UBC Theses and Dissertations

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UBC Theses and Dissertations

Sensitivity analysis of capital projects Poveda, David 1988

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S E N S I T I V I T Y A N A L Y S I S OF C A P I T A L P R O J E C T S by DAVID POVEDA A T H E S I S SUBMITTED IN P A R T I A L F U L F I L M E N T OF T H E REQUIREMENTS FOR THE D E G R E E OF MASTER OF A P P L I E D S C I E N C E i n THE F A C U L T Y OF GRADUATE S T U D I E S C I V I L E N G I N E E R I N G DEPARTMENT We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE U N I V E R S I T Y OF B R I T I S H COLUMBIA NOVEMBER 1988 © DAVID POVEDA, 1988 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia Vancouver, Canada DE-6 (2/88) ABSTRACT T h i s t h e s i s p r e s e n t s a very g e n e r a l i z e d model u s e f u l i n the economic e v a l u a t i o n of c a p i t a l p r o j e c t s . Net Present Value and the I n t e r n a l Rate of Return are used as the performance measures. A t h e o r e t i c a l framework to perform s e n s i t i v i t y a n a l y s i s i n c l u d i n g b i v a r i a t e a n a l y s i s and s e n s i t i v i t y to f u n c t i o n a l forms i s presented. During the development of the model, emphasis i s given to the f i n a n c i a l mechanisms a v a i l a b l e to fund l a r g e c a p i t a l p r o j e c t s . A l s o , mathematical f u n c t i o n s that can be used to represent cash flow p r o f i l e s generated in each p r o j e c t phase are i n t r o d u c e d . These p r o f i l e s are a p p l i c a b l e to a number of p r o j e c t types i n c l u d i n g o i l and gas, mining, r e a l e s t a t e and chemical process p r o j e c t s . F i n a l l y , a computer program has been developed which t r e a t s most of the t h e o r e t i c a l concepts e x p l o r e d in t h i s t h e s i s , and an example of i t s a p p l i c a t i o n i s presented. T h i s program c o n s t i t u t e s a u s e f u l t e a c h i n g t o o l . i i T a b l e o f C o n t e n t s A B S T R A C T i i L I S T OF T A B L E S . . . . . v i i L I S T OF F I G U R E S ' . . v i i i ACKNOWLEGEMENTS x 1. T H E S I S O B J E C T I V E S AND B A S I C CONCEPTS 1 1.1 T H E S I S O B J E C T I V E S 1 1.2 ECONOMIC E V A L U A T I O N OF P R O J E C T S 2 1 .2 .1 I n t r o d u c t i o n 2 1 . 2 . 2 E c o n o m i c p e r f o r m a n c e m e a s u r e s 3 1 . 2 . 3 Net P r e s e n t V a l u e 5 1 . 2 . 3 . 1 T h e d i s c o u n t r a t e 6 1 . 2 . 3 . 2 T h e d i s c o u n t i n g m e t h o d 7 1 . 2 . 4 T h e I n t e r n a l R a t e o f R e t u r n 8 1.3 IMPLEMENTATION IN THE COMPUTER PROGRAM 11 2 . F I N A N C I A L AND MACROECONOMIC CONSIDERATIONS . . 13 2.1 INTRODUCTION 13 2 . 2 SOURCES OF F I N A N C I N G 14 2 . 2 . 1 C o m m e r c i a l b a n k s 15 2 . 2 . 2 E x p o r t f i n a n c i n g a g e n c i e s . . . 1 7 2 . 2 . 3 D e v e l o p m e n t b a n k s 18 2 . 2 . 4 I n s u r a n c e c o m p a n i e s 19 2 . 3 T Y P E S OF LOANS 19 2 . 3 . 1 S u b o r d i n a t e d l o a n s 20 2 . 3 . 2 U n s e c u r e d l o a n s 20 2 . 3 . 3 S e c u r e d l o a n s 21 2 . 4 GUARANTEE SCHEMES 22 i i i 2 . 5 TWO F I N A N C I N G TECHNIQUES 23 2 . 5 . 1 P r o j e c t f i n a n c i n g 23 2 . 5 . 2 L e a s e f i n a n c i n g 25 2 . 6 I N F L A T I O N AND C A P I T A L BUDGETING 26 2 . 7 OVERSEAS P R O J E C T S AND F O R E I G N EXCHANGE RATES . . . 2 9 2 . 7 . 1 C o u n t r y r i s k 31 2 . 7 . 2 M a c r o e c o n o m i c r i s k a n d e x c h a n g e r a t e s . . . . 3 1 2 . 8 CASH FLOWS GENERATED BY F I N A N C I A L ARRANGEMENTS .34 2 . 9 IMPLEMENTATION ON THE COMPUTER PROGRAM 35 2 . 9 . 1 F i n a n c i a l m e c h a n i s m s 35 2 . 9 . 2 I n f l a t i o n 35 2 . 9 . 3 F o r e i g n e x c h a n g e r a t e 36 3 . CASH FLOWS GENERATED IN C A P I T A L P R O J E C T S 37 3.1 INTRODUCTION 37 3 . 2 O I L AND GAS INDUSTRY 38 3 . 2 . 1 E x p l o r a t i o n p h a s e 38 3 . 2 . 2 E c o n o m i c e v a l u a t i o n 39 3 . 2 . 3 F i e l d d e v e l o p m e n t 40 3 . 2 . 4 O p e r a t i o n 41 3 . 2 . 4 . 1 REVENUES 41 3 . 2 . 4 . 2 E X P E N S E S 49 3 . 2 . 5 D i s p o s a l 53 3 . 3 MINING P R O J E C T S 54 3 . 3 . 1 M i n e d e v e l o p m e n t 55 3 . 3 . 2 O p e r a t i o n p h a s e 56 3 . 3 . 2 . 1 R e v e n u e s 56 3 . 3 . 2 . 2 E x p e n s e s 59 i v 3 . 4 R E A L E S T A T E P R O J E C T S 60 3 . 4 . 1 F e a s i b i l i t y a n a l y s i s 60 3 . 4 . 2 D e s i g n 61 3 . 4 . 3 C o n s t r u c t i o n 61 3 . 4 . 4 A b s o r p t i o n p h a s e 72 3 . 4 . 5 O p e r a t i o n 74 3 . 4 . 6 D i s p o s a l 77 3 . 5 PROCESS I N D U S T R I E S 77 3 . 5 . 1 O p e r a t i o n 78 3 . 5 . 2 E x p e n s e s 80 3 . 6 IMPLEMENTATION ON THE COMPUTER PROGRAM 83 4 . S E N S I T I V I T Y A N A L Y S I S 86 4.1 INTRODUCTION 86 4 . 2 PARAMETER E S T I M A T I O N 87 4 . 3 R I S K MANAGEMENT 88 4 . 4 S E N S I T I V I T Y A N A L Y S I S 89 4 . 5 U N I V A R I A T E S E N S I T I V I T Y A N A L Y S I S 90 4 . 5 . 1 L i n e a r a n a l y s i s 91 4 . 5 . 2 L i n e a r a n a l y s i s : t h e c a s e o f i m p l i c i t f u n c t i o n s 95 4 . 6 E X A C T A N A L Y S I S 97 4 . 7 B I V A R I A T E S E N S I T I V I T Y A N A L Y S I S . . . 9 8 4 . 8 T H R E E V A R I A T I O N S OF S E N S I T I V I T Y A N A L Y S I S . . 1 0 1 4 . 8 . 1 B r e a k - e v e n a n a l y s i s 101 4 . 8 . 2 E x t r e m e p o i n t a n a l y s i s 102 4 . 8 . 3 S e n s i t i v i t y t o f u n c t i o n a l f o r m s 102 4 . 9 C O N C L U S I O N : THE B E N E F I T S OF S E N S I T I V I T Y A N A L Y S I S 103 v 4.10 IMPLEMENTATION ON THE COMPUTER PROGRAM 104 5. THE COMPUTER PROGRAM 106 5.1 INTRODUCTION 106 5.2 DATA INPUT . 109 5.3 BUILT-1N-FUNCTIONS 121 5.4 CALCULATION OF PERFORMANCE MEASURES 122 5.5 SENSITIVITY ANALYSIS 124 5.6 PLOTTING OF RESULTS 126 6. VALIDATION AND APPLICATION OF THE MODEL 128 6.1 INTRODUCTION 128 6.2 VALIDATION OF THE MODEL 128 6.3 ARBITRARY FUNCTIONS 139 6.4 EXAMPLE OF APPLICATION 145 6.4.1 DESCRIPTION OF THE PROJECT 146 6.4.2 PREPARATION OF DATA INPUT 149 7. CONCLUSIONS AND FUTURE WORK .158 7.1 THEORETICAL FRAMEWORK 158 7 . 2 THE COMPUTER MODEL 158 BIBLIOGRAPHY 160 APPENDIX A .170 APPENDIX B . . 216 v i LIST OF TABLES Summary of mathematical f u n c t i o n s used to represent cash flow p r o f i l e s S t r u c t u r e of v e c t o r V Matrix F: Data elements a s s o c i a t e d with flow type Matrix F: Data elements i n columns 2, 3 and 4 a c c o r d i n g to the flow type F o r e c a s t e d constant c o n s t r u c t i o n c o s t s Cash flows d e s c r i p t i o n and parameters v i i LIST OF FIGURES 1 . Production r a t e of o i l w e l l s 43 2. E x p o n e n t i a l d e c l i n e curves 44 3. Pr o d u c t i o n output of a mine 58 4. Truncated normal f u n c t i o n s 65 5. Beta d i s t r i b u t i o n 67 6. Gamma f u n c t i o n 69 7. R a y l e i g h f u n c t i o n 70 8. W e i b u l l f u n c t i o n 71 9. Cash flow p r o f i l e generated d u r i n g 73 c o n s t r u c t i o n 10. E x p l o n e n t i a l and step f u n c t i o n s 76 11. Example of product l i f e c y c l e 79 12. Gompertz curve 81 13. L o g i s t i c curve 82 14. Star diagram f o r an h y p o t e t i c a l o i l 95 f i e l d 15. Contour diagram 100 16. Surface diagram 100 17. General flow c h a r t of the program 107 18. Menu f o r the s e l e c t i o n of the p r o j e c t 112 phase 19. Menu f o r the s e l e c t i o n of flow type 112 ( f e a s i b i l i t y and design) 20. Menu f o r the s e l e c t i o n of flow type 114 ( c o n s t r u c t i o n ) v i i i 21. Menu f o r the s e l e c t i o n of flow type 114 (operation) 22. D e s c r i p t i o n and s o l u t i o n of the simple 130 example 23. Summary of r e s u l t s o b tained with the 131 computer program 24. Primary v a r i a b l e s 132 25. Information about cash flows 134 26. Economic performance measures 135 27. P e r i o d - b y - p e r i o d cash flow i n c u r r e n t 135 d o l l a r s 28. Cash flows i n currunt d o l l a r s 136 29. S e n s i t i v i t y c o e f f i c i e n t s 137 30. Exact u n i v a r i a t e a n a l y s i s 138 31. B i v a r i a t e a n a l y s i s 140 32. S e n s i t i v i t y c h a r t f o r the s i m p l i f i e d 141 example 33. P l o t of the r e s u l t s of the exact 142 a n a l y s i s (NPV) 34. P l o t of the r e s u l t s of the exact 143 a n a l y s i s (IRR) 35. Sequencing and d u r a t i o n of the work 147 packages 36. General schedule of the p r o j e c t 150 37. Subroutine VARIA 157 ix ACKNOWLEGEMENTS I.want to express my g r a t i t u d e to Dr. Alan D. R u s s e l l who su p e r v i s e d t h i s t h e s i s , f o r h i s v a l u a b l e c o n t r i b u t i o n s to the improvement of i t s content, and who a l s o p r o v i d e d me with a part time r e s e a r c h a s s i s t a n t s h i p during the p r e p a r a t i o n of t h i s work. My thanks to a l l the p r o f f e s o r s , c o l l e g u e s and f r i e n d s who helped and supported me d u r i n g my stay i n Canada. x To my mother x i CHAPTER 1 . THESIS OBJECTIVES AND BASIC CONCEPTS 1.1 THESIS OBJECTIVES The o b j e c t i v e s of t h i s t h e s i s are f o u r f o l d : 1)The development of a very general model f o r the economic e v a l u a t i o n of c a p i t a l p r o j e c t s ; 2)the i d e n t i f i c a t i o n of the a t t r i b u t e s r e q u i r e d by cash flow p r o f i l e s for each p r o j e c t phase and t h e i r statement on the form of mathematical expressions or f u n c t i o n s ; 3)a complete review of the i s s u e of s e n s i t i v i t y a n a l y s i s ; and 4)the implementation of a general model i n a computer program. The c r i t e r a f o r economic e v a l u a t i o n of a p r o j e c t are Net Present Value, NPV, and the I n t e r n a l Rate of Return, IRR. Both are t r e a t e d by d i s c o u n t i n g the cash flows generated during each p r o j e c t phase, e i t h e r at a continuous or d i s c r e t e r a t e . The model enables the user to t r e a t any type of f u n c t i o n a l form to d e s c r i b e the cash flow p r o f i l e s ( e i t h e r d i s c r e t e or con t i n u o u s ) . A l s o , a reinvestment (or e x t e r n a l investment) rate can be p r e s c r i b e d in order to c a l c u l a t e the I n t e r n a l Rate of Return for these s i t u a t i o n s when the unrecovered balance of the p r o j e c t at any stage goes to zero or become p o s i t i v e . In order to i d e n t i f y some u s e f u l mathematical f u n c t i o n s that may be used to express cash flow p r o f i l e s , four types of p r o j e c t s are stud i e d , namely those encountered i n the o i l and gas in d u s t r y , mining a c t i v i t i e s , r e a l e s t a t e developments and chemical and process i n d u s t r i e s . Each of 1 2 them i s broken down i n t o i t s basic phases and according to the kind of a c t i v i t i e s undertaken i n each phase, a mathematical f u n c t i o n i s suggested f o r t r e a t i n g the cash flow. These f u n c t i o n s are summarized i n a t a b l e . The t h i r d o b j e c t i v e i s to st a t e a complete t h e o r e t i c a l framework to perform s e n s i t i v i t y a n a l y s i s of investment proposals, based on a throughout review of the the a v a i l a b l e l i t e r a t u r e in en g i n e e r i n g economics and r e l a t e d t o p i c s . S e n s i t i v i t y a n a l y s i s i s a u s e f u l f i r s t s tep i n the assesment of r i s k i n c a p i t a l p r o j e c t s . I t s extension to b i v a r i a t e a n a l y s i s and s e n s i t i v i t y to f u n c t i o n a l forms i s developed. F i n a l l y , a computer program i s developed as a p r a c t i c a l counterpart to the t h e o r e t i c a l concepts p r e v i o u s l y discussed, and an example of i t s a p p l i c a t i o n i s given. At the end of each of the four t h e o r e t i c a l chapters, a b r i e f note d e s c r i b i n g the most important aspects of the theory t r e a t e d and how they are implemented i n the computer program, are presented. 1 . 2 ECONOMIC EVALUATION OF PROJECTS 1 . 2 . 1 INTRODUCTION Governments and p r i v a t e c o r p o r a t i o n s are co n t i n u o u s l y involved in the e v a l u a t i o n and implementation of l a r g e c a p i t a l p r o j e c t s , undertaken in order to s a t i s f y p u b l i c demand f o r goods and s e r v i c e s , and to promote economic development. Given the large amounts of human and monetary 3 resources committed to such p r o j e c t s , they should be c a r e f u l l y planned and evaluated, t a k i n g i n t o account both q u a l i t a t i v e and q u a n t i t a t i v e c o n s i d e r a t i o n s . In t h i s chapter, the b a s i c concepts d e a l i n g with the q u a n t i t a t i v e p o r t i o n of the economic e v a l u a t i o n of c a p i t a l p r o j e c t s i s presented. 1.2.2 ECONOMIC PERFORMANCE MEASURES C a p i t a l investment d e c i s i o n s , at l e a s t the q u a n t i t a t i v e p o r t i o n , are u s u a l l y based on one of s e v e r a l p o s s i b l e c r i t e r i a c a l l e d economic performance measures. A performance measure i s defi n e d as an index c o n t a i n i n g p a r t i c u l a r information about a s e r i e s of r e c e i p t s and disbursements representing the investment o p p o r t u n i t y . I t i s then compared against a predefined c u t o f f p o i n t or a s i m i l a r index of an a l t e r n a t i v e p r o j e c t in order to proceed with the a c c e p t - r e j e c t d e c i s i o n or i n order to s e l e c t between mutually e x c l u s i v e p r o j e c t s . According to Rose [46], there are over 20 "methods" of ev a l u a t i o n for c a p i t a l investments, a l l of which are s e r i o u s proposals which have t h e i r own p a r t i c u l a r advantages and disadvantages. They may have been proposed because they are p a r t i c u l a r l y simple, or emphasize the importance of c a p i t a l and i t s value over the time, or emphasize the importance of p r o f i t a f t e r i n t e r e s t repayments, or emphasize the r i s k and un c e r t a i n t y a s s o c i a t e d with the p r o j e c t , or they may be m o d i f i c a t i o n s to already e s t a b l i s h e d methods intended to 4 overcome shortcomings. The subject of e v a l u a t i o n i s made ambiguous due to the many names given to the same method or performance measure and the multitude of minor c o r r e c t i o n s that can be a p p l i e d , each r e s u l t i n g i n a new name. Some of these methods are: Estimated payback p e r i o d or payoff p e r i o d ; Return on t o t a l investment; Return on average investment; Return on c a p i t a l employed; Return on e q u i t y ; Investor's method; Machine and A l l i e d Products I n s t i t u t e -MAPI- method; P r o j e c t balance method; P r o f i t a b i l i t y index; I n t e r n a l r a t e of return or discounted cash flow r a t e of ret u r n ; Net present value or present worth or present e q u i v a l e n t ; Net future value or f u t u r e worth or f u t u r e e q u i v a l e n t ; the annual e q u i v a l e n t sum, or annual c o s t or uniform annual cost method and b e n e f i t - c o s t r a t i o , to name a f ew. In r e f e r e n c e s [30], [45], [46], [51] and [53] as w e l l as i n s e v e r a l papers in The Engi n e e r i n g Economist j o u r n a l [13], the d e t a i l s concerning these and some other techniques, t h e i r approach, advantages and disadvantages, are documented. Some of the techniques are convenient for simple s i t u a t i o n s but u n s u i t a b l e for complex ones. In a d d i t i o n , c o n f l i c t i n g c o n c l u s i o n s can be drawn f o r a p a r t i c u l a r case by employing v a r i o u s techniques. Therefore, whenever a c a p i t a l investment d e c i s i o n has to be made, the problem a r i s e s on which c r i t e r i o n the d e c i s i o n i s to be based. The s e l e c t i o n of a method may depend on the s i z e and type of the 5 investment, or simply, on the sponsor's p r e f e r e n c e s . However, two s p e c i f i c performance measures are given primary importance in the l i t e r a t u r e , and may be considered as the most adequate b a s i s of comparison and e v a l u a t i o n of engineering p r o j e c t s . They are the Net Present Value NPV and the Discounted Cash Flow Rate of Return, most commonly known as I n t e r n a l Rate of Return IRR. Both are adopted for the modelling e x e r c i s e presented i n t h i s t h e s i s . 1.2.3 NET PRESENT VALUE The ideas of i n t e r e s t , equivalence and d i s c o u n t i n g are w e l l known and broadly documented in the l i t e r a t u r e . They r e l y upon the concept of the time value of money, and standard procedures and formulas have been developed to c a l c u l a t e e q u i v a l e n t amounts at any poin t in time f o r s p e c i f i c cash flow p r o f i l e s at a s e l e c t e d i n t e r e s t or discount r a t e . The present worth of a cash flow i s the e q u i v a l e n t s i n g l e amount at time zero, d e f i n i n g the beginning of the venture. The Net Present Value of the p r o j e c t i s simply c a l c u l a t e d as the a l g e b r a i c sum of the present worth of the i n d i v i d u a l cash flows generated during the l i f e of the p r o j e c t . I t represents the e q u i v a l e n t amount by which the equivalent r e c e i p t s of a cash flow stream exceed or f a i l to equal the e q u i v a l e n t disbursements of that cash flow stream. The Net Present Value has a number of features that makes i t s u i t a b l e as an economic performance measure. F i r s t , 6 i t c o n siders the time value of money according to the discount rate s e l e c t e d for i t s c a l c u l a t i o n . Second, i t concentrates the eq u i v a l e n t value of any cash flow stream in a s i n g l e index at a p a r t i c u l a r p o i n t i n time (t=0). T h i r d , a s i n g l e unique value of the NPV i s a s s o c i a t e d with each discount rate used, no matter what may be the investment cash flow p a t t e r n . I t i s claimed that i s has the disadvantage of being an absolute number, so no r e l a t i v e judgement about the convenience of the investment can be made. There are two s p e c i f i c i s s u e s that should be co n s i d e r e d when using NPV as the performance measure. They are the s e l e c t i o n of the discount r a t e , and the d i s c o u n t i n g method. 1.2.3.1 The discount r a t e When the present worth of a s e r i e s of cash flows i s to be c a l c u l a t e d , a discount r a t e has to be p r e s c r i b e d . In c a p i t a l p r o j e c t s , t h i s rate i s the Minimum Acceptable (or A t t r a c t i v e ) Rate of Return, MARR. It i s u s u a l l y the r e s u l t of a p o l i c y d e c i s i o n made by the management of the p r o j e c t in the process of i d e n t i f y i n g a t a r g e t r a t e of i n t e r e s t that represents a " f l o o r " rate or lowest rate of return that w i l l be c o n s i d e r e d acceptable. The minimum acceptable rate of return can be viewed as a rate at which the p r o j e c t ' s sponsor can always in v e s t , since he has a l a r g e number of o p p o r t u n i t i e s that y i e l d such r e t u r n . However, i t may vary a c c o r d i n g to type and l e v e l of r i s k i n v o l v e d in each p a r t i c u l a r 7 venture. Thus, whenever any money i s committed to an investment proposal, an oppo r t u n i t y to invest that money at the MARR has been foregone. For t h i s reason, the MARR i s sometimes considered to be an "opportunity c o s t " . The s e l e c t i o n of a MARR i s b a s i c a l l y a management d e c i s i o n . One method for s e l e c t i n g i t i s to examine the proposals a v a i l a b l e f o r investment and to i d e n t i f y the maximum rate that can be earned i f the funds are not invested i n them. A complete d i s c u s s i o n about the c o n s i d e r a t i o n s that should be made i n s e l e c t i n g the MARR can be found in Thuesen and Fabrycky [53]. 1.2.3.2 The d i s c o u n t i n g method The second aspect to conside r in the c a l c u l a t i o n of the Net Present Value deals with the type of d i s c o u n t i n g that should be used, namely d i s c r e t e or continuous compounding. The va r i o u s elements that comprise a cash flow stream have a p p r e c i a b l y d i f f e r e n t frequency of occurrence. For insta n c e , tax payments and lea s e disbursements are o u t l a y s that may occur as i n f r e q u e n t l y as once a year. On the other hand, disbursements f o r labor and r e c e i p t s from s a l e s of a product, g e n e r a l l y occur f r e q u e n t l y enough so that they may be viewed as cash t r a n s a c t i o n s that are v i r t u a l l y continuous. Most investment proposals include cash elements that have d i f f e r e n t f r e q u e n c i e s of occurrence. If the a n a l y s i s were to be done as r e a l i s t i c as p o s s i b l e the type of d i s c o u n t i n g a p p r o p r i a t e for each flow would be 8 used. However, t h i s may h o p e l e s s l y complicate many problems and such refinements i n technique are in c o n s i s t e n t with the r e l a t i v e l y rough estimates u s u a l l y employed in the economic e v a l u a t i o n . In order to s i m p l i f y the process, one of two conventions i s used. Heebink [20], p o i n t s out that in p r o j e c t s f o r which a r e l a t i v e l y low MARR (up to 12 or 15%) i s s p e c i f i e d , the choice of a d i s c o u n t i n g method i s not l i k e l y to a f f e c t the a c c e p t - r e j e c t d e c i s i o n . However, i n p r o j e c t s with a high MARR, the d i s c o u n t i n g method that i s used may reverse the a c c e p t - r e j e c t d e c i s i o n , in cases when the c a l c u l a t e d rate of re t u r n i s j u s t above or j u s t below the MARR. Th i s author provides an example of such a s i t u a t i o n and suggests that i n p r o j e c t s having a high MARR, the infre q u e n t cash flows ought to be dis c o u n t e d d i s c r e t e l y and the frequent ones c o n t i n u o u s l y . 1.2.4 THE INTERNAL RATE OF RETURN The i n t e r n a l Rate of Return i s another performance measure widely used i n the economic e v a l u a t i o n of c a p i t a l investments. It i s simply d e f i n e d as the discount rate that equates the present worth of a l l disbursements and r e c e i p t s a s s o c i a t e d with the p r o j e c t , t h e r e f o r e making the NPV equal to zero. The p r o j e c t i s accepted when the IRR i s gre a t e r than or equal to the Minimum a t t r a c t i v e r a t e of r e t u r n , and r e j e c t e d otherwise. 9 Since the e a r l y 1960s, two t h e o r e t i c a l c o m p l i c a t i o n s a s s o c i a t e d with the c a l c u l a t i o n of the IRR have been discussed, by many authors, namely the issu e s of reinvestment rate and the existence of m u l t i p l e r a t e s of return f o r a s i n g l e cash flow stream. The d i s c u s s i o n i s s t i l l open and c o n t r a d i c t o r y view p o i n t s are hel d by d i f f e r e n t authors. The c o n f l i c t a r i s e s from the f a c t that investments may be e i t h e r "pure" or "mixed" as d e f i n e d by Teichroev et a l [52]. B r i e f l y , the d i s t i n c t i o n can be ex p l a i n e d by c o n s i d e r i n g a p r o j e c t with an economic l i f e of n p e r i o d s . The investment i s designated as pure i f the sponsor of the p r o j e c t s has funds committed in i t during each of the n pe r i o d s , and i s designated as mixed i f the sponsor has funds committed in the p r o j e c t during some of the n per i o d s and has an "o v e r d r a f t " on the p r o j e c t d u r i n g the r e s t of the p e r i o d s . In the case of pure investments, the i n t e r n a l rate of r e t u r n does have the meaning s t a t e d i n i t s d e f i n i t i o n , i s unique and t o t a l l y " i n t e r n a l " to the p r o j e c t , meaning that i t i s independent from the rate at which the sponsor can r e i n v e s t h i s c a p i t a l . For mixed investments the s i t u a t i o n i s q u i t e d i f f e r e n t . The fundamental meaning of IRR i s that rat e of i n t e r e s t earned each p e r i o d on the unrecovered balance of the investment so that the remaining balance at the end of the investment l i f e i s zero. Then, i f the sponsor has funds committed to the p r o j e c t , the investment balance i s compounded at the rate of r e t u r n . On the other hand, i f 10 t h e r e i s an o v e r d r a f t on the p r o j e c t , t h e b a l a n c e s h o u l d be compounded a t t h e r a t e t h a t c an be e a r n e d by t h e s p o n s o r when t h i s o v e r d r a f t i s r e i n v e s t e d . T h i s r a t e i s c a l l e d t h e r e i n v e s t m e n t r a t e o r e x t e r n a l i n t e r e s t r a t e and s e v e r a l a u t h o r s (Mao and K n o l l [ 3 1 ] , Howe [ 23 ] ) c l a i m t h a t t h e c o r r e c t r e i n v e s t m e n t r a t e i s t h e s p o n s o r ' s c o s t of c a p i t a l . As Montgomery and Raper [33] p o i n t o u t , no m a t t e r how much has been w r i t t e n or a r g u e d , t h e r e c o n t i n u e t o be c o n t r o v e r s i a l and sometimes d o g m a t i c d i f f e r e n c e s of o p i n i o n among q u a l i f i e d p r o f e s s i o n a l s and a u t h o r s c o n c e r n i n g t h e e f f e c t t h a t r e i n v e s t m e n t has or s h o u l d have on t h e c a l c u l a t i o n of t h e I n t e r n a l R ate of R e t u r n . In t h e i r p a p e r , t h e s e a u t h o r s c l a r i f y why d i f f e r e n c e s p e r s i s t i n t h e r e i n v e s t m e n t i s s u e , summarize t h e d i f f e r e n t a p p r o a c h e s t o s o l v e t h i s q u e s t i o n and p r o p o s e an a l t e r n a t i v e p e r f o r m a n c e measure: t h e e x t e r n a l r a t e of r e t u r n . The s e c o n d t h e o r e t i c a l c o m p l i c a t i o n i n v o l v e d i n t h e IRR c a l c u l a t i o n i s t h e e x i s t e n c e of m u l t i p l e r a t e s of r e t u r n . T h i s s i t u a t i o n i s a l s o p r e s e n t i n t h e c a s e s of mixed i n v e s t m e n t s . The s o l u t i o n of t h e IRR i s o b t a i n e d by s o l v i n g and n t h d e g r e e p o l y n o m i a l where n i s t h e number of p e r i o d s of t h e i n v e s t m e n t . The D e s c a r t e s ' r u l e of s i g n s s t a t e s t h a t a p o l y n o m i a l w i t h r e a l c o e f f i c i e n t s and m s i g n changes has m-2k p o s i t i v e r o o t s where k i s a p o s i t i v e i n t e g e r or z e r o . I t means t h a t the p o s s i b l e p o s i t i v e r o o t s cannot e x c e e d t h e number of s i g n c h a n g e s , or s t a t e d i n a d i f f e r e n t way, t h e r e may be as many p o s i t i v e v a l u e s of IRR as t h e r e a r e s i g n 11 c hanges i n the c a s h f l o w s t r e a m . Newnan [36] c l a i m s t h a t i n t h e c a s e s where t h e r e a r e m u l t i p l e r a t e s o f r e t u r n , none of them s h o u l d be c o n s i d e r e d a s u i t a b l e measure of t h e r a t e of r e t u r n , or a t t r a c t i v e n e s s of t h e c a s h f l o w , and p r o p o s e s a method t o r e d u c e the number of s i g n c h a n g e s i n a c a s h f l o w t o one by u s i n g a r e i n v e s t m e n t r a t e , t h e r e f o r e o b t a i n i n g a s i n g l e IRR v a l u e . The c o m p u t a t i o n of t h e IRR g e n e r a l l y r e q u i r e s a t r i a l - a n d - e r r o r p r o c e d u r e . However, s i n c e i t i s t h e s o l u t i o n of an n t h d e g r e e p o l y n o m i a l , v a r i o u s m a t h e m a t i c a l methods t h a t s y s t e m a t i c a l l y c o n v e r g e on t h e r o o t s t h a t s a t i s f y s u c h a p o l y n o m i a l can be u s e d . 1.3 IMPLEMENTATION IN THE COMPUTER PROGRAM In the computer program d e v e l o p e d as p a r t of t h i s t h e s i s , the p e r f o r m a n c e measures a r e t h e Net P r e s e n t V a l u e , t h e I n t e r n a l Rate of R e t u r n and T o t a l C o n s t r u c t i o n C o s t . The NPV i s o b t a i n e d as t h e a l g e b r a i c sum of t h e p r e s e n t w o r t h a t time z e r o of a l l the c a s h f l o w s a s s o c i a t e d w i t h t h e p r o j e c t , u s i n g c o n t i n u o u s d i s c o u n t i n g . The IRR i s computed u s i n g t h e method p r o p o s e d by Newnan [ 3 6 ] , whereby an e x t e r n a l i n v e s t m e n t r a t e s h o u l d be s p e c i f i e d i f the net c a s h f l o w s t r e a m has more than one s i g n change. T o t a l C o n s t r u c t i o n C o s t i s c a l c u l a t e d as the t o t a l a r e a under the c u r v e d e f i n i n g t h e c u r r e n t d o l l a r c o n s t r u c t i o n e x p e n d i t u r e f u n c t i o n p l u s t h e i n t e r e s t on the c o n s t r u c t i o n 12 l o a n . CHAPTER 2 . FINANCIAL AND MACROECONOMIC CONSIDERATIONS 2 . 1 INTRODUCTION One of t h e key i s s u e s i n v o l v e d i n t h e e v a l u a t i o n of c a p i t a l i n v e s t m e n t s i s t h e d e f i n i t i o n of t h e s o u r c e s and mechanisms of f i n a n c i n g f o r the l a r g e amounts of monies t h a t must be spe n t b e f o r e t h e r e v e n u e s g e n e r a t e d by t h e p r o j e c t a r e c o l l e c t e d . T h i s t a s k c o n s i s t s of d e t e r m i n i n g how much money and from whom i t s h o u l d be borrowed, a t what i n t e r e s t r a t e and under what k i n d of g u a r a n t e e s , agreements and payback s t r u c t u r e s . G e n e r a l l y , l a r g e p r o j e c t s r e q u i r e complex f i n a n c i a l schemes, where s e v e r a l l e n d i n g and f i n a n c i a l i n s t i t u t i o n s from d i f f e r e n t c o u n t r i e s a r e i n v o l v e d , p r o v i d i n g c r e d i t s i n d i f f e r e n t c u r r e n c i e s , w i t h d i f f e r e n t i n t e r e s t r a t e s ( o f t e n , not f i x e d ) and w i t h d i f f e r e n t m a t u r i t i e s . T h i s f a c t makes a l m o s t i m p o s s i b l e t o s i m p l i f y t h e f i n a n c i a l a n a l y s i s i n t o a s i m p l e b a s i c model. However, t h e p r o b l e m can be broken down i n t o i t s p r i m a r y components and e a c h of them a n a l y z e d s e p a r a t e l y . In t h i s c h a p t e r , t h e c o n s i d e r a t i o n s r e l e v a n t t o eac h of t h e s e components w i l l be p r e s e n t e d . They i n c l u d e s o u r c e s of f i n a n c i n g , t y p e s of l o a n s and g u a r a n t e e schemes. A d d i t i o n a l l y , two f i n a n c i n g t e c h n i q u e s t h a t a r e u s u a l l y employed i n c a p i t a l p r o j e c t s and t h a t d i f f e r from t r a d i t i o n a l l e n d i n g , a r e p r e s e n t e d . They a r e t h e p r o j e c t 13 1 4 f i n a n c i n g t e c h n i q u e and l e a s e f i n a n c i n g . Two o t h e r v a r i a b l e s t h a t s h o u l d be c a r e f u l l y c o n s i d e r e d d u r i n g the economic e v a l u a t i o n a r e a l s o d i s c u s s e d , namely, i n f l a t i o n r a t e s and t h e a d d i t i o n a l r i s k s i n t r o d u c e d i n o v e r s e a s p r o j e c t s w i t h s p e c i a l a t t e n t i o n t o exchange r a t e s . These two f a c t o r s a r e t h e outcome of the i n t e r a c t i o n of complex mechanisms of the macroeconomic s y s t e m . The f i r s t one w i l l a l m o s t i n e v i t a b l y be p r e s e n t i n any economic a c t i v i t y . The s e c o n d may have a v e r y s t r o n g i mpact on t h e i m p l e m e n t a t i o n and o p e r a t i o n of o v e r s e a s p r o j e c t s , and even on d o m e s t i c ones, when i m p o r t e d r e s o u r c e s (monetary or m a t e r i a l ) a r e u s e d . 2.2 SOURCES OF FINANCING I r r e s p e c t i v e of t h e e x a c t n a t u r e o f f i n a n c i n g c o n s i d e r e d f o r any i n v e s t m e n t o p p o r t u n i t y , t h e p r o j e c t has t o be c o m m e r c i a l l y and f i n a n c i a l l y v i a b l e . The s p o n s o r of t h e p r o j e c t has t o c a r r y out a c o m p l e t e f e a s i b i l i t y a n a l y s i s t o d e m o n s t r a t e t h a t t h e r e v e n u e s g e n e r a t e d d u r i n g t h e o p e r a t i o n o f the v e n t u r e a r e l a r g e enough t o c o v e r t h e o p e r a t i o n a l c o s t s and t o r e p a y the i n t e r e s t s and p r i n c i p a l of l o a n s n e g o t i a t e d w i t h l e n d i n g i n s t i t u t i o n s . The f e a s i b i l i t y a n a l y s i s w i l l a l s o h e l p t o d e f i n e t h e f i n a n c i a l r e q u i r e m e n t s of the p r o j e c t . W i t h t h i s i n f o r m a t i o n a l r e a d y a v a i l a b l e , t h e s p o n s o r can l o o k a t t h e s p e c t r u m of l e n d i n g i n s t i t u t i o n s and shop a r o u n d f o r t h e b e s t f i n a n c i a l package t h a t meets t h e needs of the i n v e s t m e n t . S o u r c e s of l o n g term f i n a n c i n g f o r 1 5 c a p i t a l p r o j e c t s i n c l u d e c o m m e r c i a l banks, e x p o r t f i n a n c i n g a g e n c i e s , development banks and i n s u r a n c e c o m p a n i e s . 2.2.1 COMMERCIAL BANKS P r i v a t e c o m m e r c i a l banks (and i n g e n e r a l , p r i v a t e f i n a n c i a l i n s t i t u t i o n s ) a r e c r e a t e d t o t r a n s f e r c u r r e n t p u r c h a s i n g power i n t h e form of money from s a v e r s t o b o r r o w e r s , i n exchange f o r t h e p r o m i s e of g r e a t e r f u t u r e p u r c h a s i n g power, and t o a l l o c a t e t h o s e f u n d s among t h e p o t e n t i a l u s e r s on t h e b a s i s of r i s k - a d j u s t e d r e t u r n s . .The l i k e l i h o o d of o b t a i n i n g a c o m m e r c i a l bank l o a n , and a c h e a p one, d e c r e a s e s w i t h th e l e v e l of r i s k of t h e p r o j e c t . A l m o s t a l l d o m e s t i c , s m a l l and medium s i z e p r o j e c t s a r e f i n a n c e d by means of medium and l o n g t e r m debt n e g o t i a t e d w i t h p r i v a t e banks. As i n any o t h e r f i n a n c i n g a l t e r n a t i v e , t h e r e a r e s e v e r a l key i s s u e s t h a t s h o u l d be c a r e f u l l y a n a l y z e d when d e s i g n i n g t h e f i n a n c i a l package of any p r o j e c t . They a r e t h e amount of t h e l o a n , i n t e r e s t r a t e , c u r r e n c y u s ed, g r a c e p e r i o d , drawdown and repayment schemes, r e q u i r e d g u a r a n t e e s , f i n a n c i n g of c o s t o v e r r u n s , and a d d i t i o n a l r e l a t e d c h a r g e s l i k e c o m m i s s i o n s on unused f u n d s , l o a n s t u d y f e e s and t h e l i k e . However, repayment p e r i o d and i n t e r e s t r a t e may be r e g a r d e d as the most i m p o r t a n t v a r i a b l e s t o c o n s i d e r . F o r most l a r g e , o v e r s e a s p r o j e c t s , i n t e r n a t i o n a l f i n a n c i n g i s u s u a l l y r e q u i r e d . A c c o r d i n g t o R a d e t z k y and Zorn [ 4 2 ] , i n t h e l a t e 1960s and e a r l y 1970s, p r o j e c t f i n a n c e l o a n s were 16 a v a i l a b l e f o r p e r i o d s up t o 12 o r 15 y e a r s . In t h e l a t e 1970s, the t y p i c a l l o a n repayment p e r i o d was r e d u c e d t o f i v e t o seven y e a r s , a l t h o u g h th e i n c r e a s i n g l i q u i d i t y i n t h e i n t e r n a t i o n a l f i n a n c i a l m a r k e t s due t o t h e g e n e r a l r e a c t i v a t i o n of t h e w o r l d economy d u r i n g the 1980s has pushed a v e r a g e m a t u r i t i e s t o 8 and 10 y e a r s . I t s h o u l d , however, be kept i n mind t h a t t h e a t t i t u d e s of i n d i v i d u a l banks d i f f e r , a c c o r d i n g t o t h e t y p e and l o c a t i o n of t h e p r o j e c t , the p o t e n t i a l b o r r o w e r and t h e g e n e r a l s t a t e of t h e economy. These f a c t o r s d e f i n e t h e l e v e l of r i s k a s s o c i a t e d w i t h t h e i n v e s t m e n t and a r e key d e t e r m i n a n t s i n any d e c i s i o n made by p r i v a t e l e n d i n g i n s t i t u t i o n s . I n t e r e s t r a t e s f o r the c o m m e r c i a l bank l o a n s i n v o l v e d i n p r o j e c t f i n a n c i n g t e n d t o be f l o a t i n g , r e f l e c t i n g a s p r e a d between t h e bank's own c o s t of b o r r o w i n g and t h e r a t e p a i d by t h e b o r r o w e r . U s u a l l y , l o a n s a r e o f f e r e d a t r a t e s w i t h a f i x e d s m a l l p e r c e n t a g e (0.5-2%) o v e r th e L i b o r or t h e US Prime R a t e . L i b o r i s the London I n t e r b a n k o f f e r i n g r a t e , t h e r a t e c h a r g e d i n l o a n s between major banks i n t h e E u r o c u r r e n c y m a r k e t . The US Prime r a t e i s t h e i n t e r e s t r a t e c h a r g e d t o t h e l a r g e s t and most c r e d i t w o r t h y c o r p o r a t e b o r r o w e r s by major US banks. The s p r e a d w i l l v a r y w i t h t h e s t r e n g t h of o v e r a l l l o a n demand and w i t h t h e b a n k e r ' s p e r c e p t i o n of t h e r i s k i n v o l v e d i n t h e p r o j e c t . F i n a l l y , i n some c a s e s , banks r e q u i r e g i v e n l e v e l s of l o a n - t o - e q u i t y r a t i o s i n the p r o j e c t , i n o r d e r t o a p p r o v e l o a n s . Such r e q u i r e m e n t s a r e i n t e n d e d t o o b t a i n a h i g h e r 17 commitment of t h e sponsor,' so r e d u c i n g t h e r i s k assumed by the l e n d e r . In r e f e r e n c e [ 4 2 ] , t h e s t r u c t u r e of s e v e r a l bank l o a n s t h a t have been n e g o t i a t e d t o f i n a n c e m i n i n g p r o j e c t s i n d e v e l o p i n g c o u n t r i e s i s p r e s e n t e d . 2.2.2 EXPORT FINANCING AGENCIES These a g e n c i e s a r e b a s i c a l l y banks c r e a t e d by t h e governments of seven w e s t e r n i n d u s t r i a l i z e d c o u n t r i e s (Canada, F r a n c e , Germany, I t a l y , J a p a n , UK and U S ) . They p r o v i d e t h e s o - c a l l e d " e x p o r t c r e d i t s " i n t e n d e d t o f i n a n c e the a c q u i s i t i o n of goods and equipment p r o d u c e d i n t h o s e c o u n t r i e s by i m p o r t e r s i n a s e c o n d c o u n t r y . M i n i n g , o i l and gas p r o j e c t s and p r o c e s s i n d u s t r i e s b e n e f i t from t h i s t y p e of c r e d i t , g i v e n the c o n s i d e r a b l e v a l u e of t h e m a c h i n e r y and equipment r e q u i r e d i n t h o s e p r o j e c t s . U s u a l l y , e x p o r t c r e d i t s i n v o l v e f a i r l y l o n g repayment p e r i o d s and f i x e d i n t e r e s t r a t e s . In a d d i t i o n , t h i s f i n a n c i n g scheme n o r m a l l y r e q u i r e s a government g u a r a n t e e mechanism. The o v e r a l l g u a r a n t e e schemes a r e d i s c u s s e d l a t e r i n t h i s c h a p t e r . In t h e US, t h e E x p o r t - I m p o r t bank (Eximbank) p r o v i d e s t h i s t y p e of c r e d i t s . N o r m a l l y , i t p r o v i d e s h a l f of the e x p o r t f i n a n c i n g f o r l a r g e s c a l e p r o j e c t s d i r e c t l y , and w i l l e n s u r e t h e r e m a i n i n g h a l f w h i c h i s p r o v i d e d by US c o m m e r c i a l b a n k s . A d d i t i o n a l l y , t h e l o c a l c o s t s of p r o j e c t s e m p l o y i n g US c a p i t a l goods can be f i n a n c e d t h r o u g h a companion a g e n c y , the P r i v a t e E x p o r t F i n a n c i n g C o r p o r a t i o n . The l o a n s a r e c o v e r e d by a US government agency 18 g u a r a n t e e . 2.2.3 DEVELOPMENT BANKS To h e l p p r o v i d e t h e huge f i n a n c i a l r e s o u r c e s r e q u i r e d to promote t h e development of e c o n o m i c a l l y backward r e g i o n s , some i n d u s t r i a l i z e d c o u n t r i e s have e s t a b l i s h e d a v a r i e t y of development banks, whose l e n d i n g i s d i r e c t e d t o i n v e s t m e n t s t h a t would not o t h e r w i s e be f u n d e d by p r i v a t e f i n a n c i n g i n s t i t u t i o n s . T hese p r o j e c t s i n c l u d e dams, c o m m u n i c a t i o n s y s t e m s , r o a d s and o t h e r i n f r a s t r u c t u r e f a c i l i t i e s and p r o c e s s i n d u s t r i e s whose v a l u e l i e s m a i n l y i n p e r c e i v e d p o l i t i c a l and s o c i a l a d v a n t a g e s t o t h e n a t i o n such as s u b s t i t u t i o n of i m p o r t e d goods and j o b c r e a t i o n . The l o a n s o f f e r e d by t h e s e i n s t i t u t i o n s g e n e r a l l y a r e medium t o l o n g term and a t a below market or c o n c e s s i o n a r y r a t e s ; t h e y a r e n e g o t i a t e d d i r e c t l y w i t h g o v e r n m e n t s . T h e r e a r e t h r e e d i f f e r e n t t y p e s of d e v e l o p m e n t banks: 1. The W o r l d Bank group, w h i c h i s a m u l t i n a t i o n a l f i n a n c i a l i n s t i t u t i o n e s t a b l i s h e d a t t h e end of W o r l d War II t o f a c i l i t a t e p r o v i s i o n of l o n g term c a p i t a l f o r t h e r e c o n s t r u c t i o n and d e v e l o p m e n t of member c o u n t r i e s . I t s i m p o r t a n c e l i e s i n the f a c t t h a t i t p r o v i d e s much of t h e p l a n n i n g and f i n a n c i n g f o r economic development p r o j e c t s c o n t i n u o u s l y b e i n g u n d e r t a k e n i n t h i r d w o r l d c o u n t r i e s . 2. R e g i o n a l development banks p r o v i d e f u n d s f o r m a n u f a c t u r i n g , m i n i n g , a g r i c u l t u r a l and i n f r a s t r u c t u r e p r o j e c t s c o n s i d e r e d i m p o r t a n t t o the development of t h e 19 c o u n t r i e s i n an s p e c i f i c g e o g r a p h i c a r e a . The E u r o p e a n Investment Bank, the I n t e r - A m e r i c a n Development Bank and t h e A f r i c a n Development Bank f a l l under t h i s c a t e g o r y . 3. N a t i o n a l d e v e l o p m e n t banks c o n c e n t r a t e on a p a r t i c u l a r i n d u s t r y or r e g i o n w i t h i n a c o u n t r y , but t h e y have t h e same b a s i c f u n c t i o n s as t h e r e g i o n a l b anks. 2.2.4 INSURANCE COMPANIES In many of t h e i n d u s t r i a l i z e d c o u n t r i e s , i n s u r a n c e companies a r e major s o u r c e s of c a p i t a l . In p a r t i c u l a r , t h e s t a b l e and more p r e d i c t a b l e f i n a n c i a l s t r u c t u r e of t h e s e companies (as opposed t o f i n a n c i a l banks where d e p o s i t s a r e f o r r e l a t i v e l y s h o r t t e r m s ) a l l o w s t h e s e h i g h l y l i q u i d c o r p o r a t i o n s t o c o n s i d e r v e r y l o n g term l e n d i n g . Such l e n d i n g can c l e a r l y be a d v a n t a g e o u s t o l a r g e c a p i t a l p r o j e c t s t h a t u s u a l l y c a r r y a heavy d e b t s e r v i c e b u r d e n i n the e a r l y y e a r s of o p e r a t i o n s . On t h e o t h e r hand, t h i s t y p e o f f i n a n c i n g has t h e d i s a d v a n t a g e t h a t t h e i n t e r e s t r a t e s t r u c t u r e t e n d s t o be h i g h e r t h an t h a t o f f e r e d by t h e g e n e r a l b a n k i n g system, and the s e c u r i t y and g u a r a n t e e a g r e e m e n t s demanded by i n s u r a n c e companies a r e e x t r e m e l y s t r i n g e n t . 2.3 TYPES OF LOANS Loans o b t a i n e d by i n v e s t o r s i n o r d e r t o f i n a n c e c a p i t a l p r o j e c t s f a l l i n t o t h r e e c a t e g o r i e s : S u b o r d i n a t e d l o a n s , u n s e c u r e d l o a n s and s e c u r e d l o a n s . They w i l l be b r i e f l y 20 d e s c r i b e d . A c o m p l e t e t r e a t m e n t o f t h i s t o p i c may be f o u n d i n N a v i t t [ 3 5 ] . 2.3.1 SUBORDINATED LOANS A s u b o r d i n a t e d l o a n i s o f t e n used by a s p o n s o r t o p r o v i d e c a p i t a l t o a p r o j e c t w h i c h w i l l s u p p o r t s e n i o r b o r r o w i n g from t h i r d p a r t y l e n d e r s . In t h i s c a s e , t h e spo n s o r can be t h e owner of t h e p r o j e c t , a s u p p l i e r p r o v i d i n g s u b o r d i n a t e d t r a d e c r e d i t s , a u s e r t r y i n g t o g e t th e p r o j e c t t o i t s o p e r a t i o n a l phase o r a government i n t e r e s t e d i n g e t t i n g t h e p r o j e c t b u i l t . When a s u b o r d i n a t e d l o a n i s n e g o t i a t e d , the p a r t i e s a g r e e on t h e p r e c i s e e x t e n t and c i r c u m s t a n c e s of s u b o r d i n a t i o n , i n c l u d i n g repayment of p r i n c i p a l , repayment of i n t e r e s t , term of s u b o r d i n a t i o n and a d e s c r i p t i o n of l e n d e r s and c r e d i t o r s t o w h i c h t h e l o a n i s s u b o r d i n a t e d . 2.3.2 UNSECURED LOANS U n s e c u r e d d e b t i s s i m p l y a de b t b a c k e d by the g e n e r a l c r e d i t of the b o r r o w e r and not s e c u r e d by any a s s e t or p o o l of a s s e t s a c t i n g as c o l l a t e r a l f o r the l o a n . An u n s e c u r e d l o a n agreement may c o n t a i n c o v e n a n t s t h a t l i m i t i n v e s t m e n t and o t h e r l o a n s , l e a s e s and deb t o b l i g a t i o n s which t h e sp o n s o r may i n c u r . Because of t h e l a c k of any c o l l a t e r a l w i t h which t h e l e n d e r may r e c o v e r h i s money i n c a s e t h e borrower f a i l s t o r e p a y , l a r g e u n s e c u r e d l o a n s a r e a v a i l a b l e o n l y t o the most c r e d i t w o r t h y companies w i t h l o n g r e c o r d s of 21 s u c c e s s f u l o p e r a t i o n s and good r e l a t i o n s h i p s w i t h t h e i r l e n d e r s . T h e r e f o r e , t h i s l o a n t y p e i s a v a i l a b l e o n l y f o r p r o j e c t s h a v i n g r e l a t i v e l y low r i s k , f o r t h o s e s p o n s o r s , owners and managers who have e s t a b l i s h e d a good r e p u t a t i o n w i t h the f i n a n c i a l community, and where s u f f i c i e n t c a p i t a l or s u b o r d i n a t e d l o a n s have been p r o v i d e d t o meet the e q u i t y c a p i t a l of t h e p r o j e c t . U n s e c u r e d l o a n s f o r p r o j e c t s a r e o f t e n p r o v i d e d by s p o n s o r s as an a l t e r n a t i v e t o t a k e l a r g e e q u i t y r i s k . In s i t u a t i o n s where t h e p r o j e c t t e n d s t o r a i s e s i g n i f i c a n t amounts of c a p i t a l by s e c u r e d l o a n s or l e a s i n g , i t w i l l s e r v e a p u r p o s e s i m i l a r t o a s u b o r d i n a t e d l o a n , meaning t h a t i t w i l l be j u n i o r t o t h e s e c u r i t y p r o t e c t i o n of l e a s e o b l i g a t i o n s and s e c u r e d l o a n s . 2.3.3 SECURED LOANS S e c u r e d l o a n s a r e t h e most common t y p e of f i n a n c i n g used i n c a p i t a l p r o j e c t s . The a s s e t s of t h e p r o j e c t , o r any o t h e r i n p o s s e s s i o n of the b o r r o w e r a r e used t o s e c u r e t h e d e b t . Such a s s e t s have v a l u e as c o l l a t e r a l , w h ich means t h a t t h e y a r e m a r k e t a b l e and can be r e a d i l y c o n v e r t e d t o c a s h . A c c e p t a b l e c o l l a t e r a l c o n s i s t s of r e a l p r o p e r t y , p e r s o n a l p r o p e r t y and payments due under a t a k e - o r - p a y c o n t r a c t . In a f u l l y s e c u r e d l o a n , the v a l u e of t h e c o l l a t e r a l e q u a l s or e x c e e d s th e amount borrowed, and t h e l e n d e r r e l i e s p r i m a r i l y upon i t s v a l u e f o r repayment; however, the r e p u t a t i o n of the b o r r ower and c o m m e r c i a l and f i n a n c i a l v i a b i l i t y of t h e p r o j e c t a r e c o n s i d e r e d i n t h e l e n d i n g d e c i s i o n s i n c e banks 22 w i l l not l e n d t o a p r o j e c t or company where t h e y e x p e c t t o have t o s e i z e and s e l l t h e s e c u r e d a s s e t s i n o r d e r t o c o l l e c t t h e l o a n . The s e c u r i t y i n t e r e s t i s r e g a r d e d by l e n d e r s as a p r o t e c t i o n of l o a n repayment i n t h e u n l i k e l y e v e n t t h a t the l o a n i s n o t r e p a i d d u r i n g the n o r m a l o p e r a t i o n of the p r o j e c t . 2.4 GUARANTEE SCHEMES L e n d e r s a r e w i l l i n g t o a p p r o v e c r e d i t s and l o a n s f o r t h o s e i n v e s t m e n t s and p r o j e c t s p o n s o r s which p r e s e n t the l o w e s t p o s s i b l e r i s k t o t h e l e n d i n g i n s t i t u t i o n s . . I n v e s t m e n t g u a r a n t e e schemes p e r m i t s h i f t i n g c e r t a i n s p e c i f i c r i s k s i n h e r e n t t o t h e f i n a n c i n g of p r o j e c t s t o i n t e r e s t e d p a r t i e s who have no d e s i r e t o become d i r e c t l y i n v o l v e d i n t h e o p e r a t i o n of t h e p r o j e c t , or t o d i r e c t l y p r o v i d e the c a p i t a l f o r the p r o j e c t . G u a r a n t o r s of p r o j e c t d e b t a r e u s u a l l y t h e owner a c t i n g as a p a r e n t company of t h e v e n t u r e , but t h i r d p a r t y i n s t i t u t i o n s l i k e s u p p l i e r s , s e l l e r s , u s e r s and i n t e r e s t e d governments a l s o a c t as g u a r a n t o r s . G u a r a n t e e s c o v e r b o t h e q u i t y and l o a n i n v e s t m e n t s a g a i n s t c o m m e r c i a l , p o l i t i c a l , c a s u a l t y and war r i s k as w e l l as a c t s of God. In some c a s e s , t h e y a l s o c o v e r t h e v a l u e of l i c e n c e s , s e r v i c e s , l o y a l t i e s and know-how payments. In g e n e r a l , most of t h e schemes r e s t r i c t c o v e r a g e t o new i n v e s t m e n t s and major expansions,, and t h e y do n o t , as a r u l e , c o v e r r o u t i n e m o d e r n i z a t i o n where new t e c h n o l o g y i s r e q u i r e d , s i n c e the l e v e l of r i s k i n v o l v e d i n such p r o j e c t s 23 i s h i g h e r than t h e a v e r a g e . In a d d i t i o n , g u a r a n t e e schemes n o r m a l l y i n c l u d e p r o v i s i o n s f o r w r i t i n g down the v a l u e o f t h e c o v e r e d i n v e s t m e n t o v e r t i m e . F o r i n s t a n c e , t h e O v e r s e a s P r i v a t e I n v e s t m e n t C o r p o r a t i o n , OPIC, t h e l a r g e s t p r i v a t e g u a r a n t e e company i n t h e US, r e d u c e s i t s c o v e r a g e of m i n i n g p r o j e c t s t o a maximum of 50 p e r c e n t of t h e o r i g i n a l i n v e s t m e n t a f t e r a p e r i o d o f 12 y e a r s and e l i m i n a t e s c o v e r a g e e n t i r e l y a f t e r 20 y e a r s . T h e r e a r e two t y p e s of g u a r a n t e e s : D i r e c t g u a r a n t e e s , under which t h e g u a r a n t o r assumes t h e r e s p o n s i b i l i t y t o p e r f o r m a l l t h e o b l i g a t i o n s o f t h e g u a r a n t e e d p a r t y ; and L i m i t e d g u a r a n t e e s , i n which t h e g u a r a n t e e i s not a l l encompassing i n o r d e r t o p r o v i d e s u f f i c i e n t s u p p o r t t o t h e t r a n s a c t i o n i n o r d e r t o e n a b l e i t t o be f i n a n c e d . G u a r a n t e e s may be l i m i t e d as t o amount and as t o t i m e and may be i n d i r e c t , c o n t i n g e n t o r i m p l i e d . A d e t a i l e d d e s c r i p t i o n o f t h e s e v a r i a t i o n s as w e l l as s p e c i f i c g u a r a n t e e schemes may be f o u n d i n r e f e r e n c e s [35] and [ 4 7 ] . 2.5 TWO FINANCING TECHNIQUES 2.5.1 PROJECT FINANCING In the 1960s, the s o - c a l l e d " P r o j e c t f i n a n c i n g " t e c h n i q u e became e s t a b l i s h e d as a major s t r a t e g y f o r f u n d i n g l a r g e c a p i t a l p r o j e c t s . I t emerged be c a u s e c a p i t a l needs f o r new p r o j e c t s were g r o w i n g beyond th e i n t e r n a l c a s h g e n e r a t i o n and b o r r o w i n g c a p a c i t y of i n v e s t o r s and 24 c ompanies. N e v i t t [35] d e f i n e s P r o j e c t f i n a n c i n g as t h e f i n a n c i n g of a p a r t i c u l a r economic u n i t i n w h i c h a l e n d e r i s s a t i s f i e d t o l o o k i n i t i a l l y t o t h e c a s h f l o w s and e a r n i n g s of t h a t economic u n i t as t h e s o u r c e of f u n d s from w h i c h a l o a n w i l l be r e p a i d and t o t h e a s s e t s of t h e economic u n i t as c o l l a t e r a l f o r t h e l o a n . P r o j e c t f i n a n c i n g c o n t a i n s t h e f o l l o w i n g e l e m e n t s : 1. A b a s i c r e l i a n c e on t h e a n t i c i p a t e d c a s h f l o w s of t h e p r o j e c t i t s e l f t o r e p a y the d e b t , i n c o n t r a s t t o t h e r e l i a n c e on the o v e r a l l c r e d i t w o r t h i n e s s of the p r o j e c t s p o n s o r s , t h e i r b a l a n c e s h e e t s o r income s t a t e m e n t ; 2. I t i s c o n c e r n e d w i t h w e l l - d e f i n e d p r o j e c t s and not w i t h the t o t a l f i n a n c i a l needs of i t s s p o n s o r s . The f i n a n c i a l needs of t h e p r o j e c t a r e matched by s e v e r a l d i f f e r e n t s o u r c e s of c a p i t a l r a t h e r t h an by a s i n g l e one; 3. The l e n d i n g r i s k i s s h a r e d , u s u a l l y by s y n d i c a t i n g t h e p r o j e c t l o a n as w i d e l y as p o s s i b l e ; 4. The drawdown of t h e l o a n o c c u r s over a p e r i o d of t i m e as t h e p r o j e c t i s c o m p l e t e d ; and 5. The e s s e n t i a l g u a r a n t e e of repayment l i e s i n t h e s u c c e s s f u l o p e r a t i o n of the p r o j e c t . T h i s t e c h n i q u e i s a t t r a c t i v e t o p a r e n t c o r p o r a t i o n s s i n c e i t s u l t i m a t e o b j e c t i v e i s t o a r r a n g e a b o r r o w i n g f o r a p r o j e c t w h i c h w i l l b e n e f i t t h e s p o n s o r and a t the same t i m e , be c o m p l e t e l y n o n - r e c u r s i v e t o t h e l a t t e r , not i n any way a f f e c t i n g h i s b o r r o w i n g c a p a c i t y o r b a l a n c e s h e e t . However, not e v e r y p r o j e c t i s e l i g i b l e f o r t h i s t y p e of f i n a n c i n g . 25 L e n d e r s a r e not i n t h e v e n t u r e c a p i t a l b u s i n e s s nor a r e t h e y e q u i t y r i s k t a k e r s . Then, o n l y t h o s e p r o j e c t s w i t h an a s s o c i a t e low l e v e l of r i s k may be a c c e p t e d f o r t h i s k i n d of f i n a n c i n g . F u r t h e r d e t a i l s about t h i s t e c h n i q u e may be f o u n d i n H a r r i s o n [19] and N e v i t t [ 3 5 ] . 2.5.2 LEASE FINANCING Equipment l e a s i n g i s a l s o a f i n a n c i n g t e c h n i q u e t h a t has been used i n l a r g e and s m a l l c a p i t a l p r o j e c t s . The use of a l e a s e t o f i n a n c e a l l t h e equipment and f a c i l i t i e s of a p r o j e c t may be r e g a r d e d as a v a r i a t i o n of t h e p r o j e c t f i n a n c i n g t e c h n i q u e s i n c e many of t h e o b j e c t i v e s of t h e l a t t e r a r e a c h i e v e d by u s i n g a l e a s e . However, i t c o u l d be u sed i n c o n j u n c t i o n w i t h some o t h e r f i n a n c i n g mechanisms. L e s s o r s can be e i t h e r t h i r d p a r t y l e a s i n g companies o r s p o n s o r p a r t i e s i n t e r e s t e d i n the c o m p l e t i o n of t h e p r o j e c t . The key i s s u e i n a l e a s i n g d e c i s i o n i s t h e t a x r e g u l a t i o n s r e l a t e d t o d e p r e c i a t i o n w r i t e - o f f s i n a p a r t i c u l a r c o u n t r y and how i m p o r t a n t t h e s e t a x s h i e l d s a r e t o t h e p r o j e c t . O b v i o u s l y , s i n c e t h e l e a s i n g company b e n e f i t s from the d e p r e c i a t i o n c h a r g e s a p p l i e d t o t h e equipment , the i n t e r e s t r a t e c h a r g e d i n t h i s t r a n s a c t i o n i s lower then the n o rmal r a t e f o r o t h e r t y p e s of f i n a n c i n g t e c h n i q u e s . A d e t a i l e d d e s c r i p t i o n of t h e l e a s i n g mechanism as a f i n a n c i n g a l t e r n a t i v e may be f o u n d i n B a y l e s and D i l t z [ 8 ] , and Levy and L a n d s k r o n e r [ 2 8 ] . 26 2.6 INFLATION AND CAPITAL BUDGETING A f t e r the 1973 o i l c r i s i s , t h e e c o n o m i e s of t h e i n d u s t r i a l i z e d w e s t e r n w o r l d r e g i s t e r e d h i g h i n f l a t i o n r a t e s , r a n g i n g between 8 and 15%, t h e commonly c a l l e d d o u b l e - d i g i t i n f l a t i o n r a t e . In d e v e l o p i n g c o u n t r i e s , i n f l a t i o n t e n d s t o be h i g h e r and i n some c a s e s , t h r e e - d i g i t i n f l a t i o n r a t e s have been r e p o r t e d . T h i s r e a l i t y r e q u i r e s t h a t t h e c o n s e q u e n c e s of a g e n e r a l i n c r e m e n t of p r i c e s a r e r e f l e c t e d i n t h e economic e v a l u a t i o n of c a p i t a l p r o j e c t s . In t h e g e n e r a l l i t e r a t u r e i n e n g i n e e r i n g e c o n o m i c s , t h e f a c t t h a t any s e r i o u s i n v e s t m e n t a n a l y s i s s h o u l d be c a r r i e d out i n an a f t e r - t a x b a s i s i s e m p h a s i z e d . I t may be added, t h a t s u c h an a n a l y s i s s h o u l d a l s o i n c l u d e i n f l a t i o n r a t e s and c a s h f l o w s s h o u l d be e x p r e s s e d i n c u r r e n t t e r m s . U s u a l l y , c o n s t a n t - d o l l a r e v a l u a t i o n s a r e p e r f o r m e d b a s e d on the a s s u m p t i o n t h a t i n t h e l o n g r u n , s i m u l t a n e o u s c h a n g e s i n p r i c e l e v e l s and i n t h e d i s c o u n t r a t e w i l l e f f e c t i v e l y c a n c e l o u t , l e a v i n g t h e i n v e s t m e n t d e c i s i o n unchanged. T h e r e a r e , however, some i m p o r t a n t d i s t u r b a n c e s i n t r o d u c e d by t h e e x i s t e n c e of p r i c e i n f l a t i o n . In a paper p u b l i s h e d i n 1982, LeRoy and F o w l e r [27] d i s c u s s what t h e y c a l l t h r e e s e c o n d a r y e f f e c t s of i n f l a t i o n on a p r e s e n t v a l u e a n a l y s i s and on c a p i t a l r e c o v e r y f a c t o r s . These e f f e c t s a r e : 1. Under t h e tax p r o v i s i o n t h a t p r e v a i l i n many c o u n t r i e s , which a l l o w f u l l t a x d e d u c t i b i l i t y of i n t e r e s t payments, a s i m u l t a n e o u s i n c r e a s e i n p r i c e l e v e l s and the d i s c o u n t 27 r a t e w i l l make any g i v e n p r o j e c t more a t t r a c t i v e ; 2. Those same t a x p r o v i s i o n s do not a l l o w f o r i n d e x a t i o n of the t ax s h i e l d from d e p r e c i a t i o n , t h e r e b y r e d u c i n g t h e v a l u e of the t a x s h i e l d and hence, of a p r o j e c t e x p o s e d t o p r i c e i n c r e m e n t s ; and 3. I n f l a t i o n r e s u l t s i n a d e c r e a s e of t h e n o m i n a l l e v e l of s a l e s (even t h o u g h u n i t s s a l e s maybe be u n a f f e c t e d ) t h e r e b y r e q u i r i n g an i n c r e a s e d i n v e s t m e n t i n w o r k i n g c a p i t a l i n n o m i n a l t e r m s . A d e t a i l e d d i s c u s s i o n of t h e s e p o i n t s may be fo u n d i n t h e a f o r e m e n t i o n e d p a p e r . But maybe even more i m p o r t a n t i s t h e e f f e c t of d i f f e r e n t i a l i n f l a t i o n r a t e s , b o t h w i t h r e s p e c t t o s p e c i f i c c a s h f l o w s and t i m e . R e p o r t e d i n f l a t i o n i n d e x e s l i k e t h e Consumer P r i c e Index i n t h e US and s i m i l a r i n d i c a t o r s i n o t h e r c o u n t r i e s , r e f l e c t a w e i g h t e d a v e r a g e of p r i c e i n c r e m e n t s . An a v e r a g e i s n e c e s s a r y b e c a u s e t h e i n f l a t i o n r a t e f o r s p e c i f i c goods and s e r v i c e s i s not e q u a l . T h i s d i f f e r e n c e w i l l have a s t r o n g impact on t h e economic a t t r a c t i v e n e s s of a p r o j e c t i f i t i s p r e s e n t f o r e x p e n s e s and r e v e n u e s . F o r example, i f d u r i n g the o p e r a t i o n a l p hase of a r e a l e s t a t e d e v e l o p m e n t , r e n t p r i c e s r i s e a t a h i g h e r r a t e than o p e r a t i n g e x p e n s e s , the owner of t h e p r o j e c t w i l l see h i s p r o f i t i n c r e a s e , or d e c r e a s e i f t h e c o n t r a r y o c c u r s . A s e c o n d s i t u a t i o n i s more l i k e l y t o happen. T h a t i s , t h a t i n f l a t i o n r a t e s change d u r i n g t h e l i f e of the p r o j e c t . L a r g e c a p i t a l p r o j e c t s have p l a n n i n g h o r i z o n s as l o n g as 50 28 y e a r s . Even f o r t h e more common c a s e s w i t h p r o j e c t l i v e s of 20 y e a r s , the l i k e l i h o o d t h a t i n f l a t i o n r a t e s r e m a i n c o n s t a n t d u r i n g such p e r i o d s of t i m e i s a l m o s t none. The normal c y c l e s of the economy and change of governments c a u s e i n f l a t i o n l e v e l s t o change o v e r t i m e . C a p i t a l p r o j e c t s a r e c h a r a c t e r i z e d by h a v i n g l a r g e amounts of money s p e n t d u r i n g t h e f i r s t few y e a r s and a more smooth f l o w of r e v e n u e s and o p e r a t i n g e xpenses d u r i n g t h e r e s t of t h e i r l i v e s . . A g r e a t d i f f e r e n c e between i n f l a t i o n i n t h e e a r l y and l a t e r y e a r s of t h e p r o j e c t l i f e would i m p l y a d d i t i o n a l n o n - o p e r a t i o n a l g a i n s or l o s s e s f o r t h e i n v e s t m e n t d e p e n d i n g on t h e d i r e c t i o n of the d i f f e r e n c e . F i n a l l y , h i g h i n f l a t i o n r a t e s may pose a t h r e a t t o t h e a c q u i s i t i o n of f u n d s i n o r d e r t o f i n a n c e t h e p r o j e c t . The e l a p s e d t i m e between the moment when the c o s t of t h e p r o j e c t i s d e f i n e d and i t s f i n a n c i n g a p p r o v e d may be i n t h e range of y e a r s . T h e r e f o r e , i n h y p e r i n f l a t i o n a r y e c o n o m i e s , the amount n e g o t i a t e d would be f a r l e s s t h a n t h e u p d a t e d c o s t of t h e p r o j e c t . R a d e t z k i and Zorn [ 4 2 ] , m e n t i o n th e c a s e of a l a r g e m i n i n g p r o j e c t l o c a t e d i n a t h i r d w o r l d c o u n t r y w i t h h i g h i n f l a t i o n r a t e s t h a t n e g o t i a t e d i t s f i n a n c i n g t h r e e t i m e s as i t s c o s t r o s e w i t h i n f l a t i o n , u n t i l i t was abandoned b e c a u s e of the l a c k of f u n d i n g r e q u i r e d t o c o v e r t h o s e i n c r e m e n t s . 29 2.7 OVERSEAS PROJECTS AND FOREIGN EXCHANGE RATES A common c h a r a c t e r i s t i c of many l a r g e c a p i t a l p r o j e c t s i s t h a t they f a l l under the c a t e g o r y of m u l t i n a t i o n a l o p e r a t i o n s , where t h e s p o n s o r or p a r e n t company i s b a s e d i n a d i f f e r e n t c o u n t r y t o t h a t where t h e p r o j e c t w i l l be u n d e r t a k e n . M i n i n g , o i l and c h e m i c a l p r o c e s s i n d u s t r y p r o j e c t s a r e commonly o v e r s e a s v e n t u r e s . The economic e v a l u a t i o n of f o r e i g n i n v e s t m e n t s o p p o r t u n i t i e s i s s u b j e c t t o a w i d e r and more c o m p l i c a t e d s e t of economic, p o l i t i c a l and s t r a t e g i c c o n s i d e r a t i o n s t h a n t h o s e which i n f l u e n c e most d o m e s t i c i n v e s t m e n t d e c i s i o n s . New s o u r c e s of r i s k c o m p l i c a t e t h e d e c i s i o n making p r o c e s s g i v e n the h i g h l e v e l s of u n c e r t a i n t y i n v o l v e d i n t h e s e p r o j e c t s . These new f a c t o r s i n c l u d e d i f f e r e n c e s between p r o j e c t and p a r e n t company c a s h f l o w s , f o r e i g n t a x r e g u l a t i o n s , l i k e l i h o o d of e x p r o p r i a t i o n , a b i l i t y t o r e p a t r i a t e f u n d s , exchange ' r a t e c h a n g e s , d i f f e r e n t i a l i n f l a t i o n r a t e s and b a s i c b u s i n e s s r i s k of f o r e i g n and d o m e s t i c p r o j e c t s . T h e r e f o r e , b e s i d e s t h e r e l e v a n t q u a l i t a t i v e c o n s i d e r a t i o n s , an a n a l y t i c a l framework t h a t a l l o w s t h e measurement and r e d u c t i o n of a l l t h e s e complex f a c t o r s t o a common d e n o m i n a t o r s h o u l d be implemented i n o r d e r t o d e t e r m i n e the d e s i r a b i l i t y of t h e p r o j e c t u nder c o n s i d e r a t i o n . F i v e a l t e r n a t i v e methods a r e d i s c u s s e d i n t h e l i t e r a t u r e . They a r e : a ) S h o r t e n i n g t h e minimum p a y b a c k p e r i o d ; b ) r a i s i n g t h e r e q u i r e d r a t e of r e t u r n ; c ) a d j u s t i n g 30 the c a s h f l o w s f o r t h e c o s t of r i s k r e d u c t i o n , eg. c h a r g i n g a premium f o r o v e r s e a s p o l i t i c a l r i s k i n s u r a n c e ; d ) a d j u s t i n g c a s h f l o w s t o r e f l e c t the s p e c i f i c impact of a g i v e n r i s k ; and e ) u s i n g c e r t a i n t y e q u i v a l e n t s i n p l a c e of e x p e c t e d c a s h f l o w s . I t i s a l s o c l a i m e d i n t h e l i t e r a t u r e ( S h a p i r o [ 4 8 ] , F o l k s [15]) t h a t i n a n a l y z i n g o v e r s e a s p r o j e c t s , a t w o - s t a g e e v a l u a t i o n a p p r o a c h t h a t d i f f e r e n t i a t e s between t h e p r o j e c t and the p a r e n t ' s c a s h f l o w s s h o u l d be u s e d . In t h e f i r s t s t a g e the p r o j e c t s h o u l d be fo u n d e c o n o m i c a l l y v i a b l e i n t h e l o c a l e n v i r o n m e n t . The o v e r a l l p r o j e c t c a s h -flows i n l o c a l c u r r e n c y a r e d e v e l o p e d from market d a t a and e n g i n e e r i n g and p r o d u c t i o n s t u d i e s and a t r a d i t i o n a l e v a l u a t i o n t e c h n i q u e i s used t o make t h e a c c e p t - r e j e c t d e c i s i o n . I f t h e i n v e s t m e n t i s a c c e p t e d , i t goes t o t h e s e c o n d s t a g e where i t has t o pr o v e i t s v i a b i l i t y i n terms of c a s h f l o w s t o t h e p a r e n t . In o v e r s e a s p r o j e c t s , t h e s t r e a m of c a s h f l o w s r e a l i z e d by t h e p a r e n t d i f f e r s i n t i m i n g and amount from t h a t r e a l i z e d by the p r o j e c t b e c a u s e of fund r e p a t r i a t i o n and tax r e g u l a t i o n s e s t a b l i s h e d by l o c a l governments, b e c a u s e of d i f f e r e n c e s i n i n f l a t i o n r a t e s and because of d i f f e r e n c e s i n t h e p u r c h a s i n g power of money i n t r o d u c e d by exchange r a t e s . In t h i s way, two main s o u r c e s o f r i s k a r e i d e n t i f i e d and c o n s i d e r e d i n t h e se c o n d s t a g e . They a r e t h e c o u n t r y r i s k and t h e macroeconomic u n c e r t a i n t i e s . They w i l l be b r i e f l y d e f i n e d . 31 2.7.1 COUNTRY RISK The c o n c e p t of c o u n t r y r i s k c a p t u r e s t h e e x p o s u r e t o u n c e r t a i n t y about a l a r g e number of f a c t o r s a f f e c t i n g t h e p o l i t i c a l and t h e economic e n v i r o n m e n t of a c o u n t r y . O x h e l h e i m and W i h l b o r g [39] d i v i d e c o u n t r y r i s k i n t o p o l i t i c a l and r i s k r e l a t e d t o economic development i n t h e in v e s t m e n t c o u n t r y . P o l i t i c a l r i s k i s d e f i n e d as t h e p o s s i b i l i t y of changes i n l e g i s l a t i o n and r e g u l a t i o n s t h a t may i n f l u e n c e t h e r e t u r n on t h e p r o j e c t . I t i n v o l v e s u n c e r t a i n t y about o w n e r s h i p r i g h t s , a b o u t exchange r a t e regime, monetary and tax p o l i c i e s , p o l i t i c a l p r e s s u r e s , t e r r o r i s m , e t c . The most extreme p o l i t i c a l r i s k i s t h a t of e x p r o p r i a t i o n . R i s k s r e l a t e d t o economic development r e f e r t o the f a c t t h a t i n t h e l o n g r u n , t h e c o u n t r y ' s economic development would be d e t e r m i n e d by t h e p r o d u c t i v i t y i n c r e m e n t s i n t h e i n d u s t r i a l f i e l d . These i n c r e m e n t s would d e f i n e the growth p e r s p e c t i v e s of t h e p r o j e c t i n t h e l o n g term. A l l t h e s e f a c t o r s a r e p u r e l y q u a l i t a t i v e and d i f f i c u l t t o f o r e s e e . Some m i t i g a t i o n s t r a t e g i e s s u c h as o b t a i n i n g p a r t n e r s h i p from l o c a l i n v e s t o r s or governments, b o r r o w i n g l o c a l l y , or b u y i n g i n s u r a n c e s a r e g e n e r a l l y s u g g e s t e d . 2.7.2 MACROECONOMIC RISK AND EXCHANGE RATES Macroeconomic r i s k i s d i s t i n g u i s h e d from the f a c t t h a t i t i s not f i r m - s p e c i f i c or i n d u s t r y - s p e c i f i c . S o u r c e s of macroeconomic u n c e r t a i n t y a r e exchange r a t e l e v e l s , 32 i n f l a t i o n and i n t e r e s t r a t e s , p r i c e s o f . some c o m m o d i t i e s l i k e o i l and the a g g r e g a t e l e v e l of p r o d u c t i o n and demand. These v a r i a b l e s a r e o f t e n r e f l e c t e d i n exchange r a t e s and, t h e r e f o r e , a t t e n t i o n i s u s u a l l y f o c u s e d on t h e l a t t e r . M acroeconomic e x p o s u r e depends p a r t i c u l a r l y on two e q u i l i b r i u m r e l a t i o n s h i p s . One i s t h e P u r c h a s i n g Power P a r i t y , t h a t r e f e r s t o the e q u a l i t y of good's p r i c e s a c r o s s c o u n t r i e s when measured i n one c u r r e n c y . When t h i s p a r i t y e x i s t s , t h e r e a r e no u n e x p l o i t e d i n t e r n a t i o n a l t r a d e o p p o r t u n i t i e s and t h e exchange r a t e r i s k d i s a p p e a r s . The s e cond r e l a t i o n s h i p i s t h e F i s h e r Open. I t s t a t e s t h a t t h e e x p e c t e d r e t u r n s on f i n a n c i a l i n v e s t m e n t s and the b o r r o w i n g c o s t s a c r o s s c o u n t r i e s and c u r r e n c i e s a r e e q u a l . O x e l h e i m [39] d e m o n s t r a t e s t h a t f o r a l a r g e number of c o u n t r i e s , t h e r e a r e s u b s t a n t i a l d e v i a t i o n s from t h e s e r e l a t i o n s h i p s , a t l e a s t t e m p o r a r i l y and t h e n , p r o j e c t s and i n v e s t m e n t s do f a c e t h i s a d d i t i o n a l r i s k e x p o s u r e . E x c h a n g e r a t e r i s k e x p o s u r e has been d i v i d e d i n t o two t y p e s , namely a c c o u n t i n g and e c o n o m i c . A c c o u n t i n g e x p o s u r e a r i s e s from t h e need, f o r p u r p o s e s of r e p o r t i n g and c o n s o l i d a t i o n of t h e p a r e n t company, t o c o n v e r t the r e s u l t s of t h e o v e r s e a s p r o j e c t from t h e l o c a l c u r r e n c y t o t h e home c u r r e n c y . The most i m p o r t a n t t y p e i s t h e economic e x p o s u r e , t h a t i s b a s e d on t h e p o s s i b i l i t y t h a t t h e Net P r e s e n t V a l u e of the p r o j e c t w i l l change when t h e exchange r a t e c h a n g e s . T h i s change can o c c u r t h r o u g h one or b o t h of the f o l l o w i n g e f f e c t s : a change i n the c a s h f l o w s or 33 a change i n t h e d i s c o u n t r a t e . The exchange r a t e i s assumed t o be time i n v a r i a n t . S h a p i r o [48] s e p a r a t e s economic e x p o s u r e i n t o t r a n s a c t i o n and r e a l o p e r a t i o n e x p o s u r e . T r a n s a c t i o n e x p o s u r e r e s u l t s from the p o s s i b i l i t y of exchange g a i n s or l o s s e s (upon s e t t l e m e n t s a t a f u t u r e d a t e ) o f t r a n s a c t i o n s d enominated i n f o r e i g n c u r r e n c y , f o r example, d e b t i n f o r e i g n c u r r e n c y . R e a l o p e r a t i n g e x p o s u r e a r i s e s b e c a u s e c u r r e n c y f l u c t u a t i o n s , i n c o m b i n a t i o n w i t h p r i c e c h a n g e s , c o u l d a l t e r t h e amounts and r i s k i n e s s of the f u t u r e o p e r a t i n g c a s h f l o w s of t h e p r o j e c t . C o n s e q u e n t l y , m e a s u r i n g the economic e x p o s u r e of t h e p r o j e c t r e q u i r e s m e a s u r i n g i t s s e n s i t i v i t y t o exchange r a t e c h a n g e s . In g e n e r a l , r e a l c a s h f l o w s can be a l t e r e d by one o f t h e f o l l o w i n g e v e n t s : a ) t h e p r e v i o u s l y m e n t i o n e d d e v i a t i o n s from t h e p u r c h a s i n g power p a r i t y ; b ) e x c h a n g e r a t e c h a n g e s c a u s e r e l a t i v e p r i c e c h a n g e s ; c ) g o v e r n m e n t s tax n o m i n a l r a t h e r than r e a l p r o f i t s ; and d)some c a s h f l o w s a r e f i x e d i n n o m i n a l t e r m s . D e t a i l s c o n c e r n i n g t h e s e c i r c u m s t a n c e s a r e documented i n S h a p i r o [ 4 8 ] . F i n a l l y , an a n a l y t i c a l p r o c e d u r e i n o r d e r t o i n c o r p o r a t e exchange r a t e s i n t o t h e economic e v a l u a t i o n p r o c e s s u s i n g t h e NPV as t h e p e r f o r m a n c e measure has been d e v e l o p e d by L e s s a r d [ 2 7 ] . In h i s work, t h i s a u t h o r s u g g e s t s and a d j u s t e d p r e s e n t v a l u e a p p r o a c h t h a t h o l d s f o r i n d e p e n d e n t p r o j e c t s i n c o m p l e t e c a p i t a l m a r k e t s , p r o v i d i n g a r e l a t i v e l y s i m p l e framework f o r e v a l u a t i n g most 34 i n t e r n a t i o n a l c a p i t a l p r o j e c t s . 2.8 CASH FLOWS GENERATED BY FINANCIAL ARRANGEMENTS As m e n t i o n e d b e f o r e , the c a s h f l o w p a t t e r n g e n e r a t e d by t h e f i n a n c i a l mechanisms i n c a p i t a l p r o j e c t s c an have a v e r y d i v e r s e v a r i e t y of shapes a c c o r d i n g t o t h e f i n a n c i n g a r r a n g e d w i t h t h e l e n d i n g i n s t i t u t i o n s . However, a g e n e r a l i z a t i o n can be done i n t h e sen s e t h a t t h e a m o r t i z a t i o n of l o a n s c o m p r i s e s a s e t of d i s c r e t e payments of v a l u e and t i m i n g d e t e r m i n e d by t h e repayment s c h e d u l e . In any c a s e , t h e p r e s e n t worth of t h i s s e t of payments has t o be e q u a l t o the p r e s e n t worth of t h e amount borrowed, b o t h d i s c o u n t e d a t the i n t e r e s t r a t e n e g o t i a t e d f o r t h e l o a n . T h r e e s i m p l e repayment s c h e d u l e s t h a t a r e us e d i n t h e f i n a n c i n g of c a p i t a l p r o j e c t s a r e : 1. U n i f o r m repayment f u n c t i o n , where t h e l o a n i s r e p a i d i n e q u a l amounts. 2. S t e p f u n c t i o n , where t h e payments a r e e q u a l f o r a g i v e n number of p e r i o d s n, and t h e n i n c r e a s e d i n a f i x e d v a l u e . T h i s new amount i s p a i d f o r a n o t h e r n p e r i o d s a f t e r w hich the payment i s i n c r e a s e d a g a i n . T h i s p a t t e r n i s f o l l o w e d u n t i l the l o a n i s c o m p l e t e l y r e p a i d . 3. G r a d i e n t f u n c t i o n , where e a c h payment i s i n c r e a s e d by a f i x e d amount w i t h r e s p e c t t o t h e p r e v i o u s payment. 2.9 IMPLEMENTATION ON THE COMPUTER PROGRAM 35 2.9.1 FINANCIAL MECHANISMS The computer program c o n s i d e r s two d i f f e r e n t t y p e s o f l o a n s : one t a k e n t o f i n a n c e t h e c o n s t r u c t i o n p h a s e ( c o n s t r u c t i o n l o a n ) and a n o t h e r t a k e n t o be r e p a i d w i t h t h e r e v e n u e s g e n e r a t e d by the p r o j e c t ( l o n g term l o a n ) . F o r t h e f o r m e r , the u s e r s p e c i f y t h e f r a c t i o n o f c o n s t r u c t i o n f i n a n c e d w i t h borrowed f u n d s , t h e n o m i n a l i n t e r e s t r a t e and the p e r i o d when t h i s l o a n i s t o be r e p a i d . I t i s assumed i n t h e model, t h a t t h e i n p u t from b o r r o w e d f u n d s f o l l o w s t h e form of the c o n s t r u c t i o n e x p e n d i t u r e f u n c t i o n , and t h a t no repayment of i n t e r e s t or c a p i t a l i s done p r i o r t o t h a t p e r i o d . F o r the l o n g term l o a n , t h e u s e r s p e c i f i e s the amount borrowed, or s i m p l y s e t s i t e q u a l t o t h e v a l u e o f t h e c o n s t r u c t i o n l o a n p l u s i t s a c c r u e d i n t e r e s t s . Then, t h e i n t e r e s t r a t e and t h e t y p e of repayment f u n c t i o n ( u n i f o r m , s t e p or g r a d i e n t ) a r e s p e c i f i e d , as w e l l as t h e f r e q u e n c y and number of payments. U s i n g t h i s i n f o r m a t i o n , a c o m p l e t e repayment s c h e d u l e i s c a l c u l a t e d , i n c l u d i n g payment o f i n t e r e s t s and p r i n c i p a l and l o a n b a l a n c e . 2.9.2 INFLATION In the program, i n f l a t i o n r a t e s a r e . c o n s i d e r e d f o r i n d i v i d u a l c a s h f l o w s , u n i t s a l e p r i c e s and f i x e d and v a r i a b l e o p e r a t i n g c o s t s . The model assumes them t o be 36 c o n s t a n t , not v a r y i n g w i t h t i m e . 2.9.3 FOREIGN EXCHANGE RATE The i s s u e of f o r e i g n exchange r a t e i s i n c l u d e d i n t h e program by s p e c i f y i n g t h e v a l u e of t h e exchange r a t e and t h o s e f l o w s t h a t a r e e x p r e s s e d i n f o r e i g n c u r r e n c y . They a r e s i m p l y c o n v e r t e d i n t o d o l l a r s by m u l t i p l y i n g the v a l u e of t h o s e f l o w s by t h e exchange r a t e . CHAPTER 3. CASH FLOWS GENERATED IN CAPITAL PROJECTS 3. 1 INTRODUCTION The most i m p o r t a n t t a s k i n p r o j e c t e v a l u a t i o n i s , p e r h a p s , t h e d e f i n i t i o n of t h e c a s h f l o w s t h a t w i l l be g e n e r a t e d t h r o u g h o u t - t h e l i f e t i m e of t h e p r o j e c t . Those c a s h f l o w s w i l l be t h e i n p u t t o w e l l known m a t h e m a t i c a l models and t e c h n i q u e s t h a t i n t u r n w i l l y i e l d t h e i n f o r m a t i o n r e q u i r e d -in the d e c i s i o n - m a k i n g p r o c e s s . Thus, t h e q u a l i t y of t h i s i n f o r m a t i o n (and by e x t e n s i o n , t h e d e c i s i o n s made upon i t ) depends on t h e a c c u r a c y a c h i e v e d i n t h e p r e d i c t i o n of t h e c a s h f l o w s . The r e c e i p t s and d i s b u r s e m e n t s r e l a t e d t o a p r o j e c t a r e r e p r e s e n t e d by m a t h e m a t i c a l f u n c t i o n s , e i t h e r d i s c r e t e or c o n t i n u o u s . The p a r a m e t e r s of such f u n c t i o n s d e f i n e the magnitude of t h e c a s h f l o w and t h e way i n t h a t i t w i l l be d i s t r i b u t e d o v e r t i m e , t h a t i s , s c a l e and shape p a r a m e t e r s r e s p e c t i v e l y . A l t h o u g h e a c h p r o j e c t i s a u n i q u e one, some s p e c i a l f u n c t i o n s can be us e d t o r e p r e s e n t t y p i c a l c a s h f l o w p r o f i l e s a c c o r d i n g t o t h e t y p e of t h e p r o j e c t and t h e f l o w i n c o n s i d e r a t i o n . In t h i s c h a p t e r , t h e t y p i c a l f l o w p a t t e r n s or p r o f i l e s t h a t has been r e c o g n i z e d as l i k e l y t o o c c u r i n each p r o j e c t phase and t h e f u n c t i o n s t h a t may be used t o d e s c r i b e them w i l l be p r e s e n t e d . Cash f l o w s p r o f i l e s a s s o c i a t e d w i t h t h e f i n a n c i n g of the p r o j e c t a r e not c o n s i d e r e d i n t h e 37 38 d i s c u s s i o n s i n c e t h e y were p r e s e n t e d i n t h e l a s t c h a p t e r . T h e r e f o r e , t h i s a n a l y s i s c o r r e s p o n d s t o a s i t u a t i o n when no borrowed f u n d s a r e u s e d . S i n c e t h e s e f l o w s a r e c h a r a c t e r i s t i c of t h e t y p e of p r o j e c t b e i n g e v a l u a t e d , f o u r m a j o r f i e l d s where i n t e n s i v e c a p i t a l p r o j e c t s a r e e n c o u n t e r e d have been c h o s e n f o r d i s c u s s i o n , namely t h e o i l and g a s , m i n i n g , r e a l e s t a t e and p r o c e s s i n d u s t r i e s . 3.2 OIL AND GAS INDUSTRY The o i l and gas d r i l l i n g and p r o d u c t i o n p r o j e c t s c o m p r i s e the f o l l o w i n g major p h a s e s : e x p l o r a t i o n , e conomic e v a l u a t i o n , f i e l d d e v e l o p m e n t , o p e r a t i o n and d i s p o s a l . The c a s h f l o w s g e n e r a t e d i n each of them a r e d i s c u s s e d below. 3.2.1 EXPLORATION PHASE The f i r s t s t a g e i n an o i l and gas e x t r a c t i o n p r o j e c t i s the i d e n t i f i c a t i o n of f e a s i b l e e x t r a c t a b l e r e s e r v e s . The s e a r c h f o r o i l b e g i n s w i t h p r e l i m i n a r y e x a m i n a t i o n on t h e s u r f a c e i n the a r e a c o n c e r n e d and i n v o l v e s mapping and g e o p h y s i c a l s u r v e y s , which l e a d s t o an e v a l u a t i o n o f t h e p r o b a b i l i t y t h a t o i l i s i n a p a r t i c u l a r l o c a t i o n . D u r i n g t h i s t i m e , money f l o w s a t a more o r l e s s u n i f o r m r a t e . Once i t seems p r o b a b l e t h a t t h e r e r e a l l y i s o i l i n t h e a r e a , t e s t w e l l s a r e d r i l l e d and the c o s t s r i s e r a p i d l y a t t h i s s t a g e . D r i l l i n g of t e s t w e l l s i s the most s i n g l e c o s t l y o p e r a t i o n of o i l e x p l o r a t i o n , s i n c e i t r e q u i r e s e x p e n s i v e d r i l l i n g and 39 pumping equipment and q u a l i f i e d l a b o r t o do the j o b . The d r i l l i n g c o s t s i n c r e a s e e x p o n e n t i a l l y w i t h d r i l l i n g d e p t h s . Crew c o s t s may v a r y a c c o r d i n g t o complex s h o o t i n g p a t t e r n s . O t h e r c o s t s i n c u r r e d d u r i n g the e x p l o r a t i o n phase a r e r i g h t - o f - w a y p e r m i t s , l e a s e bonus payments t o gove r n m e n t s , s e i s m i c c r ews, t r a n s p o r t a t i o n and l a n d r e n t a l c o s t s . A l l of them c o n t i n u e t o happen u n t i l a l a r g e r e s e r v o i r t h a t i s c o m m e r c i a l l y f e a s i b l e i s d e f i n e d . G i v e n t h e randomness i n v o l v e d i n t h e e v e n t of f i n d i n g o i l , an e x p e n d i t u r e p a t t e r n c a n n o t be e x a c t l y d e f i n e d . At b e s t , i t might be s a i d t h a t d u r i n g t h e e x p l o r a t i o n p h a s e , money i s s p e n t i n a more o r l e s s u n i f o r m way, and from t i m e t o t i m e , some up o r down jumps a r e i n t r o d u c e d by t h e d r i l l i n g or abandonment of t e s t w e l l s , which may c r e a t e a s t e p f u n c t i o n . 3.2.2 ECONOMIC EVALUATION D u r i n g t h i s p h a s e , t h e economic m e r i t s of the v e n t u r e a r e q u a n t i f i e d . A f o r e c a s t of r e v e n u e s and ex p e n s e s i s n e c e s s a r y t o a s s e s the p r o f i t a b i l i t y of the f i e l d , and t h e p r o j e c t i s a c c e p t e d or r e j e c t e d . T h i s phase has a v e r y s h o r t d u r a t i o n when compared w i t h t h e t o t a l l i f e of the p r o j e c t and c o n s e q u e n t l y , a d e t a i l e d d e s c r i p t i o n of the c a s h f l o w i s m e a n i n g l e s s . In g e n e r a l , t h e r e a r e o n l y e xpenses g e n e r a t e d d u r i n g t h i s phase c o r r e s p o n d i n g t o t h e c o s t of p e r f o r m i n g the economic e v a l u a t i o n . I t may be assumed t h a t money f l o w s o u t s i d e t h e p r o j e c t f o l l o w i n g an u n i f o r m d i s t r i b u t i o n , or i n 40 two d i s c r e t e payments (one a t t h e b e g i n n i n g and the o t h e r a t the end of t h e p h a s e ) , or even more s i m p l y , i n one d i s c r e t e payment e q u a l t o t h e t o t a l c o s t of t h e e v a l u a t i o n . 3.2.3 FIELD DEVELOPMENT The economic e v a l u a t i o n w i l l d e t e r m i n e i f the p r o j e c t i s a c c e p t e d or r e j e c t e d . I f i t i s a c c e p t e d , t h e n e x t s t a g e i s t o d e s i g n and c o n s t r u c t t h e f a c i l i t i e s t h a t a r e needed f o r t h e o p e r a t i o n of the p r o j e c t ; t h i s i s the o b j e c t i v e of the d e v elopment p h a s e . In a d d i t i o n , t h e a c q u i s i t i o n of t h e l a n d can be done s i m u l t a n e o u s l y t o t h e d e s i g n p r o c e s s . S i m i l a r t o t h e economic e v a l u a t i o n phase, d e s i g n e x penses a r e i n c u r r e d d u r i n g a v e r y s h o r t p e r i o d of t i m e , and may be assumed t o be u n i f o r m l y d i s t r i b u t e d o v e r t i m e , or a s e t of d i s c r e t e payments. In o r d e r t o s t a r t the c o n s t r u c t i o n a c t i v i t i e s , t h e l a n d has t o be a l r e a d y p u r c h a s e d . I t s v a l u e i s an i m p o r t a n t c h a r g e , and t h e c a s h flow g e n e r a t e d w i t h t h i s t r a n s a c t i o n may be a s i n g l e payment, or a s e r i e s of d i s c r e t e payments a c c o r d i n g t o t h e c o n d i t i o n s of t h e c o m m e r c i a l agreement c o n v e n e d w i t h t h e former owner of t h e l a n d . However, a s e r i e s of payments can be r e p l a c e d by i t s p r e s e n t w orth ( d i s c o u n t e d t o the time when t h e c o n s t r u c t i o n b e g i n s ) , and a s i m i l a r s i t u a t i o n t o the s i n g l e payment c a s e i s o b t a i n e d . F o l l o w i n g the d e s i g n and t h e a c q u i s i t i o n of t h e l a n d i s the p h y s i c a l development of t h e f i e l d . The c o s t s of development i n c l u d e c a s i n g of w e l l s , d r i l l i n g , w e l l 41 equipment, pumping u n i t s , g a t h e r i n g l i n e s , tank b a t t e r i e s , water- or g a s - i n j e c t i o n s y s t e m s , e l e c t r i f i c a t i o n , a c c e s s r o a d s , b u i l d i n g s , e t c . In g e n e r a l , i t i n c l u d e s a l l t h e e x p e n d i t u r e s r e q u i r e d t o d r i l l and c o m p l e t e the w e l l and t o p r o v i d e i t w i t h p r o d u c t i o n f a c i l i t i e s r e q u i r e d t o l i f t t h e o i l and gas from th e bottom o f t h e w e l l t o t h e s u r f a c e and t o t r a n s p o r t i t from the w e l l head t o t h e f i e l d t e r m i n a l . The c a s h f l o w g e n e r a t e d d u r i n g t h i s p r o c e s s t e n d s t o have a b e l l - s h a p e d form. The d e s c r i p t i o n of t h e t y p e s o f f l o w s and t h e m a t h e m a t i c a l f u n c t i o n s t h a t may be u s e d t o r e p r e s e n t them i s g i v e n i n s e c t i o n 3.4.3. A d d i t i o n a l l y , t h e a c q u i s i t i o n o f some p i e c e s of c o s t l y equipment may j u s t i f y the i n c l u s i o n of d i s c r e t e payments t o r e p r e s e n t t h e s e t r a n s a c t i o n s . 3.2.4 OPERATION The o p e r a t i o n a l s t a g e of t h e o i l and gas f i e l d d e a l s w i t h t h e g e n e r a t i o n of t h e income of t h e p r o j e c t as a r e s u l t of the s a l e s of e x t r a c t e d c r u d e o i l and g a s . D i f f e r e n t t y p e s of e x p e n s e s o c c u r d u r i n g t h i s p hase. They a r e t h e w o r k i n g c a p i t a l , o p e r a t i o n a l c o s t s , t a x e s , repayment of l o a n s and non-cash e x p e n s e s : d e p r e c i a t i o n , d e p l e t i o n and a m o r t i z a t i o n . The d i s b u r s e m e n t s r e l a t e d t o f i n a n c i a l i t e m s w i l l not be t r e a t e d h e r e as t h e y were d i s c u s s e d i n t h e l a s t c h a p t e r . 3.2.4.1 REVENUES The r e v e n u e s g e n e r a t e d by t h e p r o j e c t may be d e r i v e d from f u t u r e p r o d u c t i o n e s t i m a t e s by m u l t i p l y i n g 42 the s a l e a b l e p r o d u c t i o n by t h e a p p r o p r i a t e o i l o r n a t u r a l gas v a l u e . T h e r e f o r e , t h e s e two f a c t o r s s h o u l d be e s t i m a t e d . A c c o r d i n g t o I k o k u [ 2 5 ] , f u t u r e o i l income u s u a l l y employs the c u r r e n t l y p o s t e d p r i c e of c r u d e o i l . C u r r e n t p r i c e s a r e a l s o employed f o r n a t u r a l - g a s l i q u i d s . . However, i n t h e gas of n a t u r a l g as, e x i s t i n g c o n t r a c t s s h o u l d be examined f o r t h e gas p r i c e t o u s e . A t y p i c a l p r o d u c t i o n p a t t e r n of o i l w e l l s i s shown i n f i g u r e 1. In the f i r s t s t a g e of p r o d u c t i o n , t h e f i e l d o p e r a t e s a t a c o n s t a n t r a t e qQ, known as maximum e f f i c i e n t , r a t e or w e l l a l l o w a b l e , d u r i n g a p e r i o d of t y e a r s . Then, p r o d u c t i o n b e g i n s t o d e c l i n e e x p o n e n t i a l l y f o r y e a r s b e f o r e r e a c h i n g a non-economic p r o d u c t i o n r a t e a when t h e o p e r a t i o n s a r e not l o n g e r j u s t i f i e d and the p r o j e c t i s abandoned. The p r o d u c t i o n r a t e d u r i n g t h e d e c l i n i n g p e r i o d may be d e s c r i b e d by one of t h r e e commonly r e c o g n i z e d t y p e s of f u n c t i o n s t h a t r e l a t e t h e l e v e l of p r o d u c t i o n q w i t h t i m e t, d e p e n d i n g on how t h e decrement on the p r o d u c t i o n r a t e happens. These f u n c t i o n s a r e r e f e r r e d t o as c o n s t a n t - p e r c e n t a g e d e c l i n e , h a rmonic d e c l i n e and h y p e r b o l i c d e c l i n e . In f i g u r e 2, t h e t y p i c a l shape of the f u n c t i o n s d u r i n g t h e e x p o n e n t i a l d e c l i n e phase, i s d e p i c t e d . I t can be shown t h a t t h e n o m i n a l r a t e of d e c l i n e D, i n the p r o d u c t i o n r a t e q, i s d e s c r i b e d by the e q u a t i o n : FIGURE 1. Produc t ion rate of oil w e l l s FIGURE 2 . P roduc t ion dec l ine curves 45 D = 1 dq q d t (3. 1) Now, t h e p r o d u c t i o n f u n c t i o n s can be deduced a s s u m i n g d i f f e r e n t c h a r a c t e r i s t i c forms of t h e d e c l i n e r a t e D. 1. C o n s t a n t - p e r c e n t a g e d e c l i n e . The c o n s t a n t - p e r c e n t a g e d e c l i n e c u r v e i s t h e s i m p l e s t , most c o n s e r v a t i v e and most w i d e l y u s e d d e c l i n e c u r v e e q u a t i o n i n t h e o i l and gas i n d u s t r y , g i v e n t h a t many w e l l s and f i e l d s a c t u a l l y f o l l o w a c o n s t a n t - p e r c e n t a g e d e c l i n e o v e r a g r e a t p o r t i o n of t h e i r p r o d u c t i v e l i f e , and then,- o n l y d e v i a t e s i g n i f i c a n t l y t o w a r d t h e end of t h i s p e r i o d . When t h i s d e v i a t i o n i s d i s c o u n t e d t o p r e s e n t t i m e , i t i s not u s u a l l y s i g n i f i c a n t . In a d d i t i o n , t h e mat h e m a t i c s i n v o l v e d i n t h i s t y p e of d e c l i n e a r e much s i m p l e r and e a s i e r t o use t h a n the o t h e r two t y p e s of d e c l i n e c u r v e s . Here, i t i s assumed t h a t t h e i n s t a n t a n e o u s o r n o m i n a l d e c l i n e r a t e D, i s a c o n s t a n t p e r c e n t a g e of th e i n s t a n t a n e o u s p r o d u c t i o n r a t e q. M a t h e m a t i c a l l y : w i t h k b e i n g a c o n s t a n t . I n t e g r a t i n g t h i s e q u a t i o n , t h e r a t e - t i m e r e l a t i o n can be o b t a i n e d . ' I t i s : (3. 2) q = q 0 e -Dt 46 (3. 3) where q i s t h e p r o d u c t i o n r a t e a t t i m e t t a k i n g t h e time o r i g e n a t t h e b e g i n n i n g of t h e d e c l i n e , and q 0 i s the p r o d u c t i o n r a t e a t t i m e z e r o . S i n c e Eqn. 3.3 i s an e x p o n e n t i a l f u n c t i o n , t h e c o n s t a n t - p e r c e n t a g e d e c l i n e i s a l s o known as e x p o n e n t i a l d e c l i n e . The c u m u l a t i v e p r o d u c t i o n Q c a n be o b t a i n e d by i n t e g r a t i n g Eqn. 3.3. T h a t y i e l d s : q 0 ( l - e " D t ) q 0 - q Q = = (3.4) D D 2. Harmonic d e c l i n e . In t h e h armonic d e c l i n e t y p e of c u r v e , t h e n o m i n a l d e c l i n e r a t e i s not c o n s t a n t but d e c r e a s e s p r o p o r t i o n a l l y w i t h t h e p r o d u c t i o n r a t e . T h i s i s e x p r e s s e d by the d i f f e r e n t i a l e q u a t i o n : D = -1 5 = kg (3.5) q d t k b e i n g a c o n s t a n t . S i n c e D 0 = k q 0 from Eqns 3.5 and 3.6 (3. 6) 47 D b -15 q d t i n t e g r a t i n g Eqn 3.7 and r e a r r a n g i n g t e r m s : 1+D 0t D f Q o (3. 7) t h a t i s t h e h a r m o n i c d e c l i n e f u n c t i o n . The c u m u l a t i v e f u n c t i o n i s o b t a i n e d by i n t e g r a t i n g Eqn. 3.8; t h a t i s : Q = J i i l n O + D o t ) (3. 9) D 0 Harmonic d e c l i n e i s not w i d e l y u s e d i n r e s e r v e e s t i m a t i o n . However, t h e r e a r e s e v e r a l c o n d i t i o n s under w h i c h i t has been o b s e r v e d i n c r u d e o i l p r o d u c t i o n as would be t h e c a s e o f e x t r a c t i o n of h i g h v i s c o s i t y o i l d r i v e n by e n c r o a c h i n g e d g e w a t e r , or under some t e r m i n a l o p e r a t i o n s s u c h as steam soak i n t h i c k g r a v i t y d r a i n a g e r e s e r v o i r s . 3. H y p e r b o l i c d e c l i n e . In t h i s t y p e of p r o d u c t i o n c u r v e , t h e d e c l i n e r a t e i s d e f i n e d a s : 48 D = - V (3. 10) be where b i s a number in the i n t e r v a l [0,1] and c i s : c = _ L _ (3. i i ) bD 0 Going through the mathematics, the production r a t e at time t i s : q = q 0 ( 1 + b D 0 t ) " ( l / b ) (3. 12) and the cumulative f u n c t i o n i s : Q = — 1- _ 3 ( l _ b ) (3.13) ( l-b)Do q 0 Under c e r t a i n c o n d i t i o n s , o i l production obtained by g r a v i t y drainage w i l l d e c l i n e with a h y p e r b o l i c d e c l i n e constant equal to 0.5. A l s o , the h y p e r b o l i c f u n c t i o n i s a g e n e r a l i z a t i o n of the other two types of f u n c t i o n s . The exponential d e c l i n e can be obtained with b=0, whereas a value of b=1 w i l l y i e l d the harmonic d e c l i n e . 49 2.4.2 EXPENSES Working c a p i t a l Once the f i e l d has been d e v e l o p e d and i t i s r e a d y f o r p r o d u c t i o n , w o r k i n g c a p i t a l i s i n j e c t e d i n t o t h e p r o j e c t , i n o r d e r t o have a r e s e r v o i r of money t o be drawn on as needed t o f a c i l i t a t e and i n s u r e smooth o p e r a t i o n s . W o rking c a p i t a l i n p u t i s modeled by a s i n g l e d i s c r e t e payment l o c a t e d a t t h e b e g i n n i n g of the o p e r a t i o n a l phase and a l t h o u g h i t goes i n t o t h e p r o j e c t , i t i s c o n s i d e r e d an o u t - c a s h i t e m i n t h e economic e v a l u a t i o n . O p e r a t i n g c o s t s O p e r a t i n g c o s t s a r e a l l t h o s e c o s t s i n c u r r e d i n t h e o p e r a t i o n s of e x t r a c t i n g , p r o d u c i n g , s t o r i n g , t r a n s p o r t i n g and s e l l i n g o i l and g a s . They may be f u r t h e r d i v i d e d i n t o two c a t e g o r i e s : d i r e c t o p e r a t i n g c o s t s and i n d i r e c t o p e r a t i n g c o s t s . The former i n c l u d e s l a b o r and m a t e r i a l s c o s t s f o r o p e r a t i o n , m a i n t e n a n c e , w o r k o v e r s , gas p r o c e s s i n g p l a n t s , s a l t - w a t e r d i s p o s a l s y s t e m s , g a s - or w a t e r - i n j e c t i o n p l a n t s and pumping s t a t i o n s . The i n d i r e c t o p e r a t i n g c o s t s a r e t h o s e e x p e n d i t u r e s i n c u r r e d on b e h a l f of t h e o p e r a t i o n i n g e n e r a l . Items c o n s i d e r e d h e r e a r e p l a n t and home o f f i c e o v e r h e a d s , a d m i n i s t r a t i o n and management, r e s e a r c h and d evelopment, s e l l i n g e x p e n s e s , r o y a l t i e s , i n s u r a n c e and l o c a l t a x e s , b o n u s e s , d o n a t i o n s , e t c . 50 T h e r e i s no s t r a i g h t f o r w a r d r e l a t i o n s h i p between i n d i r e c t and d i r e c t c o s t s but t h e y a r e a l l o c a t e d t o v a r i o u s p h a s e s by means of s i m p l e r u l e s t h a t v a r y from company t o company. I t i s a common p r a c t i c e t o e x p r e s s i n d i r e c t c o s t s as a p e r c e n t a g e on t o p of d i r e c t c o s t s i n c u r r e d d u r i n g t h e s t e a d y p r o d u c t i o n p e r i o d and keep them c o n s t a n t a l o n g t h e p r o j e c t . D i r e c t c o s t can be d e f i n e d by m u l t i p l y i n g t h e u n i t c o s t by t h e p r o d u c t i o n o u t p u t . They a r e p r o p o r t i o n a l t o t h e volume of o i l and gas p r o d u c e d , which i n t u r n i s d e t e r m i n e d u s i n g one of t h e c u r v e s p r e s e n t e d i n t h e l a s t s e c t i o n . Taxes Taxes t o which o i l and gas p r o d u c t i o n p r o j e c t s a r e s u b j e c t e d v a r y w i d e l y t h r o u g h o u t t h e w o r l d . They may i n c l u d e c o n s e r v a t i o n , p r o p e r t y and e x c i s e t a x e s c a l c u l a t e d on t h e b a s i s of p r o d u c t i o n v a l u e , p r o d u c t i o n volume or b o t h , and p a i d e i t h e r t o m u n i c i p a l , s t a t e or n a t i o n a l g o vernments. The t a x l e g i s l a t i o n i t s e l f c h a n g e s from t i m e t o time w i t h i n t h e same c o u n t r y and i t i s d i f f i c u l t t o make g e n e r a l i z a t i o n s r e g a r d i n g t h i s t o p i c . E a c h p a r t i c u l a r c a s e s h o u l d be a n a l y z e d a c c o r d i n g t o t h e l o c a t i o n of t h e p r o j e c t and t h e c u r r e n t l e g i s l a t i o n , i n o r d e r t o e s t a b l i s h t h e i r t y p e and v a l u e . D e p r e c i a t i o n , D e p l e t i o n and A m o r t i z a t i o n . These a r e s p e c i a l e x p e n d i t u r e s s i n c e t h e y do not 51 i m p l y a c t u a l f l o w of c a s h . However, t h e y s h o u l d be c o n s i d e r e d i n the a n a l y s i s b ecause t h e i r i mpact on t h e p r o f i t i s i m p o r t a n t , and i n c l u d i n g or e x c l u d i n g them may r e v e r s e t h e a c c e p t - r e j e c t d e c i s i o n made d u r i n g the economic e v a l u a t i o n . D e p r e c i a t i o n , d e p l e t i o n and a m o r t i z a t i o n a r e t h e means of r e c o v e r i n g t h e i n v e s t m e n t i n c e r t a i n t y p e of a s s e t s i n b e f o r e - t a x d o l l a r s . D e p r e c i a t i o n i s the p r o c e s s of p r o r a t i n g as e x p e n s e s t h e c a p i t a l i z e d c o s t of c e r t a i n i t e m s o v e r a p e r i o d of y e a r s . As . i t was p r e v i o u s l y n o t e d , i t i s a n o n - c a s h c h a r g e , but i t i s d e d u c t i b l e from th e t a x b a s e , which r e p r e s e n t s a r e a s o n a b l e a l l o w a n c e f o r t h e e x h a u s t i o n , wear and t e a r and o b s o l e s c e n c e of d e p r e c i a b l e p r o p e r t y u s e d i n b u s i n e s s o r h e l d f o r t h e p r o d u c t i o n of income. T h i s e n a b l e s t h e p r o j e c t s p o n s o r t o r e c o v e r t h e c o s t of a d e p r e c i a b l e a s s e t d u r i n g i t s e s t i m a t e d u s e f u l l i f e . In the o i l and gas i n d u s t r y , d e p r e c i a b l e i t e m s n o r m a l l y i n c l u d e w e l l equipment and s u r f a c e e q u i p m e n t . In g e n e r a l , an i t e m may be d e c l a r e d d e p r e c i a b l e i f i t r e t a i n s a u s a b l e or r e u s a b l e v a l u e a f t e r a p e r i o d of t i m e . T h e r e a r e s e v e r a l commonly us e d methods of d e t e r m i n i n g d e p r e c i a t i o n c h a r g e s , a l t h o u g h any c o n s i s t e n t method i s a c c e p t a b l e as l o n g as i t c onforms t o c e r t a i n g overnment-imposed l i m i t a t i o n s . F o r the U n i t e d S t a t e s , t h e y a r e t h e s t r a i g h t - l i n e 52 method, t h e d e c l i n i n g b a l a n c e method, t h e sum of t h e y e a r s d i g i t s method and t h e u n i t of p r o d u c t i o n method. A d e t a i l e d d e s c r i p t i o n of a l l of them c a n be fou n d e l s e w h e r e ( [ 1 ] ) . V a l l e - R i e s t r a [54] s u g g e s t s t h a t the method s e l e c t e d i n t h e p r o j e c t s h o u l d be t h e one f o r which t h e p r e s e n t v a l u e of a l l d e p r e c i a t i o n c h a r g e s i s a maximum. T h i s r u l e d o e s not l e a d t o t h e c h o i c e of a u n i q u e method s i n c e t h e p r e s e n t v a l u e depends upon t h e p r o j e c t l i f e t i m e , t h e s a l v a g e v a l u e and the t i m e v a l u e of money. T h i s a u t h o r a l s o s u g g e s t t h a t f o r t h e sake of s i m p l i c i t y d u r i n g t h e e a r l y - s t a g e p r o j e c t e v a l u a t i o n , t h e s t r a i g h t - l i n e method w i t h z e r o s a l v a g e v a l u e may be u s e d . The s e c o n d t y p e of n o n - c a s h c h a r g e s i s t h e d e p l e t i o n a l l o w a n c e . I t i s a d e p r e c i a t i o n l i k e c h a r g e t o a c c o u n t f o r t h e e x h a u s t i o n of a n a t u r a l r e s o u r c e a s a r e s u l t of i t s e x t r a c t i o n . The i d e a b e h i n d d e p l e t i o n i s t h a t as some m i n e r a l r e s o u r c e i s e x t r a c t e d and s o l d , the r e s e r v e s of the m i n e r a l s h r i n k s and the v a l u e of t h e p r o p e r t y d i m i n i s h e s . U n l e s s some p r o v i s i o n such as d e p l e t i o n c h a r g e s i s made t o r e c o v e r t h e i n v e s t m e n t as t h e c r u d e o i l i s pumped and s o l d , t h e net r e s u l t w i l l be the l o s t of c a p i t a l . The d e p l e t i o n a l l o w a n c e may be computed on e i t h e r a f i x e d p e r c e n t a g e b a s i s of a c o s t - p e r - u n i t 53 b a s i s . A d e s c r i p t i o n o f t h e s e two methods can be found i n G e n t r y and O ' N e i l [ 1 6 ] . F i n a l l y , a m o r t i z a t i o n a p p l i e s t o c e r t a i n c a p i t a l e x p e n d i t u r e s . The c a p i t a l e x p e n d i t u r e s t o which i t a p p l i e s v a r i e s from p l a c e t o p l a c e and from time t o t i m e a c c o r d i n g t o v a r i a t i o n i n t h e f i s c a l p o l i c y o f the c o u n t r y where the p r o j e c t i s u n d e r t a k e n . In the U n i t e d S t a t e s , f o r example, a m o r t i z a t i o n can be a p p l i e d t o o r g a n i z a t i o n e x p e n s e s of the company, r e s e a r c h and d e v elopment e x p e n s e s , trademark and tradename e x p e n d i t u r e s , and some o t h e r e x p e n s e s . The f i r m may d e d u c t e a c h y e a r a p a r t of t h e s e e x p e n d i t u r e s and t h u s , r e c o v e r them i n a manner s i m i l a r t o t h e s t r a i g h t - l i n e d e p r e c i a t i o n . 3.2.5 DISPOSAL When the r a t e of p r o d u c t i o n of an o i l and gas f i e l d has d e c l i n e d t o a v a l u e when the p r o d u c t i o n r e v e n u e s w i l l j u s t meet the o p e r a t i n g e x p e n s e s of t h e w e l l , known as t h e economic l i m i t , t h e p r o j e c t i s abandoned. At t h i s t i m e , t h e equipment can be s c r a p p e d or s o l d and t h e l a n d may be a l s o s o l d . These a r e n o n - o p e r a t i o n a l r e v e n u e s t h a t s h o u l d be i n c l u d e d i n the a n a l y s i s s i n c e t h e i r v a l u e ( m a i n l y t h e r e v e n u e o b t a i n e d w i t h t h e l a n d t r a n s a c t i o n ) c o u l d be c o n s i d e r a b l e . However, i t w i l l depend on the l o c a t i o n of t h e p r o j e c t and the a c t u a l q u a n t i t y of s a l e a b l e equipment. F o r p u r p o s e s of p r e l i m i n a r y economic e v a l u a t i o n , the s a l v a g e 54 v a l u e of the p r o j e c t can be assumed t o be a s i n g l e payment f l o w i n g i n t o t h e p r o j e c t a t the end of t h e o p e r a t i o n a l p h a s e . In c a s e s when the l a n d has a h i g h v a l u e , c e r t a i n k i n d s of c o m m e r c i a l a g r e e m e n t s might t a k e e f f e c t and a s e t of payments or a d i s c r e t e f u n c t i o n may be a p p r o p r i a t e f o r m o d e l l i n g the s a l v a g e v a l u e o f t h e v e n t u r e . 3.3 MINING PROJECTS The p h ases i n a m i n i n g p r o j e c t a r e the same as t h o s e i n an o i l and gas e x p l o i t a t i o n p r o j e c t d i s c u s s e d i n the p r e v i o u s s e c t i o n . The s e a r c h f o r an e c o n o m i c a l l y e x t r a c t a b l e o r e i s c o n d u c t e d i n t h e f i r s t p l a c e , t h e n the p r o f i t a b i l i t y of t h e i n v e s t m e n t i s e v a l u a t e d and t h e mine i s d e v e l o p e d . A f t e r a r e l a t i v e l y l o n g p e r i o d of o p e r a t i o n , t h e p r o j e c t i s abandoned. The c a s h f l o w s g e n e r a t e d d u r i n g e x p l o r a t i o n , e v a l u a t i o n and d i s p o s a l a r e v e r y s i m i l a r t o t h o s e o f an o i l p r o j e c t , s i n c e t h e k i n d of a c t i v i t i e s and the work i n v o l v e d i n t h e i r e x e c u t i o n i s p r a c t i c a l l y e q u a l i n b o t h c a s e s . Then, t h e s e phases w i l l not be t r e a t e d i n m i n i n g p r o j e c t s . The d i s c u s s i o n c o n c e r n i n g t h e l a n d a c q u i s i t i o n p r e s e n t e d i n t h e l a s t s e c t i o n a l s o a p p l i e s h e r e . The l i k e l y t y p e of f l o w s o c c u r r i n g d u r i n g the d e v e l o p m e n t and o p e r a t i o n p h a s e s a r e p r e s e n t e d below. 55 3.3.1 MINE DEVELOPMENT The c o n s t r u c t i o n and d e v e l o p m e n t of a mine o n l y , i s a g i a n t c i v i l e n g i n e e r i n g p r o j e c t . L a r g e amounts of e a r t h a r e moved and b u i l d i n g s and t r a n s p o r t a t i o n f a c i l i t i e s s uch as r o a d s , r a i l w a y s and p o r t s a r e c o n s t r u c t e d . In a d d i t i o n , c o s t l y h a n d l i n g and sometimes p r o c e s s i n g e q u i p m e n t , have t o be p u r c h a s e d . The d e v e l o p m e n t of a mine c a n be v i e w e d as t h e sum of s e v e r a l s u b - p r o j e c t s v a r y i n g i n s i z e , t y p e and number a c c o r d i n g t o the t y p e and s i z e of t h e mine i t s e l f . The c a s h f l o w p r o f i l e g e n e r a t e d d u r i n g t h e c o n s t r u c t i o n of c i v i l p r o j e c t s t e n d s t o have a b e l l - s h a p e d form t h a t c a n be r e p r e s e n t e d by s e v e r a l m a t h e m a t i c a l f u n c t i o n s l i k e t h e Normal, B e t a , Gamma and W e i b u l l f u n c t i o n s . T h e s e c o n s t r u c t i o n e x p e n d i t u r e f u n c t i o n s and t h e i r c o r r e s p o n d i n g e q u a t i o n s w i l l be i n t r o d u c e d i n s e c t i o n 3.2.3. E a r t h movement i s a more or l e s s c o n t i n u o u s o p e r a t i o n and w h i l e i t t a k e s p l a c e , money i s s p e n t u n i f o r m l y . The a c q u i s i t i o n o f heavy and e x p e n s i v e equipment can be r e p r e s e n t e d by d i s c r e t e payments d i s t r i b u t e d a l o n g t h e t i m e a x i s a c c o r d i n g t o a p r o c u r e m e n t s c h e d u l e . These s u b - p r o j e c t s a r e u n d e r t a k e n f o l l o w i n g t h e g e n e r a l mine development s c h e d u l e , and t h e y a r e u s u a l l y o v e r l a p p e d i n t i m e . T h e r e f o r e , t h e g e n e r a l c a s h f l o w p r o f i l e of t h e development phase i s made up of s e v e r a l o v e r l a p p e d b e l l - s h a . p e d s u b f l o w s p l u s some d i s c r e t e payments. 56 3.3.2 OPERATION PHASE 3.3.2.1 Revenues E s t i m a t i n g m i n e r a l p r o j e c t r e v e n u e s i s a d i f f i c u l t and r i s k y t a s k . A n n u a l mine revenue i s c a l c u l a t e d by m u l t i p l y i n g t h e number of u n i t s p r o d u c e d and s o l d d u r i n g the y e a r by t h e s a l e s u n i t p r i c e . In p r a c t i c e , t h e number of u n i t s s o l d u s u a l l y d i f f e r s by a s m a l l amount from the u n i t s mined due t o c h a n g es i n i n v e n t o r y l e v e l s , but t h i s d i f f e r e n c e i s g e n e r a l l y i g n o r e d i n v a l u a t i o n s t u d i e s . T h i s i s a l s o v a l i d i n any p r o j e c t i n w hich t h e r e v e nue i s o b t a i n e d by t h e p r o d u c t i o n and s e l l i n g o f any k i n d of commodity. W h i l e the a r i t h m e t i c i n v o l v e d i n c a l c u l a t i n g r e v e n u e s i s t r i v i a l , d e t e r m i n i n g th e b e s t v a l u e t o use f o r e a c h of t h o s e two c r i t i c a l v a r i a b l e s i s much more d i f f i c u l t . B e s i d e s , i t has been p o i n t e d out many t i m e s i n the l i t e r a t u r e , t h a t t h e s e v a r i a b l e s a r e i n t h e s e t of h i g h l y s e n s i t i v e v a r i a b l e s i n any p r o f i t a b i l i t y measure and s h o u l d be c a r e f u l l y e v a l u a t e d . The a n n u a l p r o d u c t i o n r a t e may be e a s i e r t o d e f i n e s i n c e most of i t s components a r e t e c h n i c a l i s s u e s t h a t a r e d e t e r m i n e d u s i n g c l a s s i c a l m i n i n g e n g i n e e r i n g t e c h n i q u e s . G e n e r a l l y , a mine o p e r a t e s a t a c o n s t a n t p r o d u c t i o n r a t e t h r o u g h o u t most of i t s l i f e . I t i s an optimum r a t e e s t a b l i s h e d by m i n i n g e n g i n e e r s d e p e n d i n g of t h e p a r t i c u l a r c h a r a c t e r i s t i c s of t h e p r o j e c t . O n l y a t t h e b e g i n n i n g and towards the end of o p e r a t i o n does the o u t p u t d i f f e r from the o p t i m a l p r o d u c t i o n r a t e due 57 t o a d j u s t m e n t s and i n c r e m e n t s o f p r o d u c t i v i t y d u r i n g t h e s t a r t - u p of the mine and t o d e c r e m e n t s of r e c o v e r a b l e m i n e r a l near t h e e x h a u s t i o n of t h e o r e . In t h e s i m p l e s t c a s e , t h e p r o d u c t i o n f u n c t i o n may be c o n s i d e r e d t o be c o n s t a n t d u r i n g t h e e n t i r e d u r a t i o n of the o p e r a t i o n phase. F o r t h e sake of s i m p l i c i t y , t h i s i s assumed i n many p r e l i m i n a r y e a r l y s t a g e economic e v a l u a t i o n s . Then, r e f i n e m e n t s can be i n t r o d u c e d by a s s i g n i n g a f u n c t i o n a l f o r m t o t h e p r o d u c t i o n o u t p u t a t the s t a r t and f i n i s h of o p e r a t i o n s . D u r i n g t h e s t a r t - u p p e r i o d , the p r o d u c t i o n c an be assumed t o i n c r e a s e l i n e a r l y from z e r o t o t h e o p t i m a l r a t e i n a g i v e n t i m e , or f o l l o w i n g some t y p e of e x p o n e n t i a l f u n c t i o n l i k e t h e l o g i s t i c or Gompertz c u r v e s ( t h e s e s p e c i a l f u n c t i o n s w i l l be d e s c r i b e d when t h e p r o d u c t i o n f u n c t i o n s o f p r o c e s s i n d u s t r i e s a r e d i s c u s s e d ) . S i m i l a r l y , when t h e s a l e a b l e p r o d u c t i o n commences t o d e c l i n e a t the l a t e r s t a g e s of t h e p r o j e c t , i t may be assumed t o happen l i n e a r l y from the o p t i m a l r a t e u n t i l t h e economic l i m i t i s r e a c h e d and c o n t i n u e d o p e r a t i o n i s no l o n g e r j u s t i f i e d . O t h e r w i s e , a p a r a b o l i c or e x p o n e n t i a l d e c l i n e can be used. In f i g u r e 3, an h y p o t h e t i c a l p r o d u c t i o n s c h e d u l e f o r a c o a l mine i s p r e s e n t e d . A l o g i s t i c c u r v e i s u s e d d u r i n g the e a r l y o p e r a t i o n ; when the o p t i m a l p r o d u c t i o n r a t e i s o b t a i n e d , the o u t p u t r e m a i n s c o n s t a n t d u r i n g a l o n g p e r i o d of ti m e ; t h e n , i t s t a r t s t o d e c l i n e l i n e a r l y - IGURE 3 . Example of output of a m ine Time CJI 00 59 u n t i l the economic l i m i t i s r e a c h e d . The s e c o n d major component of mine r e v e n u e c a l c u l a t i o n i s the u n i t s a l e s p r i c e , and i t i s an e x e r c i s e f o r which a h i g h e r r o r of e s t i m a t i o n i n v a r i a b l y e x i s t s . A v e r y s i m p l i s t i c a s s u m p t i o n may be made by a d o p t i n g t h e c u r r e n t m i n e r a l p r i c e and use i t t o e s t i m a t e t o t a l r e v e n u e s . However, t h i s c a n l e a d t o even more s e r i o u s e r r o r s . Some m a t h e m a t i c a l t e c h n i q u e s a r e a v a i l a b l e t o p r o d u c e f o r e c a s t s of f u t u r e p r i c e s b a s e d on p a s t v a l u e s . They i n c l u d e w e i g h t e d , moving or l o g a r i t h m i c a v e r a g e s , h i g h e r o r d e r r e g r e s s i o n i n c l u d i n g F o u r i e r s e r i e s and e c o n o m e t r i c m o d e l l i n g . A g r e a t d e a l of judgement i s a b a s i c i n g r e d i e n t i n t h i s p r o c e s s . 3.3.2.2 Ex p e n s e s O p e r a t i n g c o s t a r e d e f i n e d as t h o s e o n g o i n g , r e c u r r i n g c o s t s i n c u r r e d d u r i n g the no r m a l f u n c t i o n i n g of t h e mine. In m i n i n g p r o j e c t s , t h e i r s t r u c t u r e i s v e r y s i m i l a r t o t h a t i n o i l and gas p r o j e c t s . The same d i f f e r e n t i a t i o n between d i r e c t and i n d i r e c t c o s t s i s made; t a x e s , d e p r e c i a t i o n , a m o r t i z a t i o n and d e p l e t i o n a r e o t h e r o p e r a t i o n a l c h a r g e s t h a t a l s o a p p l y t o t h i s t y p e of p r o j e c t . T h e r e f o r e , t h e c a s h f l o w p r o f i l e of o p e r a t i o n a l e x p e n s e s i s v e r y s i m i l a r t o the one p r e s e n t e d i n s e c t i o n 3.2.4.2. 60 3.4 REAL ESTATE PROJECTS R e a l e s t a t e p r o j e c t s a r e u n d e r t a k e n as a r e s p o n s e t o c e r t a i n market o p p o r t u n i t i e s . They i n c l u d e s h o p p i n g c e n t e r s , o f f i c e b u i l d i n g s , h o u s i n g d e v e l o p m e n t s and t h e l i k e . These p r o j e c t s c o m p r i s e s i x b a s i c p h a s e s s t a r t i n g w i t h t h e f e a s i b i l i t y a n a l y s i s and f o l l o w e d by t h e d e s i g n , c o n s t r u c t i o n , a b s o r p t i o n , o p e r a t i o n and d i s p o s a l . The c a s h f l o w g e n e r a t e d d u r i n g each of them w i l l be now p r e s e n t e d . 3.4.1 F E A S I B I L I T Y ANALYSIS The o b j e c t i v e i n t h i s s t a g e of t h e work i s t o p r o d u c e a f e a s i b i l i t y s t u d y of t h e p r o p o s e d i n v e s t m e n t . A f e a s i b i l i t y s t u d y i s an a n a l y s i s i n t e n d e d t o d i s c o v e r whether or n o t t h e p r o j e c t can be c a r r i e d out s u c c e s s f u l l y , w i t h s u c c e s s u s u a l l y meaning s u f f i c i e n t r e t u r n on t h e c a p i t a l i n v e s t e d by t h e s p o n s o r of t h e p r o j e c t . I t r e q u i r e s two i n t e r d e p e n d e n t a n a l y s e s : a market r e s e a r c h and a f i n a n c i a l e v a l u a t i o n . The e x p e n s e s i n c u r r e d d u r i n g t h i s phase c o r r e s p o n d t o the c o s t of c o l l e c t i n g and a n a l y z i n g t h e i n f o r m a t i o n r e q u i r e d i n the p r o d u c t i o n of the f e a s i b i l i t y r e p o r t . I t i s a r e l a t i v e l y low f i g u r e when compared w i t h c a s h f l o w s g e n e r a t e d i n o t h e r p h a s e s . B e s i d e s , t h i s phase has a r e l a t i v e l y s h o r t d u r a t i o n . Because of t h e s e two r e a s o n s , i t may be assumed t h a t t h e c a s h f l o w p r o f i l e has one o f t h e t h r e e f o l l o w i n g s i m p l e f o r m s : 1. A s i n g l e d i s c r e t e payment; 2. Two d i s c r e t e payments, one a t t h e b e g i n n i n g and one a t 61 the end of t h e phase; or 3. A u n i f o r m d i s t r i b u t i o n , a s s u m i n g t h a t money f l o w s u n i f o r m l y d u r i n g t h e p r e p a r a t i o n of t h e f e a s i b i l i t y s t u d y . 3.4.2 DESIGN D u r i n g t h e d e s i g n s t a g e , t h e p h y s i c a l s p e c i f i c a t i o n s of the p r o j e c t a r e d e f i n e d . F o u r major components a r e i n c l u d e d i n i t s t o t a l c o s t : a r c h i t e c t u r a l , s t r u c t u r a l , e l e c t r i c a l and m e c h a n i c a l d e s i g n . In some l a r g e h o u s i n g p r o j e c t s , t h e c o s t of d e s i g n i n g some r e q u i r e d u t i l i t y o r i n f r a s t r u c t u r e f a c i l i t i e s s u c h as water and sewage s y s t e m s and i n t e r n a l r o a d s s h o u l d be i n c l u d e d . G i v e n t h i s phase has a r e l a t i v e l y s h o r t d u r a t i o n and t h a t i t s c o s t i s a l s o r e l a t i v e l y low i n r e l a t i o n t o t h e c o n s t r u c t i o n p h a s e , the c a s h f l o w g e n e r a t e d d u r i n g i t s e x e c u t i o n may be e x p r e s s e d i n one of t h e t h r e e ways m e n t i o n e d i n t h e p r e v i o u s s e c t i o n . The d e s i g n c o s t may be t r e a t e d as a g l o b a l q u a n t i t y or brok e n down t o p r o d u c e a s e t of s u b - f l o w s a n a l y z e d i n d e p e n d e n t l y . 3.4.3 CONSTRUCTION D u r i n g t h e c o n s t r u c t i o n phase, a l l t h e f a c i l i t i e s c o n s i d e r e d t o be i n t e g r a l p a r t of t h e p r o j e c t a r e b u i l t . In o r d e r t o p r o c e e d w i t h t h e s e a c t i v i t i e s , t h e l a n d has t o be. a c q u i r e d . T h i s t a s k i s r e a l l y i n d e p e n d e n t of t h e c o n s t r u c t i o n phase and make t a k e p l a c e a nytime b e f o r e 62 b e g i n n i n g of c o n s t r u c t i o n . In most e v a l u a t i o n s t u d i e s , t h e l a n d v a l u e i s r e p r e s e n t e d by a s i n g l e payment o c c u r r i n g a t the b e g i n n i n g of t h e c o n s t r u c t i o n p h a s e . T h i s i s a r e a s o n a b l e a s s u m p t i o n , but i n some c a s e s , t h e a c q u i s i t i o n of the l a n d on which a r e a l s t a t e d e v e l o p m e n t i s b e i n g p l a n n e d i s s u b j e c t t o s p e c i a l c o n t r a c t u a l a greements between t h e p a r t i e s i n v o l v e d i n t h e n e g o t i a t i o n . Such a g r e e m e n t s may s p e c i f y a s c h e d u l e of payments a l o n g s e v e r a l y e a r s . Thus, a s e r i e s of s i n g l e f l o w s o r i t s p r e s e n t w o r t h d i s c o u n t e d t o the time when t h e c o n s t r u c t i o n s t a r t s , may be employed. When the p r e s e n t worth method i s u s e d , i t s h o u l d be o b t a i n e d by d i s c o u n t i n g t h e o u t f l o w s a s s o c i a t e d w i t h t h e l a n d a c q u i s i t i o n a t t h e same r a t e u s e d i n the c a l c u l a t i o n o f t h e net p r e s e n t v a l u e of t h e p r o j e c t , g i v e n t h a t t h i s i s an i n t e g r a l component of t h e i n v e s t m e n t . The c o n s t r u c t i o n of any c i v i l p r o j e c t i s s u b j e c t t o a p r e d e f i n e d s c h e d u l e , i n w h i c h a c t i v i t i e s a r e l i n k e d t o e a c h o t h e r a c c o r d i n g t o l o g i c a l r e l a t i o n s h i p s . Those a c t i v i t i e s a r e a l s o r e f e r r e d t o as work p a c k a g e s ( g e n e r a l l y , a work package i s a c o l l e c t i o n of a c t i v i t i e s ) and f o l l o w i n g l o g i c a l p r e c e d e n c e r u l e s , t h e y a r e a r r a n g e d i n a network t h a t d e f i n e s the c o n s t r u c t i o n s c h e d u l e . One c h a r a c t e r i s t i c of such a network i s t h a t i t t e n d s t o have an a g g l o m e r a t i o n of a c t i v i t i e s t h a t have t o be e x e c u t e d towards the m i d d l e of the c o n s t r u c t i o n p e r i o d , and l e s s of them towards b o t h t h e b e g i n n i n g and e n d i n g of c o n s t r u c t i o n . 63 The l a t t e r i m p l i e s t h a t d u r i n g c o n s t r u c t i o n , money i s more h e a v i l y s p e n t a t the m i d d l e s t a g e s o f the p r o c e s s and l e s s h e a v i l y s p e n t a t the b e g i n n i n g and end of t h i s p e r i o d . A l s o , due t o t h e n a t u r e of t h e n e t w o r k s , t h e t r a n s i t i o n between t h e s e two d i f f e r e n t p a t t e r n s of e x p e n d i t u r e t e n d s t o be e x p o n e n t i a l , and the c o n s t r u c t i o n e x p e n d i t u r e f u n c t i o n t u r n s out t o be a b e l l - s h a p e d c u r v e . However, t h i s t y p e of f u n c t i o n o n l y r e p r e s e n t s t h e d i r e c t c o n s t r u c t i o n c o s t s . T h e r e a r e two o t h e r major c o s t i t e m s i n c u r r e d d u r i n g c o n s t r u c t i o n , namely t h e i n d i r e c t c o s t s and t h e m o b i l i z a t i o n - d e m o b i l i z a t i o n c o s t s . The f o r m e r can be assumed t o be c o n s t a n t and u n i f o r m l y d i s t r i b u t e d d u r i n g c o n s t r u c t i o n . They i n c l u d e a d m i n i s t r a t i o n , management, o v e r h e a d s , t e m p o r a r y u t i l i t i e s and so f o r t h . M o b i l i z a t i o n and d e m o b i l i z a t i o n c o s t s a r e i n c u r r e d a t t h e b e g i n n i n g and end of c o n s t r u c t i o n and t h e y may be assumed t o be s i n g l e payments or u n i f o r m l y d i s t r i b u t e d d u r i n g the s h o r t p e r i o d of t i m e when t h e y o c c u r . S i n c e d i r e c t c o s t a r e t h e g r e a t e s t component of t h e c a s h f l o w g e n e r a t e d d u r i n g c o n s t r u c t i o n , d i s c u s s i o n w i l l f o c u s on them. I t was p r e v i o u s l y m e n t i o n e d t h a t d i r e c t c o n s t r u c t i o n c o s t s can be e x p r e s s e d by a b e l l - s h a p e d t y p e of c u r v e . S e v e r a l m a t h e m a t i c a l f u n c t i o n s may be us e d f o r t h i s p u r p o s e . They i n c l u d e t h e Normal, B e t a , Gamma, R a y l e i g h and W e i b u l l f u n c t i o n s . 1. Normal d e n s i t y f u n c t i o n T h i s i s t h e well-known p r o b a b i l i t y d i s t r i b u t i o n 64 f u n c t i o n , a l s o c a l l e d G a u s s i a n c u r v e . I t i s d e f i n e d by t h e e q u a t i o n : C U ) = _ ^ e x p " ( t ' M ) 2 (3.14) ay/2-n 2a2 where u i s t h e mean and o t h e s t a n d a r d d e v i a t i o n i n a p r o b a b i l i t y d i s t r i b u t i o n . In o r d e r t o r e p r e s e n t c o n s t r u c t i o n e x p e n d i t u r e f u n c t i o n s , n s h o u l d be viewed as the time when t h e peak of e x p e n d i t u r e s i s o b t a i n e d and a as a shape p a r a m e t e r . S m a l l v a l u e s of a w i l l y i e l d narrow p r o f i l e s whereas h i g h v a l u e s w i l l r e s u l t i n w i d e r , smoother c u r v e s . Eqn 3.14 i s t h e s t a n d a r d normal f u n c t i o n , i e . t h e v a l u e s of the v a r i a b l e t a r e o n l y i n t h e i n t e r v a l [ 0 , 1 ] . T h e r e f o r e , an a p p r o p r i a t e t r a n s f o r m a t i o n s h o u l d be made t o o b t a i n a c t u a l v a l u e s of time and c a s h f l o w . A l s o , s i n c e C ( t ) t a k e s t h e v a l u e of z e r o a t p l u s and minus i n f i n i t y , t h e f u n c t i o n has t o be t r u n c a t e d a t t h e time p o i n t s where c o n s t r u c t i o n commences and ends. The normal f u n c t i o n i s symmetric w i t h r e s p e c t t o i t s mean. T h i s may be a r e s t r i c t i o n when u s i n g i t , s i n c e p e r f e c t l y symmetric e x p e n d i t u r e p a t t e r n s a r e more t h e e x c e p t i o n t h a n t h e r u l e . T h i s d i s a d v a n t a g e may be overcome by t h e B e t a f u n c t i o n as w i l l be seen l a t e r . In f i g u r e 4, some t r u n c a t e d and t r a n s f o r m e d n ormal c u r v e s a r e p r e s e n t e d f o r d i f f e r e n t v a l u e s of u and o. FIGURE 4-- T r u n c a t e d n o r m a l c u r v e s 0.1 0.03 H T f m * 66 The Beta d i s t r i b u t i o n The Beta d i s t r i b u t i o n i s a v e r y v e r s a t i l e f u n c t i o n , and pe r h a p s , t h e most u s e f u l e q u a t i o n t o e x p r e s s c o n t i n u o u s f l o w s a s s o c i a t e d w i t h c a p i t a l p r o j e c t s i n g e n e r a l . M a t h e m a t i c a l l y , i t t a k e s t h e for m : C ( t ) = _ L _ ( a + b + l ) fc'A 8 ^ b (3.15) Z-A a b Z-A Z-A d e f i n e d f o r v a l u e s of t between A and Z, and where C ( t ) i s t h e flo w of money a t time t , A and Z a r e t h e extreme v a l u e s of t h e f u n c t i o n and a and b a r e shape p a r a m e t e r s . W i t h a p r o p e r c o m b i n a t i o n of a and b, t h e B e t a f u n c t i o n can be u s e d t o r e p r e s e n t u n i f o r m , e x p o n e n t i a l , t r i a n g u l a r and symmetric or skewed b e l l - s h a p e d e x p e n d i t u r e p a t t e r n s . In f i g u r e 5, s e v e r a l c a s e s of t h e Beta d i s t r i b u t i o n a r e shown f o r d i f f e r e n t c o m b i n a t i o n s of the shape p a r a m e t e r s . The Gamma f u n c t i o n The Gamma f u n c t i o n has t h e f o r m : C ( t ) - b ( b t ) ! 6 X p ( - b t ) (3.16) n! The v a l u e of t h e par a m e t e r n d e t e r m i n e s t h e shape of t h e flow w h i l e b i s a s c a l i n g p a r a m e t e r . I t s h o u l d be n o t i c e d t h a t t h i s f u n c t i o n i s e q u a l t o z e r o f o r v a l u e s FIGURE 5. Beta d i s t r i b u t i o n 0.0+5 0.04 H 0.035 H 0.03 H 0.025 H • a=1, b = : + a = 3. b=3 O a = 3, b=1 68 of t<0. V a l u e s of t^O a r e , however, of no i n t e r e s t t o examine. The shape of t h e Gamma f u n c t i o n f o r d i f f e r e n t v a l u e s of n i s p r e s e n t e d i n f i g u r e 6. The R a y l e i g h f u n c t i o n I t may be a d v a n t a g e o u s t o use t h i s f u n c t i o n t o r e p r e s e n t c o n t i n u o u s f l o w s , g i v e n t h a t i t c o n t a i n s o n l y one p a r a m e t e r . M a t h e m a t i c a l l y , t h e e x p r e s s i o n of t h e R a y l e i g h f u n c t i o n i s : where a i s t h e p a r a m e t e r of t h e f u n c t i o n . In f i g u r e 7, i t has been a s s i g n e d d i f f e r e n t v a l u e s t o p r e s e n t t h e shape of t h i s f u n c t i o n . The W e i b u l l f u n c t i o n C o n c l u d i n g t h i s e n u m e r a t i o n , t h e W e i b u l l f u n c t i o n i s g i v e n as an a l t e r n a t i v e t o r e p r e s e n t t h e c o n s t r u c t i o n e x p e n d i t u r e f u n c t i o n . I t has t h e form: C ( t ) = — e x p a 2 (3. 17) 2 a 2 b t - T s (b-1 ) t - T s b C ( t ) = 1 (3. 18) n n n d e f i n e d f o r t > T g , where n i s a s c a l e p a r a m e t e r , b i s t h e shape f a c t o r and T g i s a l o c a t i o n p a r a m e t e r . F i g u r e 8 p r e s e n t s some examples of t h e W e i b u l l f u n c t i o n . 0.1 F I G U R E 6 . G a m m a d i s t r i b u t i o n Paramatars: b=5ca l« , n = 5 h a p « 0.09 H b*.1 ,n=0 + b = .15rn=1 b = .2+,n=3 b = .33,n=6 cn F I G U R E 7 , R a y l e i g h f u n c t i o n 0.8 F I G U R E 8 . W e i b u l l f u n c t i o n Param«t«rs: b = S h a p « , n = Scal« 6 -i — : 0 10 20 30 40 b = 2,n=3 + b = 2.5 rn=2 O b = 3,n=1.5 72 One of t h e p r e v i o u s l y d e s c r i b e d f u n c t i o n s may be s e l e c t e d t o r e p r e s e n t the d i r e c t c o n s t r u c t i o n c o s t p r o f i l e , but i t i s n e c e s s a r y t o make a s u i t a b l e t r a n s f o r m a t i o n t o i t i n o r d e r t o o b t a i n m e a n i n g f u l v a l u e s of t i m e and money. I t s h o u l d be reminded t h a t t h e t o t a l a r e a under t h e c u r v e e q u a l s t h e t o t a l d i r e c t c o s t s . In a d d i t i o n t o t h e s e d i s t r i b u t i o n s , p o l y n o m i a l d i s t r i b u t i o n s c an be a d o p t e d , but t h e y have t h e d i s a d v a n t a g e t h a t the c o n t r i b u t i o n of t h e c o e f f i c i e n t s and powers of e a c h term combine t o r e n d e r c o n c e p t u a l v i s u a l i z a t i o n of s c a l e and shape a d j u s t m e n t s more d i f f i c u l t , e x c e p t f o r v e r y low o r d e r p o l y n o m i a l s . At t h i s p o i n t , an example of the c a s h f l o w p r o f i l e g e n e r a t e d d u r i n g t h e c o n s t r u c t i o n phase of r e a l e s t a t e p r o j e c t s can be i n t r o d u c e d . In f i g u r e 9, t h e m o b i l i z a t i o n and d e m o b i l i z a t i o n c o s t s a r e d i s c r e t e payments; i n d i r e c t c o s t a r e u n i f o r m l y d i s t r i b u t e d d u r i n g c o n s t r u c t i o n and d i r e c t c o s t s f o l l o w a B e t a d i s t r i b u t i o n w i t h p a r a m e t e r s a=3 and b=3. 3.4.4 ABSORPTION PHASE The a b s o r p t i o n phase i s t h e i n t e r f a c e between c o n s t r u c t i o n and s t e a d y s t a t e o p e r a t i o n of t h e p r o j e c t . D u r i n g t h i s p e r i o d some a c t i v i t i e s l i k e m a r k e t i n g and s a l e s g e n e r a t e n e g a t i v e c a s h f l o w s . But a t t h e same t i m e , t h e r e v e n u e s of t h e p r o j e c t s t a r t b e i n g c o l l e c t e d by means o f s e l l i n g or l e a s i n g some a r e a s o r u n i t s . A b s o r p t i o n r a t e i s FIGURE 9. C a s h flow dur ing c o n s t r u c t i o n 74 d e f i n e d as t h e r a t e a t w hich t h e p r o j e c t i s l e a s e d or s o l d . F o r i n s t a n c e , i n an a p a r t m e n t b u i l d i n g , t h a t r a t e would be the number of u n i t s s o l d or l e a s e d e v e r y month u n t i l t h e f a c i l i t y i s c o m p l e t e l y m a r k e t e d . O b v i o u s l y , t h e a b s o r p t i o n r a t e depends upon the p a r t i c u l a r c h a r a c t e r i s t i c s of t h e r e a l e s t a t e market a t t h e time when t h e c o n s t r u c t i o n i s f i n i s h e d , but i n g e n e r a l i t i s assumed t o be c o n s t a n t . T h e r e f o r e , t h e c a s h f l o w p r o f i l e has two components. A n e g a t i v e p o r t i o n c o r r e s p o n d i n g t o t h e s t a r t - u p e x p e n s e s , t h a t may be assumed t o be u n i f o r m , and a p o s i t i v e p a r t r e p r e s e n t i n g t h e r e v e n u e s o b t a i n e d by t h e p a r t i a l o p e r a t i o n of the p r o j e c t . T h i s revenue f u n c t i o n w i l l depend on t h e n a t u r e of t h e a b s o r p t i o n r a t e , s i n c e t h e income i s c a l c u l a t e d by m u l t i p l y i n g t h e a l r e a d y s o l d o r , l e a s e d a r e a by the u n i t p r i c e . I f the r a t e i s c o n s i d e r e d t o be c o n s t a n t , t h i s f u n c t i o n i s a s t r a i g h t l i n e . O t h e r w i s e i t w i l l t a k e t h e form of an e x p o n e n t i a l e q u a t i o n . The l o g i s t i c c u r v e , p r e s e n t e d l a t e r i n t h i s c h a p t e r , may be c o n s i d e r e d f o r t h a t p u r p o s e . 3.4.5 OPERATION A r e a l e s t a t e v e n t u r e i s u n d e r t a k e n w i t h t h e o b j e c t i v e of l e a s i n g or s e l l i n g a f i x e d u s e f u l a r e a w i t h i n t h e p r e m i s e s of t h e p r o j e c t . The a n a l y s i s of t h i s phase i s o n l y of i n t e r e s t when the p r o j e c t i s t o be l e a s e d s i n c e i t i s o n l y i n t h i s c a s e when the owner s t i l l has h i s o r i g i n a l c a p i t a l c ommitted t o the p r o j e c t . 75 C o n c e p t u a l l y , t h e form of t h e c a s h f l o w s g e n e r a t e d d u r i n g t h e o p e r a t i o n of t h i s t y p e of p r o j e c t i s v e r y s i m p l e . Revenues a r e c a l c u l a t e d by m u l t i p l y i n g t h e l e a s a b l e a r e a by t h e u n i t r e n t p r i c e . E x p e n s e s a r e a l m o s t f i x e d m a i n t e n a n c e and o p e r a t i n g c o s t s . T h e r e a r e two a s p e c t s t o t a k e i n t o a c c o u n t i n t h e c a l c u l a t i o n of r e v e n u e s . F i r s t , i t i s c o n v e n i e n t t o assume a v a c a n c y r a t e . T h i s means t h a t t h e f a c i l i t y i s not c o m p l e t e l y l e a s e d a t any t i m e . Thus, i f t h e v a c a n c y r a t e i s 5%, t h e a r e a used i n the c a l c u l a t i o n of income s h o u l d be 95% of a l l t h e t o t a l l e a s a b l e s p a c e . And s e c o n d , t h e a n a l y s i s can be done i n e i t h e r c o n s t a n t or c u r r e n t d o l l a r s . I f i t i s i n c o n s t a n t d o l l a r s , c u r r e n t r e n t p r i c e s m ight be employed. O t h e r w i s e , a mechanism of r e n t e s c a l a t i o n s h o u l d be p r o v i d e d . I t can e i t h e r c o n s i d e r t h e i n c r e m e n t of r e n t p r i c e s a t a c o n t i n u o u s r a t e , or a r e v i s i o n of them e v e r y c e r t a i n amount of t i m e . The f i r s t method would y i e l d an e x p o n e n t i a l c a s h f l o w p r o f i l e . The s e c o n d would i m p l y a s t e p w i s e f u n c t i o n . T h i s two a l t e r n a t i v e s a r e p r e s e n t e d i n f i g u r e 10. O p e r a t i n g c o s t s i n r e a l e s t a t e p r o j e c t s can be assumed t o be f i x e d a t a g i v e n v a l u e , i n c o n s t a n t d o l l a r s . They i n c l u d e t a x e s , i n s u r a n c e , m a i n t e n a n c e , u t i l i t i e s , j a n i t o r i a l and a d m i n i s t r a t i o n . I t i s w o r t h w h i l e t o d i f f e r e n t i a t e between t h o s e items t h a t a r e dependent on t h e l e a s e d a r e a ( u t i l i t i e s and j a n i t o r i a l ) o n l y when t h e v a c a n c y r a t e i s u n u s u a l l y h i g h . Then, the o u t f l o w o c c u r r i n g d u r i n g t h i s 77 phase may be r e p r e s e n t e d by a u n i f o r m d i s t r i b u t i o n . 3 . 4 . 6 DISPOSAL When the u s e f u l l i f e of t h e p r o j e c t has come t o an end, the f a c i l i t i e s a r e d e m o l i s h e d and t h e l a n d i s s o l d . T h a t i m p l i e s a n e g a t i v e and a p o s i t i v e s i n g l e d i s c r e t e f l o w . The l a n d v a l u e can be c a l c u l a t e d by i n f l a t i n g i t s c u r r e n t v a l u e t o t h e time when i t i s i n t e n d e d t o be s o l d . A l s o , i t s h o u l d be s t u d i e d i f t h e r e i s an a d d i t i o n a l b e n e f i t due t o v a l o r i z a t i o n of t h e p r o p e r t y due t o d e v e l o p m e n t s i n t h e a d j a c e n t a r e a s d u r i n g t h e l i f e of t h e p r o j e c t . 3 . 5 PROCESS INDUSTRIES The l a s t t y p e of c a p i t a l p r o j e c t c o n s i d e r e d i n t h i s r e v i e w , a r e t h o s e u n d e r t a k e n i n t h e p r o c e s s i n d u s t r i e s , d e f i n e d as any p r o p o s a l which w i l l r e q u i r e t h e i n v e s t m e n t of c a s h f o r new or m o d i f i e d p r o c e s s i n g f a c i l i t i e s . They can be b r o k e n down i n t o f i v e main s t a g e s : f e a s i b i l i t y , d e s i g n , i m p l e m e n t a t i o n o r c o n s t r u c t i o n , o p e r a t i o n and d i s p o s a l . The c a s h p r o f i l e s g e n e r a t e d d u r i n g a l l of them a r e s i m i l a r t o the ones g e n e r a t e d d u r i n g t h e a n a l o g o u s phase i n a r e a l e s t a t e v e n t u r e , w i t h t h e o n l y e x c e p t i o n b e i n g t h e o p e r a t i n g phase. The f e a s i b i l i t y a n a l y s i s and d e s i g n phase a r e r a t h e r s h o r t , i n w h i c h money may be assumed t o f l o w u n i f o r m l y . The p u r c h a s e of l a n d can be r e p r e s e n t e d by a s i n g l e d i s c r e t e payment and d u r i n g i m p l e m e n t a t i o n , a b e l l - s h a p e d e x p e n d i t u r e p a t t e r n i s g e n e r a t e d . G i v e n t h e 78 n a t u r e of p r o c e s s i n d u s t r i e s , d i s c r e t e payments may be r e q u i r e d t o p o r t r a y the a c q u i s i t i o n of c o s t l y equipment items d u r i n g c o n s t r u c t i o n . The d i s p o s a l of t h e p r o j e c t w i l l y i e l d a p o s i t i v e s i n g l e d i s c r e t e c a s h f l o w c o r r e s p o n d i n g t o the s a l v a g e v a l u e of the equipment p l u s t h e s e l l i n g p r i c e o f the l a n d . These c o n c e p t s have a l r e a d y been d i s c u s s e d e a r l i e r . T h e r e f o r e , o n l y t h e c a s h f l o w s g e n e r a t e d d u r i n g o p e r a t i o n w i l l be s t u d i e d . 3.5.1 OPERATION The a n n u a l revenue i s t h e p r o d u c t of t h e number o f u n i t s s o l d p e r y e a r and t h e s e l l i n g p r i c e p e r u n i t . G e n e r a l l y , i n t h e p r o c e s s i n d u s t r i e s , t h e s e two f a c t o r s a r e not i n d e p e n d e n t . When a new p r o d u c t i s i n t r o d u c e d , i t i s n e c e s s a r y f o r a p o t e n t i a l c u s t o m e r t o know of i t s e x i s t e n c e b e f o r e he or she can buy. I f e a c h s a t i s f i e d c u s t o m e r i n f l u e n c e s more than one p o t e n t i a l p u r c h a s e r , and due t o t h e e f f e c t s of m a r k e t i n g c a m p a i g n s , t h e s a l e s c u r v e r i s e s e x p o n e n t i a l l y u n t i l t h e t o t a l p o t e n t i a l demand i s s a t u r a t e d and t h e p r o d u c t r e a c h e s a g i v e n l e v e l and growth, i f any, i s mo d e r a t e d . F i n a l l y , t h e r e i s a p e r i o d of d e c l i n e due t o t h e p r o d u c t o b s o l e s c e n c e and c o m p e t i t i o n from a l t e r n a t i v e s . T h i s whole p r o c e s s i s c a l l e d t h e p r o d u c t l i f e c y c l e , and o f c o u r s e , i s d i f f e r e n t f o r e a c h p a r t i c u l a r p r o d u c t , but i t s g e n e r a l p a t t e r n i s shown i n f i g u r e 11. T h e r e a r e two w i d e l y used f u n c t i o n s t h a t r e p r e s e n t t h e s a l e s volume d u r i n g i n t r o d u c t i o n , growth and m a t u r i t y of a F I G U R E 11. P r o d u c t l i f e c y c l e 2.4-0 20 40 60 80 100 120 Tfm* (months) 80 p r o d u c t . They a r e the Gompertz and t h e L o g i s t i c c u r v e s . The Gompertz c u r v e has t h e form: In y = In A1 - A 2 e x p ( - A 3 * t ) (3.19) where y i s t h e s a l e s volume a t t i m e t , A1 i s an a s y m p t o t i c l i m i t e q u a l t o the demand of a s a t u r a t e d m arket, and A2 and A3 a r e shape p a r a m e t e r s . In f i g u r e 12, The Gompertz c u r v e i s p r e s e n t e d f o r d i f f e r e n t v a l u e s o f A2 and A3. When t h e s a l e s t r e n d i s n o t e x p e c t e d t o be skewed d u r i n g t h e e a r l y y e a r s of t h e l i f e c y c l e , t h e l o g i s t i c c u r v e may be employed. M a t h e m a t i c a l l y , i t t a k e s t h e form: y = hi (3m 20) 1+A2exp(-A3*t) The meaning of t h e terms i n t h i s e x p r e s s i o n i s the same as f o r Eqn. 3.19. Some t y p i c a l s h apes of t h e l o g i s t i c c u r v e and the i n f l u e n c e of t h e p a r a m e t e r s A2 and A3 a r e p r e s e n t e d i n f i g u r e 13. 3.5.2 EXPENSES C o s t i n c u r r e d i n t h e o p e r a t i n g of p r o c e s s i n d u s t r i e s can a l s o be d i v i d e d i n t o d i r e c t and i n d i r e c t c o s t s . A l s o , a t the b e g i n n i n g of t h i s p h a s e , w o r k i n g c a p i t a l i s added t o t h e p r o j e c t . The r e p r e s e n t a t i o n of c a s h f l o w s r e l a t e d t o t h e s e F I G U R E 12. G o m p e r t z c u r v e A1=2, A3=0.15 O A2 = 5 + A2 = 10 O A2 = 15 • A 3 = 0 . 0 8 + A 3 = 0 .12 O A 3 = 0 .16 CD 83 i t e m s a l s o has been p r e v i o u s l y d i s c u s s e d i n t h i s c h a p t e r . In T a b l e 1, t h e summary of a l l t h e f u n c t i o n s t h a t c a n be used t o r e p r e s e n t c a s h f l o w p a t t e r n s , a c c o r d i n g t o p r o j e c t t y p e and p r o j e c t phase, i s p r e s e n t e d . 3.6 IMPLEMENTATION ON THE COMPUTER PROGRAM The computer program has some of t h e p r e v i o u s l y d e s c r i b e d f u n c t i o n s as b u i l t - i n f u n c t i o n t h a t can be s e l e c t e d by t h e u s e r t o r e p r e s e n t c a s h f l o w p r o f i l e s . A c c o r d i n g t o e a c h p r o j e c t phase, t h o s e f u n c t i o n s a r e : 1. I n i t i a l i n v e s t m e n t (Land) and d i s p o s a l : S i n g l e d i s c r e t e payment. 2. F e a s i b i l i t y and D e s i g n : S i n g l e d i s c r e t e payment, two d i s c r e t e payments and u n i f o r m f u n c t i o n . 3. C o n s t r u c t i o n : S i n g l e d i s c r e t e payment, two d i s c r e t e payments, u n i f o r m f u n c t i o n , l i n e a r f u n c t i o n ( t r a p e z o i d a l f l o w s ) , B e t a f u n c t i o n and e x p o n e n t i a l f u n c t i o n . 4. O p e r a t i o n : S i n g l e d i s c r e t e payment, two d i s c r e t e payments, u n i f o r m f u n c t i o n , l i n e a r f u n c t i o n , B e t a f u n c t i o n , e x p o n e n t i a l f u n c t i o n and Gompertz c u r v e . Any number of c a s h f l o w s of any t y p e can be a s s i g n e d t o e a c h phase as l o n g as the t o t a l number of c a s h f l o w s do not e x c e e d 50. F o r example, t h e c o n s t r u c t i o n phase can be r e p r e s e n t e d by 12 f l o w s of which 3 a r e B e t a f u n c t i o n s , 7 a r e u n i f o r m f u n c t i o n s an 2 a r e d i s c r e t e payments. A l s o , f i x e d and v a r i a b l e o p e r a t i n g c o s t s can be s p e c i f i e d . F i x e d c o s t s a r e assumed t o t a k e e f f e c t a t t h e end TABLE 1. Summary of mathematical functions used to express cash flow p r o f i l e s PROJECT TYPE PHASE O i l and Gas Mining Real Estate Process Industries Exploration Uniform Uniform Step function Step function Straight l i n e Straight l i n e F e a s i b i l i t y and design Single payment, Two discrete payments. Uniform function I n i t i a l Inves tment One discrete : payment Construction Set of discrete payments, Uniform, Beta, Normal, Gamma, Rayleigh, Weibull Operation Exponential Uniform, straight decline curves l i n e , l o g i s t i c Uniform Uniform, Exponential, Gompertz, L o g i s t i c Disposal One discrete payment 85 of each y e a r . V a r i a b l e c o s t s are m u l t i p l i e d by the p r o d u c t i o n output t o o b t a i n the t o t a l c o s t s . Taxes are t r e a t e d by m u l t i p l y i n g the income tax r a t e by the t a x a b l e income. The l a t t e r i s o b t a i n e d by. s u b s t r a c t i n g the o p e r a t i n g c o s t s , d e p r e c i a t i o n and l o n g term debt repayment from the revenues g e n e r a t e d by the p r o j e c t . In the program, two d e p r e c i a t i o n methods have been implemented: the s t r a i g h t l i n e method and the d e c l i n i n g , balance method. CHAPTER 4. SENSITIVITY ANALYSIS 4.1 INTRODUCTION The development of mathematical models t o compute economic performance measures i n a d e t e r m i n i s t i c f a s h i o n i s a f i r s t s t e p i n the d e c i s i o n making p r o c e s s and e v a l u a t i o n of c a p i t a l p r o j e c t s . Along w i t h v e r y i mportant q u a l i t a t i v e c o n s i d e r a t i o n s such as s o c i a l c o n v e n i e n c e , d i v e r s i f i c a t i o n of p o r t f o l i o i n v e s t m e n t , e t c . , t h e s e models w i l l g e n e rate the r e q u i r e d i n f o r m a t i o n f o r d e c i d i n g between p r o c e e d i n g w i t h or r e j e c t i n g a p r o j e c t . As seen i n the l a s t c h a p t e r , the cash fl o w s a s s o c i a t e d w i t h the phases of a p r o j e c t have d i f f e r e n t shape and s i z e a c c o r d i n g t o the investment t y p e . Furthermore, when c o n s i d e r i n g s i m i l a r types of p r o j e c t s , the shape and s i z e of a g i v e n cash flow p r o f i l e may change a c c o r d i n g t o p a r t i c u l a r p r o j e c t c h a r a c t e r i s t i c s and/or management s t r a t e g i e s . One of the most c r i t i c a l and important t a s k s i n the e v a l u a t i o n of any p r o j e c t i s the d e f i n i t i o n of the cash f l o w s p r o f i l e s t o be used i n the e v a l u a t i o n p r o c e s s . T h i s i n v o l v e s s e l e c t i n g the f u n c t i o n a l forms i n v o l v e d i n the c a l c u l a t i o n of the performance measures and a s s i g n i n g v a l u e s to t h e i r parameters, which we may c a l l primary v a r i a b l e s . Examples of p r i m a r y v a r i a b l e s a r e i n f l a t i o n and t a x a t i o n r a t e s , market p r i c e s , l a n d v a l u e and c o n s t r u c t i o n d u r a t i o n . 86 87 4.2 PARAMETER ESTIMATION The e s t i m a t i o n and f o r e c a s t of f u t u r e e v e n t s i n l a r g e p r o j e c t s i s not an e a s y t a s k ( n o r i s i t i n a l m o s t any o t h e r e n v i r o n m e n t ) . A d e t a i l e d d i s c u s s i o n of t h e methods o f e s t i m a t i o n and f o r e c a s t i n g i s beyond the s c o p e of t h i s t h e s i s . B r i e f l y , however t h e r e a r e t h r e e b a s i c a p p r o a c h e s t o making e s t i m a t e s about the f u t u r e , a c c o r d i n g t o H u l l [ 2 4 ] : 1. The use of h i s t o r i c a l d a t a ; 2. The use of t h e judgement and e x p e r i e n c e of one p e r s o n ; and 3. The use of t h e judgement and e x p e r i e n c e of s e v e r a l p e o p l e . H i s t o r i c a l d a t a can be used i n c o m b i n a t i o n w i t h s t a t i s t i c a l and e c o n o m e t r i c models t o i d e n t i f y p o s s i b l e r e l a t i o n s h i p s between v a r i a b l e s known w i t h c e r t a i n t y and t h e v a r i a b l e s t o be e s t i m a t e d . The s e c o n d method c o n s i s t s i n a s k i n g a q u a l i f i e d p r o f e s s i o n a l t o draw a p a r a l l e l between t h e s i t u a t i o n c u r r e n t l y f a c i n g him o r h e r and a s i t u a t i o n w h i c h he or she has p r e v i o u s l y e n c o u n t e r e d e i t h e r d i r e c t l y o r i n d i r e c t l y . T h i s a p p r o a c h has t h e d i s a d v a n t a g e o f p o s s i b l e p e r s o n a l b i a s or l a c k of c o n s i d e r a t i o n of f a c t o r s o u t s i d e the e s t i m a t o r ' s knowledge. In o r d e r t o overcome t h e s e d i s a d v a n t a g e s , a g r o u p of i n d i v i d u a l s not a l l h e a v i l y committed t o t h e p r o j e c t and w i t h d i f f e r e n t r e w a r d s t r u c t u r e s may be a s k e d t o p r o d u c e the b e s t e s t i m a t e f o r t h e p r i m a r y v a r i a b l e s . The d i f f e r e n t a p p r o a c h e s t o g r o u p f o r e c a s t i n g may be found e l s e w h e r e [ 2 4 ] , [ 4 0 ] . 88 4.3 RISK MANAGEMENT Independent from which t e c h n i q u e i s u s e d t o p r o v i d e e s t i m a t e s about the p r i m a r y v a r i a b l e s , t h e r e w i l l i n e v i t a b l y be an element of u n c e r t a i n t y a s s o c i a t e d w i t h s u c h e s t i m a t e s . They a r e o n l y e s t i m a t e s no m a t t e r how p r e c i s e and r e l i a b l e the d a t a on which t h e y a r e b a s e d o r how e x p e r t t h e f o r e c a s t e r s a r e . A l t h o u g h t h e r e e x i s t s e v e r a l s o u r c e s o f r i s k s u c h as t e c h n o l o g i c a l change, p o l i t i c a l e n v i r o n m e n t , e t c . , i t i s w i d e l y r e c o g n i z e d i n t h e l i t e r a t u r e t h a t t h e r i s k i n an i n v e s t m e n t p r o j e c t a r i s e s , e s s e n t i a l l y , from the u n c e r t a i n t y about the p r i m a r y v a r i a b l e s , w h i c h i n - t u r n , g i v e s r i s e t o u n c e r t a i n t y about the c a s h f l o w e s t i m a t e s . S i n c e t h e p e r f o r m a n c e measures a r e computed as f u n c t i o n s of t h e c a s h f l o w s , the i n i t i a l u n c e r t a i n t y i s t r a n s f e r r e d t o t h e i r c a l c u l a t e d v a l u e s . T h e r e f o r e , a f u r t h e r s t e p i n t h e economic e v a l u a t i o n p r o c e s s i s t o a s s e s s and t h e n r e d u c e t h e r i s k s i n v o l v e d i n t h e p r o j e c t . T h i s a c t i v i t y i s r e f e r r e d t o as r i s k management. Two a n a l y t i c a l p r o c e d u r e s f o r q u a n t i f y i n g r i s k have been d e v e l o p e d . The f i r s t one i s s e n s i t i v i t y a n a l y s i s and i t w i l l be d i s c u s s e d i n d e t a i l i n t h e r e m a i n d e r of t h i s c h a p t e r . The s e c o n d one c o n s i s t s i n c a r r y i n g out what i s known as r i s k s i m u l a t i o n . B r i e f l y , t h i s t e c h n i q u e c o n s i s t s i n p e r f o r m i n g Monte C a r l o s i m u l a t i o n i n o r d e r t o f i n d t h e p r o b a b i l i t y d i s t r i b u t i o n of t h e p e r f o r m a n c e measure. The p r o c e d u r e i n v o l v e s f o u r b a s i c s t e p s : a ) D e f i n e a p r o b a b i l i t y 89 d i s t r i b u t i o n most s u i t e d t o e a c h p r i m a r y v a r i a b l e ; b)draw a random v a l u e from e a c h d i s t r i b u t i o n and a s s i g n i t t o e a c h v a r i a b l e ; c ) r u n a d e t e r m i n i s t i c a n a l y s i s u s i n g t h e c o m b i n a t i o n of v a l u e s s e l e c t e d i n t h e p r e v i o u s p o i n t ; and d ) r e p e a t a number of t i m e s t o o b t a i n t h e p r o b a b i l i t y d i s t r i b u t i o n of t h e p e r f o r m a n c e measure. 4.4 SENSITIVITY ANALYSIS In t h e l a s t s e c t i o n , s e n s i t i v i t y a n a l y s i s was i n t r o d u c e d as m a t h e m a t i c a l t e c h n i q u e f o r q u a n t i f y i n g r i s k . At a c o n c e p t u a l l e v e l , F l a n a g a n e t a l . [ 1 4 ] , d e f i n e - i t as a d e t e r m i n i s t i c m o d e l l i n g t e c h n i q u e which p r i m a r i l y answers "What i f . . . " q u e s t i o n s , f o r i n s t a n c e , "What would t h e v a l u e of t h e p e r f o r m a n c e measure be i f t h e p r i m a r y v a r i a b l e x assumes a d i f f e r e n t v a l u e than t h a t e s t i m a t e d f o r i t ? " The t e c h n i q u e i n v o l v e s f i r s t c a l c u l a t i n g a p e r f o r m a n c e measure ( u s u a l l y NPV or IRR) on t h e b a s i s of c a s h f l o w s c a l c u l a t e d from most l i k e l y or " b e s t " e s t i m a t e s o f t h e p r i m a r y v a r i a b l e s and t h e n o b s e r v i n g t h e e f f e c t on t h e p e r f o r m a n c e measure of c h a n ges of t h o s e most l i k e l y e s t i m a t e s . The b a s i c o b j e c t i v e of s e n s i t i v i t y a n a l y s i s i s s i m p l e : i f t h e change i n an e s t i m a t e has v e r y l i t t l e e f f e c t on t h e NPV or IRR, t h e n the i n v e s t m e n t d e c i s i o n i s not l i k e l y t o depend t o any g r e a t e x t e n t on t h e a c c u r a c y of t h a t e s t i m a t e . On t h e o t h e r hand, i f a change i n the e s t i m a t e p r o d u c e s a l a r g e change i n t h e p e r f o r m a n c e m e a s u r e s , then t h e 90 u n c e r t a i n t y s u r r o u n d i n g th e e s t i m a t e may w e l l be a s i g n i f i c a n t c o n s i d e r a t i o n when t h e i n v e s t m e n t d e c i s i o n i s b e i n g made. Thus, a s e n s i t i v i t y a n a l y s i s can be r e g a r d e d as a way o f q u i c k l y i d e n t i f y i n g t h o s e p r i m a r y v a r i a b l e s w h i c h c o n t r i b u t e most t o t h e r i s k of t h e p r o j e c t . U s i n g t h i s i n f o r m a t i o n , t h e management of t h e p r o j e c t w i l l p r o c e e d t o r e d u c e r i s k and u n c e r t a i n t y making a t r a d e - o f f between t h e v a l u e of i n f o r m a t i o n t h a t r e d u c e s r i s k e x p o s u r e , and t h e c o s t o f t h a t i n f o r m a t i o n , meaning t h a t i t s h o u l d be c o l l e c t e d o n l y i f i t s v a l u e a t l e a s t e q u a l s i t s c o s t of c o l l e c t i o n , s t o r a g e and a n a l y s i s . The r e s u l t of t h e a n a l y s i s w i l l a l s o be h e l p f u l i n d e f i n i n g a p p r o p r i a t e r i s k m i t i g a t i o n s t r a t e g i e s s u c h as l o n g term c o n t r a c t s , i n s u r a n c e s , e t c . 4.5 UNIVARIATE SENSITIVITY ANALYSIS The most g e n e r a l i z e d a p p r o a c h t o s e n s i t i v i t y a n a l y s i s q u a n t i f i e s the change i n t h e p e r f o r m a n c e measure when one p r i m a r y v a r i a b l e i s changed and t h e r e s t a r e h e l d t o t h e i r o r i g i n a l v a l u e s . T h i s i s b a s i c a l l y a u n i v a r i a t e a n a l y s i s : o n l y one v a r i a b l e i s changed a t a t i m e . In t h i s s e c t i o n , t h e two d i f f e r e n t ways of c a r r y i n g out u n i v a r i a t e s e n s i t i v i t y a n a l y s i s w i l l be d i s c u s s e d . They a r e the l i n e a r and t h e e x a c t a n a l y s i s . 91 4.5.1 LINEAR ANALYSIS L i n e a r s e n s i t i v i t y a n a l y s i s i s a s i m p l i f i e d way of o b t a i n i n g an a p p r o x i m a t e e s t i m a t e o f t h e d e g r e e o f s e n s i t i v i t y of each p r i m a r y v a r i a b l e . I t may r e p l a c e a c o m p l e t e (or e x a c t ) a p p r o a c h when t h e l a t t e r would be h i g h l y e x p e n s i v e or t i m e c o n s u m i n g . A t e c h n i q u e from l i n e a r c o n t r o l t h e o r y i n s y s t e m s e n g i n e e r i n g c a l l e d q u a s i 1 i n e a r i z a t i o n i s u s e d t o o b t a i n t h e s e r e s u l t s . In q u a s i l i n e a r i z a t i o n , an o p e r a t i n g p o i n t o r benchmark i s i d e n t i f i e d and t h e n t h e s e n s i t i v i t y a n a l y s i s i s c o n d u c t e d by e v a l u a t i n g t h e f i r s t - o r d e r l i n e a r d e v i a t i o n s from t h e benchmark u s i n g t h e f u n d a m e n t a l f o r m u l a o f t h e t o t a l d i f f e r e n t i a l from c a l c u l u s : n 3f dP = Z • dx . (4. 1) i=1 3 X i where P i s t h e p e r f o r m a n c e measure e x p r e s s e d as a f u n c t i o n f of n p r i m a r y v a r i a b l e s . The p a r t i a l d e r i v a t i v e of t h i s f u n c t i o n w i t h r e s p e c t t o e a c h p r i m a r y v a r i a b l e x^ i s e v a l u a t e d a t t h e p o i n t P Q . I t may be n o t i c e d t h a t t h e same r e s u l t can be o b t a i n e d by e x p a n d i n g t h e f u n c t i o n f i n a T a y l o r ' s s e r i e s a b o u t t h e p o i n t P Q and n e g l e c t i n g t h e terms of s e c o n d o r d e r and h i g h e r . F o r s u f f i c i e n t l y s m a l l d e v i a t i o n s , t h e n o n - l i n e a r terms a r e n e g l i g i b l e compared w i t h t h e f i r s t o r d e r terms ( o r l i n e a r t e r m s , from which t h e name of t h i s a p p r o a c h i s 92 t a k e n ) . We n o t e , however, t h a t we w i s h t o i n v e s t i g a t e l a r g e d e v i a t i o n s from the bench mark v a l u e . Thus, an i m p o r t a n t i s s u e i s t h e range o v e r w h i c h t h e l i n e a r a n a l y s i s i s v a l i d . From a g e o m e t r i c a l p o i n t of view, t h i s a p p r o x i m a t i o n c an be j u s t i f i e d by s a y i n g t h a t i n t h e immediate v i c i n i t y of P Q , t h e t a n g e n t p l a n e d e f i n e d by t h e l i n e a r terms of t h e T a y l o r ' s e x p a n s i o n a p p r o x i m a t e s v e r y c l o s e l y t h e b e h a v i o r of t h e p e r f o r m a n c e measure. In a c t u a l p r a c t i c e , t h e d i f f e r e n t i a l s dx^ can be s u b s t i t u t e d by s m a l l d e v i a t i o n s Ax^. T h e r e f o r e , Eqn. 4.1 may be r e w r i t t e n a s : n 3f AP = I Ax. (4. 2) 1 = 1 3 x i 1 S i n c e the u n i v a r i a t e c a s e i s b e i n g c o n s i d e r e d , o n l y t h e j t h v a r i a b l e i s a l l o w e d t o change, i e . Ax^=0, i * j , t h e n : AP = £ £ Ax . (4. 3) 3 X j Now, the f i r s t - o r d e r p a r t i a l d e r i v a t i v e of t h e f u n c t i o n d e s c r i b i n g the p e r f o r m a n c e w i t h r e s p e c t t o e a c h p r i m a r y v a r i a b l e x^, i s d e f i n e d as t h e absolute s e n s i t i v i t y c o e f f i c i e n t of t h e v a r i a b l e x^, and w i l l be r e p r e s e n t e d as s-; m a t h e m a t i c a l l y : 93 3f (4. 4) However, t h i s c o e f f i c i e n t c an be o n l y u s e d t o q u a n t i f y a b s o l u t e changes b o t h i n t h e p r i m a r y v a r i a b l e s and t h e p e r f o r m a n c e measure. U s i n g the d e f i n i t i o n o f s e n s i t i v i t y c o e f f i c i e n t g i v e n by Bode and q u o t e d i n S i n h a [ 5 0 ] , t h e magnitude of t h e p e r c e n t a g e or r e l a t i v e change i n a v a r i a b l e and a p e r f o r m a n c e measure can be l i n k e d . T h i s s e n s i t i v i t y c o e f f i c i e n t w i l l be r e f e r r e d t o as t h e relative s e n s i t i v i t y c o e f f i c i e n t and w i l l be r e p r e s e n t e d by S^. Bode d e f i n e s a s : 9 ( l n P) 9P x • l = (4. 5) P P t h e n : AP (4. 6) P which i s the d e s i r e d e x p r e s s i o n . A g a i n , we can a r r i v e a t t h e same p o i n t i n a d i f f e r e n t way: d i v i d i n g b o t h s i d e s of Eqn. 4.3 by P and the n by x^, y i e l d s : 94 A P r . j. 3x i P.x i (4. 7) r e a r r a n g i n g t e r m s : A P A x . (4. 8) l P E q u a t i o n s 4.6 and 4.8 a r e e q u i v a l e n t a c c o r d i n g t o t h e d e f i n i t i o n o f S^. The r e l a t i v e s e n s i t i v i t y c o e f f i c i e n t s c a n be o b t a i n e d f o r a l l the p r i m a r y v a r i a b l e s and shown i n a t a b u l a r f o r m a t . However, a g r a p h of t h e r e s u l t s i s a u s e f u l p r e s e n t a t i o n w h i c h q u i c k l y i n d i c a t e s t h e most s e n s i t i v e o r c r i t i c a l v a r i a b l e s . The a p p l i c a t i o n of Eqn. 4.8 t o n p r i m a r y v a r i a b l e s w i l l r e s u l t i n t h e same number of e q u a t i o n s o f s t r a i g h t l i n e s p a s s i n g t h r o u g h t h e o r i g i n . These l i n e s a r e drawn i n a s i n g l e g r a p h w i t h one of t h e a x i s r e p r e s e n t i n g p e r c e n t a g e change i n t h e p r i m a r y v a r i a b l e s and t h e o t h e r r e p r e s e n t i n g p e r c e n t a g e change i n t h e p e r f o r m a n c e measure. T h i s k i n d of g r a p h i s known as " s p i d e r " or " s t a r " d i a g r a m , and an example f o r an h y p o t h e t i c a l o i l f i e l d e x t r a c t e d f r o m [24] i s g i v e n i n f i g u r e 14. In t h i s example th e p e r f o r m a n c e measure under c o n s i d e r a t i o n i s the Net P r e s e n t V a l u e of t h e p r o j e c t . As n o t e d p r e v i o u s l y , t h e range o v e r which t h e s t r a i g h t l i n e a p p r o x i m a t i o n h o l d s i s unknown. 95 FIGURE 14. S e n s i t i v i t y d i a g r a m f o r an o i l f i e l d S o u r c e : P e r r y and Hayes [ 4 0 ] . 4.5.2 LINEAR ANALYSIS: THE CASE OF IMPLICIT FUNCTIONS The l a t t e r r a t i o n a l e can be a p p l i e d w i t h o u t any d i f f i c u l t y when the f u n c t i o n d e s c r i b i n g the p e r f o r m a n c e measure i s e x p l i c i t on the p r i m a r y , v a r i a b l e s . However, when the i n t e r n a l r a t e of r e t u r n i s used, an a d d i t i o n a l c o n s i d e r a t i o n i s r e q u i r e d . 96 The i n t e r n a l r a t e of r e t u r n i s d e f i n e d a s t h e d i s c o u n t r a t e t h a t makes the NPV e q u a l t o z e r o . T h e r e f o r e , IRR i s an i m p l i c i t f u n c t i o n of t h e p r i m a r y v a r i a b l e s and i t s p a r t i a l d e r i v a t i v e s a r e c a l c u l a t e d d i f f e r e n t l y . In t h i s c a s e , t h e i m p l i c i t f u n c t i o n theorem has t o be u s e d . B r i e f l y , t h a t theorem s t a t e s t h e f o l l o w i n g : L e t : P = f ( X , y ) , and y=g(X) (4. 9) i n which g(x) i s the i m p l i c i t f u n c t i o n . Then, !l = -E w i t h p= ££ and q= !£ (4. 10) 3x^ q 3x^ 3y The a p p l i c a t i o n t o s e n s i t i v i t y a n a l y s i s i s s t r a i g h t f o r w a r d . In Eqn. 4.9, P r e p r e s e n t s t h e NPV ( i n t h i s c a s e e q u a l t o z e r o ) , t h e v e c t o r X c o n t a i n s t h e p r i m a r y v a r i a b l e s and y i s the IRR. Thus, when the p e r f o r m a n c e measure i s t h e IRR, t h e a b s o l u t e s e n s i t i v i t y c o e f f i c i e n t i s c a l c u l a t e d u s i n g Eqn 4.10. T h i s c o e f f i c i e n t w i l l be d e n o t e d by s^. The r e l a t i v e c o e f f i c i e n t i s : x . s ( i , y ) = S ( i , y ) - J (4. 11) 97 and t h e r e l a t i v e c h a n g e s i n IRR g i v e n a p e r c e n t a g e change i n v a r i a b l e i i s : A y - c A x i /, „ , — " s U , y ) — ( 4 - I 2 ) y x i U s i n g t h i s e q u a t i o n , a s i m i l a r s p i d e r d i a g r a m c a n be p r o d u c e d t o r e p r e s e n t th e d e g r e e of s e n s i t i v i t y o f e a c h p r i m a r y v a r i a b l e when the IRR i s s e l e c t e d as t h e p e r f o r m a n c e measure. 4.6 EXACT ANALYSIS The l i n e a r a n a l y s i s d e s c r i b e d i n t h e p r e v i o u s s e c t i o n p r o v i d e s some i n s i g h t i n t o w hich v a r i a b l e s c o n t r i b u t e t h e most t o t h e o v e r a l l r i s k of t h e p r o j e c t . The r e l a t i v e s e n s i t i v i t y c o e f f i c i e n t s r e l a t e p e r c e n t a g e changes i n t h e p r i m a r y v a r i a b l e s t o t h o s e i n t h e p e r f o r m a n c e measure. However, the s e n s i t i v i t y of t h e v a r i a b l e s does not f o l l o w an e x a c t l i n e a r p a t t e r n . An e x a c t a n a l y s i s can be p e r f o r m e d t o e v a l u a t e t h e s e n s i t i v i t y of t h e v a r i a b l e s f o r a g i v e n r e l a t i v e change ( i e . the s e n s i t i v i t y c o e f f i c i e n t i s now a f u n c t i o n of the magnitude of the r e l a t i v e c h a n g e ) . The i d e a i s t o r e c a l c u l a t e t h e p e r f o r m a n c e measure when the p r i m a r y v a r i a b l e s a r e v a r i e d between -w% and +z% w i t h a f i x e d i n c r e m e n t ( a g a i n , o n l y one a t a t i m e ) . The v a l u e s of w and z s h o u l d be s e l e c t e d a c c o r d i n g t o what the management of the p r o j e c t c o n s i d e r s t h e "most p e s s i m i s t i c " and "most 98 o p t i m i s t i c " e s t i m a t e s of e a c h v a r i a b l e . T h i s c o n c e p t may be b e t t e r e x p l a i n e d w i t h an example. In t h e e v a l u a t i o n of a c o p p e r mine d e v e l o p m e n t , one of t h e p r i m a r y v a r i a b l e s i s t h e c o n s t a n t d o l l a r p r i c e p e r pound of t h i s m i n e r a l o v e r t h e l i f e of t h e p r o j e c t , v a l u a t e d i n t o d a y ' s d o l l a r s . A f t e r r e v i e w i n g th e b e h a v i o r of c o p p e r p r i c e s and c o n s i d e r i n g t h e p o s s i b l e f u t u r e c h a r a c t e r i s t i c s of t h i s - market, management d e f i n e s an e x p e c t e d p r i c e of US$1.3 per pound, and t h a t i t i s not l i k e l y t h a t t h i s v a l u e w i l l be lower t h a n US$1.0 or h i g h e r t h a n US$2.0. T h i s f i g u r e s a r e r e f e r r e d t o as t h e b e s t e s t i m a t e , t h e most p e s s i m i s t i c and t h e most o p t i m i s t i c e s t i m a t e s r e s p e c t i v e l y . Thus, i n t h i s c a s e , th e e x a c t a n a l y s i s s h o u l d be c a r r i e d o u t f o r v a l u e s of t h e c o p p e r p r i c e between US$1 and US$2 w i t h i n c r e m e n t s o r say, t e n c e n t s . The changes may be e x p r e s s e d i n p e r c e n t a g e terms and t h e r e s u l t s p l o t t e d i n a s p i d e r d i a g r a m . Note t h a t i f t h e p e r f o r m a n c e measure i s l i n k e d i n a n o n l i n e a r f a s h i o n w i t h t h e p r i m a r y v a r i a b l e b e i n g s t u d i e d , the s e n s i t i v i t y c u r v e w i l l not be n e c e s s a r i l y a s t r a i g h t l i n e . 4.7 BIVARIATE SENSITIVITY ANALYSIS One l i m i t a t i o n of s e n s i t i v i t y a n a l y s i s i s t h a t , i n . i t s c u r r e n t a p p l i c a t i o n s , i t i s o n l y u n i v a r i a t e . A b i v a r i a t e s e n s i t i v i t y a n a l y s i s m o d e r a t e s t h i s l i m i t a t i o n t o a t l e a s t some e x t e n t . The c o n c e p t of b i v a r i a t e s e n s i t i v i t y a n a l y s i s i s the e x t e n s i o n of t h e u n i v a r i a t e a p p r o a c h . In t h i s c a s e , 99 the impacts on t h e p e r f o r m a n c e measure a r e q u a n t i f i e d when two v a r i a b l e s a r e a l l o w e d t o change a t a t i m e . In the u n i v a r i a t e c a s e , t h e r e i s an a s s u m p t i o n of ind e p e n d e n c e between t h e v a r i a b l e s s i n c e e a c h of them i s a l l o w e d t o v a r y w h i l e t h e o t h e r s r e m a i n c o n s t a n t . T h i s may not a l w a y s be the c a s e . F o r i n s t a n c e , t h e s a l v a g e v a l u e c an be dependent on t h e c o s t of t h e l a n d , o r t h e t o t a l c o s t s on t h e p r o d u c t i o n o u t p u t . L e t t i n g two p o s s i b l e r e l a t e d v a r i a b l e s or two h i g h l y s e n s i t i v e ones change s i m u l t a n e o u s l y , t h e new v a l u e s of t h e p e r f o r m a n c e measure can be c a l c u l a t e d and d i s p l a y e d g r a p h i c a l l y by means of a c o n t o u r diagram, l i k e the one shown i n f i g u r e 15, or a s u r f a c e d i a g r a m ( f i g u r e 16). U s i n g t h e b i v a r i a t e a p p r o a c h , o t h e r t y p e s of q u e s t i o n s d i f f e r e n t from t h e "What i f . . . " t y p e c a n be answered. In o r d e r t o implement m a n a g e r i a l s t r a t e g i e s t o d e a l w i t h e v e n t u a l v a r i a t i o n s i n the p r i m a r y v a r i a b l e s d u r i n g t h e l i f e of the p r o j e c t , i t may be of i n t e r e s t t o know t h e r e q u i r e d change i n one v a r i a b l e i i n o r d e r t o o f f s e t c hanges i n a sec o n d v a r i a b l e j , w h i l e m a i n t a i n g t h e o r i g i n a l v a l u e of t h e p e r f o r m a n c e measure. F o r e a c h p a r t i c u l a r v a r i a b l e , one or two o t h e r v a r i a b l e s may be i d e n t i f i e d as t h e i r " o f f s e t t i n g " c o u n t e r p a r t s , p r o v i d i n g management w i t h a v a l u a b l e t o o l f o r r i s k m i t i g a t i o n . 1 00 Contour LCC 1 1 000 2 2 000 3 ' 3 000 4 4 000 5 5 000 6 6 000 7 7 000 8 8 000 9 9000 10 10 000 11 11 000 12 12000 13 13 000 14 14 000 15 15 000 16 16 000 17 17 000 18 18 000 19 19 000 20 20 000 20 JO Project lite (y) FIGURE 15 . Contour diagram (source: Flanagan [14 ] ) FIGURE 16. Surface diagram ( s o u r c e : Flanagan [14]) 101 4.8 THREE VARIATIONS OF SENSITIVITY ANALYSIS Some v a r i a t i o n s o f t h e b a s i c c o n c e p t of u n i v a r i a t e s e n s i t i v i t y a n a l y s i s have been d e v e l o p e d t o p r o v i d e more i n s i g h t i n t o t h e r i s k s and u n c e r t a i n t i e s a s s o c i a t e d w i t h c a p i t a l p r o j e c t s . T h r e e of them w i l l be p r e s e n t e d h e r e i n , namely b r e a k - e v e n a n a l y s i s , extreme p o i n t s a n a l y s i s and s e n s i t i v i t y t o f u n c t i o n a l f o r m s . The f i r s t two methods have been t r e a t e d i n t h e l i t e r a t u r e but t h e name of "extreme p o i n t s " i s p r o p o s e d s i n c e no o t h e r has been f o u n d . S e n s i t i v i t y t o f u n c t i o n a l forms i s b a r e l y t r e a t e d i n t h e l i t e r a t u r e . As i n t h e whole i s s u e of s e n s i t i v i t y a n a l y s i s , t h e c o n c e p t s i n v o l v e d h e r e a r e r a t h e r s i m p l e . 4 . 8 . 1 BREAK-EVEN ANALYSIS The o b j e c t i v e of b r e a k - e v e n a n a l y s i s i s t o i d e n t i f y t h a t l e v e l of e a c h u n c e r t a i n p r i m a r y v a r i a b l e t h a t r e v e r s e s t h e a c c e p t - r e j e c t d e c i s i o n of t h e p r o j e c t . When th e Net P r e s e n t V a l u e i s t h e p e r f o r m a n c e measure, t h e b r e a k - e v e n a p p r o a c h w i l l f i n d t h e v a l u e of e a c h v a r i a b l e t h a t r e v e r s e s i t s s i g n when t h e r e s t of the v a r i a b l e s a r e h e l d c o n s t a n t a t t h e i r b e s t e s t i m a t e s . T h i s l e v e l i s c a l l e d t h e b r e a k - e v e n p o i n t . S i m i l a r l y , i f IRR i s used as t h e p e r f o r m a n c e measure, t h e b r e a k - e v e n p o i n t w i l l y i e l d an IRR e q u a l t o t h e minimum a c c e p t a b l e r a t e of r e t u r n . I ndeed, t h e I n t e r n a l Rate o f R e t u r n i s t h e b r e a k - e v e n p o i n t f o r t h e p r i m a r y v a r i a b l e d i s c o u n t r a t e , when the NPV i s t h e p e r f o r m a n c e measure. 102 The b r e a k - e v e n p o i n t i s t h e n compared w i t h the i n t e r v a l d e f i n e d by t h e p e s s i m i s t i c and o p t i m i s t i c e s t i m a t e s t o g i v e a b e t t e r i d e a a bout the p o t e n t i a l r i s k a s s o c i a t e d w i t h e a c h u n c e r t a i n v a r i a b l e . 4.8.2 EXTREME POINT ANALYSIS I t was m e n t i o n e d p r e v i o u s l y t h a t management s h o u l d a s s e s s t h r e e d i f f e r e n t e s t i m a t e s f o r e a c h u n c e r t a i n p r i m a r y v a r i a b l e : t h e most l i k e l y , t h e most p e s s i m i s t i c and t h e most o p t i m i s t i c e s t i m a t e s . The extreme p o i n t a n a l y s i s c o n s i s t s i n c a l c u l a t i n g t h e p e r f o r m a n c e measure c o m b i n i n g a l l t h e p e s s i m i s t i c and t h e n a l l t h e o p t i m i s t i c e s t i m a t e s . The a s s u m p t i o n t h a t a l l t h e v a r i a b l e s w i l l t a k e t h e i r l o w e s t v a l u e a t the same time i s o v e r l y - p e s s i m i s t i c . C o n v e r s e l y , i t i s o v e r l y - o p t i m i s t i c t o e x p e c t them t o s i m u l t a n e o u s l y t a k e t h e i r h i g h e s t v a l u e . In s p i t e of t h i s , i t i s s t i l l w o r t h c a r r y i n g out t h i s c a l c u l a t i o n . I f t h e i n v e s t m e n t i s u n a c c e p t a b l e when o p t i m i s t i c e s t i m a t e s a r e combined, i t i s a l m o s t c e r t a i n not worth c o n s i d e r i n g any f u r t h e r . I f i t i s a c c e p t a b l e when p e s s i m i s t i c e s t i m a t e s a r e combined, i t can be a c c e p t e d w i t h o u t any f u r t h e r a n a l y s i s , a ssuming t h a t t h e r a n ges have been a c c u r a t e l y e s t i m a t e d . 4.8.3 SENSITIVITY TO FUNCTIONAL FORMS S e n s i t i v i t y a n a l y s i s examines t h e changes i n a p e r f o r m a n c e measure due t o v a r i a t i o n s i n p r i m a r y v a r i a b l e s s i n c e t h e former i s o b v i o u s l y a f u n c t i o n of the l a t t e r . 103 However, the NPV, IRR or any o t h e r p e r f o r m a n c e measure, depends not o n l y on the v a l u e of t h e v a r i a b l e s , but a l s o on the f u n c t i o n a l forms t h a t d e s c r i b e t h e shape of the c a s h f l o w s . These f u n c t i o n s d e f i n e when and how much money w i l l f l o w i n t o or o u t s i d e the p r o j e c t . T h e r e f o r e , i t th e y change, so w i l l the p e r f o r m a n c e measure. I t may be a l s o of i n t e r e s t t o know how s e n s i t i v e t h e i n v e s t m e n t i s t o s u c h v a r i a t i o n s . The p r i n c i p l e i s the f o l l o w i n g . F o r e a c h c a s h f l o w , a f u n c t i o n a l form i s d e f i n e d . Then, a s e t of f u n c t i o n a l forms (or t h e i r p a r a m e t e r s ) t h a t a r e t h o u g h t t o be l i k e l y t o d e s c r i b e t h e f l o w a r e s e l e c t e d and t h e p e r f o r m a n c e measure i s computed f o r a l l of them. The r e s u l t s a r e u s e d t o a i d i n the s t u d y and s e l e c t i o n of d i v e r s e management s t r a t e g i e s , such as f r o n t - o r back-end l o a d e d c o n s t r u c t i o n p r o j e c t s . The r e p r e s e n t a t i o n of t h i s t y p e of a n a l y s i s c a n n o t be done by means of a s p i d e r d i a g r a m , u n l e s s t h e changes i n one parameter a r e c o n s i d e r e d . 4.9 CONCLUSION: THE BENEFITS OF SENSITIVITY ANALYSIS Throughout t h i s c h a p t e r , s e n s i t i v i t y a n a l y s i s has been p r e s e n t e d as a s i m p l e t e c h n i q u e u s e d as one of the f i r s t s t e p s i n t h e e v a l u a t i o n and q u a n t i f i c a t i o n of r i s k i n c a p i t a l p r o j e c t s . D e s p i t e i t s s i m p l i c i t y and i t s p r e l i m i n a r y n a t u r e , i t b r i n g s i m p o r t a n t b e n e f i t s . Those b e n e f i t s , as p r e s e n t e d by P e r r y and Hayes [ 4 0 ] , a r e : 1. The p o w e r f u l impact on management of t h e r e a l i z a t i o n t h a t t h e r e i s a range of p o s s i b l e outcomes f o r t h e 104 p r o j e c t ; 2. D e c i s i o n making i s made more r e a l i s t i c a l t h o u g h t h e i n f o r m a t i o n on wh i c h d e c i s i o n s a r e made becomes more complex; 3. The r o b u s t n e s s o f p r o j e c t s t o s p e c i f i c u n c e r t a i n t i e s c an be compared; and 4. The r e l a t i v e i m p o r t a n c e of e a c h v a r i a b l e i s i m m e d i a t e l y a p p a r e n t , t h e r e f o r e h i g h l i g h t i n g t h o s e a r e a s which most b e n e f i t from a t t e m p t s t o r e d u c e o r c o n t r o l u n c e r t a i n t y , or need f u r t h e r d e v e l o p m e n t work. 4.10 IMPLEMENTATION ON THE COMPUTER PROGRAM In t h e computer program d e v e l o p e d as p a r t of t h i s t h e s i s , t h e l i n e a r , e x a c t , b r e a k - e v e n and b i v a r i a t e s e n s i t i v i t y a n a l y s e s have been implemented. In t h e l i n e a r a n a l y s i s , t h e a b s o l u t e and r e l a t i v e s e n s i t i v i t y c o e f f i c i e n t w i t h r e s p e c t t o NPV, IRR and TCC a r e computed f o r e a c h s e l e c t e d v a r i a b l e . In the e x a c t a n a l y s i s , t h e NPV i s c a l c u l a t e d f o r 10 d i f f e r e n t v a l u e s on t h e range s e t by t h e p e s s i m i s t i c and o p t i m i s t i c e s t i m a t e s of the v a r i a b l e , and t h e b r e a k - e v e n p o i n t i s c a l c u l a t e d i f i t e x i s t s i n t h a t r a n g e . The b i v a r i a t e a n a l y s i s i s p e r f o r m e d by computing t h e NPV f o r the r e s u l t i n g 100 c o m b i n a t i o n s of p o i n t s t a k i n g 10 p o i n t s i n t h e range s e t by t h e p e s s i m i s t i c and o p t i m i s t i c e s t i m a t e s f o r each of the two v a r i a b l e s b e i n g s t u d i e d . A m a t r i x c o n t a i n i n g t h i s r e s u l t s i s p r e s e n t e d . No a t t e m p t i s made t o i n t e r p o l a t e c o n t o u r s of c o n s t a n t NPV v a l u e s . S i m i l a r l y , c o n t o u r s of c o n s t a n t IRR a r e not i d e n t i f i e d . CHAPTER 5. THE COMPUTER PROGRAM 5.1 INTRODUCTION A computer program u s i n g the FORTRANVS c o m p i l e r a v a i l a b l e a t the main computer of UBC (FORTRAN 77 p r o g r a m i n g l a n g u a g e ) was implemented i n c l u d i n g most of t h e t o p i c s t r e a t e d i n t h e p r e v i o u s c h a p t e r s . The b a s i c o b j e c t i v e o f the model i s t o p r o v i d e the u s e r w i t h i n f o r m a t i o n a b o u t t h e s e n s i t i v i t y of any of the v a r i a b l e s and p a r a m e t e r s i n v o l v e d i n t h e c a s h f l o w s a s s o c i a t e d w i t h t y p i c a l c a p i t a l p r o j e c t s . S p e c i f i c a l l y , a s t a r d-iagram, b r e a k - e v e n p o i n t s and e x a c t u n i v a r i a t e and b i v a r i a t e s e n s i t i v i t y a n a l y s i s a r e p r o d u c e d . The program a l s o computes a p e r i o d - b y - p e r i o d c a s h f l o w i n c u r r e n t d o l l a r s . The program i s made up of f i v e m a j o r modules w i t h a t o t a l of 49 s u b r o u t i n e s . The main p a r t s a r e : i ) d a t a i n p u t ; i i ) c a l c u l a t i o n of t h e p e r f o r m a n c e measures (Net P r e s e n t V a l u e , I n t e r n a l R ate of R e t u r n , T o t a l c o n s t r u c t i o n c o s t s and p e r i o d - b y - p e r i o d c a s h f l o w ; i i i ) t h e b u i l t - i n f u n c t i o n s u s e d t o d e s c r i b e c a s h f l o w p a t t e r n s ; i v ) t h e s e n s i t i v i t y a n a l y s i s ; and v ) t h e p l o t of r e s u l t s . The g e n e r a l a r c h i t e c t u r e of the program and i t s b a s i c f l o w c h a r t i s d e p i c t e d i n f i g u r e 17. A main segment c a l l e d Flow c o n t r o l r o u t i n e i n i t i a t e s the program by c a l l i n g t h e d a t a i n p u t s u b r o u t i n e ( s t e p 1 ) . Once t h i s p r o c e s s i s 106 I I I Data | j input j I I I I | Menus 1 I. 3 T I Flow | c o n t r o l j r i i I 4| i i. NPV IRR TCC I I. B u i l t - i n | fu n c t i o n s j FIGURE 17. Program b a s i c flow c h a r t 12 .1. 10 I Output | f i l e I 11 S e n s i t i v i t y A n a l y s i s I. L i n e a r j j Exact I P l o t t i n g r o u t i n e s | | B i v a r i a t e | o 108 c o m p l e t e d , t h e program r e t u r n s t o t h e c o n t r o l r o u t i n e ( s t e p 2) and the p e r f o r m a n c e measures a r e c a l c u l a t e d ( s t e p 3 ) . These v a l u e s a r e t r a n s f e r r e d t o t h e c o n t r o l r o u t i n e ( s t e p 4) and p r i n t e d i n t h e o u t p u t f i l e ( s t e p 5 ) . Then, t h e u s e r s e l e c t s t h e t y p e o f s e n s i t i v i t y a n a l y s i s t o be p e r f o r m e d ( s t e p 6) and from t h i s b l o c k , t h e p e r f o r m a n c e measures a r e r e c a l c u l a t e d ( s t e p 7 ) . The s e n s i t i v i t y r o u t i n e s make use of t h e s e v a l u e s ( s t e p 8) t o c a l c u l a t e t h e s e n s i t i v i t y c o e f f i c i e n t s and t o p e r f o r m the e x a c t and b i v a r i a t e a n a l y s e s ( s t e p 9 ) . These r e s u l t s a r e p l o t t e d i n s t e p 10 and s e n t t o the o u t p u t f i l e i n s t e p 11. Then, t h e program r e t u r n s t o t h e c o n t r o l r o u t i n e ( s t e p 12) and s t e p s 6 t h r o u g h 12 a r e r e p e a t e d as many t i m e s as d e s i r e d . The major a s s u m p t i o n s and r e s t r i c t i o n of t h e program a r e : 1. A maximum of 50 c a s h f l o w s and 100 p e r i o d s a r e a l l o w e d . 2. Any c o n s i s t e n t system of u n i t s f o r money and time c a n be us e d . 3. O n l y one f o r e i g n exchange r a t e c an be s p e c i f i e d . 4. The i n p u t from borrowed f u n d s f o l l o w s the form of t h e c o n s t r u c t i o n e x p e n d i t u r e f u n c t i o n . 5. I n f l a t i o n and i n t e r e s t r a t e s a r e c o n s t a n t and n o m i n a l ones. 6. Two a r b i t r a r y f u n c t i o n s t o d e s c r i b e c a s h f l o w p a t t e r n s can be p r e s c r i b e d . One f o r t h e c o n s t r u c t i o n phase and a n o t h e r f o r t h e o p e r a t i n g p h a s e . 7. N e g a t i v e f l o w s ( d i s b u r s e m e n t s ) a r e e n t e r e d as n e g a t i v e v a l u e s ; p o s i t i v e f l o w s ( r e v e n u e s ) a r e e n t e r e d a s 109 p o s i t i v e ones, e x c e p t f i x e d and v a r i a b l e o p e r a t i n g c o s t s a r e always e n t e r e d as p o s i t i v e but a r e t r e a t e d a s d i s b u r s e m e n t s . 8. T h e r e i s no r e s t r i c t i o n on the t i m e v a l u e s a s s i g n e d t o c a s h f l o w s . I t means t h a t t h e y c an be s u p e r i m p o s e d i n t i m e . 9. As many as n i n e d i f f e r e n t u n i t s a l e p r i c e s w i t h t h e i r c o r r e s p o n d e n t i n f l a t i o n r a t e s can be s p e c i f i e d . 10. F i x e d and v a r i a b l e o p e r a t i n g c o s t s a r e c o n s t a n t (as of the p e r i o d when o p e r a t i o n s t a r t s ) but an i n f l a t i o n r a t e can be a t t a c h e d t o e a c h of them. 11 . C o n t i n u o u s compounding i s us e d t h r o u g h o u t t h e program. The f i v e major b o d i e s of t h e program a r e d e s c r i b e d below. 5.2 DATA INPUT The i n p u t b e g i n s w i t h g e n e r a l i n f o r m a t i o n a b o u t t h e p r o j e c t , namely p r o j e c t i d e n t i f i c a t i o n , i n i t i a l number of c a s h f l o w s ( c a s h f l o w s may be added l a t e r o n ) , d i s c o u n t r a t e , f o r e i g n exchange r a t e and p r o j e c t l i f e . The i n f o r m a t i o n about the c o n s t r u c t i o n l o a n i s n e x t . I t i s assumed t h a t f o r t h o s e c a s e s when s u c h a l o a n i s u s e d , the i n p u t from borrowed funds w i l l f o l l o w t h e form of t h e c o n s t r u c t i o n e x p e n d i t u r e f u n c t i o n . The repayment of t h e l o a n w i l l o c c u r i n a p e r i o d not n e c e s s a r i l y e q u a l t o the end o f c o n s t r u c t i o n , w h i c h i s i n p u t by t h e u s e r . 1 10 Then, t h e g e n e r a l i n f o r m a t i o n a b o u t t h e o p e r a t i n g phase i s r e q u e s t e d by t h e program. Up t o n i n e d i f f e r e n t u n i t s a l e p r i c e s can be s p e c i f i e d , e ach of them w i t h i t s c o r r e s p o n d i n g i n f l a t i o n r a t e . I t i s i m p o r t a n t t o n o t e t h a t t h e v a l u e of  the u n i t p r i c e s c o r r e s p o n d s t o t h e c u r r e n t d o l l a r r a t e when  the o p e r a t i n g phase commences. I f t h e p r i c e s has been e s t i m a t e d i n c u r r e n t d o l l a r s f o r a l a t e r ( e a r l i e r ) p e r i o d , they have t o be d e f l a t e d ( i n f l a t e d ) t o t h e p e r i o d when o p e r a t i o n s s t a r t . Then, t h e f i x e d and v a r i a b l e o p e r a t i n g c o s t s w i t h t h e i r r e s p e c t i v e i n f l a t i o n r a t e s a r e s p e c i f i e d . These c o s t s s h o u l d a l s o be s p e c i f i e d i n c u r r e n t d o l l a r s as of t h e s t a r t of o p e r a t i o n s . They a r e assumed t o be i n e f f e c t d u r i n g any p e r i o d when r e v e n u e s from o p e r a t i o n s a r e p r o d u c e d . I n f o r m a t i o n about d e p r e c i a t i o n f o l l o w s . The model r e q u i r e s t h e v a l u e of d e p r e c i a b l e a s s e t s , the p e r i o d when d e p r e c i a t i o n s t a r t s and t h e l i f e of t h e a s s e t . A c c o r d i n g t o t h e s e v a l u e s , d e p r e c i a t i o n c h a r g e s f o r each p e r i o d a r e computed u s i n g t h e s t r a i g h t l i n e d e p r e c i a t i o n method. Then, t h e income t a x r a t e and t h e c h a r a c t e r i s t i c s of the l o n g term f i n a n c i n g a r e e n t e r e d . The program o f f e r s t h r e e o p t i o n s t o t h e u s e r : a ) t h e c a s e when no l o n g term l o a n i s t a k e n ; b ) t h e l o n g term l o a n i s t a k e n t o repay t h e c o n s t r u c t i o n l o a n ( i n c l u d i n g i n t e r e s t d u r i n g c o n s t r u c t i o n ) ; and c) t h e u s e r may e n t e r an a r b i t r a r y amount borrowed. When o p t i o n s b) or c) a r e s e l e c t e d , t h e u s e r s p e c i f i e s the i n t e r e s t r a t e , the p e r i o d when t h e l o a n i s t a k e n and the 111 t y p e of repayment f u n c t i o n . The repayment f u n c t i o n can be s e l e c t e d from: 1. U n i f o r m payments. 2. S t e p f u n c t i o n ( i n c r e m e n t s e v e r y g i v e n number o f p a y m e n t s ) . 3. G r a d i e n t f u n c t i o n . The u s e r a l s o s p e c i f i e s the number of p e r i o d s between two payments, the d a t e of t h e f i r s t payment (which a l l o w s a g r a c e p e r i o d i n t h e f i n a n c i n g s t r a t e g y ) and t h e t o t a l number of payments. For the c a s e s of s t e p and g r a d i e n t repayment f u n c t i o n s , t h e v a l u e of t h e f i r s t payment s h o u l d be e n t e r e d as w e l l . Then, t h e i n f o r m a t i o n about c a s h f l o w s i s e n t e r e d . T h i s i s done w i t h the a i d of menus and t h e p r o g r a m w i l l r e q u e s t the a p p r o p r i a t e i n f o r m a t i o n a c c o r d i n g t o t h e c h o i c e s made by the u s e r . The f i r s t of t h e s e menus i s p r e s e n t e d i n f i g u r e 18. At t h i s p o i n t , the phase t o w h i c h th e c a s h f l o w b e l o n g s i s s p e c i f i e d . A c c o r d i n g t o t h e p r o j e c t p h a s e s e l e c t e d , t h e i n p u t p r o c e e d s as f o l l o w s : 1. F e a s i b i l i t y and D e s i g n : When e i t h e r of t h e s e p hases i s s e l e c t e d , t h e u s e r a s s i g n s a name t o t h e c a s h f l o w and s e l e c t s i t s t y p e from a menu l i k e t h e one shown i n f i g u r e 1 9 . Then, the p a r a m e t e r s of t h e c a s h f l o w a r e e n t e r e d . 2. I n i t i a l I n vestment and D i s p o s a l : The model o n l y a l l o w s s i n g l e d i s c r e t e payments t o d e s c r i b e t h e s e f l o w s . They can be l o c a t e d a t any p o i n t i n t i m e . 1 12 FIGURE 18. Menu f o r the s e l e c t i o n of p r o j e c t phase PROJECT PHASE 1. FEASIBILITY 2. DESIGN 3. INITIAL INVESTMENT 4. CONSTRUCTION 5. OPERATION 6. DISPOSAL FIGURE 19. Menu f o r t h e s e l e c t i o n of f l o w t y p e ( F e a s i b i l i t y and Desi g n ) SELECT ONE OF THE FOLLOWING: 1. SINGLE PAYMENT 2. TWO DISCRETE PAYMENTS 3. UNIFORM FLOW 113 3. C o n s t r u c t i o n : F o r e a c h c a s h f l o w , t h e u s e r s p e c i f i e s a name and s e l e c t s i t s t y p e from a menu l i k e t h e one shown i n F i g u r e 20. One of t h e c a s h f l o w s of t h e c o n s t r u c t i o n phase can be an a r b i t r a r y f u n c t i o n programmed by t h e u s e r and l i n k e d t o t h e o b j e c t code of t h e main program. T h i s f u n c t i o n subprogram s h o u l d have t h e f o l l o w i n g FORTRAN c o d i n g : FUNCTION CO(X,F,I) DIMENSION F(50,9) CO= ( A r b i t r a r y f u n c t i o n ; C O = f ( x , F , I ) ) RETURN END The f u n c t i o n may have a maximum of t h r e e p a r a m e t e r s g i v e n t h e i n t e r n a l s t r u c t u r e of t h e program. They a r e s p e c i f i e d as t h e s e c o n d , t h i r d and f o u r t h columns of t h e I t h row of m a t r i x F. F o r example, i f the a r b i t r a r y f u n c t i o n i s t h e e q u a t i o n of a s t r a i g h t l i n e , t h e p a r a m e t e r s a r e the i n t e r c e p t b and t h e s l o p e m. In s u c h a c a s e , t h e u s e r may w r i t e the F u n c t i o n subprogram d e s c r i b e d above, i n wh i c h t h e f u n c t i o n i s e x p r e s s e d a s : CO = F ( I , 2 ) + F ( I , 3 ) * X r e p r e s e n t i n g : F u n c t ion,= b + mx FIGURE 20 . Menu f o r t h e s e l e c t i o n o f f l o w t y p e ( C o n s t r u c t i SELECT ONE OF THE FOLLOWING: 1. SINGLE PAYMENT 2 . TWO DISCRETE PAYMENTS 3. UNIFORM FLOW 4. TRAPEZOIDAL 5. BETA FUNCTION 6. EXPONENTIAL 7. OTHER FIGURE 2 1 . Menu f o r t h e s e l e c t i o n o f f l o w t y p e ( O p e r a t i o n ) SELECT ONE OF THE FOLLOWING: 1. SINGLE PAYMENT 2 . TWO DISCRETE PAYMENTS 3. UNIFORM FLOW • 4. TRAPEZOIDAL 5. BETA FUNCTION 6. EXPONENTIAL 7. GOMPERTZ CURVE 8. OTHER 115 The n u m e r i c a l v a l u e of t h e p a r a m e t e r s i s i n p u t d u r i n g t h e e x e c u t i o n of the program. 4. O p e r a t i o n : The t y p e of e a c h c a s h f l o w b e l o n g i n g t o t h i s phase i s s e l e c t e d from a menu l i k e t h a t shown i n f i g u r e 21. A l s o , one of t h e s e f l o w s c an be an a r b i t r a r y f u n c t i o n programmed by t h e u s e r i n a manner s i m i l a r t o the e x p l a i n e d f o r t h e a r b i t r a r y f u n c t i o n of t h e c o n s t r u c t i o n p h a s e . The o n l y d i f f e r e n c e i s t h a t t h e name of the f u n c t i o n subprogram i s RE i n t h i s c a s e ( i n s t e a d of CO). A f t e r t h e name and t h e p a r a m e t e r s of the c a s h f l o w have been e n t e r e d , t h e program w i l l ask f o r t h e u n i t s a l e p r i c e a p p l i c a b l e t o t h e re v e n u e f u n c t i o n . T h i s w i l l n ot be done i f t h e r e i s o n l y one u n i t s a l e p r i c e f o r t h e e n t i r e p r o j e c t . In t h i s c a s e , t h e p r o g r a m assumes t h a t t h e p r i c e a p p l i e s t o a l l the c a s h f l o w s e n t e r e d under t h e o p e r a t i n g p h a s e . In the c a s e t h a t a f u n c t i o n e n t e r e d under t h e o p e r a t i o n a l phase does n o t c o r r e s p o n d t o an o u t p u t p r o f i l e t h a t has t o be m u l t i p l i e d by a u n i t s a l e p r i c e , a dummy u n i t p r i c e e q u a l t o one s h o u l d be a s s i g n e d t o t h a t f u n c t i o n . Some c o n s i d e r a t i o n s about t h e c a s h f l o w p a r a m e t e r s a r e i n o r d e r . F i r s t l y , t h e v a l u e of t h e f l o w s h o u l d be n e g a t i v e f o r d i s b u r s e m e n t s or o u t f l o w s and p o s i t i v e f o r r e v e n u e s o r i n f l o w s . The program does not assumes t h e s i g n of any c a s h f l o w ( i t i s not assumed t h a t t h e s a l v a g e v a l u e i s a l w a y s p o s i t i v e o r t h a t c o n s t r u c t i o n f l o w s a r e always n e g a t i v e ) e x c e p t f o r the c a s e of o p e r a t i o n a l c o s t s and repayment of 1 1 6 t h e l o n g term l o a n . The f i x e d and v a r i a b l e c o s t s a r e e n t e r e d as p o s i t i v e v a l u e s but t h e c a s h f l o w o r i g i n a t e d by them i s assumed t o be n e g a t i v e . S e c o n d l y , t h e v a l u e of t h e c a s h f l o w s i s assumed t o be i n c u r r e n t d o l l a r s as of t h e p e r i o d when the c a s h f l o w s t a r t s f o r t h e c a s e of c o n t i n u o u s f l o w s and of t h e p e r i o d when the c a s h f l o w happens i n t h e c a s e of d i s c r e t e f l o w s . I f an i n f l a t i o n r a t e a p p l i e s t o a c o n t i n u o u s c a s h f l o w , t h e flo w w i l l be i n f l a t e d w i t h r e s p e c t t o t h e s t a r t i n g p e r i o d o f the f l o w . T h i r d l y , t h e r e i s no r e s t r i c t i o n a bout t h e t i m e p e r i o d when any c a s h f l o w s t a r t s and f i n i s h e s ( o b v i o u s l y , t h e former s h o u l d be b e f o r e t h e l a t t e r ) . T hat f l e x i b i l i t y p e r m i t s t h e u s e r t o s u p e r i m p o s e d i f f e r e n t p h a s e s and d i f f e r e n t c a s h f l o w s w i t h i n t h e same p h a s e . Two i m p o r t a n t f e a t u r e s of t h e model c o n c e r n i n g the d a t a i n p u t s h o u l d be c a r e f u l l y c o n s i d e r e d . The f i r s t one r e f e r s t o the e x i s t e n c e of some p r i m a r y v a r i a b l e s not a s s o c i a t e d w i t h the b a s i c p a r a m e t e r s of any c a s h f l o w , but t h a t can be i n c l u d e d i n the model. They a l s o may be us e d t o s e t f u n c t i o n a l r e l a t i o n s h i p s between t h e p a r a m e t e r s o f t h e c a s h f l o w s t r e a m . F o r example, the s t a r t i n g d a t e of a g i v e n c a s h f l o w may o c c u r x p e r i o d s a f t e r t h e f i n i s h i n g d a t e of a n o t h e r f l o w . Then, t h i s v a r i a b l e x i s s p e c i f i e d i n a v e c t o r c a l l e d V. The program a l l o w s as many as 20 of t h e s e v a r i a b l e s and the y a r e s t o r e d i n e l e m e n t s 20 t h r o u g h 39 of t h e a f o r e m e n t i o n e d v e c t o r V. A f t e r t h e i n f o r m a t i o n about t h e 1 1 7 c a s h f l o w s has been e n t e r e d , t h e p r o g r a m w i l l r e q u e s t t h e u s e r t o i n p u t the v a l u e s of t h e s e p r i m a r y v a r i a b l e s i n c a s e t h e y e x i s t . The f i r s t 20 e l e m e n t s o f t h i s v e c t o r c o n t a i n p r i m a r y v a r i a b l e s c o n s i d e r e d by t h e program t h a t a r e n o t a s s o c i a t e d t o any s p e c i f i c c a s h f l o w . The g e n e r a l s t r u c t u r e of the v e c t o r i s shown i n T a b l e 2. The s e c o n d f e a t u r e r e f e r s t o a s u b r o u t i n e w r i t t e n and c o m p i l e d by the u s e r where f u n c t i o n a l r e l a t i o n s h i p s between any of t h e v a r i a b l e s and p a r a m e t e r s can be s p e c i f i e d i n c l u d i n g such v a r i a b l e s i n v e c t o r V. T h i s works as f o l l o w s : The b a s i c i n f o r m a t i o n about t h e c a s h f l o w s i s s t o r e d i n a m a t r i x c a l l e d F. I t has 50 rows (maximum 40 c a s h f l o w s ) and 9 columns c o n t a i n i n g t h e p a r a m e t e r s of e a c h c a s h f l o w . The f i r s t column of row I r e f e r s t o t h e t y p e of f u n c t i o n t h a t d e s c r i b e s t h e c a s h f l o w I; t h e r e f o r e , t h i s column w i l l a lways have a number between 1 and 8. The r e m a i n i n g c o l u m n s c o n t a i n i n f o r m a t i o n d e p e n d i n g on t h e t y p e of f l o w as d e s c r i b e d i n T a b l e s 3 and 4. In T a b l e 3, t h e i n f o r m a t i o n s t o r e d i n each o f t h e e i g h t columns of any row I i s p r e s e n t e d . The v a l u e of I c o r r e s p o n d s t o t h e number of t h e c a s h f l o w as e n t e r e d by t h e u s e r d u r i n g t h e d a t a i n p u t . In a l l c a s e s , columns 7, 8 and 9 have t h e same i n f o r m a t i o n , i e . t h e i n f l a t i o n r a t e t h a t a p p l i e s f o r t h e f l o w , t h e f o r e i g n exchange r a t e and the u n i t s a l e p r i c e . Column f i v e f o r F ( I , 1 ) = 1 c o n t a i n s t h e p e r i o d when t h e s i n g l e f l o w o c c u r s . Columns f i v e and s i x f o r F ( I , 1)= 2 r e f e r t o the p e r i o d when t h e f i r s t and s e c o n d 1 18 TABLE 2 S t r u c t u r e of the v e c t o r V Element D e s c r i p t i o n 1 D i s c o u n t r a t e 2 F o r e i g n exchange r a t e 3 F r a c t i o n of c o n s t r u c t i o n f i n a n c e d w i t h b o r r o w e d funds 4 I n t e r e s t r a t e on c o n s t r u c t i o n l o a n 5 P e r i o d when c o n s t r u c i o n l o a n i s due 6 Not used 7 F i x e d o p e r a t i o n a l c o s t s 8 V a r i a b l e o p e r a t i o n a l c o s t s 9 V a l u e of d e p r e c i a b l e a s s e t s 10 P e r i o d when d e p r e c i a t i o n s t a r t s 11 L i f e of d e p r e c i a b l e a s s e t s 12 Income t a x r a t e 13 Amount o f l o n g term l o a n 14 I n t e r e s t r a t e on l o n g term l o a n 15 e q u a l 1 i f t h e l o n g term l o a n i s t a k e n t o r e p a y the c o n s t r u c t i o n l o a n . E q u a l 0 o t h e r w i s e . 16 P e r i o d when t h e l o n g term l o a n i s t a k e n 17 P e r i o d when o p e r a t i o n s b e g i n 18 I n f l a t i o n r a t e f o r f i x e d o p e r a t i o n a l c o s t s 19 I n f l a t i o n r a t e f o r v a r i a b l e o p e r a t i o n a l c o s t s 20-39 Other p r i m a r y v a r i a b l e s a s s i g n e d by t h e u s e r 119 TABLE 3 M a t r i x F: Data e l e m e n t s a s s o c i a t e d w i t h f l o w t y p e Flow Type Column number 1 2 3 4 5 6 7 8 9 S i n g l e payment 1 P - - T - - FE SP Two d i s c r e t e 2 PI P2 - TI T2 - FE SP payments U n i f o r m 3 C - - T i T f IR FE SP T r a p e z o i d a l 4 PI P2 - T i T f IR FE SP Beta f u n c t i o n 5 c a b T i T f IR FE SP E x p o n e n t i a l 6 c b - T i T f IR FE SP Gompertz c u r v e 7 A l A2 A3 T i T f IR FE SP A r b i t r a r y 8 PI P2 P3 T i T f IR FE SP (CO or RE) TABLE 4 M a t r i x F: D a t a e l e m e n t s i n columns 2, 3 and 4 a c c o r d i n g t o t h e f l o w t y p e F(I,1) F ( I , 2 ) F ( I , 3 ) F ( I , 4 ) 1 V a l u e o f payment — — 2 V a l u e o f f i r s t paym. Second payment -3 V a l u e o f t h e f l o w - -4 S t a r t i n g v a l u e F i n i s h i n g v a l u e -5 A m p l i f i c a t i o n c o n s t . P a r a m e t e r 1 P a r a m e t e r 2 6 I n i t i a l v a l u e Growth r a t e -7 A s y m p t o t i c l i m i t Shape p a r a m e t e r Growth r a t e 8 Parameter 1 P a r a m e t e r 2 Pa r a m e t e r 3 120 payments o c c u r , r e s p e c t i v e l y . The r e s t of f l o w t y p e s a r e c o n t i n u o u s ( F ( I , 1 ) = 3 t h r o u g h 8 ) , f o r t h e s e c a s e s , columns 5 and 6 c o n t a i n t h e s t a r t i n g and f i n i s h i n g p e r i o d s of t h e c a s h f l o w r e s p e c t i v e l y . The r e s t o f t h e i n f o r m a t i o n , i e . columns 2, 3 and 4 f o r a l l f l o w t y p e s , i s summarized i n T a b l e 4. The i n f o r m a t i o n about t h e u n i t s a l e p r i c e s i s s t o r e d i n a m a t r i x c a l l e d P c o n t a i n i n g 10 rows and 2 c o l u m n s . Each row s t o r e s i n i t s f i r s t column t h e v a l u e of one of t h e n i n e p o s s i b l e d i f f e r e n t u n i t a r y p r i c e s (row 10 i s r e s e r v e d f o r o t h e r i n t e r n a l i n f o r m a t i o n ) , and i t s c o r r e s p o n d i n g i n f l a t i o n r a t e o c c u p i e s t h e s e c o n d c olumn. H a v i n g t h i s s t r u c t u r e i n mind, t h e u s e r a s s i g n s a number t o each c a s h f l o w and w r i t e s a s u b r o u t i n e c a l l e d VARIA d e s c r i b i n g the f u n c t i o n a l r e l a t i o n s h i p s between t h e p r i m a r y v a r i a b l e s . F o r t h e example m e n t i o n e d b e f o r e ( t h e s t a r t i n g p e r i o d of say c a s h f l o w 3 o c c u r s 0.5 p e r i o d s a f t e r the f i n i s h i n g d a t e of c a s h f l o w 2) and a d d i n g t h e c o n d i t i o n t h a t t h e i n f l a t i o n r a t e of c a s h f l o w s 5 and 7 s h o u l d be a l w a y s the same, the s u b r o u t i n e VARIA s h o u l d l o o k l i k e : SUBROUTINE VARIA(F,V,P,NC) DIMENSION F ( 5 0 , 9 ) , V ( 4 0 ) , P ( 1 0 , 2 ) F ( 3 , 5 ) = F ( 2 , 6 ) + V ( 2 0 ) F ( 7 , 7 ) = F ( 5 , 7 ) RETURN END 121 i n w h i c h : F ( 3 , 5 ) = S t a r t i n g p e r i o d (column 5) of c a s h f l o w 3 (row 3) F ( 2 , 6 ) = F i n i s h i n g p e r i o d (column 6) of c a s h f l o w 2 (row 2) V(20)=0.5; t h i s v a l u e i s e n t e r e d from t h e program F ( 5 , 7 ) = I n f l a t i o n r a t e (column 7) of c a s h f l o w 5 (row 5) F (7 , 7) = I n f l a t i o n r a t e (column 7) of c a s h f l o w 7 (row 7) I t s h o u l d be n o t i c e d t h a t i n t h e s u b r o u t i n e , F ( 3 , 5 ) = F ( 2 , 6 ) + V ( 2 0 ) , c o u l d a l s o have been w r i t t e n as F(3 , 5 ) = F ( 2 , 6 ) + 0 . 5 , but a s s i g n i n g a p o s i t i o n i n v e c t o r V t o t h i s q u a n t i t y e n a b l e s t h e u s e r t o p e r f o r m a s e n s i t i v i t y a n a l y s i s on t h i s p a r a m e t e r . In t h e same way as p r e s e n t e d i n t h i s b r i e f example, t h e u s e r may s p e c i f y any f u n c t i o n a l r e l a t i o n s h i p s between t h e p r i m a r y v a r i a b l e s . In t h e n e x t c h a p t e r , the way i n which t h i s s u b r o u t i n e i s w r i t t e n w i l l be e x p l a i n e d i n more d e t a i l w i t h t h e a i d of a more c o m p l i c a t e d example. 5.3 BUILT-IN-FUNCTIONS The s e c o n d main b l o c k of t h e program c o n t a i n s t h e m a t h e m a t i c a l d e f i n i t i o n of t h e b u i l t - i n f u n c t i o n s of t h e model. I t i s s t a n d a r d FORTRAN c o d i n g of m a t h e m a t i c a l f u n c t i o n and no s p e c i a l t o p i c s d e s e r v e t o be m e n t i o n e d . 122 5 . 4 CALCULATION OF PERFORMANCE MEASURES Once t h e d a t a i n p u t i s c o m p l e t e d , t h e program p r o c e e d s t o compute t h e Net P r e s e n t V a l u e , t h e I n t e r n a l Rate of R e t u r n of the c a s h f l o w s t r e a m and t h e T o t a l c o n s t r u c t i o n c o s t s , a s w e l l as t h e p e r i o d - b y - p e r i o d c u r r e n t d o l l a r c a s h f l o w . F i r s t , t h e c a s h f l o w s a r e c o n v e r t e d i n t o e q u i v a l e n t d i s c r e t e amounts u s i n g t h e e q u a t i o n : m i n ( i + 1 , T f ) C i + 1 = { ; C ( t ) . e x p ( - r t + 0 ( t - T s ) ) d t }* e x p [ r ( i + 1 ) ] ( 5 . 1) m a x ( i , T s ) where: C ( i + 1 ) = E q u i v a l e n t d i s c r e t e v a l u e of c a s h f l o w C ( t ) between time i and i+1 computed a t p e r i o d i+1 r = D i s c o u n t r a t e 0 = l n f l a t i o n r a t e T s = S t a r t i n g p e r i o d f o r c a s h f l o w C ( t ) T f = F i n i s h i n g p e r i o d f o r c a s h f l o w C ( t ) In f i g u r e 17A, t h e t r a n s f o r m a t i o n done by e q u a t i o n 5.1 i s e x p l a i n e d . The c o n t i n u o u s c a s h f l o w i s decomposed i n e q u i v a l e n t d i s c r e t e payments a t t h e end of e a c h p e r i o d . The NPV of t h e u n i f o r m f l o w i s e q u a l t o the NPV of t h e s e t o f payments. Then, f o r each p e r i o d , t h e f o l l o w i n g f i g u r e s a r e computed. 1. I n i t i a l i n v e s t m e n t . 2. F e a s i b i l i t y e x p e n s e s . 1 23 T i m e P2A P34 P I P 4 i T i m e F I G U R E 21 A . T r a n s f o r m a t i o n d o n e -with, e q u a t i o n 5 . 1 3. D e s i g n e x p e n s e s . 4. C o n s t r u c t i o n c o s t s ( e q u i t y i n p u t ) . 5. C o n s t r u c t i o n c o s t s ( i n p u t from borrowed f u n d s ) . 6. Revenues. 7. F i x e d o p e r a t i o n a l c o s t s . 8. V a r i a b l e o p e r a t i o n a l c o s t s . 9. D e p r e c i a t i o n c h a r g e s . 10. Long term debt payment. 1 1 . T a x a b l e income. 12. Income t a x . 13. S a l v a g e v a l u e 14. Net c a s h f l o w 124 T a x a b l e income i s c a l c u l a t e d a s t h e r e v e n u e s minus f i x e d c o s t s minus v a r i a b l e c o s t s , minus d e p r e c i a t i o n c h a r g e s minus l o a n a m o r t i z a t i o n . The net c a s h f l o w i s c a l c u l a t e d as t h e t a x a b l e income p l u s t h e a l g e b r a i c sum of i t e m s 1,2,3,4 and 12 of the p r e v i o u s l i s t . The NPV i s o b t a i n e d by d i s c o u n t i n g t h e p e r i o d - b y - p e r i o d c a s h f l o w t o z e r o u s i n g c o n t i n u o u s compounding. The i n t e g r a l s a r e computed n u m e r i c a l l y u s i n g t h e Gauss q u a d r a t u r e method. Then, the I n t e r n a l R ate o f R e t u r n i s computed u s i n g t h e method p r o p o s e d by Newnan [ 3 6 ] . In c a s e t h e p r o j e c t i s a mixed i n v e s t m e n t , an e x t e r n a l r e i n v e s t m e n t r a t e i s r e q u e s t e d by the program. The r e s u l t i s o b t a i n e d u s i n g a s y s t e m a t i c p r o c e d u r e of t r i a l and e r r o r . 5.5 SENSITIVITY ANALYSIS As was m e n t i o n e d b e f o r e , t h e main o b j e c t i v e of t h e program i s t o p e r f o r m d i f f e r e n t t y p e s of s e n s i t i v i t y a n a l y s i s u s i n g a f a i r l y g e n e r a l model f o r t h e c a l c u l a t i o n of t h e NPV and IRR and T o t a l c o n s t r u c t i o n c o s t s (TCC) of c a p i t a l p r o j e c t s . Those t y p e s a r e l i n e a r u n i v a r i a t e a n a l y s i s , e x a c t u n i v a r i a t e a n a l y s i s i n c l u d i n g b r e a k - e v e n p o i n t s and b i v a r i a t e a n a l y s i s . The f i r s t t y p e i s c a r r i e d out by s e l e c t i n g any v a r i a b l e from the m a t r i x F c o r r e s p o n d i n g t o the i n f o r m a t i o n a b o u t c a s h f l o w s , or from t h e v e c t o r V c o n t a i n i n g o t h e r p r i m a r y v a r i a b l e s and u s e r - d e f i n e d v a r i a b l e s . The model computes t h e a b s o l u t e and r e l a t i v e l i n e a r s e n s i t i v i t y c o e f f i c i e n t s f o r 125 t h e NPV, IRR and TCC c a s e s as d e f i n e d i n t h e p r e v i o u s c h a p t e r . The u s e r has t h e o p t i o n of p r o d u c i n g a s t a r d i a g r a m or s e n s i t i v i t y c h a r t by i n c l u d i n g any of t h e a n a l y z e d v a r i a b l e s i n i t . In any c a s e , t h e r e s u l t s w i l l be w r i t t e n b o t h on the s c r e e n and i n a f i l e a t t a c h e d t o u n i t 8. The e x a c t a n a l y s i s i s p r o d u c e d by c a l c u l a t i n g t h e NPV f o r a range of v a l u e s a s s i g n e d t o t h e s e l e c t e d v a r i a b l e s between t h e i r p e s s i m i s t i c or l o w e r e s t i m a t e and t h e i r o p t i m i s t i c or h i g h e r e s t i m a t e . The b r e a k - e v e n p o i n t i s c a l c u l a t e d by t r i a l - a n d - e r r o r . F i n a l l y , t h e u s e r i s g i v e n t h e o p t i o n of p r o d u c i n g a p l o t of t h e r e s u l t s o b t a i n e d i n t h i s a n a l y s i s . The b i v a r i a t e a n a l y s i s i s s i m i l a r t o t h e e x a c t a n a l y s i s w i t h t h e e x c e p t i o n t h a t t h e p r o d u c e d o u t p u t i s a m a t r i x of 10 rows and 10 c o l u m n s . Ten p o i n t s i n the range s e t by t h e lower and h i g h e r e s t i m a t e s of e a c h v a r i a b l e a r e u s e d and t h e NPV i s computed f o r t h e r e s u l t i n g 100 c o m b i n a t i o n s . The e l e m e n t s of the r e s u l t i n g m a t r i x r e p r e s e n t t h e the change i n p e r c e n t a g e of the r e s u l t i n g NPV w i t h r e s p e c t t o t h e o r i g i n a l NPV, or NPV c a l c u l a t e d a t t h e " b e s t " e s t i m a t e s . A g a i n , t h e r e s u l t i s s e n t b o t h t o t h e s c r e e n and t o a f i l e a t t a c h e d t o u n i t 8. F i n a l l y , t h e u s e r has t h e o p t i o n of r e s e t t i n g t h e v a l u e of any c a s h f l o w p a r a m e t e r o r p r i m a r y v a r i a b l e , as w e l l as c h a n g i n g or a d d i n g new c a s h f l o w s i n o r d e r t o e x p l o r e a d d i t i o n a l b e h a v i o r s of t h e i n v e s t m e n t . 126 5.6 PLOTTING OF RESULTS The l a s t main p a r t of t h e program c o m p r i s e s t h e p l o t t i n g s u b r o u t i n e s . I t s h o u l d be m e n t i o n e d t h a t t h e program has been w r i t t e n u s i n g an a l m o s t s t a n d a r d v e r s i o n of t h e FORTRAN 77 p r o g r a m i n g l a n g u a g e , so i t may be e a s i l y c o m p i l e d and u s e d ( w i t h a l m o s t no change) i n o t h e r m a c h i n e s . The p l o t t i n g s u b r o u t i n e s a r e t h e e x c e p t i o n t o t h e s e c r i t e r i a s i n c e t h i s f e a t u r e makes use o f t h e ALGRAF s i m p l e p l o t t i n g p a c k a g e a v a i l a b l e f o r p u b l i c use i n t h e FORTRAN l i b r a r y of t h e computing c e n t e r a t UBC. U s i n g t h i s r o u t i n e , s i m p l e but s e l f e x p l a i n e d and c o n v e n t i o n a l s t a r d i a g r a m and v a r i a b l e v e r s u s NPV diagrams a r e p r o d u c e d . The p l o t t i n g p r o c e d u r e r e q u i r e s t h a t the f i l e i n w h i c h t h e p l o t s a r e t o be p r o d u c e d i s a t t a c h e d t o u n i t 9 a t t h e time when t h e main program i s c a l l e d f o r e x e c u t i o n . A h a r d copy of t h e p l o t i s o b t a i n e d a f t e r the e x e c u t i o n i s c o m p l e t e d i s s u i n g t h e MTS command: $RUN *QMSPLOT 0 = P l o t f i l e Where P l o t f i l e i s t h e name of t h e f i l e a t t a c h e d t o u n i t n i n e . G i v e n the r e s t r i c t i o n i n t h e a p p l i c a t i o n of t h i s p l o t t i n g r o u t i n e s t o t h e a v a i l a b i l i t y o f an s p e c i f i c k i n d of g r a p h i c s o f t w a r e , t h i s a s p e c t of t h e program has not been g i v e n g r e a t e mphasis. Graphs o f much b e t t e r q u a l i t y can be o b t a i n e d even u s i n g m i c r o c o m p u t e r s . The i n t e r f a c e between o t h e r g r a p h i c p a c k a g e s and t h e program s h o u l d be made f o r 127 e v e r y p a r t i c u l a r h a r d w a r e - s o f t w a r e c o n f i g u r a t i o n . The c o m p l e t e p r o g r a m l i s t i n g c a n be f o u n d i n A p p e n d i x A. CHAPTER 6. VALIDATION AND APPLICATION OF THE MODEL 6.1 INTRODUCTION The o b j e c t i v e s of t h i s c h a p t e r a r e t o v a l i d a t e the computer model d e v e l o p e d and t o show an example o f i t s a p p l i c a t i o n . F i r s t , an e x t r e m e l y s i m p l e example i s s o l v e d i n o r d e r t o d e m o n s t r a t e t h e a c c u r a c y of the r e s u l t s o b t a i n e d w i t h t h e model. Second, t h e program i s us e d t o compute the economic p e r f o r m a n c e measures and s e n s i t i v i t y a n a l y s i s of an h i g h l y s i m p l i f i e d model of an a c t u a l p r o j e c t , t h e p r o p o s e d b r i d g e l i n k i n g New B r u n s w i c k and P r i n c e Edward I s l a n d a c r o s s N o r t h u m b e r l a n d S t r a i t i n A t l a n t i c Canada. A l l the e s t i m a t e s and f i g u r e s used i n t h i s example a r e h y p o t h e t i c a l . 6.2 VALIDATION OF THE MODEL D u r i n g the development of t h e model, i t was c o n t i n u o u s l y t e s t e d f o r a c c u r a c y u s i n g p r e v i o u s l y s o l v e d examples. In t h i s s e c t i o n , t h i s a c c u r a c y i s d e m o n s t r a t e d u s i n g a v e r y s i m p l e c a s e , i n which a f a c i l i t y i s b u i l t and then s o l d . At time z e r o , t h e l a n d i s a c q u i r e d a t a c o s t of $5 m i l l i o n s . C o n s t r u c t i o n b e g i n s and the t o t a l c o n s t r u c t i o n c o s t s a r e e s t i m a t e d t o be $8.5 m i l l i o n s , o v e r a c o n s t r u c t i o n p e r i o d o f 1.5 y e a r s . The f a c i l i t y c o m p r i s e s 44 ap a r t m e n t s u i t e s t h a t can be s o l d f o r $400000 e a c h d u r i n g a p e r i o d of one y e a r s t a r t i n g when 90% of c o n s t r u c t i o n has been c o m p l e t e d . No 1 28 129 f i n a n c i n g i s t a k e n t o f u n d t h e c o n s t r u c t i o n phase o r as l o n g term d e b t . The a n a l y s i s i s t o be done i n c o n s t a n t d o l l a r s and on a p r e t a x b a s i s . In f i g u r e 22, t h e i n f o r m a t i o n about t h e p r o j e c t i s summarized, as w e l l as t h e r e s u l t s o b t a i n e d when the p r o b l e m was s o l v e d by hand. Then, the e x e r c i s e was s o l v e d w i t h t h e program u s i n g t h e f o l l o w i n g p r o c e d u r e : 1. The c a s h f l o w s a r e numbered: 1. Land a c q u i s i t i o n . 2. C o n s t r u c t i o n c o s t s . 3. Revenues 2. The p r i m a r y v a r i a b l e s p a r t i c u l a r t o t h i s p r o b l e m a r e a s s i g n e d a p o s i t i o n i n v e c t o r V, s t a r t i n g w i t h t h e 2 0 t h e l e m e n t : V(20)=C V ( 2 l ) = x V(22)=Ta 3. The s u b r o u t i n e VARIA d e s c r i b i n g t h e f u n c t i o n a l r e l a t i o n s h i p s between t h e v a r i a b l e s i s w r i t t e n . I t i s : C FUNCTIONAL RELATIONSHIPS BETWEEN VARIABLES SUBROUTINE VARIA(F,V,P,NC) DIMENSION F ( 5 0 , 9 ) , V ( 4 0 ) , P ( 1 0 , 2 ) C V a l u e of t h e s e c o n d flow=C/Tc F ( 2 , 2 ) = V ( 2 0 ) / F ( 2 , 6 ) C V a l u e of t h e t h i r d flow=44/Ta F(3,2)=44/V(22) C S t a r t t i m e of t h i r d flow=x.Tc 130 1 D e f i n i t i o n of the problem xTc Ta Area=44*S Area=C Tc Land MARR-0.18 L=$ 5 m i l l i o n s Tc=1.5 years time C=$ 8.5 m i l l i o n s x=0.9 Ta=l year S=$ 0.4 m i l l i o n s S o l u t i o n Net Present value= $183028.0 I n t e r n a l Rate o f Return= 19.04% L i n e a r s e n s i t i v i t y c o e f f i c i e n t s ( r e l a t i v e ) V a r i a b l e NPV IRR L -27 32 -1.52 Tc -11 45 -0.659 C -40 75 -2.251 X -16 66 -0.962 Ta -5 99 -0.345 S 69 24 3.781 FIGURE 22. D e s c r i p t i o n and manual s o l u t i o n of the simple example. 131 ECONOMIC PERFORMANCE MEASURES: Net p r e s e n t v a l u e = 183027.0 I n t e r n a l R ate o f Return= 19.04% L i n e a r s e n s i t i v i t y c o e f f i c i e n t s : V a r i a b l e V a l u e NPV IRR L -5000.0 -27.318 -1.505 Tc 1.5 -11.526 -0.635 C 8500.0 -40.701 -2.242 X 0.9 -16.772 -0.924 Ta 1.0 -6.025 -0.332 S 400.0 69.017 3.802 FIGURE 23. Summary o f r e s u l t s o b t a i n e d w i t h t h e program. F ( 3 , 5 ) = V ( 2 1 ) * F ( 2 , 6 ) C F i n a l p e r i o d of t h i r d flow=x.Tc+Ta F(3,6)=V(22)+F(3,5) RETURN END The time and monetary u n i t s a r e y e a r s and t h o u s a n d d o l l a r s r e s p e c t i v e l y . A f t e r p e r f o r m i n g l i n e a r , e x a c t and b i v a r i a t e a n a l y s e s , the program gave the r e s u l t s summarized i n f i g u r e 23. The complete o u t p u t f o r t h i s example i s p r e s e n t e d i n f i g u r e s 24 t o 34. F i g u r e 24 shows the v a l u e of the p r i m a r y v a r i a b l e s c o n s i d e r e d by the program. F i g u r e 25 summarizes SENSITIVITY AND ECONOMIC ANALYSIS OF PROJECT: SIMPLE EXAMPLE PRIMARY VARIABLES DISCOUNT RATE=0.1800 FOREIGN EXCHANGE RATE= 0.0 FRACTION OF CONSTRUCTION FINANCED WITH BORROWED FUNDS=0.0 INTEREST RATE ON CONSTRUCTION LOAN=0.0 PERIOD WHEN THE CONSTRUCTION LOAN IS DUE= 0 .0 FIXED OPERATING C0STS= 0.0 VARIABLE C0STS= . 0 .0 VALUE OF DEPRECIABLE ASSETS= 0 .0 PERIOD WHEN ASSETS ARE ACQUIRED= 0.0 LIFE OF DEPRECIABLE ASSETS= 0.0 TAX RATE=0.0 INFLATION RATE FOR FIXED C0STS=0.0 INFLATION RATE FOR VARIABLE COSTS= 0 .0 UNIT SALE PRICES # PRICE INFLATION 1 400.0000000 0.0 FIGURE 24. Primary variables 133 the i n f o r m a t i o n a b o u t th e c a s h f l o w s . F i g u r e 26 p r e s e n t s t h e economic p e r f o r m a n c e m e a s u r e s . I t s h o u l d be n o t e d t h a t t h e T o t a l C o n s t r u c t i o n C o s t s a r e n e g a t i v e , f o l l o w i n g t h e c o n v e n t i o n used by t h e program ( n e g a t i v e f l o w s s h o u l d be p r o c e e d e d by a minus s i g n ) . F i g u r e 27 p r e s e n t s t h e p e r i o d - b y - p e r i o d c a s h f l o w i n c u r r e n t d o l l a r s . F o r example, d u r i n g t h e s e c o n d p e r i o d of t h e p r o j e c t , a t o t a l of $11440000.0 i s r e c e i v e d as r e v e n u e s . The u s e r s h o u l d be c a r e f u l i n r e a d i n g t h e s e f i g u r e s , s i n c e t h e r e s u l t s a r e i n the system of u n i t s s e l e c t e d d u r i n g t h e d a t a i n p u t . In f i g u r e 28 t h e c o n t r i b u t i o n of e a c h c a s h f l o w t o t h e p e r i o d - b y - p e r i o d c a s h f l o w i n c u r r e n t d o l l a r s i s p r e s e n t e d . F i g u r e 29 p r e s e n t s t h e s e n s i t i v i t y c o e f f i c i e n t s f o r t h e i n d e p e n d e n t p r i m a r y v a r i a b l e s of t h e p r o b l e m . The a b s o l u t e c o e f f i c i e n t w i t h r e s p e c t t o t h e NPV and TCC i s t h a t d e f i n e d i n e q u a t i o n 4.4. The r e l a t i v e c o e f f i c i e n t w i t h r e s p e c t t o t h e s e two p e r f o r m a n c e measures i s d e f i n e d by e q u a t i o n 4.5. For the IRR c a s e , t h e a b s o l u t e c o e f f i c i e n t i s d e f i n e d i n e q u a t i o n 4.10 and t h e r e l a t i v e c o e f f i c i e n t i s d e f i n e d i n e q u a t i o n 4.11. F i g u r e 30 p r e s e n t s t h e o u t p u t of the e x a c t u n i v a r i a t e a n a l y s i s f o r v a r i a b l e S. F i r s t , t h e b r e a k - e v e n p o i n t (NPV=0 and IRR=MARR) i s p r i n t e d . Then, the e x a c t a n a l y s i s f o r 10 p o i n t s i n t h e range d e f i n e d by t h e p e s s i m i s t i c and o p t i m i s t i c e s t i m a t e s i s p r e s e n t e d . F i g u r e 31 p r e s e n t s t h e b i v a r i a t e s e n s i t i v i t y a n a l y s i s . The t o p row and l e f t column of t h e m a t r i x p r e s e n t the p e r c e n t a g e changes i n the v a r i a b l e s , t a k i n g 10 p o i n t s i n the range s e t by t h e INFORMATION ABOUT CASH FLOWS » NAME TYPE PHASE INIT. PEP. . FINAL PER. INF. RATE CURRENCY I L A NO SINGLE PA YM. INITIAL INV 0 .0 0 .0 0 .0 DOLLARS VALUE= - 5000.000(THOUS. $ ) 2 COfJS1nUC TI ON UNIFORM CONSTRUCTION 0 .0 1.50 0 .0 DOLLARS VALUE= •5666.664(THOUS. $ /PERIOD) 3 REVENUES UNIFORM OPERATION 1.35 2 .35 0 .0 DOLLARS VALUE= 44.0001THOUS. $ /PERIOD) UNIT SALE PRICE= 4 00.00000001THQUS. $ ) FIGURE 25. Information about cash flows E C O N O M I C P E R F O R M A N C E M E A S U R E S N E T P R E S E N T V A L U E C O N S T A N T D O L L A R C O N S T R U C T I O N C O S I S = E S C A L A T I O N D U R I N G C O N S T R U C T I O N -I N T E R E S I S C U R I N G C O N S T R U C T I O N : : T O T A L C O N S T R U C T I O N C O S T S = 183 .027 •8499.988 0 .0 0 .0 •8499.988 I N T E R N A L R A T E OF R E T U R N : 19.040 FIGURE 26. Economic performance measures CURRENT DOLLAR CASH FLOW INITIAL INVESTMENT -5000.000 FEASIBILITY DESIGN CONST. (EOUITY) CONST. LOAN REVENUES FIXED COSTS VARIABLE COSTS DEPRECIATION LONG TERM DEBT SALVAGE VALUE GROSS INCOME INCOME TAX NET CASH FLOW 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0 .0 0 .0 0 .0 -5666.660 -2833.330 0 .0 0.0 11440.000 0 .0 0 .0 0 .0 0 .0 0 .0 0.0 11440.000 0 .0 10666.660 8606.668 0 .0 0 .0 0 .0 0 .0 0 .0 6159.984 0 .0 0 .0 0 .0 0 .0 0 .0 6159.984 0 .0 6159 .984 FIGURE 27. Period-by-period cash flow i n current d o l l a r s 1 36 CURRENT DOLLAR CASH FLOWS CASH FLOW LAND CONSTRUC11 ON REVENUES 1 • 5000.000 • 5666.660 0 .0 2 0 .0 -2833.330 1 1440.000 3 0.0 0.0 6159.984 FIGURE 28. Cash flows in current dollars 0 LINEAR SENSITIVITY COEFICIENTS FOR VARIABLE S = -5000.0000000 ABSOLUTE RELATIVE NPV -1.00000 -27.31831 IRR -0.00006 -1.50486 TCC 0.0 0.0 LINEAR SENSITIVITY COEFICIENTS FOR VARIABLE C 8500.0000000 NPV IRR TCC ABSOLUTE -0.87640--0.00005 - 1.00000 RELATIVE -40.701 10 -2.24207 1.00000 LINEAR SENSITIVITY COEFICIENTS FOR VARIABLE Tc 1.5000000 NPV IRR TCC ABSOLUTE - 1406.42896 -0.08060 0.0 RELATIVE - 1 1 .52638 -0.63495 0.0 LINEAR SENSITIVITY COEFICIENTS FOR VARIABLE x = 0.9000000 ABSOLUTE RELATIVE NPV -3410.88940 -16.77235 IRR -0.19546 -0.92393 TCC 0.0 0.0 LINEAR SENSITIVITY COEFICIENTS FOR VARIABLE Ta 1.0000000 NPV IRR TCC ABSOLUTE - 1 102.81982 -0.06320 0.0 RELATIVE -6.02544 -0.33192 0.0 LINEAR SENSITIVITY COEFICIENTS FOR VARIABLE S 400.0000000 NPV IRR TCC ABSOLUTE 31.58008 0.00181 0.0 RELATIVE 69.01717 3.80190 0.0 FIGURE 29. Se n s i t i v i t y coefficients 138 EXACT UNIVARIATE ANALYSIS FOR VARIABLE S BREAK EVEN POINT= 394.1838379 VARIABLE NPV IRR (%) 370.0000000 377.7775879 385.5554199 393.3332520 401.1110840 408.8886719 416.6665039 424.4443359 432.2221680 439.9997559 -764.385 -518.766 -273.137 -27.509 218.113 463.738 709.363 954.988 1200.617 1446.234 13.483 14.968 16.423 17.839 19.235 20.593 21.931 23.239 24 .528 25.778 FIGURE 30. Exact univariate analysis 139 p e s s i m i s t i c and o p t i m i s t i c e s t i m a t e s of e a c h v a r i a b l e . The numbers i n t h e m a t r i x a r e p e r c e n t a g e change i n the NPV, when b o t h v a r i a b l e s a r e changed a t a t i m e . F i g u r e 32 p r e s e n t s t h e s t a r d i a g r a m p r o d u c e d by t h e program. In f i g u r e s 33 and 34, t h e p l o t of t h e r e s u l t s f r o m t h e e x a c t a n a l y s i s w i t h r e s p e c t t o t h e NPV and IRR r e s p e c t i v e l y i s p r e s e n t e d . F i n a l l y , i t i s n o t e d t h a t c o m p a r i n g t h e r e s u l t s o b t a i n e d by t h e program and t h o s e o b t a i n e d by hand, i t c a n be c o n c l u d e d t h a t the model p r o v i d e s a c c u r a t e r e s u l t s . The d i f f e r e n c e s between t h e two s e t s o f answers can be e x p l a i n e d by r o u n d i n g e r r o r s i n c u r r e d i n b o t h methods, m a i n l y i n t h e manual s o l u t i o n . 6.3 ARBITRARY FUNCTIONS In o r d e r t o p r o v i d e an example of t h e way how t h e a r b i t r a r y f u n c t i o n s a l l o w e d by t h e program a r e u s e d , the c a s h f l o w p r o f i l e s of t h e s i m p l e example were m o d i f i e d as shown i n f i g u r e 35.A. A l t h o u g h t h e program i n c l u d e s t h i s t y p e o f p r o f i l e s ( t r a p e z o i d a l f l o w s ) , t h e c a s h f l o w s w i l l be e n t e r e d as t h e a r b i t r a r y f u n c t i o n s c o n s i d e r e d by t h e model. The c a s h f l o w s a r e numbered as b e f o r e , i e . Land i s c a s h f l o w 1, C o n s t r u c t i o n i s c a s h f l o w 2, and Revenues i s c a s h f l o w 3. The p a r a m e t e r s of c a s h f l o w s 2 and 3 a r e a,b and c , d as i n f i g u r e 35A, r e s p e c t i v e l y . T h e r e f o r e , the p o s i t i o n of t h e s e q u a n t i t i e s i n m a t r i x F i s as f o l l o w s : 1. a = F ( 2 , 2 ) : F i r s t p a r a m e t e r (j=2) of c a s h f l o w 2 ( i = 2) BIVARIATE SENSITIVITY MATRIX - PERCENTAGE CHANGE IN THE NPV VARIABLE 1: S CONSTANT ALONG ROWS VARIABLE 2: C CONSTANT ALONG COLUMNS PERCENTAGE CHANGE IN VARIABLE C • 5 . 8 8 2 -4 .412 -2 .041 -1.471 0 .0 1.471 2.941 4 .412 5.882 S ( %) - 7 . 5 0 0 -278 .230 -338 .078 -397 .935 -457 .786 -517.634 -577.491 -637 .340 -697 .195 -757 .050 -5 .313 -127 .252 -187.101 -246 .958 -306 .808 -366.657 -426 .516 -486 .365 -546 .219 -606 .072 - 3 . 1 2 5 23 .723 -36 .126 -95 .983 -155.833 -215 .682 -275 .538 -335 .387 -395 .242 -455 .097 -0 .938 174.698 114.850 54.995 -4 .855 -64 .704 -124 .563 -184.411 -244 .266 -304.121 0 .0 239.404 179.556 119.699 59.848 0 .0 -59 .859 -119 .708 -179 .560 -239 .415 1.250 325.677 265.828 205.972 146.121 86 .273 26 .413 - 3 3 . 4 3 5 -93 .288 -153 .143 3.437 476.651 416.803 356.948 297.095 237.247 177.390 117.541 57.686 -2 .168 5.625 627.630 567.781 507.927 448.076 388.227 328.368 268.520 208.665 148.810 7.813 778.606 718.758 658.901 599.050 539.202 479.343 419.494 359.641 299.786 10.000 929.583 869.734 809.879 750.029 690.180 630.321 570.473 510.618 450.763 FIGURE 31. Bivariate analysis 141 FIGURE 32. S e n s i t i v i t y c h a r t L i n e a u a n a l y s i s f o r s i m p l i f i e d e xample 1 42 FIGURE 33. Plot: of r e s u l t s from the exact analysis (NPV FIGURE 34 P l o t o f r e s u l t s from the e x a c t a n a l y s i s (IRR case 1 44 2. b=F(2,3): Second p a r a m e t e r (j=3) of c a s h f l o w 2 (i=2) 3. c = F ( 3 , 2 ) : F i r s t p a r a m e t e r (j=2) of c a s h f l o w 3 (i=3) 4. d = F ( 3 , 3 ) : Second p a r a m e t e r (j=3) of c a s h f l o w 3 (i=3) The f u n c t i o n a l forms of c a s h f l o w s 2 and 3 a r e shown i n f i g u r e 35A. The v e c t o r V has t h e same s t r u c t u r e as b e f o r e : 1. V(20)=C 2. V ( 2 1 ) = X 3. V(22)=Ta Then, t h e s u b r o u t i n e VARIA and t h e F u n c t i o n subprograms CO and RE f o r t h i s example a r e : SUBROUTINE VARIA(F,V,P,NC) DIMENSION F ( 5 0 , 9 ) , V ( 4 0 ) , P ( 1 0 , 2 ) C b=(2*C)/Ta-a F ( 2 , 3 ) = 2 * V ( 2 0 ) / F ( 2 , 6 ) - F ( 2 , 2 ) C d=88/Ta-c F ( 3 , 3 ) = 8 8 / V ( 2 2 ) - F ( 3 , 2 ) C S t a r t t i m e of revenues=x.Tc F ( 3 , 5 ) = V ( 2 1 ) * F ( 2 , 6 ) C F i n i s h time of revenues=x.Tc+Ta F ( 3 , 6 ) = F ( 3 , 5 ) + V ( 2 2 ) RETURN END FUNCTION CO(X,F,I) DIMENSION F(50,9) C C O = - a - ( ( b - a ) / T c ) * t 145 C O = - F ( 2 , 2 ) - ( ( F ( 2 , 3 ) - F ( 2 , 2 ) ) / F ( 2 , 6 ) ) * X RETURN END FUNCTION RE( X , F , I ) DIMENSION F ( 5 0 , 9 ) C R E = c + ( ( d - c ) / T a ) * ( t - x T c ) C O = F ( 3 , 2 ) + ( ( F ( 3 , 3 ) - F ( 3 , 2 ) ) / ( F ( 3 , 6 ) - F ( 3 , 5 ) ) * ( X - F ( 3 , 5 ) ) RETURN END A f t e r r u n n i n g t h e example i n t h e c o mputer, th e NPV r e s u l t s t o be $210137 and the IRR goes up t o 19.21%. 6.4 EXAMPLE OF APPLICATION A l t h o u g h t h e example p r e s e n t e d i n t h i s s e c t i o n i s b a s i c a l l y i n t e n d e d t o show the use of t h e model f o r t h e c a l c u l a t i o n o f t h e s e n s i t i v i t y c o e f f i c i e n t s of a p r o p o s e d i n v e s t m e n t , t h e model can a l s o be used t o p e r f o r m o t h e r k i n d s of a n a l y s e s . In i t s p r e s e n t s t a t e , t h e computer program can be used as a v e r y p o w e r f u l t e a c h i n g t o o l . By r u n n i n g an example i n w h i c h v a r i a b l e s a r e r e s e t and c a s h f l o w s added, d e l e t e d o r changed, th e u s e r can g a i n i m p o r t a n t i n s i g h t s i n t o t h e b e h a v i o r of t h e model employed f o r t h e economic e v a l u a t i o n of c a p i t a l p r o j e c t s . A l s o , t h e model can be used t o a s s i s t i n c o n t i n g e n c y a l l o w a n c e a l l o c a t i o n and f a s t - t r a c k i n g p r oblems as w e l l as a l m o s t any p r o b l e m i n v o l v i n g time v a l u e 146 of money. 6.4.1 DESCRIPTION OF THE PROJECT The p r o j e c t s e l e c t e d f o r t h i s example i s t h e P r i n c e Edward I s l a n d b r i d g e . In t h e f i r s t s t a g e of t h e p r o j e c t , a p r o p o s a l i s p r e p a r e d a t a t o t a l c o s t of $1.5 m i l l i o n s and w i t h a t o t a l d u r a t i o n of 9 months. The s t a r t i n g d a t e of t h i s phase w i l l be tim e z e r o (1 period=1 y e a r ) . T h r e e months a f t e r t i m e z e r o (0.25 y e a r s ) , t h e d e s i g n phase commences. T o t a l d e s i g n c o s t s a r e $20 m i l l i o n and t h i s phase w i l l have a d u r a t i o n of 2.25 y e a r s . D u r i n g t h e s e two i n i t i a l p h a s e s , money f l o w s f o l l o w i n g a u n i f o r m d i s t r i b u t i o n . I n f l a t i o n r a t e s f o r b o t h i t e m s a r e e s t i m a t e d t o be 5%. C o n s t r u c t i o n b e g i n s a t t i m e t=1.5 y e a r s . F o r p u r p o s e s of an a p p r o x i m a t e a n a l y s i s , t h e p r o j e c t has been d e s c r i b e d i n terms of t h r e e major work pack a g e s and an i n d i r e c t expense c a t e g o r y ( a l l management c o s t s , s i t e f a c i l i t i e s , e t c . ) which span t h e e n t i r e l e n g t h , T c of t h e c o n s t r u c t i o n p h ase. The work p a c k a g e s , t h e i r s e q u e n c i n g and d u r a t i o n s a r e shown i n f i g u r e 35. C o n s t a n t d o l l a r c o s t s as of A p r i l 1, 1989, the f o r e c a s t s t a r t o f c o n s t r u c t i o n , have been e s t i m a t e d and p r e s e n t e d i n T a b l e 5. W h i l e some v a r i a b i l i t y i n the i n f l a t i o n r a t e f o r c o n s t r u c t i o n c o s t s i s a n t i c i p a t e d , i t has been s u g g e s t e d t h a t a c o n s t a n t r a t e e q u a l t o t h e e x p e c t e d a v e r a g e r a t e o f i n f l a t i o n be used f o r a l l work package c o s t s , i n c l u d i n g i n d i r e c t c o s t s , f o r p r e l i m i n a r y a n a l y s i s p u r p o s e s . 147 BRIDGE APPROACHES y T c BRIDGE SUPERSTRUCTURE x Tr BRIDGE FOOTINGS AND PIERS I N D I R E C T C O S T S A p r i l 1/89 FIGURE 35. Sequencing and d u r a t i o n of work packages d u r i n g c o n s t r u c t i o n p h a s e . TABLE 5 E s t i m a t e d c o n s t a n t d o l l a r c o n s t r u c t i o n c o s t s Work Package Cost Symbol U n i t s I n d i r e c t c o s t s 50.0 F o o t i n g s and P i e r s 120.0 S u p e r s t r u c t u r e 200.0 Approaches 70.0 C o i $ m i l l i o n / y e a r Co f $ m i l l i o n Cos $ m i l l i o n Coa $ m i l l i o n 148 A p r e f e r e n t i a l r a t e f o r f i n a n c i n g has been a r r a n g e d i n exchange f o r e q u i t y p a r t i c i p a t i o n by t h e l e n d i n g o r g a n i z a t i o n . G i v e n t h e s i z e of t h e p r o j e c t , and a g u a r a n t e e by the f e d e r a l government of a s u b s i d y and c l o s u r e of t h e p r e s e n t f e r r y s y s t e m upon c o m p l e t i o n of t h e p r o j e c t , 90% o f the funds r e q u i r e d f o r c o n s t r u c t i o n c an be borrowed, w i t h the b a l a n c e b e i n g d e r i v e d from t h e members of t h e c o n s o r t i u m . D u r i n g t h e c o n s t r u c t i o n p e r i o d , t h e shape of t h e l o a n drawdown p r o f i l e w i l l c o r r e s p o n d t o t h a t of the p r o j e c t c a s h f l o w p r o f i l e . No payments of a c c r u e d i n t e r e s t w i l l be made d u r i n g c o n s t r u c t i o n . The i n t e r e s t r a t e d u r i n g c o n s t r u c t i o n has been s e t t o t h e i n f l a t i o n r a t e d u r i n g c o n s t r u c t i o n p l u s 6 p e r c e n t . The c o n s o r t i u m u n d e r t a k i n g t h e p r o j e c t p l a n s t o t a k e a l o n g term l o a n a t t h e end of c o n s t r u c t i o n p e r i o d . The s i z e of the l o a n w i l l be e q u a l t o t h e t o t a l c o n s t r u c t i o n c o s t s , i n c l u d i n g i n t e r e s t d u r i n g c o n s t r u c t i o n . The l o a n w i l l be used t o d i s c h a r g e t h e c o n s t r u c t i o n l o a n ( i n c l u d i n g a c c r u e d i n t e r e s t s ) and t o repay t h e e q u i t y c o n t r i b u t i o n of t h e c o n s o r t i u m members. The l o a n w i l l have a f i x e d i n t e r e s t r a t e e q u a l t o 10% and i t w i l l be r e p a i d o v e r 35 y e a r s , t h e o p e r a t i n g l i f e of t h e p r o j e c t . The repayment f u n c t i o n w i l l be a g r a d i e n t f u n c t i o n w i t h a f i r s t payment e q u a l t o $45 m i l l i o n . The v a l u e of the g r a d i e n t w i l l be d e r i v e d and i t i s e x p e c t e d t o be p o s i t i v e . T h i s repayment s c h e d u l e r e f l e c t s f o r e c a s t s of i n c r e a s i n g r e v e n u e . 149 C o n s t a n t d o l l a r a n n u a l o p e r a t i n g and m a i n t e n a n c e c o s t s of t h e b r i d g e a r e f o r e c a s t t o be $10 m i l l i o n s as of t h e d a t e when o p e r a t i o n s b e g i n s (0.25 p e r i o d s b e f o r e t h e end of c o n s t r u c t i o n ) . They a r e e x p e c t e d t o i n c r e a s e a t a r a t e of 5.5% per y e a r . Revenue w i l l be g e n e r a t e d t h r o u g h u s e r t o l l s and an a n n u a l s u b s i d y from t h e f e d e r a l government which i s n o t t o e x c e e d the i n f l a t i o n a d j u s t e d o p e r a t i n g and c a p i t a l c o s t s of the f e r r y s y s t e m t h a t t h e government i s co m m i t t e d t o r u n . F i r s t o p e r a t i n g y e a r p a s s e n g e r and c o m m e r c i a l v e h i c l e t r i p s a r e f o r e c a s t t o be 6000000 and 3000000 r e s p e c t i v e l y . They a r e f o r e c a s t t o grow a t 1.5% and 1.8% r e s p e c t i v e l y . T o l l r a t e s a r e f o r e c a s t t o s t a r t a t $3 and $6 r e s p e c t i v e l y and b o t h i n c r e a s e a t 5.5% p e r y e a r . The f i r s t y e a r o p e r a t i n g s u b s i d y , as of t h e time when o p e r a t i o n b e g i n s , i s f o r e c a s t t o be $25 m i l l i o n and i t i s p r o j e c t e d t o i n c r e a s e a t 5% p e r y e a r . In f i g u r e 36, the g e n e r a l s c h e d u l e of t h e p r o j e c t i s summarized. At t h e end of t h e y e a r 35 o f t h e o p e r a t i n g p e r i o d , t h e c o n s o r t i u m w i l l s e l l the p r o j e c t t o t h e government f o r $1. 6.4.2 PREPARATION OF DATA INPUT P r i o r t o t h e use of t h e program, t h e s u b r o u t i n e t h a t s e t s t h e f u n c t i o n a l r e l a t i o n s h i p s between the v a r i a b l e s ( s u b r o u t i n e VARIA) as w e l l as the s t r u c t u r e of t h e v e c t o r c o n t a i n i n g p r i m a r y v a r i a b l e s s p e c i f i c t o the p r o b l e m s h o u l d be d e f i n e d . A l s o , t h e time u n i t i s d e f i n e d as one y e a r . o O P E R A T I O N T s = 4 . 7 5 T f = 3 9 . 7 5 C O N S T R U C T I O N T s = l . 5 T f = 5 . 0 D E S I G N T s = 0 2 5 T f = 2 . 5 PROPOSAL T s = 0 T f = 0 . 7 5 t i m e ( y e a r s ) FIGURE 36 General schedule of Che project; 15! M o n e t a r y q u a n t i t i e s w i l l be e x p r e s s e d i n m i l l i o n s o f d o l l a r s . S i n c e we w i s h t o c o n d u c t e x t e n s i v e s e n s i t i v i t y a n a l y s i s , we s e t t h e r e l a t i o n s h i p s between p r i m a r y v a r i a b l e s and f l o w p a r a m e t e r s by f i r s t i n c l u d i n g t h e v a r i a b l e s p a r t i c u l a r t o t h e p r o b l e m i n v e c t o r V, and t h e n w r i t i n g a s u b r o u t i n e l i n k i n g them w i t h t h e p r o b l e m . In t h a t way, when a v a r i a b l e i s changed, t h e t o t a l impact of s u c h a change i s measured by the program. The p r i m a r y v a r i a b l e s t h a t s h o u l d be i n c l u d e d i n v e c t o r V and i t s p o s i t i o n i n t h a t v e c t o r a r e a s s i g n e d s t a r t i n g i n p o s i t i o n 20 as f o l l o w s : V(20)=120 ( C o n s t a n t d o l l a r c o s t of f o o t i n g s and p i e r s , C Q F ) V(21)=200 ( C o n s t a n t d o l l a r c o s t of s u p e r s t r u c t u r e , C Q S ) V(22)=0.65 ( V a r i a b l e x as d e f i n e d i n f i g u r e 35) V(23)=2.20 ( V a r i a b l e T g as d e f i n e d i n f i g u r e 35) V(24)=70 ( C o n s t a n t d o l l a r c o s t of a p p r o a c h e s , C Q A ) V(25)=0.50 ( V a r i a b l e y as d e f i n e d i n f i g u r e 35) V(26)=1.10 ( V a r i a b l e T A as d e f i n e d i n f i g u r e 35) V(27)=2.0 ( V a r i a b l e T p as d e f i n e d i n f i g u r e 35) The p r o c e s s of w r i t i n g the s u b r o u t i n e VARIA i s as f o l l o w s . F i r s t , the c a s h f l o w s a s s o c i a t e d w i t h t h e p r o j e c t a r e numbered: 1. P r o p o s a l . 2. D e s i g n . 3. I n d i r e c t c o n s t r u c t i o n c o s t s . 4. B r i d g e f o o t i n g s and p i e r s c o n s t r u c t i o n c o s t s . 5. S u p e r s t r u c t u r e c o n s t r u c t i o n c o s t s . 152 6. A p p r o a c h e s c o n s t r u c t i o n c o s t s . 7. Revenue from t o l l s p a i d by p a s s e n g e r v e h i c l e s . 8. Revenue from t o l l s p a i d by c o m m e r c i a l v e h i c l e s . 9. Revenue from government s u b s i d y . The s a l v a g e v a l u e of t h e p r o j e c t i s n e g l e c t e d . Then, t h e p a r a m e t e r s of e a c h of t h e f l o w s a r e d e f i n e d . They a r e shown i n T a b l e 6. The u n i t s a l e p r i c e s a r e numbered as f o l l o w s : 1. T o l l r a t e f o r p a s s e n g e r v e h i c l e s . 2. T o l l r a t e f o r c o m m e r c i a l v e h i c l e s . 3. Dummy p r i c e f o r government s u b s i d y ( e q u a l 1.0) The f u n c t i o n a l r e l a t i o n s h i p s between t h e v a r i a b l e s and t h e way t h e y a r e e x p r e s s e d i n t h e s u b r o u t i n e VARIA, a r e : 1. V a l u e of f o u r t h c a s h f l o w = C Q F / d u r a t i o n , i s e x p r e s s e d a s : F ( 4 , 2 ) = - V ( 2 0 ) / V ( 2 7 ) , where F ( 4 , 2 ) = v a l u e (j=2) of t h e f o u r t h c a s h f l o w (i=4) V ( 2 7 ) = T F as d e f i n e d p r e v i o u s l y . 2. F i n i s h i n g d a t e of c a s h f l o w 4=Its i n i t i a l p e r i o d + T p , i s e x p r e s s e d a s : F(4,6)=V(27)+1.5, where: F ( 4 , 6 ) = f i n a l p e r i o d (j=6) of c a s h f l o w 4 (i=4) V ( 2 7 ) = T F as d e f i n e d p r e v i o u s l y . 3. S t a r t i n g d a t e of c a s h f l o w 5=x*Tp+Toc, i s e x p r e s s e d a s : F ( 5 , 5 ) = V ( 2 2 ) * V ( 2 7 ) + F ( 3 , 5 ) , where F ( 5 , 5 ) = s t a r t i n g d a t e (j=5) of c a s h f l o w 5 ( i = 5) 1 53 TABLE 6 Cash flows description and parameters ; Name Type Value ( m i l l i o n $) Ts (Period) Tf (Period) I n f l a t (%) 1 Proposal Uniform -1.5/.75 0.0 0.75 5.0 2 Design Uniform -20.0/2.25 0.25 2.5 5.0 3 Ind. costs Uniform -50.0 Toc=1.5 Tc=5.0 5.0 4 Footings Uniform -Cof/Tf 1.5 1.5+Tf 5.0 5 Superstructure Uniform -Cos/Ts To5-Toc+xTf To5+Ts 5.0 6 Approaches Uniform -Coa/Ta To6-To5+yTs To6+Ta 5.0 7 Pass, t r i p s Uniform 6.0E06 Tc-0.25 Tc -0.25+35 .0 1.5 8 Comm. t r i p s Uniform 3.0E06 Tc-0.25 Tc -0.25+35. ,0 1.8 9 Subsidy Uniform 25.0 Tc-0.25 Tc -0.25+35. ,0 5.0 V ( 2 2 ) = v a r i a b l e x as d e f i n e d p r e v i o u s l y . V(27)=T_ as d e f i n e d p r e v i o u s l y . r F(3,5)=Toc: S t a r t i n g d a t e (j=5) of c a s h f l o w 3 (i=3) 4. F i n i s h i n g d a t e of c a s h flow 5 = i t s s t a r t i n g d a t e + T g : F ( 5 , 6 ) = V ( 2 3 ) * F ( 5 , 5 ) , where F ( 5 , 6 ) = f i n i s h i n g d a t e (j=6) o f c a s h f l o w 5 (i=5) F(5,5)= same as above V ( 2 3 ) = v a r i a b l e T c as d e f i n e d p r e v i o u s l y . 154 V a l u e of c a s h f l o w 5 = C 0 S / T g : F ( 5 , 2 ) = - V ( 2 1 ) / V ( 2 3 ) , where F ( 5 , 2 ) = v a l u e (j=2) of t h e c a s h f l o w 5 ( i = 5 ) V ( 2 1 ) = C Q S as d e f i n e d p r e v i o u s l y . V ( 2 3 ) = v a r i a b l e T g as d e f i n e d p r e v i o u s l y . S i m i l a r l y , the r e l a t i o n s h i p s f o r v c a s h f l o w 6 can be w r i t t e n a s : F ( 6 , 2 ) = - V ( 2 4 ) / V ( 2 6 ) F ( 6 , 5 ) = F ( 5 , 5 ) + V ( 2 5 ) * V ( 2 3 ) F ( 6 , 6 ) = F ( 6 , 5 ) + V ( 2 6 ) The i n f l a t i o n r a t e s o f c a s h f l o w s 3 t o 6 a r e e q u a l . T h a t i s e x p r e s s e d a s : F ( 4 , 7 ) = F ( 3 , 7 ) , where F(4 , 7) = i n f l a t i o n r a t e ( j = 7) of c a s h f l o w 4 ( i = 4) F ( 3 , 7 ) = i n f l a t i o n r a t e (j=7) of c a s h f l o w 3 (i=3) and s i m i l a r l y f o r c a s h f l o w s 5 and 6: F( 5 , 7 ) = F ( 3 , 7 ) F ( 6 , 7 ) = F ( 3 , 7 ) The i n t e r e s t of t h e c o n s t r u c t i o n l o a n i s e q u a l t o t h e i n f l a t i o n r a t e p l u s 6%. That i s e x p r e s s e d a s : V(4)=F(3,7)+0.06, where V( 4) = I n t e r e s t on c o n s t r u c t i o n l o a n ( s e e s t r u c t u r e o f V e c t o r V) F ( 3 , 7 ) = i n f l a t i o n r a t e (j=7) of c a s h f l o w 3 (i=3) 1 55 The r e v e n u e s s t a r t b e i n g c o l l e c t e d 0.25 p e r i o d s b e f o r e t h e end of c o n s t r u c t i o n . T h a t means t h a t t h e s t a r t i n g p e r i o d of c a s h f l o w s 7, 8 and 9 i s e q u a l t o t h e f i n a l p e r i o d of c a s h f l o w 3 minus 0.25. Then: F ( 7 , 5 ) = F ( 3 , 6 ) - 0 . 2 5 , where F ( 7 , 5 ) = s t a r t i n g p e r i o d (j=5) of c a s h f l o w 7 (i=7) and s i m i l a r l y : F ( 8 , 5 ) = F ( 3 , 6 ) - 0 . 2 5 F ( 9 , 5 ) = F ( 3 , 6 ) - 0 . 2 5 The o p e r a t i o n a l phase of t h e p r o j e c t has a d u r a t i o n of 35 y e a r s : F ( 7 ,6)=F(7,5)+35 where: F ( 7 , 6 ) = F i n i s h i n g d a t e (j=6) of c a s h f l o w 7 (i=7) F ( 7 , 5 ) = a s d e f i n e d a b o v e . and s i m i l a r l y : F(8,6).=F(8,5)+35 F(9,6)=F(9,5)+35 . F i n a l l y , the s t a t e m e n t of t h e p r o b l e m s a y s t h a t t h e i n f l a t i o n r a t e f o r b o t h t y p e s of t o l l r a t e s i s e q u a l . T h i s i s e x p r e s s e d a s : P(2,2)=P(1,2) where P(2,2) = i n , f l a t i o n r a t e ( j = 2) of u n i t p r i c e 2 ( i = 2) P(1 ,2) = i n f l a t i o n r a t e ( j = 2) of u n i t p r i c e 1 ( i = l ) i s r e s t a t e d a t t h i s p o i n t , t h a t i n the s u b r o u t i n e VARIA, 1 56 the m a t r i x F r e f e r s t o c a s h f l o w s p a r a m e t e r s , t h e v e c t o r V c o n t a i n p r i m a r y v a r i a b l e s b o t h c o n s i d e r e d by the program and a s s i g n e d by t h e u s e r (see s t r u c t u r e of v e c t o r V i n c h a p t e r 5) and t h e m a t r i x P c o n t a i n s the i n f o r m a t i o n about t h e u n i t a r y s a l e p r i c e s . Summarizing, t h e s u b r o u t i n e VARIA f o r t h i s example i s the one shown i n f i g u r e 37. A f t e r r u n n i n g t h e program i n t h e computer, t h e c o m p l e t e r e s u l t s and o u t p u t o b t a i n e d a r e p r e s e n t e d i n Appendix B. SUBROUTINE VARIA(F,V,P,NC) DIMENSION F(50,9),V(40),P(10,2) F(4,2)--V(20)/V(27) F(4,6)=1.5+V(27) F(5,2)=-V(21)/V(23) F(5,5)-F(3,5)+V(22)*V(27) F(5,6)=F(5,5)+V(23) F(6,2)=-V(24)/V(26) F(6,5)-F(5,5)+V(25)*V(23) F(6,6)=F(6,5)+V(26) F(7,5)-F(3,6)-0.25 F(7,6)-F(7,5)+35 F(8,5)-F(3,6)-0.25 F(8,6)-F(8,5)+35 F(9,5)=F(3,6)-0.25 F(9,6)=F(9,5)+35 P ( 2 , 2)-P(l , 2 ) F(4 ,7)-F(3 ,7 ) F(5 ,7)-F(3 ,7 ) F(6 ,7)-F(3 ,7 ) V(4)=F(3,7)+0.06 RETURN END FIGURE 37. Subroutine VARIA CHAPTER 7. CONCLUSIONS AND FUTURE WORK The t h e o r y and t h e computer model d e v e l o p e d i n t h i s work c o v e r a wide range of a s p e c t s d e a l i n g w i t h t h e economic e v a l u a t i o n and s e n s i t i v i t y a n a l y s i s o f l a r g e c a p i t a l p r o j e c t s . However, t h e r e s t i l l i s room f o r improvement, e s p e c i a l l y i n t h e computer m o d e l . Some recommendations a b o u t a d d i t i o n s t h a t c o u l d be made a r e as f o l l o w s : 7.1 THEORETICAL FRAMEWORK 1 . The development of a more d e t a i l e d d e s c r i p t i o n of t h e c a s h f l o w s g e n e r a t e d by t h e f i n a n c i a l s t r u c t u r e , i e . l o n g term d e b t repayment s c h e d u l e s and i n p u t f r o m borrowed f u n d s . 2. Development of a s y s t e m a t i c t h e o r y t o p e r f o r m s e n s i t i v i t y a n a l y s i s t o f u n c t i o n a l f o r m s . 3. Development of a model t h a t can be used t o q u a n t i f y d i f f e r e n c e s between t h e l i n e a r and e x a c t s e n s i t i v i t y c o e f f i c i e n t s f o r l a r g e c h a n g es i n t h e p r i m a r y v a r i a b l e s . 7.2 THE COMPUTER MODEL 1. I n c l u s i o n of more b u i l t - i n f u n c t i o n s t o r e p r e s e n t c a s h f l o w p r o f i l e s . 2. C o n s i d e r a t i o n of s e v e r a l f o r e i g n exchange r a t e s . 3. I n c l u s i o n of more e r r o r c h e c k i n g c o n d i t i o n s . 4. A l l o w c o n s t a n t assumed q u a n t i t i e s ( i n f l a t i o n , i n t e r e s t , 158 1 59 t a x and f o r e i g n exchange r a t e s , s a l e s p r i c e s and o p e r a t i n g c o s t s ) t o t a k e f u n c t i o n a l forms w i t h r e s p e c t t o t i m e . I n c l u d e a b u i l t - i n s e l e c t i o n f o r s y s t e m of u n i t s p l u s a c a l e n d a r . Improve t h e q u a l i t y of t h e g r a p h i c o u t p u t i n c l u d i n g a bar c h a r t s c h e d u l e and a g e n e r a l c a s h f l o w d i a g r a m . I n c l u d e t h e o p t i o n of h a v i n g more t h a n one l o n g t e r m l o a n and d e p r e c i a t i o n scheme, and add more b u i l t - i n repayment f u n c t i o n s and d e p r e c i a t i o n methods. 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APPENDIX A PROGRAM LISTING 1 70 1 71 c _ C C ECONOMIC EVALUATION AND SENSITIVITY" ANALYSIS C OF CAPITAL PROJECTS C C DAVID POVEDA - NOVEMBER 1988 C c  C VARIABLE DEFINITION C " CN: VECTOR OF THE CASH FLOWS NAMES C NA: NAME OF A VARIABLE C PRONA: PROJECT IDENTIFICATION C F: MATRIX CONTAINING THE INFORMATION ABOUT CASH FLOWS C IT: VECTOR CONTAINING THE PHASE TO WHICH EACH CASH FLOW BELONGS C C: MATRIX CONTAINING THE EQUIVALENT DISCRETE CASH FLOWS C CF: VECTOR WITH THE NET CASH FLOW AT THE END OF EACH PERIOD C V: VECTOR OF PRIMARY VARIABLES C P: MATRIX OF UNIT SALE PRICES AND THEIR INFLATION RATES C B: MATRIX CONTAINING THE LONG TERM DEBT REPAYMENT SCHEDULE c  CHARACTER*25 CN CHARACTER*10 UNIT CHARACTER*6 NA CHARACTER*40 PRONA EXTERNAL CF3,CF4,CF5,CF6,CF7,CO,RE,FINT,FESC,FINT1 DIMENSION F ( 2 0 , 9 ) , I T ( 2 0 ) , C ( 3 5 , 5 0 ) , C F ( 5 0 ) , V ( 4 0 ) DIMENSION P ( 1 0 , 2 ) , C N ( 2 0 ) , B ( 5 0 , 7 ) , A ( 5 0 ) C C I N I T I A L I Z E VARIABLES C DO 300 1=1,20 I T ( I ) = 0 . DO 301 J=1,9 F ( I , J ) = 0 . 301 CONTINUE 300 CONTINUE DO 3 0 2 I = 1 , 1 3 DO 303 J=1,50 C ( I , J ) = 0 . 303 CONTINUE 302 CONTINUE A0 = 0. DO 304 1=1,30 V ( I ) = 0 . 304 CONTINUE C C READ PROJECT IDENTIFICATION C 1 72 WRITE(6,1) 1 FORMAT(///,'PROJECT IDENTIFICATION') READ(5,2)PRONA 2 FORMAT(A40) WRITE(8,3)PRONA 3 FORMAT(1H1,'SENSITIVITY AND ECONOMIC ANALYSIS OF PROJECT: 1 //,A40,//) C C CALL SUBROUTINE OF DATA INPUT C CALL INPUT(F,V,B,P,CN,IT,NC,IZ,UNIT) CALL VARIA(F,V,P,NC) C C WRITE THE FOREIGN EXCHANGE RATE IN COLUMN 8 C DO 108 I=1,NC I F ( F ( I , 8 ) . E Q . O ) THEN F(I,8)=1 ELSE F ( I , 8 ) = V ( 2 ) END I F 108 CONTINUE C C CALL SUBROUTINE TO PRINT THE INFORMATION ABOUT THE PROJECT C 901 CALL OUTPUT(F,V,P,IT,NC,CN,UNIT) C C COMPUTE THE PERFORMANCE MEASURES AND PRINT THEM C 10 CALL NPV(A,F,C,P,CF,V,B,IT,NC,A0,IZ,V(1),VPVO,TCCO,EDCO,XDCO) VPV=VPV0 TEI0=TCC0+EDC0+XDC0 WRITE(8, 1"38)UNIT,VPV0 WRITE(6,138)UNIT,VPVO 138 FORMAT(1H1,'ECONOMIC PERFORMANCE MEASURES' ,1 OX,' (' ,A 10,' )' ,//, 1 'NET PRESENT VALUE',T50,F12.3,/) WRITE(8,100)TCC0 WRITE(6,100)TCCO 100 FORMAT('CONSTANT DOLLAR CONSTRUCTION COSTS=',T50,F12.3,/) WRITE(8,102)EDCO WRITE(6,102)EDCO 102 FORMAT('ESCALATION DURING CONSTRUCTION*T50,F12.3,/) WRITE(8,104)XDCO WRITE(6,104)XDC0 104 FORMAT('INTERESTS DURING CONSTRUCTION=',T50,F12.3,/) WRITE(8,106)TEI0 WRITE(6,106)TEI0 106 FORMAT('TOTAL CONSTRUCTION COSTS=',T50,F12.3,/) C 173 C COMPUTE THE IRR. CHECK NUMBER OF SIGN CHANGES IN SUBROUTINE C SNSC AND REQUEST THE EXTERNAL RATE IF THERE IS MORE THAN ONE C SIGN CHANGE C 136 Y0=V(1) CALL SNSC(CF,AO,IZ,NSC) IF(NSC.EQ.I) THEN CALL SIRR1(A,F,C,P,CF,V,B,IT,NC,AO,IZ,V(1),VPV,YR) ELSE IF(NSC.EQ.O) THEN WRITE(6,140) 140 FORMAT(//,'THE INTERNAL RATE OF RETURN DOES NOT EXIST',/, 1 'NO FURTHER CALCULATIONS CAN BE PERFORMED.') GOTO 147 ENDIF WRITE(6,141) 141 FORMAT('THE PROJECT IS A MIXED INVESTMENT',/, 1 'ENTER REINVESTMENT RATE',/) READ(5,4)EXT 4 FORMAT(F4.2) CALL SIRR2(A,F,C,P,CF,V,B,IT,NC,A0,IZ,V(1),VPV,EXT,YR) ENDIF YR1=YR*100 WRITE(8,143)YR1 WRITE(6,143)YR1 143 FORMAT(//,'INTERNAL RATE OF RETURN=',3OX,F7.3,' %',//) V(1)=Y0 C C CALCULATE THE CURRENT DOLLAR CASH FLOW USING ZERO DISCOUNT RATE C 1319 WRITE(6,132) 132 FORMAT('PRINT THE PERIOD-BY-PERIOD CASH FLOW ', 1 '(YES=1, NO=0)') READ(5,133)11 13 3 FORMAT(I 1) IF(I 1.EQ.O) GOTO 137 CALL NPV(A,F,C,P,CF,V,B,IT,NC,AO,IZ,0.0,VPVO,TCC 0,EDCO,XDC 0) CALL PRCAS(C,IZ,A,AO,CN,NC,UNIT) C C PRINT THE LONG TERM REPAYMENT SCHEDULE C 137 IF(V(13).EQ.0.AND.V(15).EQ.O) GOTO 144 WRITE(6,134) 134 FORMAT('PRINT LONG TERM DEBT REPAYMENT SCHEDULE (YES=1, NO=0)', 1 /) READ(5,133)11 174 I F ( I 1.EQ.O) GOTO 144 CALL PRREP(B,V,UNIT) C C SELECTION OF TYPE OF SENSITIVITY ANALYSIS C 144 WRI.TE(6, 145) 145 FORMAT(/,'DO SENSITIVITY ANALYSIS? (YES=1, NO=0)',/) READ(5,146)1 1 146 FORMAT(I 1) I F ( I 1.EQ.O) GOTO 147 151 WRITE(6,152) 152 FORMAT(//,'SELECT TYPE OF ANALYSIS',//, 1 T2,'1. LINEAR UNIVARIATE',/,T2, 2 '2. EXACT UNIVARIATE AND BREAK-EVEN POINTS',/,T2, 3 '3. BIVARIATE' ,/,'4. RESET A VARIABLE' ,/,T2, 4 '5. CHANGE A CASH FLOW',/,T2,'6. ADD A CASH FLOW', 5 /,T2,'7. STOP',/) READ(5,146)11 C C TRANSFER CONTROL ACCORDING TO SELECTION C GOTO(154 ,155,156,157,180,200,147),11 C C LINEAR UNIVARIATE ANALYSIS C 1 54 CALL US(A,F,C,P,CF,V,B,IT,NC,AO,IZ,V(1),VPV,YR,EXT,CN,TEI0) GOTO 151 C C EXACT ANALYSIS C 1 55 CALL UEX(A,F,C,P,CF,V,B,IT,NC,A0,IZ,V(1),VPVO,YR,EXT,CN) GOTO 151 C C BIVARIATE ANALYSIS C 156 CALL BIVAR(A,F,C,P,CF,V,B,IT,NC,AO,IZ,V(1),VPVO,YR,EXT,CN) GOTO 151 C C RESET A VARIABLE C 157 CALL MENU5(F,P,B,V,IT,IL,K,IC,NA,CN) WRITE(6,160) 160 FORMAT('ENTER NEW VALUE',/) READ(5,162)VAR 162 FORMAT(F15.5) CALL .ASSVAR(F,V,P,IC,IL,K,VAR) WRITE(6,170)NA,VAR 170 FORMAT(///,'VARIABLE ',A6,* HAS BEEN RESET TO:',F15.5,/, 1 'PRINT THE NEW PERFORMANCE MEASURES? (YES=1,NO=0)',/) 175 READ(5,5)11 5 FORMAT(11) I F ( I 1.EQ.O) GOTO 151 WRITE(8,17 01)NA,VAR WRITE(6,1701)NA,VAR 1701 FORMAT(///,'VARIABLE ',A6,' HAS BEEN RESET TO:',F15.5,/, 1 'THE NEW PERFORMANCE MEASURES ARE:') GOTO 10 C C CHANGE A CASH FLOW C 180 WRITE(6,182)(J,CN(J),J=1,NC) 182 FORMAT(/,'SELECT' THE CASH FLOW' ,//,20(T2,1 2,' . \ A 2 5 , / ) , / ) READ(5,*)ICASH CALL ADDCAS(F,P,IT,CN,ICASH) WRITE(6,198)CN(ICASH) 198 FORMAT(///,'CASH FLOW ',A25,' HAS BEEN CHANGED.',/, 1 'PRINT THE NEW PERFORMANCE MEASURES? (YES=1,NO=0)',/) READ(5,5)I 1 I F ( I 1.EQ.O) GOTO 151 WRITE(8,1981)CN(ICASH) WRITE(6,1981)CN(I CASH) 1981 FORMAT(///,'CASH FLOW ',A2 5,' HAS BEEN CHANGED.',/, 1 'THE NEW PERFORMANCE ARE:') GOTO 10 C C ADD A CASH FLOW C 200 NC=NC+1 ICASH=NC CALL ADDCAS(F.,P,IT,CN,ICASH) WRITE(6,202)CN(ICASH) 202 FORMAT(///,'CASH FLOW ',A25,' HAS BEEN ADDED.',/, 1 'PRINT THE NEW PERFORMANCE MEASURES? (YES=1, NO=0)',/) READ(5,5)11 I F ( I 1.EQ.O) GOTO 151 WRITE(8,2021)CN(ICASH) WRITE(6,2021)CN(ICASH) 2021 FORMAT(///,'CASH FLOW ',A25,' HAS BEEN ADDED.',/, 1 'THE NEW PERFORMANCE ARE:') GOTO 10 C C STOP THE EXECUTION OF THE PROGRAM C 147 STOP END C C SUBROUTINE OF DATA INPUT C SUBROUTINE INPUT(F,V,B,P,CN,IT,NC,IZ,UNIT) 176 CHARACTER*25 CN,NA CHARACTER*10 UNIT DIMENSION F ( 2 0 , 9 ) , V ( 4 0 ) , I T ( 2 0 ) , P ( 1 0 , 2 ) , C N ( 2 0 ) , B ( 5 0 , 7 ) C C INPUT BASIC INFORMATION ABOUT THE PROJECT C WRITE(6,1) 1 FORMAT(////,'NUMBER OF CASH FLOWS ( 1 - 5 0 ) ' , / ) READ(6,*)NC 2 FORMAT(12) P(10,2)=NC WRITE(6,3) 3 FORMAT(/,'DISCOUNT RATE (0.##)',/) READ(5,4)V(1) 4 FORMAT(F4.2) WRITE(6,15) 15 FORMAT(/,'ARE THERE FLOWS EXPRESSED IN FOREIGN CURRENCY ', 1 '(YES=1, NO=0)',/) READ(5,2)IDE IF (IDE.. EQ.O) GOTO 19-WRITE(5,16) 16 FORMAT(/,'FOREIGN EXCHANGE RATE',/) READ ( 5 , * ) V ( 2 ) 17 FORMAT(F10.3) 19 WRITE(6,18) 18 FORMAT(/,'ENTER $ UNITS (MAX. 10 CHARACTERS)',/) READ(5,189)UNIT 189 FORMAT(A 10) WRITE(6,8) 8 FORMAT(/,'PROJECT L I F E ' , / ) READ(5,*)PFIN IZ=INT(PFIN+.99) C C INPUT INFORMATION ABOUT THE CONSTRUCTION PHASE C WRITE(6,44) 44 FORMAT(//,'GENERAL INFORMATION ABOUT CONSTRUCTION PHASE',/, 1 'FRACTION FINANCED WITH BORROWED FUNDS (0.##)',/) READ(5,4)V(3) IF(V(3).EQ.0)GOTO 220 WRITE(6,46) 46 FORMAT(/,'INTEREST RATE ON CONSTRUCTION LOAN (0.##)',/) READ(5,4)V(4) WRITE(6,47) 4 7 FORMAT(/,'PERIOD WHEN THE LOAN IS DUE*,/) READ(5,*)V(5) 48 FORMAT(F6.3) C C INPUT INFORMATION ABOUT THE OPERATIONAL PHASE C 220 WRITE(6,215) 177 215 FORMAT(//,'GENERAL INFORMATION ABOUT OPERATIONAL PHASE',/) WRITE(6,79) 7 9 FORMAT(/,'PERIOD WHEN OPERATIONS COMMENCE',/) READ(5,*)V(17) c U N I T SALE PRICES WRITE(6,201) 201 FORMAT(/,'NUMBER OF DIFFERENT UNIT SALE PRICES ( 1 - 9 ) ' , / ) READ(5,7)NP 7 FORMAT(11) P(10,1)=NP DO 210 1=1,NP WRITE(6,202)I 202 FORMAT(/,'INPUT SALE PRICE ',11,/) READ(5,*)P(I,1) 204 FORMAT(F10.3) WRITE(6,65) 65 FORMAT(/,'INFLATION RATE (0.##)',/) READ(5,4)P(I,2) 210 CONTINUE c U N I T PRODUCTION COSTS WRITE(6,74) 74 FORMAT(/,'FIXED COSTS',/) READ(5,*)V(7) 64 FORMAT(F10.3) IF(V(7).EQ.O) GOTO 779 WRITE(6,65) READ(5,4)V(18 ) 779 WRITE(6,78) 78 FORMAT(/,'UNIT VARIABLE COSTS',/) READ(5,*)V(8) IF(V(8).EQ.O) GOTO 7 99 WRITE(5,65) READ(5,4)V(19) c DEPRECIATION 799 WRITE(6,80) 80 FORMAT(//,'IS DEPRECIATION CONSIDERED (YES=1, NO=0)',/) READ(5,7)IDE IF(lDE.EQ.0)GOTO 90 WRITE(6,81) 81 FORMAT(/,'SELECT DEPRECIATION METHOD',/,T2, 1 '1. STRAIGTH LINE',/,T2,'2. DECLINING BALANCE',/) READ(5,*)ID WRITE(6,82) 82 FORMAT('VALUE OF THE DEPRECIABLE ASSETS',/) READ(5,*)V(9) WRITE(6,83) 8 3 FORMAT('PERIOD WHEN THE ASSETS ARE AQUIRED',/) READ(5,*)V(10) WRITE(6,84) 84 FORMATCLIFE OF THE ASSETS',/) READ(5,*)V(11) 1 78 IF(ID.EQ.2) THEN V(9)=-V(9) END IF c TAX RATE 90 WRITE(6,92) 92 FORMAT(//,'TAX RATE (0.##)',/) READ(5,4)V(12) c LONG TERM FINANCING 95 WRITE(6,96) 96 FORMAT(//,'LONG TERM FINANCING',//,'SELECT ONE OF THE FOLLOWING' 1 ,/,T2,'1. NO LONG TERM LOAN IS TAKEN',/,T2,'2. LOAN TAKEN ' , 2 'TO REPAY CONSTRUCTION LOAN' ,/,T2, '3 . INPUT AMOUNT BORROWED',/) READ(5 , 7 ) IB GOTO(5,101,102) , IB GOTO 95 101 V(15)=1 GOTO 103 102 READ(5,*)V(13) 98 FORMAT(F13.3) IF(V(13).EQ.O) GOTO 5 103 WRITE(6,100) 100 FORMAT(/,'NOMINAL INTEREST RATE BETWEEN PAYMENTS (0.##)',/) READ(5,4)V(14) WRITE(6,106) 106 FORMAT(/,'PERIOD WHEN THE LOAN IS TAKEN',/) READ(5,*)V(16) CALL INFIN(B) C C INFORMATION ABOUT CASH FLOWS C 5 ICASH=0 WRITE(6,6) 6 FORMAT(///,T10,'INFORMATION ABOUT CASH FLOWS',//) C 35 ICASH=ICASH+1 12 WRITE(6,10)ICASH 10 FORMAT(//,T25,'CASH FLOW NUMBER ',12,//) c SELECTION OF PHASE CALL MENU4(K) IT(ICASH)=K C C TRANFER CONTROL ACCORDING TO PHASE SELECTED •C GO TO(20,20,24 , 26,28,24) ,K GOTO 12 c F E A S I B I L I T Y AND DESIGN --. 2.0 CALL MENU 1 ( F , CN , I CASH ) GOTO 200 C INITIAL INVESTMENT AND DISPOSAL 24 IC=3 CALL FSING(F,CN,ICASH,IC) IF(IC.EQ.2) GOTO 24 GOTO 200 C CONSTRUCTION 26 CALL MENU2(F,CN,ICASH) GOTO 200 C OPERATION 28 CALL MENU3(F,CN,ICASH) IF(NP.EQ.1) THEN F(ICASH,9)=1 GOTO 200 ENDIF WRITE(6,68) 68 FORMAT(/,'SELECT UNIT SALE PRICE',/) W R I T E ( 6 , 6 9 ) ( J , P ( J , 1 ) , J = 1 , N P ) 69 FORMAT(T2,1 1 , ' . ',F15.7) WRITE(6,691) 691 FORMAT(/) READ(5,7)IU F(ICASH,9)=IU C NEXT CASH FLOW 200 IF(ICASH.NE.NC) GOTO 35 C c C INPUT OF OTHER PRIMARY VARIABLES C 110 WRITE(6,112) 112 FORMAT(//,'INPUT OTHER PRIMARY VARIABLES (YES NO=0)',/) READ(5,7)IN IF(IN.EQ.O) GOTO 140 WRITE(6,114) 114 FORMAT(/,'NUMBER OF VARIABLES ( 1 - 2 0 ) ' , / ) READ(5,*)NV DO 120 I=20,20+NV-1 WRITE(6,116)1 116 FORMAT(/,'INPUT VARIABLE ',12,' OF VECTOR V',/) READ(5,*)V(I) 118 FORMAT(F20.5) 120 CONTINUE 140 RETURN END C C SUBROUTINE TO ADD A CASH FLOW C SUBROUTINE ADDCAS(F,P,IT,CN,I CASH) CHARACTER*25 CN DIMENSION F ( 2 0 , 9 ) , I T ( 2 0 ) , C N ( 2 0 ) , P ( 1 0 , 2 ) . CALL MENU4(K) IT(ICASH)=K GOTO(10,1 0,20,30,40,20) ,K 10 CALL MENU 1 (F,CN,I CASH) GOTO 50 C 180 20 IC=3 CALL FSING(F,CN,ICASH,IC) IF(IC.EQ.2) GOTO 20 GOTO 50 C 30 CALL MENU2(F,CN,I CASH) GOTO 50 C 40 CALL MENU3(F,CN,ICASH) WRITE(6,45) 45 FORMAT('SELECT UNIT SALE . P R I C E / ) W R I T E ( 6 , 4 8 ) ( J , P ( J , 1 ) , J = 1 , 1 0 ) 48 FORMAT(T2,1 1,' . ' f F10.3) READ(5,*)IU F ( I CASH,9)=IU C 50 RETURN END C C SUBROUTINE FOR THE INPUT OF THE LONG TERM DEBT CONDITIONS C SUBROUTINE INFIN(B) DIMENSION B(50,7) 1 WRITE(6,10) 10 FORMAT(/,'SELECT TYPE OF REPAYMENT FUNCTION',/,T2, 1 '1. UNIFORM PAYMENTS',/,T2,'2. STEP FUNCTION',/,T2, 2 '3. GRADIENT FUNCTION',/) READ(5,*)IT1 I F ( I T 1 . G T . 3 ) GOTO 1 B(1,1)=IT1 50 WRITE(6,55) 55 FORMAT(/,'NUMBER OF PAYMENTS',/) READ(5,*)B(1,2) WRITE(6,60) 60 FORMAT(/,'REPAYMENT STARTING ON PERIOD',/) READ(5,*)B(1,3) WRITE(6,65) 65 FORMAT (/,' NUMBER OF PERIODS BETWEEN PAYMENTS'-,/) READ(5,*)B(1,4) I F ( I T 1 . E Q . 1 ) GOTO 200 WRITE(6,105) 105 FORMAT(/,'VALUE OF I N I T I A L PAYMENT',/) READ(5,*)B(1,5) I F ( I T 1 . E Q . 3 ) GOTO 200 WRITE(6,110) 110 FORMAT(/,'INCREMENT IN PAYMENT',/) READ(5,*)B(1,6) WRITE(6,115) 115 FORMAT(/,'NUMBER OF PAYMENTS BETWEEN INCREMENTS',/) READ(5,*)B(1,7) 200 RETURN END 181 C SUBROUTINE FOR PRINTING THE REPAYMENT SCHEDULE C SUBROUTINE PRREP(B,V,UNIT) CHARACTER*10 UNIT DIMENSION B(.50,7) ,V(40) WRITE( 8,10)UNIT,V(13),V(14) 10 FORMAT('LONG TERM DEBT REPAYMENT SCHEDULE' ,1 OX,' (' ,A10,' )' ,//, 1'AMOUNT BORROWED=',F13.3,//,'INTEREST RATE=',F6.4,///,'PERIOD', 2 T10,'AMOUNT OWED',T29,'PAYMENT',T44,'INTERESTS',T55, 3 'PRINCIPAL REPAID',T75,'LOAN BALANCE',//) NP=B(1,2) DO 100 I=2,NP+1 W R I T E ( 8 , 1 5 ) ( B ( I , J ) , J = 1 , 6 ) 1 5 FORMAT(T2,F4.1,T10,F13.3,T25,F13.3,T40,F13.3,T55,F13.3, 1 T74,F13.3) 100 CONTINUE WRITE ( 8 ,20) 20 FORMAT(1H1) RETURN END C C SUBROUTINE FOR PRINTING THE GENERAL INFORMATION C ABOUT THE PROJECT C SUBROUTINE OUTPUT(F,V,P,IT,NC,CN,UNIT) CHARACTER*7 CU CHARACTER*10 UNIT CHARACTER*25 CN CHARACTER*12 TY,PH DIMENSION F(20,9) DIMENSION V ( 4 0 ) , P ( 1 0 , 2 ) , I T ( 2 0 ) , C N ( 2 0 ) C ~ - PRIMARY VARIABLES W R I T E ( 8 , 1 ) ( V ( I ) , 1 = 1 , 5 ) , ( V ( J ) , J = 7 , 1 2 ) 1 FORMAT(//,'PRIMARY VARIABLES',//, 1 'DISCOUNT RATE=',F6.4,//,'FOREIGN EXCHANGE RATE=',F15.5,//, 2 'FRACTION OF- CONSTRUCTION FINANCED WITH BORROWED FUNDS=',F6.4, 3 //,'INTEREST RATE ON CONSTRUCTION LOAN=',F6.4,//, 4 'PERIOD WHEN THE CONSTRUCTION LOAN IS DUE=',F6.2,//, 5 'FIXED OPERATING COSTS=',F15.5,//, 6 'VARIABLE COSTS=',F15.5,//,'VALUE OF DEPRECIABLE ASSETS=', 7 F15.5,//,'PERIOD WHEN ASSETS ARE ACQUIRED=*,F6.2,//, 8 'LIFE OF DEPRECIABLE ASSETS=',F6.2,//,'TAX RATE=',F6.4,/) W R I T E ( 8 , 4 ) V ( 1 8 ) , V ( 1 9 ) 4 FORMAT('INFLATION RATE FOR FIXED COSTS=',F6.4,//, 1 'INFLATION RATE FOR VARIABLE COSTS=',F6.2) c UNIT SALE PRICES NP=P(10,1) 182 WRITE(8,5)UNIT 5 FORMAT(///,'UNIT SALE PRICES',5X,'(',A10,')',//,T2,'#',T10, 1 'PRICE',T25,'INFLATION',//) DO 7 1=1,NP W R I T E ( 8 , 6 ) I , ( P ( I , J ) , J = 1 , 2 ) 6 FORMAT(T2,I1,T6,F15.7,T28,F6.4) . 7 CONTINUE c _ _ C A S H FLOWS WRITE(8, 10) 10 FORMAT(1H1,'INFORMATION ABOUT CASH FLOWS',//,T2,'#*,T8,'NAME', •1 T34,'TYPE',T47,'PHASE',T60,'INIT. PER.',T75,'FINAL PER.', 2 T90,'INF. RATE',T105,'CURRENCY',//) DO 500 1=1,NC II 1 = F ( I , 1 ) GOTO(15,16, 1 7, 1 8 ,1 9, 20 , 21 ,22) ,1 1 1 15 TY='SINGLE PAYM.' GOTO 3 0 16 TY='TWO PAYMENTS' GOTO 30 17 TY='UNIFORM' GOTO 30 18 TY='TRAPEZOIDAL' GOTO 30 19 TY='BETA FUNCT.' GOTO 30 20 TY='EXPONENTIAL' GOTO 30 21 TY='GOMPERTZ ' GOTO 30 22 I F ( I T ( I ) . E Q . 4 ) THEN TY='ARBITR.-CO' ELSE TY='ARBITR.-RE' END IF 30 GOTO(31,32,33,34,35,36),IT(I) 31 PH='FEASIBILITY' GOTO 40 32 PH='DESIGN' GOTO 40 33 PH='INITIAL I N V GOTO 40 34 PH='CONSTRUCTION' GOTO 40 35 PH='OPERATION' GOTO 4 0 36 PH='DISPOSAL' 40 I F ( F ( I , 8 ) . E Q . 1 ) THEN CU='DOLLARS' ELSE CU='FOREIGN' ENDIF 183 C W R I T E ( 8 , 5 0 ) I , C N ( I ) , T Y , P H , F ( I , 5 ) , F ( I , 6 ) , F ( I , 7 ) , C U 50 FORMAT(T2,I2,T8,A25,T34,A12,T47,A 12,T60,F6.2,T75,F6.2,T90,F6.4, 1 T105,A7) GOTO(55,60,65,70,75,80,85,90) ,11 1 55 WRITE(8,56)F(I,2),UNIT WRITE(6,56)F(I,2),UNIT 56 FORMAT('VALUE=',F13.3,'(',A10,')',/) GOTO 300 C 60 W R I T E ( 8 , 6 1 ) F ( I , 2 ) , U N I T , F ( I , 3 ) , U N I T W R I T E ( 6 , 6 1 ) F ( I , 2 ) , U N I T , F ( I , 3 ) , U N I T 61 FORMAT('FIRST PAYMENT=',F13.3,'(',A10,')',/, 1 'SECOND PAYMENT=',F13.3,'(',A10,')',/) GOTO 300 C 65 WRITE(8,66)F(I,2),UNIT WRITE(6,66)F(I,2),UNIT 66 FORMAT('VALUE=',F13.3,'(',A10,'/PERIOD)',/) GOTO 300 C 70 W R I T E ( 8 , 7 1 ) F ( I , 2 ) , F ( I ,3) W R I T E ( 6 , 7 1 ) F ( I , 2 ) , F ( I , 3 ) 71 FORMAT('INITIAL VALUE=',F13.3,/,'FINAL VALUE=',F13.3,/) GOTO 300 C 75 W R I T E ( 8 , 7 6 ) F ( I , 2 ) , F ( I , 3 ) , F ( I , 4 ) W R I T E ( 6 , 7 6 ) F ( I , 2 ) , F ( I , 3 ) , F ( I , 4 ) 76 FORMAT('AMPLIFICATION CONSTANT=',F13.3,/,'FIRST PARAMETERS ,F5.2, 1 /,'SECOND PARAMETERS,F5.2,/) GOTO 300 80 W R I T E ( 8 , 8 1 ) F ( I , 2 ) , F ( I , 3 ) W R I T E ( 6 , 8 1 ) F ( I , 2 ) , F ( I , 3 ) 81 FORMAT('BASE VALUE=',F13.3,/,'GROWTH RATE=',F5.2,/) GOTO 3 00 C 85 W R I T E ( 8 , 8 6 ) F ( I , 2 ) , F ( I , 3 ) , F ( I , 4 ) W R I T E ( 6 , 8 6 ) F ( I , 2 ) , F ( I , 3 ) , F ( I , 4 ) 86 FORMAT('ASYMPTOTIC LIMIT=',F13.3,/,'SHAPE PARAMETERS,F9.3,/, 1 'GROWTH RATE=',F5.2,/) GOTO 300 C 90 W R I T E ( 8 , 9 1 ) F ( I , 2 ) , F ( I , 3 ) , F ( I , 4 ) W R I T E ( 6 , 9 1 ) F ( I , 2 ) , F ( I , 3 ) , F ( I , 4 ) 91 FORMAT('PARAMETER 1=',F13.3,/,'PARAMETER 2 » ' , F 1 3 . 3 , / , 1 'PARAMETER 3=',F13.3,/) C 300 I F ( I T ( I ) . E Q . 5 ) THEN IN=F(I,9) WRITE(8,301)P(IN,1),UNIT 184 WRITE(6,301)P(IN,1),UNIT 301 FORMAT('UNIT SALE PRICE=' ,F15.7,' (' , A 1 0 , ' )' ,/) ENDIF WRITE(8,305) WRITE(6,305) 305 FORMAT (' ', 1 . . j ) 500 CONTINUE RETURN END C C CALCULATION OF NPV, TCC AND CURRENT DOLLAR NET CASH FLOW C SUBROUTINE NPV(A,F,C,P,CF,V,B,IT,NC,A0,IZ,Y,VPV,TCC,EDC,XDC) EXTERNAL CF3,CF4,CF5,CF6,CF7,CO,RE,FINT,FESC,FINT 1 DIMENSION F ( 2 0 , 9 ) , I T ( N C ) , C ( 3 5 , I Z ) , C F ( I Z ) , V ( 4 0 ) , P ( 1 0 , 2 ) , B ( 5 0 , 7 ) DIMENSION A(50) c RESET VARIABLES TO ZERO A0 = 0 • TCC=0 EDC=0 XDC = 0 DO 1 J=1,IZ CF(J)=0 DO 2 1=1,35 C ( I , J ) = 0 2 CONTINUE 1 CONTINUE DO 4 J=1 ,7 DO 3 1=2,50 B( I , J ) = 0 3 CONTINUE 4 CONTINUE DO 5 1=1,50 A(I)=0 5 CONTINUE FF=V(3) DUE=V(5) RIC=V(4) C C COMPUTE FOR ALL THE FLOWS (NC=NUMBER OF FLOWS) C DO 1000 1=1,NC C FIND OUT TYPE OF FLOW AND TRANFER CONTROL I I I = I N T ( F ( I , 1 ) ) GO TO(100,100,300,300,300,300,300,300),III C FLOW IS A SINGLE OR TWO DISCRETE PAYMENTS 100 IFL=1 PP=F(I,2) -PER=F(I,5) 1 85 C 102 I F ( I T ( I ) . N E . 4 ) GOTO 110 TCC=TCC+PP XDC=XDC+FF*PP*EXP(RIC*(DUE-PER)) 110 IF(PER.EQ.O) THEN A0=A0+PP A(I)=PP GOTO 15 ELSE CALL D I S C ( P P , P E R , I T ( I ) , F ( I , 8 ) , Y , E Q U I V , I X 1 , 1 X 2 ) ENDIF C MULTIPLY BY SALE PRICE IF FLOW BELONGS TO C OPERATIONAL PHASE IF(1X1.EQ.5) THEN IN=F(I,9) PRI=P(IN,1) TEP=P(IN,2) C ( 5 , I X 2 ) = C ( 5 , I X 2 ) + E Q U I V * P R I * E X P ( ( ( I X 2 ) - V ( 1 7 ) ) * T E P ) C(7,IX2)=C(7,IX2)+EQUIV ELSE C(IX1,IX2)=C(IX1,IX2)+EQUIV ENDIF. C(I+14,IX2)=EQUIV*F(I,8) C C REPEAT THE PROCESS FOR THE SECOND PAYMENT C 15 IF(111.EQ.2.AND.IFL.EQ.1 ) THEN IFL=2 PP=F(I,3) PER=F(I,6) GOTO 102 ENDIF GOTO 1000 C C UNIFORM FLOW. DEFINE THE TYPE AND COMPUTE THE C EQUIVALENT DISCRETE PAYMENTS AT THE END OF EACH C PERIOD C 300 I X L = I N T ( F ( I , 5 ) ) IXU=INT(F(I ,6)-.05) DO 900 J=IXL,IXU XL1=J XL=MAX(XL1 ,F( I ,5) ) XU1=J+1 XU=MIN(XU1 , F ( I ,6)) J 1 = F ( l , l ) - 2 GO TO(350,400,450,500,550,600),J1 c : UNIFORM FUNCTION 350 CALL SEQU(F,C,V,P,IT,Y,I,J,FF,DUE,RIC,CF3,XL,XU,TCC,EDC,XDC) GOTO 900 c . TRAPEZOIDAL FLOW 400 CALL SEQU (F,C,V,P,IT,Y,I-,J,FF, DUE , RI C , CF 4 , XL , XU , TCC , EDC , XDC ) 186 GOTO 900 c BETA FUNCTION 4 50 CALL SEQU(F,C,V,P,IT,Y,I,J,FF,DUE,RIC,CF5,XL,XU,TCC,EDC,XDC) GOTO 900 c EXPONENTIAL FLOW 500 CALL SEQU(F,C,V,P,IT,Y,I,J,FF,DUE,RIC,CF6,XL,XU,TCC,EDC,XDC) GOTO 900 c GOMPERTZ CURVE 550 CALL SEQU(F,C,V,P,IT,Y,I,J,FF,DUE,RIC,CF7,XL,XU,TCC,EDC,XDC) GOTO 900 0 ARBITRATY FUNCTION, OPERATING PHASE 600 I F ( I T ( I ) . E Q . 4 ) GOTO 620 CALL SEQU(F,C,V,P,IT,Y,I,J,FF,DUE,RIC,RE,XL,XU,TCC,EDC,XDC) GOTO 900 c ARBITRARY FUNCTION, CONSTRUCTION PHASE -620 CALL SEQU(F,C,V,P,IT,Y,I,J,FF,DUE,RIC,CO,XL,XU,TCC,EDC,XDC) C 900 CONTINUE 1000 CONTINUE C C REORGANIZE MATRIX C AND COMPUTE FIXED AND VARIABLE COSTS C DO 1100 1=1,IZ C ( 1 3 , I ) = C ( 6 , I ) C ( 7 , I ) = C ( 7 , I ) * V ( 8 ) * E X P ( V ( 1 9 ) * ( I - V ( 1 7 ) ) ) I F ( C ( 5 , I ) . E Q . 0 ) THEN C(6,I)=0 ELSE C ( 6 , I ) = V ( 7 ) * E X P ( V ( 1 8 ) * ( I - V ( 1 7 ) ) ) ENDIF 1100 CONTINUE C C COMPUTE DEPRECIATION CHARGES C I F ( V ( 9 ) . E Q . O ) GOTO 130 IDP=INT(V(10)) IDL=INT(V(11)) I F ( V ( 9 ) . G T . 0 ) THEN C STRAIGHT LINE METHOD DEP=V(9)/V(11) DO 1110 I=IDP+1,IDP+IDL C(8,I)=DEPC 114 0 CONTINUE ELSE c DECLINING BALANCE METHOD FAC=-V(9)*2/IDL F I = ( I D L - 2 ) / I D L DO 1115 1 = 1 ,IDL DI=FAC*FI**(I-1 ) 187 C(8,IDP+1)=DI 1115 CONTINUE ENDIF C C COMPUTE LONG TERM DEBT REPAYMENT SCHEDULE C 130 IF(V(13).EQ.O.AND.V(15).EQ.O) GOTO 140 PF=ABS(FF*(TCC+EDC)+XDC) CALL REPAY(B,V,PF) NP=B(1,2) DO 135 J=2,NP+1 XPE=B(J,1 ) DFF=XPE-INT(XPE) IF(DFF.EQ.O) THEN C(9,XPE)=B(J,3) ELSE DT=1-DFF C(9,XPE+1)=B(J,3)*EXP(Y*DT) ENDIF 135 CONTINUE C C COMPUTE TAXABLE INCOME AND INCOME TAX FOR EACH PEERIOD C 140 DO 1130 I = 1 ,1Z C( 1 1 ,1 ) =C ( 5,1 ) - C ( 6 , 1 ) - C ( 7 , 1 ) - C ( 9 , 1 ) I F ( C ( 1 1 , 1 ) . L T . O ) THEN C(12,I)=0 ELSE C ( 1 2 , 1 ) = ( C ( 1 1 , 1 ) - C ( 8 , I ) - C ( 9 , I ) ) * V ( 1 2 ) ENDIF C C COMPUTE NET TOTAL CASH FLOW FOR EACH PERIOD C C( 14,1 ) = C ( 1 1 , 1 ) - C ( 1 2 , 1 ) + C ( 1 , 1 ) + C ( 2 , I ) + C ( 3 , I ) + C ( 4 , I ) + C ( 1 3 , 1 ) C F ( I ) = C ( 1 4 , 1 ) 1130 CONTINUE C C COMPUTE NPV DISCOUNTING THE NET CASH FLOW C VPV=A0 DO 114 0 I = 1 , I Z VPV=VPV+C(14,1)*EXP(-Y*I ) 1140 CONTINUE RETURN END C C SUBROUTINE TO COMPUTE EQUIVALENT DISCRETE FLOW AT THE C END OF THE PERIOD.FOR DISCRET FLOWS C SUBROUTINE DlSC(P,PER,ITF,FE,Y,EQUIV,IX 1,1X2) D l F = PER-1 NT(PER) IX1=ITF IF(DIF.EQ.O) THEN 188 IX2=PER EQUIV=P*FE ELSE IX2 = INT(PER+1 ) TX=IX2-PER EQUIV=P*EXP(Y*TX)*FE ENDIF RETURN END C C NUMERICAL INTEGRATION SUBROUTINE (GAUSS QUADRATURE) C DO NOT INCLUDE ESCALATION AND INTERESTS DURING C CONSTRUCTION C SUBROUTINE INTEG(F,XL,XU,FCT,TE,DR,Z,I) DIMENSION.F(20,9) TD=TE-DR TX=TE*F(I,5) A=.5*(XU+XL) B1=XU-XL Z=.3872983*B1 Z1=FCT(A+Z,F,I)*EXP(TD*(A+Z)-TX) Z2=FCT(A-Z,F,I)*EXP(TD*(A-Z)-TX) Z=.27777778*(Z1+Z2) Z = B1*(Z+. 4444 4 4 4 * F C T ( A , F , I ) * E X P ( ( T D * A ) - T X ) ) RETURN END C C NUMERICAL INTEGRATION SUBROUTINE (GAUSS QUADRATURE) C INCLUDE ESCALATION AND INTERESTS DURING CONSTRUCTION C SUBROUTINE INTE1(DUE,F,XL,XU,FCT,TD,RIC,FUN,Z,I) DIMENSION F(20,9) TX=TD*F(I,5) , A=.5*(XU+XL) B=XU-XL Z=.3872983*B Z1=FCT(A+Z,F,I) Z2=FCT(A-Z,F,I) X1=FUN(A + Z,DUE, RI C , TD , TX) X2=FUN(A-Z,DUE,RIC,TD,TX) Z=.27777778*(Z1*X1+Z2*X2) Z=B*(Z+.44 44 4 44*FCT(A,F,I)*FUN(A,DUE,RIC,TD,TX)) RETURN END C C SUBROUTINE TO FIND OUT THE NUMBER OF SIGN CHANGHES C FOR THE CALCULATION OF THE IRR C SUBROUTINE SNSC(CF,AO,IZ,NSC) DIMENSION C F ( 5 0 ) , I S I G ( 5 0 ) NSC = 0 DO 10 I=1,IZ I F ( C F ( I ) . E Q . O ) THEN 189 I S I G ( I ) = 0 GOTO 10 ENDIF I S I G ( I ) = C F ( I ) / A B S ( C F ( l ) ) 10 CONTINUE IF(AO.EQ.O) GOTO 15 ISO=A0*ISIG(1)/ABS(A0) IF(ISO.GT.O) GOTO 15 NSC=1 15 DO 20 1=1,IZ-1 I S = I S I G ( I ) * I S I G ( I + 1 ) IF(IS.GE.O) GOTO 20 NSC=NSC+1 2 0 CONTINUE RETURN END C C COMPUTATION OF THE IRR FOR ONE SIGN CHANGE C SUBROUTINE SIRR1(A,F,C,P,CF,V,B,IT,NC,AO,IZ,Y,VPV,YR) DIMENSION F ( 2 0 , 9 ) , C ( 3 5 , I Z ) , C F ( L Z ) , I T ( N C ) , V ( 4 0 ) , P ( 1 0 , 2 ) , B ( 5 0 , 7 ) DIMENSION A(50) YR=Y VPVO=VPV IF(VPV.GT.O) THEN DEL=.05 ELSE DEL=-.05 ENDIF 10 IF(VPVO.GT.O) THEN RI =YR ELSE RS=YR ENDIF YR=YR+DEL CALL NPV(A,F,C,P,CF,V,B,IT,NC,AO,IZ,YR,VPV,TCC,EDC,XDC) CHE 1=VPV0*VPV/ABS(VPVO) IF(CHE 1 .GT.0) GOTO 10 IF(VPVO.GT.O) THEN RS = YR ELSE RI =YR ENDIF 100 CALL NPV(A,F,C,P,CF,V,B,IT,NC,AO,IZ,YR,VPV,TCC,EDC,XDC) IF(VPV.LT.O) THEN RS = YR ELSE RI = YR ENDIF DIF=RS-RI IF(DIF.LT.0.0001)GOTO 20 190 YR=(RS+RI)/2 GOTO 100 20 YR=(RS+Rl)/2 VPV=VPV0 RETURN END C C COMPUTATION OF THE IRR USING NEWNAN METHOD C SUBROUTINE SIRR2 (A , F', C , P , CF , V, B , IT , NC , A0 ,1 Z , Y , VPV, EXT , YR) DIMENSION F ( 2 0 , 9 ) , C ( 3 5 , I Z ) , C F ( I Z ) , V ( 4 0 ) , I T ( N C ) , P ( 1 0 , 2 ) , B ( 5 0 , 7 ) DIMENSION A(50) PV=VPV VPV0=VPV YR=Y IF(VPV0.GT.0) THEN DEL=.05 ELSE DEL=-.05 ENDIF 5 IF(VPVO.GT.O) THEN RI =YR ELSE RS = YR ENDIF YR=YR+DEL CALL NPV(A,F,C,P,CF,V,B,IT,NC,AO,IZ,YR,VPV,TCC,EDC,XDC) PV=A0 DO 10 1=1,IZ IF(PV.LT.O) THEN RATE=YR ELSE RATE=EXT ENDIF PV=PV*EXP(RATE)+CF(I) 10 CONTINUE CHE 1=VPV0*PV/ABS(VPV0) IF(CHE 1 .GT.0)GOTO 5 IF(VPVO.GT.O) THEN RS = YR ELSE RI =YR ENDIF 1 5 CALL NPV(A,F,C,P,CF,V,B,IT,NC,A0,IZ,YR,VPV,TCC,EDC,XDC) PV=A0 DO 20 1=1 rIZ IF(PV.LT.O) THEN RATE=YR ELSE RATE=EXT 191 ENDIF PV=PV*EXP(RATE)+CF(I) 20 CONTINUE IF(PV.LT.O) THEN RS = YR ELSE RI =YR ENDIF DIF=RS-RI IF ( D I F . L T . 0 . 0 0 0 1 ) GOTO 100 YR=(RI+RS)/2 GOTO 15 100 YR=(RI+RS)/2 VPV=VPV0 RETURN END C C SUBROUTINE FOR PRINTING THE PERIOD-BY-PERIOD CASH FLOW C SUBROUTINE PRCAS(C,IZ,A,AO,CN,NC,UNIT) CHARACTER*25 CN CHARACTER*10 UNIT DIMENSION C ( 3 5 , 5 0 ) , C N ( 2 0 ) , A ( 5 0 ) DO 5 I=1,NC C( 3 , 1 ) = C ( 3 , 1 ) + A ( I ) C( 1 4,1)=C(14,1)+A(I) C(I + 14,1 )=C(I + 14,1 )+A(I ) 5 CONTINUE WRITE ( 8,10)UNIT 10 FORMAT(1H1 CURRENT DOLLAR CASH FLOW' ,1 OX, ' (' , A l 0 , ' ) ' ) N=INT(lZ / 8+1) DO 100 1 = 1 ,N LI= 8*(I-1)+1 LU=MIN(IZ,LI+7) WRITE ( 8,25)LI,(J,J=LI+1,LU) 25 FORMAT(//,T25,12,7(10X,I2)) W R I T E ( 8 , 3 0 ) ( C ( 3 , J ) , J = L I , L U ) 30 FORMAT(//,'INITIAL INVESTMENT',T20,8(F10.3,2X)) W R I T E ( 8 , 3 5 ) ( C ( 1 , J ) , J = LI ,LU) 35 FORMAT(//,'FEASIBILITY',T20, 8(F10.3,2X)) W R I T E ( 8 , 4 0 ) ( C ( 2 , J ) , J = LI ,LU) 40 FORMAT(//,'DESIGN',T20,8(F10.3,2X)) W R I T E ( 8 , 4 5 ) ( C ( 4 , J ) , J = L I , L U ) 4 5 FORMAT(//,'CONST. (EQUITY)',T20, 8(F10.3,2X)) W R I T E ( 8 , 7 0 ) ( C ( 1 0 , J ) , J = L I , L U ) 70 FORMAT(//,'CONST. LOAN',T20,8(F10.3,2X)) W R I T E ( 8 , 5 0 ) ( C ( 5 , J ) , J = L I , L U ) 50 FORMAT(//,'REVENUES',T20,8(F10.3,2X)) WR I T E ( 8 , 5 5 ) ( C ( 6 , J ) , J = L I , L U ) 55 FORMAT(//,'FIXED COSTS',T20, 8(F10.3,2X)) W R I T E ( 8 , 6 0 ) ( C ( 7 , J ) , J = L I , L U ) 60 FORMAT(//,'VARIABLE COSTS',T20, 8(F10.3,2X)) WRITE ( 8,65)(C ( 8,J),J=LI,LU) 65 FORMAT(//,'DEPRECIATION' ,T20,8(F1 0.3,2X)) W R I T E ( 8 , 6 8 ) ( C ( 9 , J ) , J = L I , L U ) 68 FORMAT(//,'LONG TERM DEBT',T20,8(F10.3,2X)) W R I T E ( 8 , 7 5 ) ( C ( 1 3 , J ) , J = L I , L U ) 75 FORMAT(//,'SALVAGE VALUE',T20,8(F10.3,2X)) W R I T E ( 8 , 8 0 ) ( C ( 1 1 , J ) , J = L I , L U ) 80 FORMAT(//,'GROSS INCOME',T20,8(F10.3,2X)) W R I T E ( 8 , 8 5 ) ( C ( 1 2 , J ) , J = L I , L U ) 85 FORMAT{//,'!NCOME TAX' , T20,8(F10.3,2X)) W R I T E ( 8 , 9 0 ) ( C ( 1 4 , J ) , J = L I , L U ) 90 FORMAT(//,'NET CASH FLOW',T20,8(F10.3,2X)) WRITE(8,95) 95 FORMAT(1H1) 100 CONTINUE C WRITE(8,105) 105 FORMAT('CURRENT DOLLAR CASH FLOWS',//) DO 200 1 = 1 ,N LI=8*(I-1)+1 LU=MIN(IZ,LI+7) WRITE(8,110)LI,(J,J=LI+1,LU) 110 FORMAT(//, 'CASH FLOW' ,T40,12,7(1 OX,12)) DO 150 11=1,NC WRITE(8, 120)CN(I 1 ) , ( C ( I 1 + 14,J),J=LI,LU) 120 FORMAT(/,A25,T35,8(F10.3,2X)) 150 CONTINUE WRITE(8,95) 200 CONTINUE DO 500 1=1,NC C ( 3 , 1 ) = C ( 3 , 1 ) - A ( I ) C ( 1 4 , 1 ) = C ( 1 4 , 1 ) - A ( I ) C(I + 14,1 )=C(I + 1 4 , 1 ) - A ( l ) 500 CONTINUE RETURN END C C SUBROUTINE TO COMPUTE EQUIVALENT DISCRETE FLOW AT THE C END OF EACH PERIOD FOR UNIFORM FLOWS C SUBROUTINE SEQU(F,C,V,P,IT,Y,I,J,FF,DUE,RIC,FCT,XL,XU,TCC,EDC,XDC) EXTERNAL CF3,CF4,CF5,CF6,CF7,CO,RE,FINT,FESC,FINT1 EXTERNAL FCT DIMENSION F ( 2 0 , 9 ) , C ( 3 5 , 5 0 ) , I T ( 2 0 ) , P ( l 0 , 2 ) , V ( 4 0 ) CALL INTEG(F,XL,XU,FCT,F(I,7),Y,EQUIV,I) EQUIV=EQUIV*EXP(Y*(J+1)) I F ( I T ( I ) . E Q . 4 ) THEN C(10,J+1)=C(10,J+1)+EQUIV*FF*F(I,8) EQUIV=EQUIV*(1-FF) CALL INTEG(F,XL,XU,FCT,0.,0. ,RES 1,1) TCC=TCC+RES1 CALL INTE1(DUE,F,XL,XU,FCT,F(I,7),RIC,FESC,RES2,I) EDC=EDC+RES2 IF(FF.EQ.O) GOTO 100 193 CALL INTE1(DUE,F,XL,XU,FCT,F(I,7),RIC,FINT 1,RES3,I) XDC=XDC+FF*RES3 ENDIF 100 IX1=IT(I) IF(IX1.EQ.5) THEN IN=F(I,9) PRI=P(IN,1) TEP=P(IN,2) A D D = E Q U I V * F ( l , 8 ) * P R I * E X P ( ( ( J + 1 ) - V ( 1 7 ) ) * T E P ) C(5, J+1 )=C(5,J+1)+ADD C(7,J+1)=C(7,J+1)+EQUIV*F(l,8) C(1+14,J+1)=ADD ELSE C(IX1 , J+1 )=C(IX1 ,J+1')+EQUIV*F(I ,8) C(1+14,J+1)=EQUIV*F(I,8) ENDIF RETURN END C C SUBROUTINE TO COMPUTE THE REPAYMENT SCHEDULE SUBROUTINE REPAY(B,V,PF) DIMENSION B ( 5 0 , 7 ) , V ( 4 0 ) IT 1=B(1 ,1 ) NP=B(1,2) XP=B(1,3) NPB=B(1,4) B(2,1)=XP DO 10 1=1,NP-1 B(I+2,1)=B(I+1,1)+NPB 10 CONTINUE I F ( V ( 1 5 ) . E Q . 1 ) THEN V(13)=PF ENDIF PP=V(13) R=V(14) RIN=(1+R)**NP NN=(XP-V(16))/NPB-1 OW=PP*(1+R)**NN GOTOdOO, 150,200) ,IT1 100 A=OW*(R*RIN/(RIN-1)) DO 110 1=1,NP B(I+1,3)=A 110 CONTINUE GOTO 300 C 150 B(2,3)=B(1,5) IS=B(1,7) DO 180 1=1,NP-1,IS DO 170 J=1,IS-1 B(I+J+1,3)=B(I+J,3) 170 CONTINUE B(I+IS+1,3)=B(I+IS,3)+B(1,6) 194 180 CONTINUE GOTO 300 C 200 P A = B ( 1 , 5 ) * ( ( R I N - 1 ) / ( R * R I N ) ) PG=OW-PA FAC=((RIN-1)/(R*RIN)-NP/RIN)/R B(1,6)=PG/FAC B(2,3)=B(1,5) DO 210 1=1,NP-1 B (I + 2,3)=B(I + 1 ,3)+B(1 ,6) 210 CONTINUE C 300 B(2,2)=OW DC 350 I=2,NP+1 B(I ,4)=B(I,2)*R B ( I , 5 ) = B ( I , 3 ) - B ( I , 4 ) B(I ,6)=B(I , 2 ) - B ( l , 5 ) B(I+1,2)=B(I,6) 350 CONTINUE RETURN END C C INPUT CASH FLOW NAME C SUBROUTINE NAME(CN,I CASH) CHARACTER*25 CN DIMENSION CN(20) CHARACTER*25 NA WRITE(6,10)ICASH 10 FORMAT(//,T25,'CASH FLOW NUMBER 1 ,I 2,//,'INPUT NAME 1 '(MAX. 25 CHARACTERS)',/) READ(5,11)NA 11 FORMAT(A25) CN(ICASH)=NA RETURN END C C INPUT THE PARAMETERS OF A SINGLE PAYMENT C SUBROUTINE FSING(F,CN,ICASH,IC) CHARACTER*25 CN DIMENSION F ( 2 0 , 9 ) , C N ( 2 0 ) WRITE(6,1) 1 FORMAT(//,'YOU HAVE SELECTED A SINGLE PAYMENT', 1 /,'PLEASE CONFIRM: (CORRECT=1, INCORRECT=2)',/) READ(5,2)IC 2 FORMAT(11) IF( I C . E Q . 2 ) GOTO 10 CALL NAME(CN,ICASH) 7 F ( I C A S H , 1 ) = 1 WRITE(6,3) 3 FORMAT(/,'INPUT VALUE OF THE FLOW',/) READ(5,*)F(ICASH,2) 195 WRITE(6,5) 5 FORMAT(/,'PERIOD',/) READ(5,*)F(ICASH,5) 1 0 RETURN END C C INPUT THE PARAMETERS OF TWO DISCRETE PAYMENTS-C SUBROUTINE FTWO(F,I CASH,IC) DIMENSION F(20,9) WRITE(6,1) 1 FORMAT(//,'YOU HAVE SELECTED TWO PAYMENTS', 1 /,'PLEASE CONFIRM: (CORRECT=1, INCORRECT=2)',/) READ(5,2)IC 2 FORMAT(11) IF(IC.EQ.2) GOTO 10 F(ICASH,1)=2 WRITE(6,3) 3 FORMAT(//,'INPUT VALUE OF THE FIRST FLOW',/) READ(5,*)F(ICASH,2) WRITE(6,5) 5 FORMAT('PERIOD',/) READ(5,*)F(ICASH,5) WRITE ('6, 7) 7 FORMAT('INPUT VALUE OF THE SECOND FLOW',/) READ(5,*)F(ICASH,3) WRITE(6,5) READ(5,*)F(ICASH,6) 10 RETURN END C C INPUT THE PARAMETERS OF A UNIFORM FLOW C SUBROUTINE FUNIF(F,I CASH,IC) DIMENSION F(20,9) WRITE(6,1) 1 FORMAT(//,'YOU HAVE SELECTED A UNIFORM FLOW', 1 /,'PLEASE CONFIRM: (CORRECT=1, INCORRECT=2)',/) READ(5,2 ) IC 2 FORMAT(11) IF(IC. E Q . 2 ) GOTO 10 F(ICASH,1)=3 WRITE(6,3 ) 3 FORMAT(/,'INPUT VALUE OF THE FLOW',/) READ(5,*)F(ICASH,2) CALL I TIME(F,ICASH) CALL ININF(F,ICASH) 10 RETURN END C C INPUT THE PARAMETERS OF A TRAPEZOIDAL FLOW C SUBROUTINE FTRAP(F,I CASH,IC) DIMENSION F(20,9) 196 WRITE(6,1) 1 FORMAT(//,'YOU HAVE SELECTED A TRAPEZOIDAL FLOW, 1 /,'PLEASE CONFIRM: (CORRECT=1, INCORRECT=2)',/) READ(5,2)IC 2 FORMAT(I 1 ) I F(IC.EQ.2) GOTO 10 F(ICASH,1)=4 WRITE(6,3) 3 FORMAT(/,'INPUT INITIAL VALUE OF THE FLOW',/) READ(5,*)F(ICASH,2) WRITE(6,5) 5 FORMAT('FINAL VALUE',/) READ(5,*)F(ICASH,3) CALL I TIME(F,ICASH) CALL ININF(F,ICASH) 10 RETURN END C C INPUT THE PARAMETERS OF A BETA FUNCTION C SUBROUTINE FBETA(F,I CASH,IC) DIMENSION F ( 2 0 , 9 ) WRITE(6,1) 1 FORMAT(//,'YOU HAVE SELECTED A BETA DISTRIBUTION', 1 /,'PLEASE CONFIRM: (CORRECTS, INCORRECT=2)',/) READ(5,2)IC 2 FORMAT(11) I F(IC.EQ.2) GOTO 10 F(I'CASH,1)=6 WRITE(6,3) 3 FORMAT(//,'INPUT AMPLIFICATION CONSTANT',/) READ(5,*)F(ICASH,2) WRITE(6,5) 5 FORMAT('PARAMETER 1',/) READ(5,*)F(ICASH,3) WRITE(6,7) 7 FORMAT('PARAMETER 2',/) READ(5,*)F(ICASH,4) CALL ITIME(F,ICASH) CALL ININF(F,ICASH) 1 0 RETURN END C C INPUT THE PARAMETERS OF AN EXPONENTIAL FLOW C SUBROUTINE FEXPO(F,I CASH,IC) DIMENSION F ( 2 0 , 9 ) WRITE(6,1) 1 FORMAT(//,'YOU HAVE SELECTED AN EXPONENTIAL FUNCTION', 1 /,'PLEASE CONFIRM: (CORRECT=1, INCORRECT=2)',/) READ(5,2)IC 2 FORMAT(I 1 ) I F(IC.EQ.2) GOTO 10 1 97 F ( I CASH,1) = 1 1 WRITE(6,3) 3 FORMAT(//,'INPUT BASE PARAMETER',/) READ(5,*)F(ICASH,2) WRITE(6,5) 5 FORMAT('INPUT GROWTH RATE',/) READ(5,*)F(ICASH,3) CALL ITIME(F,ICASH) CALL ININF(F,ICASH) 1 0 RETURN END C C INPUT THE PARAMETERS OF A GOMPERTZ CURVE C SUBROUTINE FGOMP(F,I CASH,IC) DIMENSION F(20,9) WRITE(6,1) 1 FORMAT(//,'YOU HAVE SELECTED A GOMPERTZ CURVE', 1 /,'PLEASE CONFIRM: (CORRECTS, INCORRECT=2)',/) READ(5,2)IC 2 FORMAT(11) ' I F ( I C . E Q . 2 ) GOTO 10 F(ICASH,1)=12 WRITE(6,3) 3 FORMAT(//,'INPUT ASYMPTOTIC LIMIT',/) READ(5,*)F(ICASH,2) WRITE(6,5) 5 FORMAT('INPUT SHAPE PARAMETER 1',/) READ(5,*)F(ICASH,3) WRITE(6,7) 7 FORMAT('SHAPE PARAMETER 2',/) READ(5,*)F(ICASH,4) CALL ITIME(F,ICASH) CALL ININF(F,ICASH) 1 0 RETURN END C C INPUT INFLATION RATE AND DEFINE CURRENCY OF THE CASH FLOW C SUBROUTINE I N I N F ( F , I CASH) DIMENSION F(20,9) WRITE(6,1) 1 FORMAT(/,'INFLATION RATE',/) READ(5,*)F(ICASH,7) WRITE(6,3) 3 FORMAT(/,'IS THE FLOW EXPRESSED IN FOREIGN CURRENCY', 1'(YES=1, NO=0)',/) READ(5,*)F(ICASH,8) RETURN END C C INPUT THE INITIAL AND FINAL PERIODS OF CONTINUOUS FLOWS 198 SUBROUTINE ITIME(F,I CASH) DIMENSION F(20,9) WRITE(6,1) 1 FORMAT(/,'INITIAL PERIOD',/) READ(5,*)F(ICASH,5) WRITE(6,3) 3 FORMAT(/,'FINAL PERIOD',/) READ(5,*)F(ICASH,6) RETURN END C C MENU FOR THE SELECTION OF FLOW TYPE DURING F E A S I B I L I T Y C AND DESIGN PHASES. ACCORDING TO THE SELECTION, THE C APPROPIATE SUBROUTINE TO INPUT THE PARAMETERS OF THE C FLOW IS CALLED C SUBROUTINE MENU1(F,CN,I CASH) CHARACTER*25 CN DIMENSION F( 2 0 , 9 ) , C N ( 2 0 ) CALL NAME(CN,ICASH) 30 WRITE(6,1)ICASH 1 FORMAT(//,'CASH. FLOW NUMBER ' ,I 2,/, 'SELECT ONE OF THE FOLLOWING' 1 ,//,T5,'1. SINGLE PAYMENT',/,T5,'2. TWO DISCRETE PAYMENTS 2 /,T5,'3. UNIFORM',/) READ(5,2)1 2 FORMAT(I 1 ) GO TO(5, 10,15) , I 5 CALL FSING(F,CN,ICASH,IC) GOTO 20 1 0 CALL FTWO(F,ICASH,IC) GOTO 20 1 5 CALL FUNIF(F,I CASH,IC) 20 IF(IC. E Q . 2 ) GOTO 30 RETURN END c C MENU FOR THE SELECTION OF FLOW TYPE IN CONSTRUCTION PHASE. C SUBROUTINE MENU2(F,CN,I CASH) CHARACTER*25 CN DIMENSION F ( 2 0 , 9 ) , C N ( 2 0 ) . CALL NAME(CN,ICASH) . 5 WRITE(6,1 )I CASH 1 FORMAT(//,'CASH FLOW NUMBER ',12,/, 1 'SELECT ONE OF THE FOLLOWING:',//,T5,'1. SINGLE PAYMENT',/, 2 T5,'2. TWO DISCRETE PAYMENTS',/,T5,'3. UNIFORM FLOW',/,T5, 3 '4. TRAPEZOIDAL',/,T5,'5. BETA FUNCTION',/,T5, 4 '6. EXPONENTIAL',/,T5,'7. OTHER',/) READ(5,3)I 199 3 FORMAT(11) GO TO(10,20,30,40,50,60,70),I GOTO 5 10 CALL FSING(F,ICASH,IC) GOTO 130 20 -CALL FTWO(F,ICASH,IC) GOTO 130 30 CALL FUNIF(F,ICASH,IC) GOTO 130 4 0 CALL FTRAP(F,ICASH,IC) GOTO 130 50 CALL FBETA(F,ICASH,IC) GOTO 130 60 CALL FEXPO(F,ICASH,IC) 130 IF(I C . E Q . 2 ) GOTO 5 GOTO 140 7 0 WRITE(6,4) 4 FORMAT('THIS FUNCTION SHOULD BE SPECIFIED AS FUNCTION CO',/) F(ICASH,1)=8 DO 90 1 = 1 , 3 WRITE(6,6)I 6 FORMAT('INPUT PARAMETER ',11) READ(5,*)F(ICASH,I+1)' 7 FORMAT(F15.4) 90 CONTINUE CALL I TIME(F,ICASH) CALL ININF(F,ICASH) 140 RETURN END C C MENU FOR THE SELECTION OF FLOW TYPE DURING OPERATIONAL C PHASE C SUBROUTINE MENU3(F,CN,I CASH) CHARACTER*25 CN DIMENSION F ( 2 0 , 9 ) , C N ( 1 0 ) CALL NAME(CN,ICASH) IC = 0 5 WRITE(6,1)ICASH 1 FORMAT(///,'CASH FLOW NUMBER ',12,/, 1 'SELECT ONE OF THE FOLLOWING:',/,T5,'1. SINGLE PAYMENT',/, 2 T5,'2. TWO DISCRETE PAYMENTS',/,T5,'3. UNIFORM FLOW',/,T5, 3 '4. TRAPEZOIDAL',/,T5,'5. BETA FUNCTION',/,T5, 4 '6. EXPONENTIAL',/,T5,'7. GOMPERTZ CURVE',/,T5,'8. OTHER',/) READ(5,2)1 GO TO(10,20,30,40 , 50 ,60,70, 8 0 ) , I 2 FORMAT(11) GOTO 5 10 CALL FSING(F,CN,ICASH,IC) GOTO 110 200 20 CALL FTWO(F,ICASH,IC) GOTO 1.1 0 30 CALL FUNIF(F,ICASH,IC) GOTO 110 40 CALL FTRAP(F,ICASH,IC) GOTO 110 50 CALL FBETA(F,ICASH,IC) GOTO 110 60 CALL FEXPO(F,ICASH,IC) GOTO 110 70 CALL FGOMP(F,ICASH,IC) 110 I F ( I C . E Q . 2 ) GOTO 5 GOTO 120 80 WRITE(6,3) 3 FORMAT('THE FUNCTION SHOULD BE SPECIFIED IN FUNCTION RE',/) F(ICASH,1)=8 DO 90 1=1,3 WRITE(6,4)1 4 FORMAT(* INPUT PARAMETER ',11) READ(5,*)F(ICASH,I + 1 ) 7 FORMAT(F15.4) 90 CONTINUE CALL ITIME(F,ICASH) CALL ININF(F,ICASH) 120 RETURN END C C MENU FOR THE SELECTION OF PROJECT PHASE C SUBROUTINE MENU4(K) WRITE(6,10) 10 FORMAT(//,'PROJECT PHASE',/,T5,'1. F E A S I B I L I T Y ' , / , T 5 , 1 '2. DESIGN',/,T5,'3. I N I T I A L INVESTMENT',/,T5, 2 '4. CONSTRUCTION',/,T5,'5. O P E R A T I O N * , / , T 5 6 . DISPOSAL',/) READ(5,12 ) K 12 FORMAT(11) RETURN END c _ C C MATHEMATICAL REPRESENTATION FLOW TYPES C C c UNIFORM FLOW FUNCTION C F 3 ( X , F , I ) DIMENSION F(20,9) CF3=F(I,2) . . RETURN END c TRAPEZOIDAL FLOW (STRAIGHT LINE) FUNCTION C F 4 ( X , F , I ) DIMENSION F(20,9) 201 C F 4 = F ( I , 2 ) + ( F ( I , 3 ) - F ( l , 2 ) ) * ( X - F ( I , 5 ) ) / ( F ( I , 6 ) - F ( I , 5 ) ) RETURN END c BETA FUNCTION FUNCTION C F 5 ( X , F , I ) DIMENSION F(20,9) K1 = 1 DO 10 J = 2 , F ( l , 3 ) K1=K1*J 10 CONTINUE K2= 1 DO 20 J = 2 , F ( I , 4 ) K2=K2*J 20 CONTINUE K3=1 K4=F(I,3)+F(I,4)+1 DO 30 J=2,K4 K3=K3*J 30 CONTINUE K 5 = F ( I , 6 ) - F ( I , 5 ) K6=K3/(K5*K1*K2) C F 5 = K 6 * ( ( ( X - F ( I , 5 ) ) / K 5 ) * * F ( l , 3 ) ) * ( ( F ( I , 6 ) - X ) * * F ( l , 4 ) ) RETURN END c EXPONENTIAL FLOW ' FUNCTION C F 6 ( X , F , I ) DIMENSION F(20,9) C F 6 = F ( I , 2 ) * E X P ( F ( I , 3 ) * X ) RETURN END c . GOMPERTZ CURVE FUNCTION C F 7 ( X , F , I ) DIMENSION F(20,9) C F 7 = E X P ( L O G ( F ( I , 2 ) ) - F ( I , 3 ) * E X P ( - F ( l , 4 ) * X ) ) RETURN END C C FACTORS TO CALCULATE ESCALATION AND INTERESTS DURING C CONSTRUCTION C FUNCTION FINT(X,DUE,RIC,TD,TX) FINT=EXP((DUE-X)*RIC)*EXP(TD*X-TX) RETURN END C FUNCTION FESC(X,DUE,RIC,TD,TX) FESC = EXP(TD*X-TX)- 1 RETURN END C FUNCTION FINT 1 (X,DUE, RI C , TD , TX) FINT1=(EXP((DUE-X)*RIC)-1)*EXP(TD*X-TX) RETURN END 202 C C SUBROUTINE TO COMPUTE THE LINEAR SENSITIVITY COEFFICIENTS C SUBROUTINE US(A,F,C,P,CF,V,B,IT,NC,A0,IZ,V1,VPVO,YR,EXT,CN,TEI 0) CHARACTER*6 NAME,NA CHARACTER*25 CN DIMENSION F ( 2 0 , 9 ) , C ( 3 5 , I Z ) , C F ( I Z ) , V ( 4 0 ) , I T ( N C ) , B ( 5 0 , 7 ) DIMENSION N A M E ( 1 0 ) , S N ( 1 0 ) , S I ( 1 0 ) , P ( 1 0 , 2 ) , C N ( 2 0 ) , A ( 5 0 ) VPVO0=VPV0 IN=1 V(1)=V1 CALL DPVDY(A,F,C,P,CF,V,B,IT,NC,AO,IZ,VPVO,YR,DY) 5 CALL MENU5(F,P,B,V,IT,IL,K,IC,NA,CN) IF(K.EQ.42) GOTO 200 CALL VARASS(F,V,P,IC,IL,K,VAR) CALL DERIV(A,F,C,P,CF,V,B,IT,NC,AO,IZ,V(1),IL,K,IC,DER,DTC). S1=DER*ABS(VAR)/VPVO S2=-DER/DY S3=S2*ABS(VAR)/YR S4=DTC*ABS(VAR)/TEI0 WRITE(8,10)NA,VAR,DER,S1,S2,S3,DTC,S4 WRITE(6,10)NA,VAR,DER,S1,S2,S3,DTC,S4 10 FORMAT(///,T15,'LINEAR SENSITIVITY COEFICIENTS FOR VARIABLE ', 1 A6,'= ',F15.7,//,T20,'ABSOLUTE', 2 T50,'RELATIVE',/,'NPV,T10,F20.5,T40,F20.5,/,'IRR',T10,F20.5, 3. T40,F2 0.5,/, 'TCC ,T10,F2 0.5,T40,F20.5) WRITE(6,20) 2 0 FORMAT(/,'DO YOU WANT TO INCLUDE THIS VARIABLE IN THE STAR ', 1 'DIAGRAM? (YES=1, NO=0)',/) READ(5,30)11 30 FORMAT(11) I F ( I 1.EQ.O) GOTO 60 SN(IN)=S1 SI(IN)=S3 NAME(IN)=NA IN=IN+1 60 WRITE(6,35) 35 FORMAT(/,'ANALYZE ANOTHER VARIABLE? (YES=1, NO=0)',/) READ(5,30)11 I F ( I 1.EQ.1) GOTO 5 IN=IN-1 IF(IN.EQ.O) GOTO 200 CALL STAR(SN,SI,NAME,IN) 200 VPV0=VPVO0 RETURN END C 203 C COMPUTATION OF THE PARTIAL DERIVATIVE OF NPV WITH C RESPECT TO THE DISCOUNT RATE C SUBROUTINE DPVDY(A,F,C,P,CF,V,B,IT,NC,AO,IZ,VPVO,YR,DY) DIMENSION F ( 2 0 , 9 ) , I T ( N C ) , C ( 3 5 , I Z ) , C F ( I Z ) , V ( 4 0 ) , P ( 1 0 , 2 ) , B ( 5 0 , 7 ) DIMENSION A(50) Y1=YR*1.01 CALL NPV(A,F,C,P,CF,V,B,IT,NC,A0,IZ,Y1,VPV1,TCC,EDC,XDC) Y1=YR*0.99 CALL NPV(A,F,C,P,CF,V,B,IT,NC,A0,IZ,Y1,VPV2,TCC,EDC,XDC) DY=(VPV1-VPV2)/(0.02*YR) RETURN END C C COMPUTATION OF THE PARTIAL DERIVATIVE OF THE NPV WITH C RESPECT TO A GIVEN VARIABLE C SUBROUTINE DERIV(A,F,C,P,CF,V,B,IT,NC,A0,IZ,VS1,IL,K,IC,DER,DTC) DIMENSION F ( 2 0 , 9 ) , I T ( N C ) , C ( 3 5 , I Z ) , C F ( I Z ) , V ( 4 0 ) , P ( 1 0 , 2 ) , B ( 5 0 , 7 ) DIMENSION A(50) V(1)=VS1 CALL VARASS(F,V,P,IC,IL,K,VAR) VAR0=VAR IF(VAR.EQ.O) THEN DER=0 GOTO 10 ENDIF VAR=1.01*VAR0 CALL ASSVAR'(F,V,P,IC,IL,K,VAR) CALL NPV(A,F,C,P,CF,V,B,IT,NC,A0,IZ,V(1),VPV1,TCC,EDC,XDC) TEI1=TCC+EDC+XDC C VAR=.99*VAR0 CALL ASSVAR(F,V,P,IC,IL,K,VAR) CALL NPV(A,F,C,P,CF,V,B,IT,NC,A0,IZ,V(1),VPV2,TCC,EDC,XDC) TEI2=TCC+EDC+XDC C DER=(VPV1-VPV2)/(0.02*ABS(VARO)) DTC=(TEI1-TEI2)/(0.02*ABS(VAR0)) CALL ASSVAR(F,V,P,IC,IL,K,VARO) 10 RETURN END C C SUBROUTINE TO PERFORM EXACT SENSITIVITY ANALYSIS C SUBROUTINE 204 UEX(A,F,C,P,CF,V,B,IT,NC,A0,IZ,VS1,VPVO,YR,EXT,CN) CHARACTER*6 NA CHARACTER*10 U CHARACTER*25 CN DIMENSION F ( 2 0 , 9 ) , C ( 3 5 , I Z ) , C F ( I Z ) , V ( 4 0 ) , I T ( N C ) , E X A ( 1 0 ) , B ( 5 0 , 7 ) DIMENSION P ( 1 0 , 2 ) , C N ( 2 0 ) , E X A N ( 1 0 ) , E X A I ( 1 0 ) , A ( 5 0 ) VPVO0=VPV0 V(1)=VS1 BREAK=0 WRITE(6,10) 10 FORMAT(///,'EXACT UNIVARIATE SENSITIVITY ANALYSIS',/) CALL MENU5(F,P,B,V,IT,IL,K,IC,NA,CN) IF(K.EQ.42) GOTO 80 WRITEC6,20) 20 FORMAT(/,'ENTER LOWER ESTIMATE ( P E S S I M I S T I C ) ' , / ) READ(5,*)V1 WRITE(6,40) 40 FORMAT(/,'ENTER HIGHER ESTIMATE (OPTIMISTIC)',/) READ(5,*)V2 C CALL SNSC(CF,A0,IZ,NSC) C EXA(1)=V1 DEL=(V2-V1)/9 CALL VARASS(F,V,P,IC,IL,K,VAR0) CALL ASSVAR(F,V,P,IC,IL,K,V1) CALL NPV(A,F,C,P,CF,V,B,IT,NC,A0,IZ,V(1),VLAST,TCC,EDC,XDC) EXAN(1)=VLAST IF(NSC.EQ.1) THEN CALL SIRR1(A,F,C,P,CF,V,B,IT,NC,A0,IZ,V(1),VLAST,YR) ELSE CALL SIRR2(A,F,C,P,CF,V,B,IT,NC,A0,IZ,V(1),VLAST,EXT,YR) ENDIF EXAI(1)=YR*100 C DO 200 1=1,9 VAR=V1+DEL*I EXA(I+1)=VAR CALL ASSVAR(F,V,P,IC,IL,K,VAR) CALL NPV(A,F,C,P,CF,V,B,IT,NC,A0,IZ,V(1),VPV,TCC,EDC,XDC) EXAN(I+1)=VPV CHE=VLAST/ABS(VLAST)*VPV IF(CHE.LT.O) THEN VL=VAR-DEL VU=VAR VIN=VPV BREAK=1 ENDIF VLAST=VPV 205 C IF(NSC.EQ.1) THEN CALL SIRR1 (A , F., C , P , CF , V, B , IT,NC , AO , I Z , V( 1 ) , VLAST, YR) ELSE CALL -SIRR2(A,F,C,P,CF,V,B,IT,NC,A0,IZ,V(1),VLAST,EXT,YR) ENDIF EXAI(1+1)=YR*100 200 CONTINUE C WRITE(8,45)NA WRITE(6,45)NA 45 FORMAT(1H1,'EXACT UNIVARIATE ANALYSIS FOR VARIABLE \ A 6 ) IF(BREAK.EQ.O) THEN WRITE(8,50) WRITE(6,50) 50 FORMAT(//,'THERE IS NOT A BREAK-EVEN POINT WITHIN THE RANGE 1 /,'DEFINED BY THE PESSIMISTIC AND OPTIMISTIC ESTIMATES',/) CALL ASSVAR(F,V,P,IC,IL,K,VAR0) GOTO 599 ENDIF CHE1=VAR/2 000 VAR=(VU+VL)/2 100 CALL ASSVAR(F,V,P,IC,IL,K,VAR) CALL NPV(A,F,C,P,CF,V,B,IT,NC,A0,IZ,V(1),VPV,TCC,EDC,XDC) CHE2=VIN/ABS(VIN)*VPV IF(CHE2.GT.O) THEN VU=VAR ELSE VL=VAR ENDIF DIF=VU-VL IF(DIF.LT.CHE1) GOTO 54 VAR=(VU+VL)/2 C VIN=VPV GOTO 100 54 BREAK=VAR 150 CALL ASSVAR(F,V,P,IC,IL,K,VAR0) C WRITE(8,55)BREAK WRITE(6,55)BREAK 55 FORMAT(/,'BREAK EVEN POINT=',F15.7,/) 599 WRITE(8,60) WRITE(6,60) 60 FORMAT('VARIABLE',T30,'NPV,T50,'IRR (%)',//) WRITE (8, 70) (EXA(I ) , EXAN (I') ,EXAI (I ) ,1 = 1 , 10) W R I T E ( 6 , 7 0 ) ( E X A ( I ) , E X A N ( I ) , E X A I ( I ) , I = 1 , 1 0 ) 70 FORMAT(F15.7,T20,F15.3,T50,F7.3) VPV0=VPVO0 206 WRITE(6,75) 75 FORMAT(/,'DO YOU WANT A PLOT OF THESE RESULTS (YES=1, NO=0)',/) READ(5,76)11 7 6 FORMAT(11) I F ( I 1.EQ.0) GOTO 80 CALL PLEXA(EXA,EXAN,EXAI,NA) 80 RETURN END C C SUBROUTINE TO PERFORM BIVARIATE SENSITIVITY ANALYSIS C SUBROUTINE BIVAR(A,F,C,P,CF,V,B,IT,NC,AO,IZ,Y,VPVO,YR,EXT,CN) CHARACTER*6 NA1,NA2 CHARACTER*25 CN DIMENSION F ( 2 0 r 9 ) , C ( 3 5 , I Z ) , C F ( I Z ) , V ( 4 0 ) , I T ( N C ) , S E N ( 1 0 , 1 0 ) , A ( 5 0 ) DIMENSION B(50,7) , BIV(2, 1 0 ) , P ( 1 0 , 2 ) , C N ( 2 0 ) ,WAR1 (10) ,WAR2( 10) WRITE(6,10) 10 FORMAT(//,'BIVARIATE SENSITIVITY ANALYSIS',/,'SELECT FIRST 1 VARIABLE',/) CALL MENU5(F,P,B,V,IT,IL1,K1,IC1,NA1,CN) IF(K1.EQ.42) GOTO 90 WRITE(6,20) 20 FORMAT(/,'ENTER LOWER ESTIMATE',/) READ(5,* ) V1 L WRITE(6,40) 40 FORMAT(/,'ENTER HIGHER ESTIMATE',/) READ(5,*)V1U WRITE(6,50) 50 FORMAT(/,'SELECT SECOND VARIABLE',/) CALL MENU5(F,P,B,V,IT,IL2,K2,IC2,NA2,CN) IF(K2.EQ.42) GOTO 90 WRITE(6,20) READ(5,*)V2L WRITE(6,40) READ(5,*)V2U WRITE(6,55) 55 FORMAT('ENTER NUMBER OF POINTS ANALYZED IN THE GIVEN RANGES',/, 1 '(9 MAXIMUM)',/) READ(5,*)NUMP NUMM1=NUMP-1 DEL 1 = (V1U-V1L)/NUMM1 DEL2=(V2U-V2L)/NUMM1 CALL VARASS(F,V,P,IC1 , IL1 ,K1 ,VAR1 ) CALL VARASS(F,V,P,IC2,IL2,K2,VAR2) NUMP1=NUMP NUMP2=NUMP CALL SWAR (WAR 1 , VAR 1 , NUMP 1 , V1 L , DEL 1 ) CALL SWAR (WAR2 , VAR2 , NUMP2 , V2L , DEL2 ) . 207 C DO 80 1=1,NUMP1 CALL ASSVAR(F,V,P,IC1 ,1 L 1 , K 1 ,WAR1 (I ) ) IF(VAR1.EQ.O) THEN BIV(1,I)=0 ELSE BIV( 1 ,1 ) = (WAR1 (I )/VAR1-1 ) * 1 00 ENDIF C DO 70 J=1,NUMP2 CALL ASSVAR(F,V,P,IC2,IL2,K2,WAR2(J)) IF(VAR2.EQ.0) THEN BIV(2,J)=0 ELSE BIV(2, J ) = (WAR2(J)/VAR2-1 ) * 1 00 ENDIF CALL NPV(A,F,C,P,CF,V,B,IT,NC,AO,I Z , Y , VPV, TCC , EDC , XDC ) SEN(I,J)=(VPV/VPV0-1)*100 7 0 CONTINUE .80 CONTINUE CALL ASSVAR(F,V,P,IC1,IL1,K1,VAR1) CALL ASSVAR(F,V,P,IC2,IL2,K2,VAR2) C WRITE(8,60)NA1,NA2,NA2,(BIV(2,I),I=1,NUMP2) WRITE(6,60)NA1,NA2,NA2,(BIV(2,I),I=1,NUMP2) 60 FORMAT(1H1,T5,'BIVARIATE SENSITIVITY MATRIX PERCENTAGE', 1' CHANGE IN THE NPV',//,'VARIABLE 1: ',A6,'CONSTANT ALONG ', 2 'ROWS',/,'VARIABLE 2: ',A6,'CONSTANT ALONG COLUMNS',//, 3 //,T15,'PERCENTAGE CHANGE IN VARIABLE ',A6,/, 4 /,T15,10(F9.3,2X)) WRITE(8,61)NA1 WRITE(6,61)NA1 61 FORMAT(//,T4,A6,/,T6,'(%)',//) DO 85 1=1,NUMP1 62 WRITE(6,65)BIV(1 , 1 ) ,(SEN(I,J),J=1,NUMP2) W R I T E ( 8 , 6 5 ) B I V ( 1 , 1 ) , ( S E N ( I , J ) , J = 1 , N U M P 2 ) 65 F0RMAT(F9.3,T15,10(F9.3,2X,/)) 85 ' CONTINUE 90 RETURN END C C SUBROUTINE TO DEFINE THE VALUE OF THE VARIABLES C FOR THE BIVARIATE SENSITIVITY ANALYSIS C SUBROUTINE S WAR (WAR, VAR , NUMP , VL , DEL ) DIMENSION WAR( 10) WAR( 1 )=VL FLA= 1 J = 2 C 208 DO 10 1=1,NUMP-1 VX=VL+I*DEL I F ( F L A . L T . 2 ) THEN CHE=VX/VAR-1 IF (CHE.EQ.O) THEN FLA = 2 GOTO 15 ENDIF IF(CHE.GT.O) THEN WAR( J)=VAR NUMP=NUMP+1 J = J+1 FLA = 2 ENDIF ENDIF C 1 5 WAR( J)=VX J=J+1 10 CONTINUE RETURN END C C ASSIGN THE VALUE IN VARIABLE "VAR" TO A GIVEN PRIMARY C VARIABLE C SUBROUTINE ASSVAR(F,V,P,IC,IL,K,VAR) DIMENSION F ( 2 0 , 9 ) , V ( 4 0 ) , P ( 1 0 , 2 ) GOTO(10, 20,30, 40, 50) ,IL 10 V(K)=VAR GOTO 50 20 F(IC,K)=VAR GOTO 50 30 P(K,1)=VAR GOTO 50 40 P(K,2)=VAR 50 CALL VARIA(F,V,P,50) RETURN END C C ASSIGN THE VALUE OF A GIVEN PRIMARY VARIABLE TO C VARIABLE "VAR" C SUBROUTINE VARASS(F,V,P,IC,IL,K,VAR) DIMENSION F ( 2 0 , 9 ) , V ( 4 0 ) , P ( 1 0 , 2 ) GOTO(10,20,30,40,50),IL 10 VAR=V(K) GOTO 50 20 VAR=F(IC,K) GOTO 50 3 0 VAR=P(K,1) GOTO 50 40 VAR=P(K,2) 50 RETURN END 209 C C MENU TO SELECT ONE VARIABLE IN ORDER TO PERFORM C SOME ANALYSIS WITH IT C SUBROUTINE MENU5(F,P,B,V,IT,IL,K,IC,NA,CN) CHARACTER*6 NA CHARACTER*25 CN DIMENSION F ( 2 0 , 9 ) , I T ( 1 2 ) , P ( 1 0 , 2 ) , C N ( 2 0 ) , B ( 5 0 , 7 ) , V ( 4 0 ) IL=0 WRITE(6,1) 1 FORMAT(//,'SELECT ONE OF THE FOLLOWING', 1 /,T6,'1. DISCOUNT RATE',/,T6,'2. FOREIGN EXCHANGE RATE' /, 2 T6,'3. FRACTION OF CONSTRUCTION FINANCED WITH BORROWED FUNDS', 3 /,T6,'4. INTEREST RATE ON CONSTRUCTION LOAN',/,T6, 4 '5. PERIOD WHEN THE CONSTRUCTION LOAN IS DUE',/,T6, 5 '6. UNIT SALE PRICE',/,T6,'7. FIXED COSTS',/,T6, 6 ' 8 . VARIABLE COSTS',/,T6,'9. VALUE OF DEPRECIABLE ASSETS',/, 7 T5,'10. PERIOD WHEN DEPRECIATION STARTS',/,T5, 8 '11. L I F E OF DEPRECIABLE ASSETS',/,T5,'12. TAX RATE',/,T5, 9 '13. AMOUNT OF THE LONG TERM LOAN') WRITE(6,4) 4 FORMAT(T5,'14. INTEREST RATE ON LONG TERM LOAN',/,T5, 1 '15. OTHER LONG TERM DEBT VARIABLES',/,T5, 2 '16. PERIOD WHEN REPAYMENT OF LONG TERM LOAN STARTS',/, 3 T5,'17. INFLATION RATE FOR SALES PRICE',/,T5, 4 ' 1 8 . INFLATION RATE FOR FIXED COSTS',/,T5, 5 '19. INFLATION RATE FOR VARIABLE COSTS',/, 6 T2, '20-40. OTHER PRIMARY VARIABLE * ,/,T5, 7 '41. CASH FLOW PARAMETER',/,T5,'42. EXIT',/) 5 READ(5,* ) K 2 FORMAT(12) IF(K.EQ.42) GOTO 200 WRITE(6,6) 6 FORMAT('ASSIGN A NAME TO THE VARIABLE (MAX. 6 CHARACTERS)',/) READ(5,7)NA 7 FORMAT(A6) IF ( K . L E . 4 0 ) THEN IF(K.EQ.6) THEN IL=3 ENDIF IF(K.EQ.17) THEN IL=4 ENDIF I F ( I L . G E . 3 ) THEN I F ( P ( 1 0 , 1 ) . E Q . 1 ) THEN K= 1 GOTO 200 ELSE 210 W R I T E ( 6 , 8 ) ( J , P ( J , 1 ) , J = 1 , P ( 1 0 , 1 ) ) 8 FORMAT(//,'SELECT THE PRICE' ,/,9(T2,1 1 ,' . ',F15.7,/)) READ(6,17)K GOTO 200 ENDIF ELSE I L= 1 GOTO 200 ENDIF IF(K.EQ.15) THEN CALL K15(B,V,IL) GOTO 200 ENDIF ENDIF C 10 IL=2 WRITE(6,3)(J,CN(J),J=1 ,P(10,2) ) 3 FORMAT(/,'SELECT THE CASH FLOW' ,//,50(T2,1 2,' . \ A 2 5 , / ) ) READ(6,* ) I C ITYPE = I N T ( F ( I C , 1 ) ) GOTO(15,25,35,45,55,65,75,85),I TYPE 15 WRITE(6,16)CN(IC) 16 FORMATCCASH FLOW ',A25,' IS A SINGLE PAYMENT',/, 1 'SELECT THE PARAMETER',/,T5,'1. VALUE OF THE FLOW', 2 /,T5,'2. PERIOD',/,T5,'3. INFLATION RATE',/) READ(5,17)11 17 FORMAT(I 1 ) GOTO(18,19,24),11 18 K=2 GOTO 200 19 K=5 GOTO 200 24 K=7 GOTO 200 25 WRITE(6,26)CN(IC) 26 FORMATCCASH FLOW ',A25,' IS TWO DISCRETE PAYMENTS',/, 1 'SELECT THE PARAMETER',/,T5,'1. FIRST PAYMENT', 2 /,T5,'2. SECOND PAYMENT',/,T5, 3 '3. PERIOD OF FIRST PAYMENT',/,T5,'4. PERIOD OF SECOND PAYMENT', 4 /,T5,'5. INFLATION RATE',/) READ(5,17)11 GOTO(27,27,29,29,29) ,1 1 27 K=I1+1 GOTO 200 29 K=I1+2 GOTO 200 35 WRITE(6,36)CN(IC) 36 FORMATCCASH FLOW ',A25,' IS A UNIFORM FLOW',/, 1 'SELECT THE PARAMETER',/,T5,'1. VALUE OF THE FLOW',/,T5, 21 1 2 '2. I N I T I A L PERIOD',/,T5,'3. FINAL PERIOD',/,T5, 3 '4. INFLATION RATE',/) READ(5,17)11 GOTO(37,38,38,38) , 11 37 K=2 GOTO 200 38 K=I1+3 GOTO 200 4 5 WRITE(6,46)CN(IC) 46 FORMATCCASH FLOW *,A25,' IS A TRAPEZOIDAL FLOW',/, 1 'SELECT THE PARAMETER',/,T5,'1. I N I T I A L VALUE', 2 /,T5,'2. FINAL VALUE',/,T5,'3. I N I T I A L ' P E R I O D ' , / , T 5 , 3 '4. FINAL PERIOD',/,T5,'5. INFLATION RATE*,/) READ(5,17)11 GOTO(47,47,49,49,49) ,11 47 K=I1+1 GOTO 200 49 K=I1+2 GOTO 200 55 WRITE(6,56)CN(IC) 56 .FORMATCCASH FLOW *,A25,' IS A BETA FUNCTION',/, 1 'SELECT THE PARAMETER',/,T5,'1. AMPLIFICATION CONSTANT',/, 2 T5,'2. PARAMETER 1',/,T5.,'3. PARAMETER 2',/,T5, 3 '4. IN I T I A L PERIOD',/,T5,'5. FINAL PERIOD',/,T5, 4 '6. INFLATION RATE',/) READ(5,17)11 K=I1+1 GOTO 200 65 WRITE(6,66)CN(IC) 66 FORMAT('CASH FLOW *,A25,' IS AN EXPONENTIAL FUNCTION',/, 1 'SELECT THE PARAMETER',/,T5,'1. AMPLIFICATION CONSTANT',/, 2 T5,'2. GROWTH RATE',/,T5,'3. I N I T I A L PERIOD',/,T5, 3 '4. FINAL PERIOD',/,T5,'5. INFLATION RATE',/) READ(5,17)11 GOTO(67,67,69,69,69) , 11 67 K=I1+1 GOTO 2 00 69 K=I1+2 GOTO 200 75 WRITE(6,76)CN(IC) 7 6 FORMATCCASH FLOW ',A25,' IS A GOMPERTZ CURVE',/, 1 . 'SELECT THE PARAMETER',/,T5,'1. ASYMPTOTIC LIMIT',/,T5, 2 '2. SHAPE PARAMETER',/,T5,'3. GROWTH RATE',/,T5, 3 '4. I N I T I A L PERIOD',/,T5,'5. FINAL PERIOD',/,T5, 4 '6. INFLATION RATE',/) READ(5,17)11 K=I1+1 GOTO 2 00 85 IF(IT('IC) .EQ.5) GOTO 95 WRITE(6,86)CN(IC) 212 86 FORMAT('CASH FLOW ',A25,' IS THE ARBITRARY FUNCTION OF THE 1 CONSTRUCTION PHASE',/) WRITE(6,87) 87 . FORMAT('SELECT THE PARAMETER',/,T5,'1. PARAMETER T , / , T 5 , 1 '2. PARAMETER 2',/,T5,'3. PARAMETER 3',/,T5, 2 '4. INITIAL PERIOD',/,T5,'5. FINAL PERIOD',/,T5, 3 '6. INFLATION RATE',/) READ(5,17)11 K=I1+1 GOTO 200 95 WRITE(6,96)CN(IC) 96 FORMATCCASH FLOW ',A25,' IS THE ARBITRARY FUNCTION OF THE 1 OPERATIONAL PHASE',/) WRITE(6,87) READ(5,17)11 K=I1+1 2 00 RETURN END C C ADDITION TO SUBROUTINE "MENU5". THIS SUBROUTINE IS C CALLED WHEN TO SELECTION MADE IN "MENU5" IS 15. C SUBROUTINE K15(B,V,IL) DIMENSION B ( 5 0 , 7 ) , V ( 4 0 ) IL=5 WRITE(6,9) 9 FORMAT(//,'SELECT ONE OF THE FOLLOWING:',/,T2,'1. NO LONG', 1 ' TERM LOAN CONSIDERED',/,T2,'2 . UNIFORM REPAYMENT FUNCTION', 2 /,T2,'3. STEP REPAYMENT FUNCTION',/,T2,'4. GRADIENT FUNCTION', 3 /,T2,'5. VALUE OF THE AMOUNT BORROWED',/,T2,'6. RESET VALUE', 4 ' OF AMOUNT BORROWED',/,T2,'7. RESET NUMBER OF PAYMENTS',/,T2, 5 '8. RESET PERIOD WHEN REPAYMENT STARTS',/,T2, 6 '9. RESET NUMBER OF PERIODS BETWEEN PAYMENTS',/,T2, 7 '10. RESET VALUE OF I N I T I A L PAYMENT',/,T2, 8 '11. RESET NUMBER OF PAYMENTS BETWEEN INCREMENTS',/) READ(5 , * ) I C GOTO(11,12,12,12,13,15,15,15,15,15,15),IC 11 V(13)=0 V(15)=0 GOTO 200 12 B(1,1)=IC-1 GOTO 200 13 V(13)=0 V ( 1 5 ) = 1 GOTO 2 00 15 WRITE(6,14) 213 14 FORMAT(/,'INPUT NEW VALUE',/) READ(5,*)VALUE IC5=IC-5 GOTO(16,161,161,161,161,18),IC5 16 V(13)=VALUE V(15)=0 GOTO 200 161 B( 1 ,IC5)=VALUE GOTO 200 18 B(1,7)=VLAUE GOTO 200 200 RETURN END C C . SUBROUTINE TO PRODUCE THE STAR DIAGRAM C SUBROUTINE STAR(SN,SI,NAME,IN) CHARACTER*6 NAME DIMENSION S N ( I N ) , S I ( I N ) , X ( 2 ) , Y ( 2 ) , N A M E ( I N ) CALL A L S I Z E ( 8 . , 8 . ) CALL A L A X I S ( ' % CHANGE IN VARIABLE',20,'% CHANGE IN NPV',15) CALL ALSCAL(-100.,100.,-100.,100.) DO 50 1=1,IN X(1)=100/SQRT(1+SN(I)**2) X(2)=-X(1) Y( 1 ) = S N ( I ) * X ( 1 ) Y(2)=-Y(1) CALL ALGRAF(X,Y,-2,0) AN = ATAN(SN(I ) ) CX=4.0+3*COS(AN) CY=4.0+3*SIN(AN)+0.1 ANG=AN*180/3.1416 CALL PSYM(CX,CY,0.17,NAME(I),ANG,6) 50 CONTINUE X(1)=0 X(2)=0 Y(1)=-100 Y(2)=100 CALL ALGRAF(X,Y,-2,0) X( 1 )=-100 X(2)=100 Y(1)=0 Y(2)=0 CALL ALGRAF(X,Y,-2,Q) CALL ALDONE C C CALL A L S I Z E ( 8 . ,8. ) CALL A L A X I S ( ' % CHANGE IN VARIABLE',20,'% CHANGE IN IRR',15) CALL ALSCAL(-100. ,100.,-100. ,100.) DO 60 1=1,IN X(1)=100/SQRT(1+SI(I)**2) 214 X(2)=-X(1) Y ( 1 ) = S I ( I ) * X ( 1 ) Y(2)=-Y(1 ) CALL ALGRAF(X,Y,-2,0) AN=ATAN(SI(I ) ) CX=4.0+3*COS(AN) CY=4.0+3*SIN(AN)+0.1 ANG=AN*180/3.1416 CALL PSYM(CX,CY,0.17,NAME(I),ANG,6) 60 CONTINUE X(1)=0 X(2)=0 Y{1)=-100 Y(2)=100 CALL ALGRAF(X,Y, -2,0) X( 1 ) =-100 X(2)=100 Y(1)=0 Y(2)=0 CALL ALGRAF(X,Y, -2,0) CALL PSYM(6.5,7. 0,0.17, CALL PSYM(6.9,6. 5,0.17, CALL ALDONE RETURN END SENSITIVITY' ,0 . , 1 1 ) CHART',0.,5) C C SUBROUTINE TO PRODUCE A PLOT OF THE EXACT ANALYSIS C SUBROUTINE PLEXA(EXA,EXAN,EXAI,NA) CHARACTER*6 NA DIMENSION EXA(10),EXAN(10),EXAI(10) XMIE=EXA(1) XMAE=EXA(1) XMIN=EXAN(1) XMAN=EXAN(1) XMII=EXAI(1) XMAI=EXAI(1) DO 1000 1=2,10 IF(EXA(I).GT.XMAE) THEN XMAE=EXA(I) ENDIF I F ( E X A ( I ) . L T . X M I E ) THEN XMIE=EXA(I) ENDIF IF(EXAN(I).GT.XMAN) THEN XMAN=EXAN(I) ENDIF IF(EXAN(I).LT.XMIN) THEN XMIP=EXAN(I) ENDIF IF(EXAI(I).GT.XMAI) THEN XMAI=EXAI (I,) ENDIF I F ( E X A I ( I ) . L T . X M I I ) THEN XMII=EXAI(I) ENDIF CONTINUE CALL A L S I Z E ( 8 . , 8 . ) CALL ALAXIS(NA,6,'NPV',3) CALL ALSCAL(XMIE,XMAE,XMIN,XMAN) CALL ALGRAF(EXA,EXAN,10,0) CALL ALDONE CALL A L S I Z E ( 8 . , 8 . ) CALL ALAXIS(NA,6,'IRR',3) CALL ALSCAL(XMIE,XMAE,XMII,XMAI) CALL ALGRAF(EXA,EXAI,10,0) CALL ALDONE RETURN END APPENDIX B COMPUTER OUTPUT FOR THE SIMPLE EXAMPLE 216 SEW I I I'.' I T V AND ECONOMIC ANALYSIS OF PROJECT.: PRINCE EDWARD ISLAND BRIDGE PRIMARY VARIABLES DISCOUNT RATE-0 . 1400 FOREIGN EXCHANGE RATE= 0.0 FRACTION OF CONSTRUCTION FINANCED WITH BORROWED FUNDS=0.9000 INTEREST RATE ON CONSTRUCTION LOAN=0.1100 PERIOD WHEN THE CONSTRUCTION LOAN IS DUE= 5.00 FIXED OPERATING C0STS= 10.00000 VARIABLE C0STS= 0.0 VALUE OF DEPRECIABLE ASSETS= 0 .0 PERIOD WHEN ASSETS ARE ACQUIRED= 0 .0 LIFE OF DEPRECIABLE ASSETS= 0.0 TAX RATE=0.0 INFLATION RATE FOR FIXED C0STS=0.05G0 INFLATION RATE FOR VARIABLE COSTS= 0 .0 UNIT SALE PRICES ( M i l l i o n $) # PRICE INFLATION 1 0.0000030 0.0550 2 0.0000060 0.0550 3 1.0000000 0.0 FCONCUIC PERFORMANCE M E A S U R E S ( M i l l i o n $) HE T P R E S E N T V A L U E 7 4 . 2 6 0 CONSTANT DOLLAR C O N S T R U C T I O N C O S I S = - 5 6 4 . 9 9 9 E S C A L A T I O N DURING C O N S T R U C T I O N - - 3 5 . 8 2 7 I N T E R E S T S DURING C O N S T R U C T I O N = 1 0 1 . 1 9 9 TOTAL C O N S T R U C T I O N C 0 S T S = - 7 0 2 . 0 2 5 INTERNAL R A T E OF RETURN= 2 1 . 1 1 4 I N F O R M H I O N A B O U I C A S H F L O W S I N A M E TYPE. PHASE I N I T . PEn. F I N A L P E R . I N F . RATE CURRENCY l P r o n o s a 1 V4t.IJE = • 7. .OOOIMi I 1 Ion J UNIFORM / P E R I O D " F E A S I B I L I T Y 2 D e s i g n VALUE= 8 . 8 B 9 ( M i I I i o n J UNIFORM / P E R I O D ) Ind t r e e X c o s Is = • SO .OOOIMI I I i o n UNIFORM J / P E H I O O ) CONSTRUCTION 4 ' F o o t i n g s UNIFORM VALUE= • 6 0 . 0 0 0 1 M i l l i o n t / P E R I O D ) CONSTRUCTION 3 . 5 0 5 S u p e r s t r u c t u r e VALUE= - 9 0 . 9 0 9 ( M t l I i o n t UNIFORM / P E R I O O ) CONSTRUCTION DOLLARS 6 V » L U E = A p p r o a c h e s • f>3 6 30 I M i 1 1 i UNIFORM / P E R I O D ) CONSTRUCT ION D O L L A R S 1 P a s s e n g e r t r i p s UNIFORM V A L U C r 6011(101)0 .OOOIMi r I i o n t / P E H I O O ) OPERATION UNI1 S A L E FRICL~ = 0 . 0 0 0 0 0 3 0 I M i I 1 i o n J ) 8 C o m m e r c i a l t r i p s V A L U C = 3 0 0 0 0 0 0 . 0 0 0 ( M i I 1 i o n I UNIFORM / P E R I O O ) U N I I S A L E r n i c E - - -OPERATION O.OOOOOGOIMi I 1 i o n $ ) 3 9 . 75 9 S u b s i d y UNIFORM OPERATION 4 . 7 5 3 9 . 7 5 O .OSOO DOLLARS VALUE= 25 .000(Mi1 1 Ion S / P E R I O D ) UNIT S A L E P R I C E = 1 .OOOOOOO(Mi 11 i o n $ ) 9 10 I N I T I A L INVESTMENT 0 . 0 0 . 0 F E A S I B I L I T Y 0 . 0 0 . 0 D E S I G N 0 . 0 0 . 0 C O N S T . ( E O U I T Y ) 0 . 0 0 . 0 C O N S T . LOAN 0 . 0 0 . 0 F I X E D COSTS 1 2 . 6 8 7 1 3 . 4 1 8 14 .19 V A R I A B L E C O S T S 0 . 0 0 . 0 0 . 0 D E P R E C I A T I O N 0 . 0 0 . 0 0 . 0 LONG TERM OEBT 5 2 . 4 2 8 5 4 . 9 0 4 5 7 . 3 8 S A L V A G E V A L U E 0 . 0 0 . 0 0 . 0 GROSS INCOME 1 3 . 4 2 8 15 .354 17 .58 INCOME TAX 0 . 0 0 . 0 0 . 0 NET CASH FLOW 1 3 . 4 2 8 15 .354 1 7 . 5 8 12 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 9 5 . 0 0 1 I 5 . 0 0 B 0 . 0 0 . 0 5 9 . 8 5 6 0 . 0 2 0 . 1 3 7 0 . 0 2 0 . 1 3 7 13 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 1 0 1 . 2 4 3 15 .872 0 . 0 0 . 0 6 2 . 3 3 2 0 . 0 2 3 . 0 3 8 0 . 0 2 3 . 0 3 8 14 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 1 0 7 . 9 0 7 1 6 . 7 8 7 0 . 0 0 . 0 6 4 . 8 0 8 0 . 0 2 6 . 3 1 2 0 . 0 2 6 . 3 12 15 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 115 .021 1 7 . 7 5 4 0 . 0 0 . 0 6 7 . 2 8 4 0 . 0 2 9 . 9 8 4 0 . 0 2 9 . 9 8 4 16 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 1 2 2 . 6 18 1 8 . 7 7 6 0 . 0 0 . 0 6 9 . 7 6 0 0 . 0 34 082 0 . 0 3 4 . 0 8 2 I N I T I A L INVESTMENT 0 . 0 0 . 0 0 . 0 F E A S I B I L I T Y 0 . 0 0 . 0 0 . 0 D E S I G N 0 . 0 0 0 0 . 0 C O N S T . ( E 0 U 1 T Y ) 0 . 0 0 . 0 0 . 0 C O N S T . LOAN 0 . 0 0 . 0 0 . 0 R E V E N U E S 130 .731 1 3 9 . 3 9 5 1 4 8 . 6 4 9 F I X E D COSTS 1 9 . 8 5 8 2 1 . 0 0 1 2 2 . 2 1 1 V A R I A B L E C O S T S 0 . 0 0 . 0 0 . 0 D E P R E C I A T I O N 0 . 0 0 . 0 0 . 0 LONG TERM DEBT 7 2 . 2 3 6 7 4 . 7 1 3 7 7 . 1 8 9 S A L V A G E V A L U E 0 . 0 0 . 0 0 . 0 GROSS INCOME 3 8 . 6 3 7 4 3 . 6 8 1 4 9 . 2 5 0 INCOME TAX 0 . 0 0 . 0 0 . 0 NET CASH FLOW 3 8 . 6 3 7 4 3 . 6 8 1 4 9 . 2 5 0 0 . 0 0 . 0 0 0 0 . 0 21 0 . 0 O 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 159 .094 2 6 . 2 7 4 0 . 0 0 . 0 7 9 . 6 6 5 0 . 0 5 5 . 3 7 9 0 . 0 5 5 . 3 7 9 e2.141 6 2 . 1 10 6 9 . 4 8 5 7 7 . 5 5 0 0 . 0 B 6 . 3 5 4 0 . 0 8 6 . 3 5 4 ro ro oo 25 26 27 I N I T I A L INVESTMENT 0 . 0 0 . 0 0 . 0 F E A S I B I L I T Y 0 . 0 0 . 0 0 . 0 D E S I G N 0 . 0 0 . 0 0 . 0 C O N S T . ( E Q U I T Y ) 0 . 0 0 . 0 0 . 0 C O N S T . LOAN 0 . 0 0 . 0 0 . 0 R E V E N U E S 2 1 9 . 0 7 6 2 3 3 . 7 8 8 2 4 9 . 5 1 2 F I X E D COSTS 3 1 . 0 8 1 3 2 . 8 7 1 3 4 . 7 6 4 V A R I A B L E COSTS 0 . 0 0 . 0 0 . 0 D E P R E C I A T I O N 0 . 0 0 . 0 0 . 0 LONG TERM DEBI 9 2 . 0 4 5 9 4 . 5 2 1 9 6 . 9 9 7 S A L V A G E V A L U E 0 . 0 0 . 0 0 . 0 GROSS INCOME 9 5 . 9 5 1 1 0 6 . 3 9 6 117 .751 INCOME TAX 0 . 0 0 . 0 0 . 0 NET CASH FLOW 9 5 . 9 5 1 1 0 6 . 3 9 6 117 .751 28 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 2 6 6 . 3 2 0 3 6 . 7 6 6 0 . 0 0 . 0 9 9 . 4 7 3 0 . 0 1 3 0 . 0 8 0 0 . 0 1 3 0 . 0 0 0 29 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 2 8 4 . 2 8 8 3 B . 8 8 4 0 . 0 0 . 0 101 .949 0 . 0 1 4 3 . 4 5 5 0 . 0 1 4 3 . 4 5 5 30 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 3 0 3 . 4 9 7 4 1.124 0 . 0 0 . 0 1 0 4 . 4 2 5 0 . 0 1 5 7 . 9 4 8 0 . 0 1 5 7 . 9 4 8 3 I 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 3 2 4 . 0 3 6 4 3 . 4 9 2 0 . 0 0 . 0 1 0 6 . 9 0 1 0 . 0 1 7 3 . 6 4 3 0 . 0 17 3 . 6 4 3 32 0 . 0 0 . 0 0 . 0 O . 0 0 . 0 3 4 5 . 9 9 8 4 5 . 9 9 7 0 . 0 0 . 0 1 0 9 . 3 7 7 0 . 0 1 9 0 . 6 5 3 0 . 0 1 9 0 . 6 2 3 tsj I N I T I A L INVESTMENT F E A S I B I L I T Y D E S I G N C O N S T . ( E Q U I T Y ) C O N S T . LOAN R E V E N U E S F I X E O C O S T S V A R I A B L E C O S T S D E P R E C I A T I O N LONG TERM DEBT S A L V A G E V A L U E c n o s s INCOME INCOME TAX NET C A S H FLOW 33 34 35 0 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 3 6 9 . 4 B 3 3 9 4 . 5 9 9 4 2 1 . 4 6 2 4 8 . 6 4 7 5 1 . 4 4 9 5 4 . 4 1 2 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 1 1 1 . 8 5 3 1 1 4 . 3 2 9 1 1 6 . 8 0 5 0 . 0 0 . 0 0 . 0 2 0 0 . 9 8 3 228 821 2 5 0 . 2 4 4 0 . 0 0 . 0 0 . 0 2 0 8 . 9 8 3 2 2 8 . 8 2 1 2 5 0 . 2 4 4 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 4 5 0 . 1 9 4 5 7 . 5 4 6 0 . 0 0 . 0 1 19 .281 0 . 0 2 7 3 . 3 G 6 0 . 0 2 7 3 . 3 0 8 0 . 0 0 . 0 0 . 0 0 . 0 4 8 0 . 9 2 9 6 0 . 8 6 1 0 . 0 0 . 0 1 2 1 . 7 5 7 0 . 0 2 9 8 . 3 1 1 0 . 0 2 9 8 . 3 1 I 0 . 0 5 1 3 . 8 0 8 6 4 . 3 6 6 0 . 0 0 . 0 1 2 4 . 2 3 3 0 . 0 3 2 5 . 2 0 9 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 4 3 8 . G 0 4 7 1 . 9 9 4 0 . 0 0 . 0 1 2 6 . 7 0 9 1 2 9 . 1 8 5 0 . 0 0 . 0 3 5 4 . 2 0 2 2 3 7 . 4 2 4 0 . 0 0 . 0 3 5 4 . 2 0 2 2 3 7 . 4 2 4 0 . 0 0 . 0 0 . 0 0 . 0 5 4 8 . 9 8 4 6 8 . 0 7 3 0 . 0 0 . 0 r o ro — (\i co O O O O O O C D O f v J O O O O O O O - - ^ f\t fu ro O CO co — 1*1 cn — <J1 LT S r. m O O ff> O CO \Tt iTi - m CJ vn O O tT> O CD ID " W t D C A S H FLOW 9 1 10 1 1 12 13 14 15 16 P r o p o s e 1 0 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 D e s i g n 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 I n d i r e c t c o s t s 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 0 0 . 0 F o o t 1 n g s 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 S u p e r s t r u c t u r e 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 0 0 . 0 A p p r o a c h e s 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 P a s s a n g e r t r i p s 24 . 056 2 5 . 800 27 . 67 1 2 9 . 677 31 . 829 34 . 137 3G . 612 3 9 . 2 6 7 C o m m e r c i a l t r i p s 24 . 328 26 . 17 1 28 . 152 3 0 . 284 32 . 578 35 . 0 4 5 37 . 699 4 0 . 5 5 4 S u b s iriy 30 . 159 31 . 705 33 . 331 35 . 040 3 6 . 836 38 . 725 40 . 7 10 4 2 . 7 98 228 O O *- f u x a •-CASH FLOW 33 34 P r o p o s e 1 0 . 0 0 . 0 O e s ig.n 0 . 0 0 . 0 I n d i r e c t c o s t s 0 . 0 0 . 0 F o o t i n g s 0 . 0 0 . 0 S u p e r s t r u c t u r e 0 . 0 0 . 0 A p p r o a c h e s 0 . 0 0 . 0 P a s s e n g e r t r i p s 129 . 0 7 3 1 3 8 . 4 3 2 C o m m e r c i a l t r i p s 140. 279 1 5 0 . 9 0 3 S u b s i d y 100 . 13 1 1 0 5 . 2 B 5 35 36 37 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 1 4 8 . 4 7 0 1 5 9 . 2 3 5 170 .781 162 .331 1 7 4 . 6 2 4 187 .848 1 1 0 . 6 6 2 1 1 6 . 3 3 6 1 2 2 . 3 0 0 38 39 40 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 0 0 . 0 0 . 0 0 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 183.. 164 136 445 157 . 720 2 0 2 . 0 7 4 2 1 7 . 3 7 7 174 .984 1 2 8 . 5 7 I I 3 5 . 163 1 0 5 . 9 0 I 231 L r'iG T E R M D E B T R E P A Y M E N T S C H E D U L E AM<;I>:II B O R R O W E D ^ 6 4 1.9-12 ( M i l l i o n S I I N T E R E S T R A T F = 0 . 1 0 0 0 P E n i O D AMOUNT OWED P A Y M E N T I N T E R E S T S P R I N C I P A L R E P A I D L O A N B A L A N C E 6 .0 6 4 1. . 9 4 2 4 5 . 0 0 0 6.) . 1 9 4 - 1 9 . 1 9 4 6 6 1 . 1 3 6 7 0' . 6 6 1 . 1 3 6 4 7 . 4 7 6 6 6 . 1 1 4 - 1 8 . 6 3 8 5 7 9 . 7 7 3 8 .0 6 " ? . 7 7 3 4 9 . 9 5 2 6 7 . 9 7 7 - 18 . 0 2 5 6 9 7 . 7 9 9 9 0 6 9 7 . 7 9 9 5 2 . 4 2 8 6 9 . 7 8 0 - 1 7 . . 3 5 2 7 1 5 . 1 5 0 1 0 .0 7 15 . 1 5 0 5 4 . 9 0 4 7 1 . 5 1 5 - 16 . 6 1 1 7 3 1 . 7 6 1 1 1 .0 73 1 . 7 6 1 5 7 . 3 8 0 7 3 . 1 7 6 - 1 5 . 7 9 6 7 4 7 . 5 5 7 12 .0 7 4 7 5 5 7 5 9 . . 8 5 6 7 4 . 7 5 6 - 14 . 8 9 9 7 6 2 . 4 5 6 13 .0 7 6 2 4 5 6 6 2 . 3 3 2 7 6 . 2 4 6 - 1 3 . 9 1 3 7 7 6 . 3 6 9 14 . .0 7 7 6 . . 3 6 9 6 4 . . 8 0 8 7 7 . 6 3 7 • 1 2 . 8 2 9 7 8 9 . 1 9 8 15 .0 7 8 9 . 1 9 8 6 7 . 2 8 4 7 8 . 9 2 0 - 1 1 . 6 3 5 6 0 0 . 8 3 3 16 .0 8 0 0 . 8 3 3 6 9 . 7 6 0 8 0 . 0 8 3 - 1 0 . . 3 2 3 8 1 1 . 1 5 6 17. .0 8 1 1 . 1 5 6 7 2 . 2 3 6 8 1 . . 1 16 - 8 . . 8 7 9 8 2 0 . 0 3 4 18 .0 8 2 0 . 0 3 4 7 4 . .7 13 8 2 . 0 0 3 - 7 . . 2 9 1 8 2 7 . 3 2 5 19 .0 8 2 7 . 3 2 5 7 7 . 1 8 9 8 2 . 7 3 3 - 5 . . 5 4 4 8 3 2 . 8 6 9 2 0 .0 8 3 2 . 8 6 9 7 9 . . 6 6 5 8 3 . 2 8 7 - 3. . 6 2 2 8 3 6 . 4 9 1 2 1 .0 8 3 6 . 4 9 1 8 2 . .14 1 8 3 . 6 4 9 - 1 . 5 0 8 8 3 8 . 0 0 0 22 .0 8 3 8 . . 0 0 0 8 4 . . 6 1 7 8 3 . 8 0 0 0. 8 1 7 8 3 7 . 1 8 3 2 3 .0 8 3 7 . . 1 8 3 8 7 . . 0 9 3 8 3 . .7 18 3. . 3 7 4 8 3 3 . 8 0 8 2 4 .0 8 3 3 . 8 0 8 8 9 . 5 6 9 8 3 . 3 8 1 .6. . 1 8 8 8 2 7 . 6 2 0 2 5 .0 8 2 7 . 6 2 0 9 2 . 0 4 5 8 2 . . 7 6 2 9 . 2 8 3 8 1 8 . . 3 3 7 2 6 .0 8 1 8 . . 3 3 7 9 4 , . 5 2 1 8 1 . . 8 3 4 1 2 . 6 6 7 8 0 5 . 6 5 0 2 7 .0 8 0 5 . . 6 5 0 9 6 : . 9 9 7 8 0 . . 5 6 5 16 . 4 3 2 7 8 9 . 2 1 8 2 8 .0 7 3 9 . 2 1 8 9 9 . 4 7 3 7 8 . 9 2 2 2 0 . 5 5 1 7 6 8 . 6 6 7 2 9 .0 7 6 6 . 6 6 7 1 0 1 . 9 4 9 7 6 . . 8 6 7 2 5 . 0 8 2 7 4 3 . . 5 8 4 3 0 .0 7 4 3 . . 5 8 4 1 0 4 . 4 2 5 7 4 . 3 5 8 3 0 . 0 6 7 7 1 3 . 5 1 8 31 .0 7 1 3 . . 5 1 8 1 0 6 . . 9 0 1 7 1 .  3 5 2 3 5 . 5 4 9 6 7 7 . 9 6 9 3 2 .0 6 7 7 . 9 6 9 1 0 9 . 3 7 7 6 7 . 7 9 7 4 1 . 5 8 0 6 3 6 . 3 S 8 3 3 .0 6 3 6 . . 3 8 8 1 1 1 . 8 5 3 6 3 . 6 3 9 4 8 . 2 1 4 5 8 8 . 1 7 4 3 4 .0 5 8 8 . . 1 7 4 1 1 4 . . 3 2 9 5 8 . . 8 1 7 5 5 . 5 1 2 5 3 2 . 6 6 2 3 5 . .0 5 3 2 . 6 6 2 1 1 6 . . 8 0 5 5 3 . 2 6 6 6 3 . 5 3 9 4 6 9 . 1 2 3 3 5 . .0 4 6 9 . 1 2 3 1 1 9 . . 2 8 1 4 6 . .9 12 7 2 . 3 6 9 3 9 6 . 7 5 3 3 7 . 0 3 9 5 . 7 5 3 1 2 1. . 7 5 7 3 9 . 6 7 5 8 2 . 0 8 2 3 1 4 . 6 7 1 3 8 .0 3 1 4 . 6 7 1 1 2 4 . 2 3 3 3 1 . . 4 6 7 9 2 . 7 6 6 2 2 1 . 9 0 5 3 9 .0 2 2 1 . 9 0 5 1 2 6 . . 7 0 9 2 2 . , 1 9 1 1 0 4 . 5 1 9 1 1 7 . 3 8 6 4 0 .0 1 1 7 . . 3 8 6 1 2 9 . . 1 8 5 1 1 . 7 3 9 1 1 7 . 4 4 7 - 0 . 0 6 1 232 LINEAR SENSITIVITY COEFICIENTS FOR VARIABLE (1 -F) 0.9000000 NPV IRR TCC ABSOLUTE 193.86804 0 . 44402 - 1 12.44034 RELATIVE 2.3496 1 1.89266 0 .14*15 LINEAR SENSITIVITY COEFICIENTS FOR VARIABLE F a r e - P = 0.0000030 ABSOLUTE RELATIVE NPV 4 1404720.00000 1.67270 IRR 94830.50000 1.34739 TCC 0.0 0.0 LINEAR SENSITIVITY COEFICIENTS FOR VARIABLE IRLTL = 0.1000000 A8S0LUTE RELATIVE NPV -1756.40B20 -2.36523 IRR -4.02276 -1.90523 TCC 0.0 0.0 LINEAR SENSITIVITY COEFICIENTS FOR VARIABLE I f f l -co= 0.0500000 ABSOLUTE RELATIVE NPV -493.68286 -0.33240 IRR -1 .13070 -0.26776 TCC -1877.44 14 1 0.13372 LINEAR SENSITIVITY COEFICIENTS FOR VARIABLE IndCos= -50.0000000 ABSOLUTE RELATIVE NPV -1.28596 -0.86586 IRR -0 .00295 -0.69746 TCC -4.55811 0.32464 232 11NE AR SENSITIVITY COEFICIENTS FOR VARIABLE (1 -F) = 0.9000000 NPV IRR TCC ABSOLUTE 193 . 86B04 0 .44402 - 1 12.44034 RELATIVE 2. 3496 1 1 .89266 0. 144 15 LINEAR SENSITIVITY COEFICIENTS FOR VARIABLE Fare -P= 0.00000 30 NPV IRR TCC ABSOLUTE 4 1404720.00000 94830.50000 0 .0 RELATIVE 1.67270 1.34739 0.0 LINEAR SENSITIVITY COEFICIENTS FOR VARIABLE IRLTL 0. 1000000 NPV IRR TCC ABSOLUTE - 1 756.40820 -4 .02276 0 .0 RELATIVE -2.36523 - 1 .90523 0.0 LINEAR SENSITIVITY COEFICIENTS FOR VARIABLE H R - c o = 0.0500000 NPV IRR TCC ABSOLUTE •493.68286 - 1 . 13070 -1877.44 14 1 RELATIVE -0.33240 -0.26776 0. 1 3372 LINEAR SENSITIVITY COEFICIENTS FOR VARIABLE lndCos= -50.0000000 NPV IRR TCC ABSOLUTE - 1 . 28596 -0 .00295 -4 . 5581 1 RELATIVE -0.86586 -0.69746 0. 32464 

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