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Sensitivity analysis of capital projects Poveda, David 1988

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SENSITIVITY  ANALYSIS  OF C A P I T A L  PROJECTS  by DAVID  A  THESIS  SUBMITTED  THE  POVEDA  IN  PARTIAL  REQUIREMENTS  F U L F I L M E N T OF  FOR T H E D E G R E E OF  MASTER OF A P P L I E D  SCIENCE  in THE  F A C U L T Y OF G R A D U A T E  CIVIL  We  accept to  THE  STUDIES  ENGINEERING  DEPARTMENT  this  as c o n f o r m i n g  thesis  the r e q u i r e d  UNIVERSITY  OF  NOVEMBER  © DAVID  standard  BRITISH  COLUMBIA  1988  POVEDA,  1988  In  presenting  degree  at the  this  thesis  in  University of  partial  fulfilment  of  of  department  this thesis for or  by  his  or  scholarly purposes may be her  representatives.  permission.  Department The University of British Columbia Vancouver, Canada  for  an advanced  Library shall make it  agree that permission for extensive  It  publication of this thesis for financial gain shall not  DE-6 (2/88)  requirements  British Columbia, I agree that the  freely available for reference and study. I further copying  the  is  granted  by the  understood  that  head of copying  my or  be allowed without my written  ABSTRACT  This  t h e s i s presents a very  economic and  the  evaluation Internal  measures. A analysis  to  the  the  Also,  represent  cash  are  analysis  project chemical  types  mathematical  of  the  t r e a t s most and  o i l and  an  Value  performance  perform  sensitivity  and  sensitivity  to  fund that  large can  be  given capital  used  i n each p r o j e c t  applicable  gas,  is  mining,  to  to  phase  a number  real estate  of and  projects.  a computer of  the  the  to  functions  These p r o f i l e s are including  Finally,  Present  model, emphasis  flow p r o f i l e s generated  process  in  i s presented. development  introduced.  thesis,  framework t o  bivariate  Net  u s e d as  f i n a n c i a l mechanisms a v a i l a b l e  projects.  model u s e f u l  projects.  Return are  theoretical  forms  During  capital  R a t e of  including  functional  of  generalized  the  been d e v e l o p e d  t h e o r e t i c a l concepts  example of  program c o n s t i t u t e s  p r o g r a m has  its application  a useful  teaching  i i  explored  in  i s presented.  tool.  which this This  Table  of  Contents  ABSTRACT  i i  LIST  OF T A B L E S  LIST  OF F I G U R E S  '..viii  ACKNOWLEGEMENTS  x  1.  THESIS  OBJECTIVES  AND B A S I C  CONCEPTS  THESIS  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  Introduction  2  1.2.2  Economic performance  1.2.3  Net P r e s e n t  1.3  OBJECTIVES  1  1.1  1.2.4  2.  . . . . . v i i  1  measures  Value  5  The d i s c o u n t  The d i s c o u n t i n g  The I n t e r n a l  Rate  of  rate method  Return  I M P L E M E N T A T I O N I N T H E COMPUTER PROGRAM  FINANCIAL AND CONSIDERATIONS  3  6 7 8 11  MACROECONOMIC . .  13  2.1  INTRODUCTION  13  2.2  SOURCES  14  2.3  2.4  OF F I N A N C I N G  2.2.1  Commercial  banks  2.2.2  Export  2.2.3  Development  2.2.4  Insurance  TYPES  OF LOANS  19  2.3.1  Subordinated loans  20  2.3.2  Unsecured  20  2.3.3  Secured  financing  15 agencies  ...17  banks  18  companies  19  loans  loans  G U A R A N T E E SCHEMES  21 22  iii  2.5  3.  TWO F I N A N C I N G  TECHNIQUES  23  2.5.1  Project  financing  23  2.5.2  Lease  2.6  INFLATION  2.7  OVERSEAS  financing  25  AND C A P I T A L B U D G E T I N G PROJECTS  AND F O R E I G N  2.7.1  Country  2.7.2  Macroeconomic r i s k  26  EXCHANGE RATES  ...29  risk  31 and exchange  rates  ....31  2.8  C A S H FLOWS G E N E R A T E D BY F I N A N C I A L  ARRANGEMENTS  2.9  I M P L E M E N T A T I O N ON T H E COMPUTER PROGRAM  35  2.9.1  Financial  35  2.9.2  Inflation  2.9.3  Foreign  mechanisms  .34  35  exchange  rate  C A S H FLOWS G E N E R A T E D I N C A P I T A L  36 PROJECTS  37  3.1  INTRODUCTION  37  3.2  O I L AND G A S I N D U S T R Y  38  3.2.1  Exploration  38  3.2.2  Economic e v a l u a t i o n  39  3.2.3  Field  40  3.2.4  Operation  41  REVENUES  41  EXPENSES  49  3.2.5 3.3  MINING  phase  development  Disposal  53  PROJECTS  3.3.1  Mine  3.3.2  Operation  54  development phase  55 56  Revenues  56  Expenses  59  iv  3.4  3.5  3.6 4.  REAL  ESTATE  PROJECTS  60  3.4.1  Feasibility  3.4.2  Design  61  3.4.3  Construction  61  3.4.4  A b s o r p t i o n phase  72  3.4.5  Operation  74  3.4.6  Disposal  77  PROCESS  analysis  60  INDUSTRIES  77  3.5.1  Operation  78  3.5.2  Expenses  80  I M P L E M E N T A T I O N ON T H E COMPUTER PROGRAM  SENSITIVITY  83  ANALYSIS  86  4.1  INTRODUCTION  86  4.2  PARAMETER E S T I M A T I O N  87  4.3  RISK  88  4.4  SENSITIVITY  4.5  UNIVARIATE  MANAGEMENT ANALYSIS  89  SENSITIVITY  4.5.1  Linear  4.5.2  Linear analysis: functions  ANALYSIS  analysis  91 the  case  of  implicit 95  4.6  EXACT  4.7  BIVARIATE SENSITIVITY  4.8  THREE VARIATIONS  OF S E N S I T I V I T Y  4.8.1  Break-even  analysis  4.8.2  Extreme  4.8.3  Sensitivity  4.9  90  ANALYSIS  CONCLUSION: ANALYSIS  97  point  THE  ANALYSIS  ...98 ANALYSIS  101  analysis  to  102  functional  BENEFITS  ..101  OF  forms  102  SENSITIVITY 103  v  5.  6.  7.  4.10 IMPLEMENTATION ON THE COMPUTER PROGRAM  104  THE COMPUTER PROGRAM  106  5.1  INTRODUCTION  106  5.2  DATA INPUT  5.3  BUILT-1N-FUNCTIONS  121  5.4  CALCULATION OF PERFORMANCE MEASURES  122  5.5  SENSITIVITY ANALYSIS  124  5.6  PLOTTING OF RESULTS  126  . 109  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  CONCLUSIONS AND FUTURE WORK 7.1  .158  THEORETICAL FRAMEWORK  7. 2  158  THE COMPUTER MODEL  158  BIBLIOGRAPHY  160  APPENDIX A  .170  APPENDIX B  . .  vi  216  L I S T OF  TABLES  Summary of m a t h e m a t i c a l to  represent  Structure Matrix flow  of v e c t o r  profiles  V  F: D a t a e l e m e n t s a s s o c i a t e d  F: D a t a e l e m e n t s  4 according  Forecasted Cash  flow  with  type  Matrix and  cash  f u n c t i o n s used  to the  constant  i n c o l u m n s 2, flow  type  construction costs  flows d e s c r i p t i o n  vii  and  parameters  3  L I S T OF FIGURES 1.  Production  r a t e of o i l w e l l s  43  2.  Exponential  3.  Production  4.  Truncated  5.  Beta  6.  Gamma f u n c t i o n  69  7.  Rayleigh  70  8.  Weibull  9.  Cash  d e c l i n e curves output  normal  44  o f a mine  58  functions  65  distribution  67  function function  flow  71  profile  generated  during  73  construction 10.  E x p l o n e n t i a l and s t e p  functions  11.  Example o f p r o d u c t  12.  Gompertz c u r v e  81  13.  Logistic  82  14.  Star diagram  life  76  cycle  79  curve f o r an h y p o t e t i c a l o i l  95  field 15.  Contour diagram  100  16.  Surface  diagram  100  17.  General  flow  107  18.  Menu f o r t h e s e l e c t i o n  c h a r t of t h e program of the p r o j e c t  112  of flow  type  112  type  114  phase 19.  Menu f o r t h e s e l e c t i o n (feasibility  20.  Menu  and  design)  f o r the s e l e c t i o n  (construction)  viii  of flow  21.  Menu f o r t h e 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 o f r e s u l t s computer  obtained with  the  131  program  24.  Primary  variables  132  25.  Information  26.  Economic p e r f o r m a n c e m e a s u r e s  135  27.  P e r i o d - b y - p e r i o d cash  135  about cash  flows  flow  in current  134  dollars 28.  Cash  flows  i n currunt d o l l a r s  29.  Sensitivity  30.  Exact  31.  Bivariate  32.  Sensitivity  coefficients  univariate  analysis  analysis  136 137 138 140  chart f o r the s i m p l i f i e d  141  example 33.  Plot  of the r e s u l t s  analysis 34.  Plot  of the exact  142  of the exact  143  (NPV)  of the r e s u l t s  a n a l y s i s (IRR) 35.  Sequencing  a n d d u r a t i o n o f t h e work  147  packages 36.  General  schedule  37.  Subroutine  of the p r o j e c t  VARIA  150 157  ix  ACKNOWLEGEMENTS  I.want  to express  supervised the with  this  improvement a  part  preparation  my g r a t i t u d e t o D r .  thesis, of time  of t h i s  Alan  f o r h i s valuable  i t s content, research  a n d who  D. R u s s e l l  contributions  to  also provided  me  assistantship  during  the  work.  My t h a n k s t o a l l t h e p r o f f e s o r s , c o l l e g u e s who h e l p e d  who  and supported  me d u r i n g  x  my s t a y  and  i n Canada.  friends  To  my  mother  xi  CHAPTER  1 . THESIS OBJECTIVES AND BASIC CONCEPTS  1.1 THESIS OBJECTIVES The  objectives  development  of  of  a  this  very  evaluation  of c a p i t a l  attributes  required  phase and  their  general  projects;  by c a s h  sensitivity  Net IRR.  critera  for  Present Value, Both  generated  are  rate.  NPV, and  The  type of f u n c t i o n a l (either  discrete  external calculate  or  when t h e u n r e c o v e r e d  the  project  mathematical  review  evaluation  of  of t h e  issue of  the  phase, e i t h e r the  Rate  user  a  balance  of  are  Return,  cash  flows  continuous  to t r e a t flow  any  profiles  a reinvestment  prescribed  of Return  of  at a  d e s c r i b e the cash  be  a project  Rate  discounting  r a t e can  the I n t e r n a l  of  implementation  continuous). Also,  investment)  of  the I n t e r n a l  by  to  economic  f o r each  form  4)the  model e n a b l e s  form  the  program.  d u r i n g each p r o j e c t  or d i s c r e t e  for  1)The  identification  the  and  economic  treated  model  3)a c o m p l e t e  analysis;  fourfold:  profiles  on  g e n e r a l model i n a computer The  are  2)the  flow  statement  e x p r e s s i o n s or f u n c t i o n s ; of  thesis  in  f o r these  the p r o j e c t  (or  order  to  situations  a t any  stage  goes t o z e r o o r become p o s i t i v e . In o r d e r t o i d e n t i f y that  may be used  to  express cash  of p r o j e c t s a r e s t u d i e d , and  gas  industry,  some u s e f u l m a t h e m a t i c a l  namely mining  d e v e l o p m e n t s and c h e m i c a l  flow p r o f i l e s ,  those encountered activities,  and p r o c e s s  1  functions  four  types  i n the o i l  real  industries.  estate Each  of  2  them i s broken down the  kind  of  mathematical f l o w . These The  into  i t s basic  activities function  functions  third  framework t o  undertaken  i s suggested  objective perform  sensitivity  literature  in  of  risk  analysis  in capital  counterpart discussed,  to  the  and an  note d e s c r i b i n g and  how  they  first  a cash  theoretical investment  and  related  step  i n the a s s e s m e n t  I t s extension forms  to  topics.  bivariate  i s developed.  i s d e v e l o p e d as a p r a c t i c a l  theoretical  concepts  previously i s given.  t h e o r e t i c a l chapters, a  important are  the  of  example o f i t s a p p l i c a t i o n  t h e most  phase,  table.  analysis  to functional  of t h e f o u r  to  r e v i e w o f t h e the a v a i l a b l e  a computer program  end of each  treated  projects.  each  a complete  economics  i s a useful  and s e n s i t i v i t y  Finally,  the  engineering  analysis  in a  i s to state  based on a t h r o u g h o u t  in  for treating  a r e summarized  proposals,  Sensitivity  p h a s e s and a c c o r d i n g  aspects  implemented  of the  in  the  At  brief theory  computer  program, a r e p r e s e n t e d .  1.2  1.2.1  ECONOMIC EVALUATION OF PROJECTS  INTRODUCTION Governments and p r i v a t e  involved capital  in  the  projects,  demand f o r  goods  development. Given  evaluation undertaken  corporations and  the large  continuously  implementation  in order  and s e r v i c e s ,  are  and  to to  of  satisfy  large public  promote  economic  amounts of human and  monetary  3  resources  committed  carefully  p l a n n e d and  qualitative In  to  and q u a n t i t a t i v e  quantitative  portion  projects,  evaluated,  t h i s chapter,  projects  such  taking  should  i n t o account  be both  considerations.  the b a s i c of t h e  they  concepts  economic  dealing  evaluation  with  of  the  capital  i s presented.  1.2.2 ECONOMIC PERFORMANCE MEASURES Capital  investment d e c i s i o n s ,  portion,  are  criteria  c a l l e d economic p e r f o r m a n c e m e a s u r e s . A p e r f o r m a n c e  measure  is  information  about  as  accept-reject  in  decision  exclusive  According  one  index  several  containing and  or  profit  simple,  after  uncertainty  order  to order  proceed to  [46],  there  a r e over  an the  between  20 "methods"  advantages  and  because they  are  the importance of  t h e t i m e , o r emphasize  with  already  the  of  a l l of which a r e s e r i o u s  own p a r t i c u l a r  or e m p h a s i z e  associated to  with  select  project,  established  capital  the importance  i n t e r e s t r e p a y m e n t s , o r emphasize  modifications  compared  or a s i m i l a r index of  in  have t h e i r  i t s v a l u e over  disbursements  I t i s then  d i s a d v a n t a g e s . They may have been p r o p o s e d  and  particular  point  f o r c a p i t a l investments,  particularly  possible  projects.  t o Rose  p r o p o s a l s which  of  opportunity.  cutoff  project  on  of r e c e i p t s  the investment  alternative  evaluation  an  a series  a predefined  mutually  based  defined  representing against  usually  at l e a s t the q u a n t i t a t i v e  the r i s k  or they  methods  of and  may  be  intended  to  4  overcome s h o r t c o m i n g s .  The s u b j e c t  of e v a l u a t i o n  ambiguous due t o t h e many names g i v e n p e r f o r m a n c e measure and t h e that  c a n be a p p l i e d , e a c h  these  methods  period;  a r e : Estimated  Return  investment;  on  Return  total on  I n v e s t o r ' s method;  Machine  return;  rate Net  of r e t u r n present  equivalent;  Net  future  equivalent;  the  annual  uniform  annual  payback  corrections  period  or  Return Return  and A l l i e d  payoff average  on  equity; Institute  method; P r o f i t a b i l i t y  or  value  cash  present or f u t u r e  equivalent  flow  worth  c o s t method and b e n e f i t - c o s t  index; rate  or  worth  sum, o r  of  on  Products  or d i s c o u n t e d  value  or  i n a new name. Some  employed;  -MAPI- method; P r o j e c t b a l a n c e Internal  o f minor  investment;  capital  made  t o t h e same method  multitude  resulting  is  present  or  annual ratio,  of  future  cost  or  t o name a  f ew. In as  references [30],  in several  [13],  the  techniques, are  details their  i n The  E n g i n e e r i n g Economist  concerning  approach,  these  advantages  and and  well  journal  some  other  disadvantages,  documented. Some  of  situations  but  conflicting by  papers  [ 4 5 ] , [ 4 6 ] , [ 5 1 ] and [53] as  arises  techniques  unsuitable for  various  investment  decision  has  the  convenient  complex  techniques.  on which c r i t e r i o n  selection  are  c o n c l u s i o n s can be drawn  employing  capital  the  to  ones.  for In  simple  addition,  for a particular Therefore, be made,  decision  case  whenever the  problem  i s t o be b a s e d .  of a method may depend on t h e s i z e  and type  a  The  of the  5  investment,  or  However, two  specific  importance most  simply,  i n the  adequate  engineering  on  performance  literature,  basis  of  projects.  Internal  Rate  of R e t u r n  exercise  1.2.3  PRESENT VALUE  NET The  i d e a s of  may  interest,  b r o a d l y documented  rely  upon  concept  standard procedures calculate  cash  discount  rate.  The  and  equivalent  specific  flow  present  of  profiles  at  a  as t h e a l g e b r a i c  individual  cash  It represents  equivalent equal  flows  receipts  Value sum  Net  Present  makes i t s u i t a b l e  are  literature. of  generated  in  Value  the  the p r o j e c t  during  the  of t h a t  a number  is  for or  the  the  of  the  by which  the  or  cash  flow  as an economic p e r f o r m a n c e  to  simply  life  exceed  of  and  equivalent  the b e g i n n i n g of  flow stream  has  time  interest  the e q u i v a l e n t amount  of a c a s h  money, developed  point  is  They  of the p r e s e n t worth of  the e q u i v a l e n t d i s b u r s e m e n t s The  discounting  been  flow  of  known the  selected  zero, d e f i n i n g  calculated  project.  have any  Present  and  for  value  at  v e n t u r e . The  adopted  the  time  a cash  of  thesis.  amounts  time  most commonly  are  in  formulas  s i n g l e amount a t Net  the  worth of  evaluation  e q u i v a l e n c e and  known and  the  P r e s e n t V a l u e NPV  Both  in this  primary  c o n s i d e r e d as  and  of R e t u r n ,  well  the  be  the Net  IRR.  presented  preferences.  measures a r e g i v e n  and  They a r e  modelling  sponsor's  comparison  the D i s c o u n t e d Cash Flow Rate as  the  fail  stream.  features measure.  to  that First,  6  it  considers  discount  the  rate  concentrates  time  value  selected  for  the e q u i v a l e n t  of  money  i t s calculation.  value  o f any c a s h  a s i n g l e index a t a p a r t i c u l a r p o i n t single  unique  discount cash  value  rate  flow  of the  used,  disadvantage  of  being  judgement about  NPV  no m a t t e r  pattern.  according  Second,  flow  i n time  It  is  claimed  (t=0).  an  absolute  the c o n v e n i e n c e  number,  of t h e  it  Third, a  with  be t h e that  the  stream i n  i s associated  what may  to  each  investment  is  has  so no  the  relative  investment  can  be  made. There a r e two s p e c i f i c when u s i n g selection  NPV as  The d i s c o u n t  should  be  considered  m e a s u r e . They  are  r a t e , and t h e d i s c o u n t i n g  method.  w o r t h of a s e r i e s of c a s h  t o be c a l c u l a t e d , a d i s c o u n t projects,  this  rate  rate  has t o be  flows i s  prescribed.  i s t h e Minimum  Acceptable  (or A t t r a c t i v e ) Rate of R e t u r n , MARR. I t i s u s u a l l y result the of  of a  project  p o l i c y d e c i s i o n made  that  r a t e of r e t u r n The as  a  that  represents  that  will  since  yield  t o type and  which t h e he has  a "floor"  be c o n s i d e r e d  minimum a c c e p t a b l e  rate at  invest,  by t h e management  i n t h e p r o c e s s of i d e n t i f y i n g a t a r g e t  interest  rate  a large  of r i s k  rate  of rate  lowest  can be v i e w e d  sponsor  number  of  can  always  opportunities  i t may v a r y  involved  or  the  acceptable.  of r e t u r n  project's  such r e t u r n . However, level  the  rate  When t h e p r e s e n t  In c a p i t a l  that  the performance  of t h e d i s c o u n t  issues  i n each  according particular  7 venture.  Thus,  investment  whenever any  money  i s committed  p r o p o s a l , an o p p o r t u n i t y t o i n v e s t  t h e MARR has been  is  sometimes c o n s i d e r e d t o be an " o p p o r t u n i t y c o s t " . The o f a MARR i s b a s i c a l l y  One method available rate  that  for selecting for  complete  a management  and  to identify  i f the funds  d i s c u s s i o n about  s h o u l d be made  in  reason,  selecting  t h e MARR  decision.  i t i s t o examine t h e  investment  t h a t c a n be e a r n e d  them. A  For this  t h a t money  at  selection  foregone.  t o an  proposals  the  maximum  a r e not i n v e s t e d i n the considerations  t h e MARR c a n be  found  i n Thuesen and F a b r y c k y [ 5 3 ] . The d i s c o u n t i n g method The  second  the Net P r e s e n t that  should  aspect Value  be  to consider deals with  used,  namely  the type discrete  compounding. The v a r i o u s e l e m e n t s flow  stream  have  occurrence.  For  disbursements as once a  appreciably instance,  y e a r . On  occur  f r e q u e n t l y enough  have d i f f e r e n t  analysis type  investment  were t o  cash  and  as i n f r e q u e n t l y  a product,  so t h a t t h e y  proposals  as  continuous. cash  occurrence.  realistic  of d i s c o u n t i n g a p p r o p r i a t e  for  generally  may be viewed  include  f r e q u e n c i e s of  of  lease  hand, d i s b u r s e m e n t s  sales of  be done as  a  frequency  t a x payments  transactions that are v i r t u a l l y Most  that  from  continuous  t h a t comprise  different  the other  and r e c e i p t s  of d i s c o u n t i n g or  a r e o u t l a y s t h a t may o c c u r  labor  cash  i n the c a l c u l a t i o n of  elements I f the  as p o s s i b l e t h e  f o r each  f l o w would  be  8  used.  However,  problems  and  inconsistent employed simplify  in  choice  the  the  calculated  (up t o 12  rate  In  of  return  author  and suggests cash  just  provides  that  likely  in  to  projects is  i n cases above  used when just  an example o f  such  in projects  ones  which  or  f l o w s ought  and t h e f r e q u e n t  for  method t h a t  is  to  specified,  i s not  decision,  usually  i s used.  o r 15%) i s  d e c i s i o n . However,  are  order  in projects  method  the accept-reject  MARR, the i n f r e q u e n t discretely  out that  many  technique  rough e s t i m a t e s  MARR, t h e d i s c o u n t i n g  reverse  a situation  in  one o f two c o n v e n t i o n s  the a c c e p t - r e j e c t  may  complicate  evaluation.  discounting  below t h e MARR. T h i s  1.2.4  refinements  points  low MARR  with a high  hopelessly  economic  [20],  of a  may  the r e l a t i v e l y  the process,  a relatively  affect  such  with  Heebink  the  this  having  t o be  a  high  discounted  continuously.  THE INTERNAL RATE OF RETURN The  internal  measure w i d e l y investments.  used  to z e r o .  defined  The  i s another evaluation  as t h e d i s c o u n t  project  therefore  i s accepted  of  capital  rate  rate  IRR i s  that  receipts  making t h e NPV  when t h e  t o t h e Minimum a t t r a c t i v e  otherwise.  performance  w o r t h o f a l l d i s b u r s e m e n t s and  with the p r o j e c t ,  than o r e q u a l rejected  of Return  i n t h e economic  I t i s simply  equates the present associated  Rate  equal greater  of r e t u r n ,  and  9  Since  the  associated  early  with  1960s,  the  calculation  d i s c u s s e d , by many a u t h o r s , r a t e and t h e single  cash  existence  flow  contradictory conflict  Briefly,  is  life  as  if  the c a s e of p u r e  meaning  for a  open  of  et  and  a l [52].  by c o n s i d e r i n g The  the p r o j e c t s  during  has  and  has f u n d s committed n  periods  a  investment  of t h e n p e r i o d s ,  the  in  return  Teichroev  each  stated  "internal"  of  of n p e r i o d s .  investments,  been  of r e i n v e s t m e n t  is still  be e x p l a i n e d  of  on t h e p r o j e c t  totally  by  i f the sponsor some  have  i n v e s t m e n t s may be e i t h e r  the sponsor  in i t during  during  independent  and  t h e r e s t of t h e  has  is in an  periods.  t h e i n t e r n a l r a t e of r e t u r n its definition,  t o the p r o j e c t ,  is  unique  meaning t h a t  i t is  from t h e r a t e a t w h i c h t h e s p o n s o r c a n  reinvest  capital. For  The  pure  as mixed  project  rates  IRR  by d i f f e r e n t a u t h o r s . The  that  defined  w i t h an economic  does have t h e  his  as  can  "overdraft"  and  are held  the d i s t i n c t i o n  designated  In  multiple  complications  the  s t r e a m . The d i s c u s s i o n  "mixed"  funds committed  the  of  view p o i n t s  designated  of  namely t h e i s s u e s  a r i s e s from t h e f a c t  " p u r e " or  project  two t h e o r e t i c a l  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 .  fundamental  earned  each  meaning of  period  investment  so t h a t  investment  life  committed  to  compounded a t  on  the  Then,  project,  the r a t e  that  rate  unrecovered  the remaining  i s zero. the  IRR i s  of  of  the  b a l a n c e a t t h e end of  the  if  the  of r e t u r n .  balance  interest  the sponsor investment On t h e  has  funds  balance  other  hand,  is if  10 there  i s an o v e r d r a f t  compounded when  this  at the  rate  overdraft  reinvestment  rate  or  (Mao  correct  reinvestment  much  and  been  controversial among effect  that  calculation these  this  measure: The  issue,  question  second  investments. and of a  and  m-2k It  number may  that  be a s  real  the p o s s i b l e  many  changes, positive  have  the  on  In t h e i r persist  be  opinion  concerning  the paper,  in  the to  performance  involved  of m u l t i p l e in  o f t h e IRR where  k  of  an a l t e r n a t i v e  n  rates  the  values  return. of  mixed solving  i s t h e number o f  periods  of signs  and m  sign  is a positive  or stated  of  cases  i s obtained  rule  positive  i n t h e IRR  by  coefficients  where  to  return.  The D e s c a r t e s '  roots  of sign  of  how  d i f f e r e n t approaches  present  polynomial  with  positive means  also  The s o l u t i o n  the investment. polynomial  rate  existence  is  nth degree  differences  propose  the  capital.  continue  of Return.  the  that  o u t , no m a t t e r  should  theoretical complication  i s the  situation  why  the  several  of  differences  or  Rate  summarize  the external  calculation This  clarify  cost  and a u t h o r s  has  of the I n t e r n a l  reinvestment solve  professionals  sponsor  and  claim  there  dogmatic  reinvestment  authors  point  or argued,  and sometimes  qualified  [33]  be  is called  rate  [23])  Howe  should  by t h e  rate  i s the sponsor's  and Raper  written  This  interest  [31],  rate  the balance  c a n be e a r n e d  external  Knoll  Montgomery  has  that  i s reinvested.  authors  As  on t h e p r o j e c t ,  roots  states changes  integer cannot  or  exceed  i n a d i f f e r e n t way, of  IRR a s  there  are  that has zero. the there sign  11  changes the  in  cases  them  the where  should  return,  cash  be  or  there  reduce  to  by  using  IRR  The  an  that a  In  nth  can  performance Rate  obtained  time using  zero  [36],  of  as  of  IRR  of  be  claims  that  in  of  return,  none  of  rate  of  measure  cash sign  of  flow,  and  changes  rate,  the  proposes  in a  therefore  cash  a  flow  obtaining  a  IRR  However,  generally  requires  a  since  various on  the  i t i s the  solution  mathematical  methods  roots  that  satisfy  such  used.  IN  THE  program measures Return the  COMPUTER developed are  and  the  Total  algebraic cash  sum  flows  PROGRAM as  part  Net  of  this  Present  Construction of  the  associated  thesis,  Value, Cost.  present with  The  worth  the  the NPV at  project,  discounting.  i s computed  i f the  the  converge  a l l the  whereby  specified  of  polynomial,  continuous The  the  [36]  rates  suitable  of  procedure.  degree  computer  Internal  a  reinvestment  IMPLEMENTATION  the  is  a  systematically  the  multiple  number  computation  polynomial  1.3  the  Newnan  value.  trial-and-error of  are  attractiveness  to  single  stream.  considered  method one  flow  an net  using  external cash  the  method  investment  flow  stream  has  proposed rate more  by  Newnan  should than  be  one  sign  total  area  change. Total under  the  expenditure  Construction curve  Cost  defining  function  plus  is calculated  the the  as  the  current  dollar  construction  interest  on  construction  the  1  loan.  2  2.  CHAPTER  FINANCIAL  2.1  INTRODUCTION  One  o f t h e key i s s u e s  investments of  f o r the  before  collected. and  from  and  under  involved  the  This  whom  large  task  kind  of  by  of guarantees,  capital  mechanisms  that  the  of determining  be b o r r o w e d ,  of  and  monies  generated  consists  i t should  what  of the sources  amounts  revenues  CONSIDERATIONS  in the evaluation  i s the definition  financing  spent  AND MACROECONOMIC  must  project  how much  a t what  are money  interest  agreements  and  be  rate  payback  structures. Generally, schemes, from  where  currencies,  fixed)  and  with  impossible  simple  basic  i t s primary  separately. each  of  sources  employed  different  chapter,  components  in  traditional  two  the problem  financing  capital  lending,  and  presented.  and  are presented.  13  that that  They  are  They  down  to  include schemes.  are differ the  a  analyzed  relevant  and guarantee  techniques  projects  makes into  them  the considerations  of loans  fact  analysis  of  in  (often,  c a n be b r o k e n  each  be  credits  rates  This  the f i n a n c i a l  will  types  interest  financial  institutions  providing  maturities.  components  of financing,  Additionally,  different  However,  In t h i s  these  with  complex  and f i n a n c i a l  are involved,  to simplify  model.  require  lending  countries  almost  into  projects  several  different  different not  large  usually from project  1 4  financing  technique  Two during  other  rates  overseas  will  almost  activity.  on  domestic  material)  2.2  and  that  shop needs  in  rates.  interaction  system. in  The  any  strong  of overseas  of  first  economic  impact  projects,  resources  on  the  and  even  (monetary  with  can look  around  for  the  or  help  With  to  the best  of the investment.  during  cover  the  of lending  of  the to  operation  of  loans  feasibility requirements  a v a i l a b l e , the i n s t i t u t i o n s and  package  of long  be  operational  The  already  to  analysis the  the f i n a n c i a l  financial Sources  sponsor  and p r i n c i p a l  information  a t the spectrum  has  feasibility  institutions.  to define  this  The  generated  enough  considered for  project  viable.  the i n t e r e s t s  lending  also  of financing  out a complete  the revenues  t o repay  will  nature  financially  are large  the p r o j e c t .  sponsor  t o exchange  present  imported  introduced  of the  a very  opportunity,  and  the venture  negotiated  of  have  when  has to c a r r y  demonstrate  analysis  may  be  namely,  FINANCING  investment  costs  risks  the macroeconomic  of t h e exact  commercially  of  discussed,  attention  t h e outcome  considered  a r e used.  Irrespective  project  are also  inevitably  ones,  be c a r e f u l l y  additional  and o p e r a t i o n  SOURCES OF  any  of  The s e c o n d  implementation  should  special  are  mechanisms  that  the  with  factors  financing.  evaluation  and  projects  two  complex one  variables  the economic  inflation  These  and l e a s e  term  that  meets  the  financing  for  15 capital  projects  agencies,  2.2.1  include  development  COMMERCIAL Private  financial  commercial  borrowers,  in  purchasing  power,  potential likelihood  of  with  by  are  on  means  They  currency  used,  large,  usually the  late  As  grace  to  transfer  current  amount  period,  long  other that  like  greater  the  the  of  returns.  .The  and  a  cheap  project. projects  debt  financing should  alternative, be  carefully of  any  interest  repayment  cost  rate,  schemes,  overruns,  commissions  on  are  negotiated  package  loan, and  future the  size  term  to  among  loan,  financial  financing  unused  and funds,  like. period  projects,  According early  of  savers  funds  medium  drawdown  overseas  and  bank  risk  of  important  1960s  of  those  and  the  from  risk-adjusted  issues  the  money  promise  and  most  required.  of  of  i n any  repayment  the  created  small  charges  and  private  commercial  medium  the  fees  However,  companies.  general,  of  level  key  are  loan  as  a  the  guarantees,  study  financing  in  allocate  designing  related  most  basis  of  additional  regarded  the  banks.  project.  export  (and  the  to  with  when  required  for  and  several  analyzed  insurance  form  a l l domestic,  private  there  the  obtaining  decreases Almost  in  are  exchange  users  and  banks  institutions) power  financed  banks  banks,  BANKS  purchasing  one,  commercial  to 1970s,  and  interest  variables  to  rate  may  consider.  international financing Radetzky project  and  Zorn  finance  [42],  loans  be For is in were  16 available 1970s, to  for  the  seven  periods  typical years,  international reactivation pushed  banks  be  loan  of  the  economy.  These  with  investment private  project  spread paid  by  with  a  US the  small  Rate.  charged  Eurocurrency to  borrowers strength  by of  the  Finally,  in  loan-to-equity loans.  Such  the  The  US  risk some  ratios  liquidity  in  the  the the  and  the  general 1980s  years.  It  of  of  individual of  state  risk  determinants  has  should,  location  general  level  be  the  of  the  associated  i n any  decision  US  loans  involved  London  are  between  banks.  rate  The  involved  in  the  in  project,  are  Libor  rate  or  offering  the  rate,  banks  i s the  interest  in  the rate  corporate  will  vary  with  the  with  the  banker's  project.  require  intended  a  rates  major  and  banks  requirements  the  the at  creditworthy  cases, the  over  spread  demand  and  offered  Interbank  most  reflecting  borrowing  (0.5-2%)  and  loan  of  loans  Prime  bank  floating,  cost  loans  overall of  to  own  largest  major  the  Usually,  is  in  and  five  attitudes  type  late  to  during 10  the  reduced  to  commercial  percentage  market. the  perception  the  key  the  bank's  Libor  due  and  the  tend  borrower.  fixed  charged  the  was  In  institutions.  for  financing  the  rate  8  that  are  lending  rates  between  Prime  to  factors define  years.  period  economy  to  and  15  increasing  p o t e n t i a l borrower  Interest in  world  according  the  or  markets  i n mind  project,  made by  the  maturities  kept  12  repayment  financial  differ,  the  to  although  average  however,  up  in to  given order  levels to  obtain  of  approve a  higher  17  commitment the  lender.  loans in  of  that  In  (Canada, provide  of  the  by  equipment  given  and  financing mechanism. in  this  The  (Eximbank)  projects  directly,  provided  costs  of  through  by  US  the and  Corporation.  The  US,  export will  are  of  from  the  In  They finance  in  those  o i l  and  this  type  machinery  and  the  covered  are  this  guarantee  discussed  later  Export-Import  for  Private a US  it  large  scale  half  which  the  local  remaining  goods  bank  Normally,  Additionally,  by  repayment  addition,  credits.  capital the  long  government  financing  banks. US  a  the  ensure  agency,  loans  to  Mining,  fairly  schemes  type  commercial  companion  US).  produced  of  rates.  requires  projects employing a  involve  the  this  value  the  projects.  guarantee  In  and  benefit  by  countries  intended  country.  industries  normally  of  bank  projects  created  UK  equipment  second  interest  half  is  in a  fixed  provides  credits"  and  credits  provides  by  several  mining  banks  Japan,  considerable  overall  finance  assumed  industrialized  Italy,  in those  chapter.  to  western  export  scheme  s t r u c t u r e of  basically  process  required  risk  AGENCIES  goods  the  the  presented.  Germany,  importers  Usually, periods  is  are  of  p r o j e c t s and credit,  the  s o - c a l l e d "export  acquisition  countries  reducing  [42],  seven  France,  so  negotiated  countries  agencies  governments  of  been  EXPORT F I N A N C I N G These  gas  sponsor,'  reference  have  developing  2.2.2  the  the  can  Export  be  financed Financing  government  agency  18  guarantee.  2.2.3  DEVELOPMENT To  to  help  promote  some  BANKS  provide  the  development  banks,  that  not  institutions. systems, process  The  loans  to long  rates;  they are  are  three  1.  The  term  t y p e s of group,  established  facilitate  provision  planning  lies  and  continuously Regional  i n the  being  mining,  job  creation.  market with  of  t h e end long  fact  nation  such  generally  or  banks  are  concessionary  of  World  There  financial War  capital  world  provide and  for  much  development  in third  II  countries.  i t provides  agricultural  as  banks:  o f member  f o r economic  and  perceived  governments.  term  that  undertaken  development  considered  at  in  is a multinational  development  financing  manufacturing, projects  and  mainly  development  which  communication  the  below  financing  facilities  institutions  of  investments  to  directly  institution  reconstruction  2.  at a  regions,  variety  private dams,  lies  and  a  to  infrastructure  these  negotiated  Bank  importance  include  advantages  and  by  required  backward  i s directed  value  by  resources  established  funded  i m p o r t e d goods  different  World  be  whose  offered  medium  lending  other  social of  have  projects  and  industries  substitution  whose  financial  economically  countries  These  and  of  otherwise  roads  political  huge  development  industrialized  would  the  of  to the Its the  projects  countries. funds  for  infrastructure  important to the development  of  the  19  countries  i n an  Investment the 3.  Bank,  African  the  development  industry  or  2.2.4  basic  region  In  many  companies stable  and  companies  the  major  more (as  lending  can  clearly  projects  that  usually  years  the  higher the  than  that  companies  are  2.3  OF  TYPES  Loans  and  unsecured  to  regional  European  this on  but  Bank  and  category.  a  particular  they  have  the  banks.  financial  financial  In  a  these  long  heavy  particular,  where  to  the  of  these  deposits highly  term  advantageous  carry  insurance  structure  banks  allows  very  be  countries,  capital.  terms)  are liquid  lending. large  Such  capital  debt  service  burden  in  of  financing  has  the  operations. hand, the  this  type  interest  offered  by  guarantee  extremely  the  rate  structure  general  agreements  banking  demanded  tends  to  system, by  be and  insurance  stringent.  LOANS  obtained  projects  of  that  security  country,  of  consider  other  disadvantage  under  industrialized  short to  On  a  The  Development  concentrate  the  predictable  opposed  relatively  early  as  sources  corporations  the  within  fall  area.  COMPANIES  of  are  Bank  banks  functions  INSURANCE  geographic  Inter-American  Development  National  same  for  specific  fall loans  by  investors  into  three  and  in  order  categories:  secured  loans.  to  finance  Subordinated They  will  be  capital loans, briefly  20  described. in  A complete  SUBORDINATED A  this  topic  may  be  found  capital  borrowing  party  lenders.  the  owner  of  subordinated  trade  interested  agree  be  to  a  the  interest,  other  sponsor  may  may  phase  a  extent  and  a  to  get  government  the  parties  circumstances  of p r i n c i p a l ,  subordination to which  supplier  trying  or  the  built.  repayment  i s simply  and a  of  repayment  description  the loan  i s subordinated.  contain  debt  by t h e  t o repay,  for  covenants and  Because  the lender  t o t h e most  a  backed  and not secured  leases  incur.  fails  a user  senior  case,  project,  i s negotiated,  as c o l l a t e r a l  loans,  which  borrower only  debt  acting  agreement  this  to  of  LOANS  of the borrower  assets  with  of  and c r e d i t o r s  UNSECURED  credit  and  including term  Unsecured  loan  precise  sponsor  support  In  credits,  loan  by a  will  the  i t s operational  subordinated  subordination,  2.3.2  which  i n g e t t i n g the p r o j e c t  on  lenders  used  third  project  When  i s often  a project  can  providing  loan  to  from  sponsor  the  LOANS  subordinated  provide  of  of  Navitt [35].  2.3.1  of  treatment  may  of  debt  creditworthy  the loan. that  An  limit  unsecured companies  loans with  pool  unsecured  which  of any  h i s money  or  investment  obligations  the lack  recover  large  by a n y a s s e t  general  the  collateral i n case  the  are available  long  records of  21  successful  operations  lenders.  Therefore,  projects  having  owners with or  and  the  often  managers  financial  of  risk.  significant it  will  meaning  who  In  of  i t will  be  lease  o b l i g a t i o n s and  2.3.3  SECURED Secured  used  loans  in c a p i t a l  Such  property fully  project  and are  good  to  by  to  the  capital  the  equity  for projects  secured a  reputation  meet  project  to  for  sponsors,  sufficient  loans  the  only  those  alternative  similar  the  to  take  tends  loans  large  to  or  raise  leasing,  subordinated  security  are  loan,  protection  of  loans.  most  loan,  amount for  the  common  assets  borrower  value  and  can  as  due the  be  borrowed,  commercial considered  in  a of  and  repayment; and the  the  are  readily  under value  of  type  real  the  the  means  that  to  property,  the  any  secure  cash.  personal  contract.  collateral  financial lending  to  converted  lender  however,  financing  which  take-or-pay the  of  p r o j e c t , or  used  collateral,  c o n s i s t s of  payments  i t s value  borrower  have  collateral  the  where  secured  of  marketable  secured  exceeds upon  assets  and  where  provided  an  p r o j e c t s . The  debt.  Acceptable  as  junior  are  in possession  are  for  their  LOANS  other  they  and  with  available  established a  capital  purpose  is  risk,  Unsecured  situations  a  type  been  sponsors  amounts  that  have  relationships  low  have  project. by  serve  loan  community,  loans  the  provided  equity  this  good  relatively  subordinated  capital  and  In  equals  relies  a or  primarily  reputation viability  decision since  of of  the the  banks  22  will  not  lend  have  to  seize  collect  the  lenders  as  event  2.4  a  and  the  of  are  the  for  the  owner  the  party  financing  as  to  repayment  i n the  loan not  repaid  during  a  parent  In  services, of  unlikely  the  loans  or  and  rule,  routine  of  normal  project of  also  act  both  as  they  loyalties  and  of  risk  risks parties  are  in  the  the  capital  usually  venture,  and  but  the third  users  loan  and  also  and  know-how  and  involved  risk the  as  new in  well  value  of  payments.  In  coverage  they  where  investments  war  cover  restrict  modernization  Investment  involved  sellers,  casualty  expansions,,  .  lowest  guarantors.  equity  schemes  the  provide  the  those  specific  debt  suppliers,  for  interested  directly  company  level  to  directly  some c a s e s ,  major  the  to  present  certain  projects  political,  the  investments  since  of  like  cover  of  most  shifting  Guarantors  as  God.  c r e d i t s and  become  project,  commercial,  required,  of  permit  governments  cover  by  institutions.  against  general,  regarded  is  lending  Guarantees  licences,  to  interest  approve  the  institutions  acts  order  to  project.  interested  in  which  the  acting  to  security  is  to  desire  of  assets  expect  sponsors  schemes  operation  secured  they  project  guarantee  no  where  project.  risk  have  company  SCHEMES  and  to  or  the  The  loan  possible  who  sell  willing  investments  inherent  project  protection  GUARANTEE  Lenders  a  loan.  that  operation  to  do  to  not,  new as  technology such  a is  projects  23  is  higher  normally the  than  include  covered  Private  the  investment  Investment company  projects  to  investment coverage  a  which  period  of  12  after  two  indirect, these be  types  2.5  TWO  2.5.1  obligations  as  to to  contingent  FINANCING  the  technique  new  in order  as  of  and  mining original  eliminates  guarantee  sufficient  i t to  implied. as  be as  A  party; is  to  time  to and  not  a l l  to  the  support  financed.  detailed  specific and  responsibility  guaranteed  the  and  guarantees,  Guarantees may  be  description  of  guarantee  and  schemes  may  [47].  TECHNIQUES  FINANCING  became  the  and  so-called  established  projects.  projects  generation  private  the  Direct  the  the  provide  [35]  1960s,  capital  of  amount  well  years  assumes  enable  or  of  of  Overseas  largest  i t s coverage  guarantees:  which  to  in references  In  large  in order  PROJECT  of  the  in  value  years.  guarantor  variations  found  20  the  limited  the  percent  a  reduces  the  schemes  i n s t a n c e , the  50  guarantees,  be  For  of  Limited  may  time.  maximum  a l l  transaction  over  guarantee down  US,  perform  encompassing  for writing  i n the  entirely are  addition,  C o r p o r a t i o n , OPIC,  after  There  In  provisions  guarantee  under  average.  were  as  a major  I t emerged  growing  borrowing  "Project strategy  because  beyond capacity  financing" for  capital  funding  needs  the  internal  of  investors  for cash and  24  companies.  Nevitt  [35]  financing  of  a  satisfied  to  look  of  that  loan as  be  following A  for  basic  on  total of  sources The  5.  be  lender  is  flows  and  earnings  source  of  funds  from  which  assets  of  the  economic  financing  a  unit  contains  the  flows  of  the  contrast  to  the  balance  sheets  or  with  well-defined needs  project  of  are  risk  the  the  project  as  loan  is  is  benefit  non-recursive  affecting  his  not  project  The  borrowing  by  occurs  a  not  financial  several  single by  with  different  one;  syndicating  the  over  a  period  of  time  as  and of  the  repayment  to the  parent arrange  sponsor  to  capacity  is eligible  lies  in  the  project.  a t t r a c t i v e to  objective will  of  i t s sponsors. by  project  statement; and  usually  guarantee  operation  the  possible;  i s completed;  essential  of  projects  than  is shared,  of  income  matched  c a p i t a l rather  drawdown  completely  in  their  The  which  debt,  worthiness  of  ultimate  the  cash  credit  the  technique  anticipated  overall  widely  every  a  the  cash  Project  the  as  project  which  as  the  the  repay  financial  successful  its  on  loan  The  This  to  in  the  lending  project 4.  the  loan.  to  i s concerned  needs  3.  the  itself  sponsors,  the  and  reliance  reliance  It  as  to  unit  financing  elements:  project  2.  unit  Project  economic  initially  repaid  collateral  1.  particular  economic  will  defines  corporations a  and  the  latter,  or  balance  for  this  since  borrowing at  the not  same in  sheet.  type  of  for  any  a  time, way  However, financing.  25 Lenders equity  are  not  risk  associate  low  level  Further  Harrison  2.5.2  [19]  LEASE  of  been a  used  lease  project  latter used  in  can  sponsor  parties  be  key  regulations  is and  by  third  country  and  project.  [8],  financing and  Levy  a  party the  may  kind  of  found  technique  that  since  detailed  rate rate  for  may  Landskroner  be  of  leasing  the  in  of  tax  of  the in  be  mechanisms. or  the  project.  is  the  tax  in  shields  a are  company  applied  types  a  the  i t could  leasing  this  of  project  write-offs  these  use  companies  decision  found  [28].  the  financing  other  description  alternative  of  objectives  charges  charged  The  facilities  completion  depreciation  normal  and  other  leasing  Obviously,  interest  a  this  an  be  However,  important  , the  as  lease.  how  equipment  A  a  depreciation  the  techniques.  they  with  projects.  and  the  to  from  the  in  capital  of  some  in  financing  variation  many  interested issue  a  using  either  related  then  for  technique  equipment  as  with  a  small  a l l the  benefits  lower  are  projects  accepted  this  nor  [35].  also  since  conjunction  the  business  those  be  about  regarded  achieved  particular  may  Nevitt  large  technique  The  capital  only  risk  details  finance  Lessors  to  of  leasing  be  are  Then,  and  in  to  may  financing  venture  FINANCING  Equipment has  the  takers.  financing. in  in  to  the  transaction  is  of  financing  leasing  mechanism  Bayles  and  Diltz  26  2.6  INFLATION  After  the  AND  CAPITAL  1973  o i l  BUDGETING crisis,  industrialized  western  world  rates,  between  8  ranging  double-digit  inflation  t o be h i g h e r  inflation  rates  have  the consequences  reflected In fact out  that  such  and  cash  Usually, the  are,  existence  and  in  some  a paper what  be  evaluations  the investment  value  call  decision  added, rates  current  will  disturbances  in  three  analysis  terms.  based  on  changes i n effectively  unchanged.  introduced  by  There the  1982, L e R o y  secondary  and Fowler  e f f e c t s of  a n d on c a p i t a l  [27]  inflation  recovery  factors.  effects are:  Under  the tax p r o v i s i o n  which  allow  a  be  are performed  rate  carried  inflation.  published  they  be  run, simultaneous  the discount  important  economics, the  inflation  in  are  projects.  I t may  include  expressed  requires  of p r i c e s  should  i s emphasized.  i n the long  of p r i c e  a present  These  that  in engineering  also  three-digit  reality  of c a p i t a l  analysis  called  countries,  cases,  increment  evaluation  should  constant-dollar  however,  discuss  general  should  out, leaving  In  of a  basis  commonly  This  the  inflation  developing  reported.  investment  analysis  flows  levels  cancel  1.  an  assumption  price  on  any s e r i o u s  of  high  the  a n d i n some  literature  i n an a f t e r - t a x  that  In  been  i n t h e economic  the general  15%,  rate.  tends  economies  registered  and  inflation  that  the  full  simultaneous  that  prevail  tax d e d u c t i b i l i t y  increase  in price  i n many  countries,  of i n t e r e s t  levels  and the  payments, discount  27  rate 2.  will  Those the  same  3.  tax provisions from  price  (even  though  capital  i n nominal  terms.  discussion  aforementioned But  flows  other  even  for  difference  estate  rate  than  operating  that Large  second  inflation  may  of the  exposed  be  level  of  unaffected) in  working  found  in  the  i f  expenses,  rent  specific  average  because  like  of  the  i s not  inflation  equal.  on  rise  This  the  economic  for  expenses phase  at a  higher  i f the contrary  likely  during  t o happen.  the l i f e  planning  of the  horizons  in  price  the o p e r a t i o n a l  prices  the  t h e owner o f t h e p r o j e c t  i s more  have  to  of  indicators  i s present  or decrease  change  capital projects  similar  during  effect  indexes  impact  i f i t  the  respect  weighted  development,  rates  and  strong  project  situation  with  and s e r v i c e s a  increase,  is  inflation  US  a  F o r example,  real  his profit  be  investment  i s necessary  have  of a  both  i n the  goods  a  A  rates,  average  will  revenues.  maybe  important  reflect  specific  attractiveness  reducing  of a p r o j e c t  points  Reported  Index  countries, An  sales  these  more  and time.  increments. rate  thereby  of the nominal  increased  of  inflation  Price  for indexation  paper.  maybe  differential  see  units an  detailed  of  i n a decrease  requiring  Consumer  do n o t a l l o w  and  thereby  cash  more a t t r a c t i v e ;  depreciation,  increments;  Inflation results  and  project  of the t a x s h i e l d and hence,  sales  A  any given  tax s h i e l d  value to  make  will occurs.  That  i s ,  project.  as long  as  50  28  years. 20  Even  f o r the  years,  constant normal  the  inflation  such  of  levels  to  by  the  years  few  operating  the  or  life  of  the  Finally, acquisition elapsed is  time  project. mining  inflation its of  cost the  be  of  the  of  i n the  early  spent  of  their and  The cause are  during  revenues  lives..  additional  investment  r a t e s may  in order the  far  and  to  moment  with  less  Zorn  located  rates that  lack  rest  none.  projects  money  flow  of  remain  governments  Capital  smooth  lives  rates  almost  of  of  later  A  and great  years  of  non-operational  depending  when  the  approved  than  in a  third  inflation,  a  on  threat  the  cost  may  the  be  required to  the  project.  The  of  the  i n the  the  updated the  world  country  i t was cover  of  range  of  amount of  the  a  large  with  high  three  abandoned  those  project  the  cost  case  i t s financing  until  to  economies,  [42], mention  negotiated  funding  pose  finance  i n hyper i n f l a t i o n a r y  Radetzki  rose  time.  imply  i t s financing  would  project  the  is  change  amounts  more  inflation  funds  Therefore,  negotiated  and  project  difference.  between  d e f i n e d and  years.  for  high  of  a  would  time  over  inflation  losses  direction  and  with  inflation  of  large  during  between  project  gains  having  expenses  difference  economy change  cases  that  periods  the  characterized first  common  likelihood  during  cycles  more  times  as  because  increments.  29  2.7 A  OVERSEAS  common  that  AND  characteristic  they  fall  operations, a  PROJECTS  FOREIGN of  under  where  the  many  the  EXCHANGE large  capital  category  sponsor  or  parent  country  to  undertaken.  Mining,  o i l  and  chemical  projects  commonly  overseas  ventures.  The  economic  evaluation  opportunities  i s subject  to  of  political  and  economic,  those New  which  influence  sources  given  of  risk  the  high  projects.  These  project  and  repatriate inflation domestic  exchange  and  more  decision  basic  rate  be  industry  set  involved  process in  differences  these between  foreign  tax  ability  changes, risk  than  decisions.  making  flows,  business  will  complicated  expropriation, '  in  investments  investment  cash  of  project  considerations  include  company  to  differential  of  foreign  and  projects. besides  considerations,  an  measurement  reduction  and  the  consideration. literature.  the  analytical  denominator  determine  period;  the  i s based  process  uncertainty  likelihood  rates  and  is  multinational  foreign  strategic  factors  funds,  of  wider  complicate  new  the  domestic  l e v e l s of  Therefore,  common  a  most  parent  regulations,  where  of  projects  company  different  are  that  RATES  of  should  They  b)raising  framework  a l l these be  desirability Five  relevant  complex  the  a l t e r n a t i v e methods are:  the  a)Shortening  required  that  implemented of  rate  qualitative  are the  of  allows factors  in  to  order  project discussed minimum  return;  the a to under  in  the  payback  c)adjusting  30  the a  cash  flows  premium  cash and  for the cost  f o r overseas  flows  to reflect  political the  e)using certainty  of r i s k  r e d u c t i o n , eg.  risk  specific  charging  insurance; d)adjusting  impact  of a given  equivalents in place  risk;  of expected  cash  flows. It Folks  is  claimed  [15]) that  evaluation and  also  the parent's the p r o j e c t  local  environment.  currency  used is  accepted,  parent  established  risk  i t  goes  briefly  from  in  to the  the stream timing  the  in  of fund  two m a i n  be u s e d .  cash  two-stage project  In t h e viable  -flows  first in the  in  local  I f the  investment  second  stage  where  of cash  flows  to the parent.  of cash  flows from  of d i f f e r e n c e s  stage.  i t has  realized that  by  realized  to In the by  and tax r e g u l a t i o n s  because  sources  and  evaluation technique i s  repatriation  t h e second  [48],  and e n g i n e e r i n g  decision.  governments,  macroeconomic  defined.  the  data  i n t r o d u c e d by e x c h a n g e  way,  between  project  a n d amount  r a t e s and because  this  a  economically  market  i n terms  by l o c a l  considered and  found  accept-reject  because  o f money In  and  the  differs  project  power  be  should  The o v e r a l l  projects,  inflation  flows  should  its viability  overseas  the  cash  (Shapiro  projects,  differentiates  s t u d i e s and a t r a d i t i o n a l  t o make  prove  that  are developed  production  literature  i n analyzing overseas  approach  stage  i n the  of d i f f e r e n c e s  in  i n the purchasing  rates. of risk They  uncertainties.  are  identified  are the They  country will  be  31  2.7.1  COUNTRY The  RISK  concept of  uncertainty  about  country  a  large  political  and  the  Oxhelheim  and  Wihlborg  political  and r i s k  possibility  of changes  uncertainty regime,  about  the fact  Risks  that  development  define  tax  e t c . The most  expropriation.  increments  and  would  extreme  i n the i n d u s t r i a l  the growth  perspectives  defined  about  into in  the  as  It  the  involves rate  pressures,  risk  i s that  development  the country's the  These  of the  that  exchange  political  by  field.  risk  project.  t o economic  determined  country.  development  political  run,  a  to the  and r e g u l a t i o n s  policies,  the long be  the  of  is  rights,  related  in  risk  on  affecting  country  legislation  return  the exposure  factors  t o economic  ownership  monetary  terrorism,  to  the  of  divide  Political in  captures  environment  [39]  related  country.  influence  number  economic  investment  may  risk  of  refer  economic  productivity  increments  project  would  i n the  long  term. All to  these  foresee.  partnership locally,  2.7.2  factors  Some m i t i g a t i o n from  local  or buying  MACROECONOMIC Macroeconomic  it  is  are purely  RISK risk  AND  uncertainty  such  are generally  EXCHANGE  as  obtaining borrowing  suggested.  RATES from  the fact  or i n d u s t r y - s p e c i f i c . are  difficult  or governments,  i s distinguished  not f i r m - s p e c i f i c  macroeconomic  strategies  investors  insurances  q u a l i t a t i v e and  exchange  that  Sources  rate  of  levels,  32  inflation like  and  interest  o i l and  These  the  variables  therefore,  rates,  aggregate are  often  attention  Macroeconomic  level  is usually exposure  relationships.  Parity,  refers  countries  there  opportunities  are and  returns  across  [39]  reporting  convert currency  the to  the  economic  the  Net  exchange both  of  been  exposure  international  trade  It  investments  disappears.  The  states  the  and  are  the  a  borrowing  large  then,  risk  that  equal.  for  divided  the  arises  consolidation  results  of  the  number from  of  these  projects  exposure.  into  Value  changes.  following  that of  from of  the the  overseas  home c u r r e n c y .  exposure,  Present  the  parity  and  has  across  this  Open.  that  two Power  prices  When  risk  currencies  on  and  Exchange  two  types,  need,  for  namely  economic.  and  rate  good's  currency.  rate  and,  Purchasing  temporarily  exposure  Accounting of  the of  this additional  rates  latter.  least  face  and  the  deviations  investments  accounting  and  on  substantial  at  risk  is  Fisher  financial  exchange  demand.  particularly  unexploited  i s the  commodities and  are  relationships,  rate  one  demonstrates  there  do  depends One  . some  production  focused  exchange  countries  Oxelheim countries,  on  of  in  equality  in  no the  relationship  expected costs  the  when m e a s u r e d  exists,  second  to  of  reflected  equilibrium that  prices  project most  i s based  the  This  The  on  project  change  effects: a  parent  purposes  company,  from  the  important  the  local  type  possibility  will  change  can  occur  change  in  cash  is that  when  through  the  to  the  one  or  flows  or  33  a  change  to  be  in the  time  [48]  transaction  losses  and  could  the  in  alter  the  cause  nominal  than  terms.  the  of  in  because  price  changes,  the  Consequently,  future measuring  r e q u i r e s measuring  p r e v i o u s l y mentioned  can  parity;  changes; and  its  be  altered  by  one  of  deviations  b)exchange  rate  changes  c)governments  tax  nominal  d)some  concerning  cash  flows  these  are  fixed  circumstances  in are  [48].  rates  NPV  as  present  into  the  [27].  procedure  In  simple  the  h i s work,  value  approach capital  framework  for  in  order  economic  performance  p r o j e c t s in complete  relatively  debt  arises  a)the  Details  Lessard  example,  with  or  transactions  flows  profits;  gains  changes.  exchange  by  of  riskiness  project  rate  exchange  exposure  into  Transaction  cash  price  the  of  for  project.  analytical  adjusted  independent  the  an  using  developed  and  power  in Shapiro  incorporate  currency,  of  real  real  Finally,  a  assumed  exposure  future date)  operating  of  purchasing  documented  process  is  exposure.  in combination  exchange  relative  rather  and  flows  general,  a  amounts  exposure to  at  Real  following events:  from  rate  economic  possibility  foreign  the  cash  sensitivity In  the  fluctuations,  economic  the  from  currency.  operating  exchange  operation  settlements  denominated  currency  The  separates real  results  (upon  foreign  rate.  invariant.  Shapiro  exposure  discount  evaluation  measure  this  author  that markets,  to  has  been  suggests  holds  for  providing  evaluating  most  34  international  capital  projects.  2.8 CASH FLOWS GENERATED As m e n t i o n e d financial diverse  before,  arranged  amortization  any  value case,  be e q u a l  financing  simple  function,  value.  This  the  have a  the  financing  sense  that  the  payments In  s e t of payments has  to  negotiated  schedules  a  schedule.  o f t h e amount  rate  very  However,  by t h e r e p a y m e n t  worth  the  borrowed,  both  f o r the loan.  that  a r e used  in  the  projects are: function,  which  Gradient  where  periods  followed  fixed  to  by  where  the loan  i s repaid  in  amounts.  of  is  can  a s e t of d i s c r e t e  of t h i s  repayment  repayment  number  after  in  comprises  worth  generated  institutions.  determined  of c a p i t a l  equal  3.  of loans  pattern projects  done  a t the i n t e r e s t  Uniform  Step  be  to the present  Three  2.  can  ARRANGEMENTS  according  lending  the present  discounted  1.  shapes  the  and timing  flow  in capital  of  with  generalization  of  the cash  mechanisms variety  BY F I N A N C I A L  new  n, a n d  amount  t h e payment until  function,  amount  t h e payments  with  then  is  paid  a r e equal  for a  given  increased  in  fixed  for  i s increased  the loan where respect  another again.  i s completely  each  payment  n  This  a  periods pattern  repaid.  i s increased  to the previous  payment.  by  a  35  2.9  IMPLEMENTATION  2.9.1  FINANCIAL The  loans:  program  taken  (construction  THE  to  loan)  generated  former,  the  user  financed  with  borrowed  by  period  when  this  the  model,  that  the  of  two  another  the taken  the p r o j e c t  loan  interest  t o be term  the nominal  from  repaid  fraction  i s t o be  input  d i f f e r e n t types construction  (long  the  funds,  the c o n s t r u c t i o n  repayment  considers  specify  the  of  PROGRAM  finance  and  revenues  form  COMPUTER  MECHANISMS  computer one  ON  borrowed  expenditure or c a p i t a l  the  For  the  rate  I t i s assumed funds  function,  is  with  construction  interest  repaid.  phase  loan). of  done  of  follows and  that  prior  to  and in the no that  period. For  the  borrowed,  or  construction interest step and  rate  long  term  simply loan  of  repayment  and  the  and  the user  i t  equal  of  is  Using  repayment  this  loan  as  the  Then,  the  (uniform,  the  information, including  amount of  function  well  calculated,  p r i n c i p a l and  value  interests.  s p e c i f i e d , as  payments.  s p e c i f i e s the to the  i t s accrued type  are  schedule  interests  2.9.2  sets  plus  or g r a d i e n t ) number  loan,  frequency a  complete  payment  of  balance.  INFLATION In  the  individual variable  program, cash  flows,  operating  inflation unit  costs.  The  rates  sale  are.  prices  model  considered  for  and  and  assumes  fixed them  to  be  36  constant,  2.9.3  FOREIGN The  program those simply those  not v a r y i n g  EXCHANGE  with  RATE  issue of f o r e i g n by s p e c i f y i n g  flows  that  converted flows  time.  exchange  the value  rate of the  i s included exchange  are expressed  in foreign  into  by m u l t i p l y i n g  dollars  by t h e e x c h a n g e  rate.  currency.  in  rate  the and  They a r e  the value  of  CHAPTER  3. CASH  FLOWS G E N E R A T E D  IN C A P I T A L PROJECTS  3. 1 INTRODUCTION The  most  important  the  definition  of the  throughout-the will  be  that  depends cash  flows.  to well  in turn  will  or  continuous.  The  be  distributed  some  special  cash  flow  profiles  flow In  that phase will  Those  the  the  in  upon  i t )  of  a  either  in that i t  i s ,scale project  t o the type  to  functions  that  f u n c t i o n s c a n be u s e d  the  such  over  each  of  functions,  a n d t h e way  Although  this  related  flow  time,  of  the prediction  parameters  and  required  quality  disbursements  flows  models  d e c i s i o n s made  mathematical  according  generated  the information  Thus,  perhaps,  cash  of the cash  respectively.  one,  be  will  yield  and by  the magnitude  that  mathematical  achieved  The r e c e i p t s  is,  known  process.  represented  parameters  the  will  accuracy  evaluation  the p r o j e c t .  are  discrete define  of  flows  ( a n d by e x t e n s i o n ,  on t h e  project  project  cash  the decision-making  information  in  lifetime  the input  techniques -in  task  and  shape  is a  unique  to represent  typical  of the p r o j e c t  and  in consideration. this  has been  chapter,  the t y p i c a l  recognized  and the f u n c t i o n s be p r e s e n t e d .  financing  of  the  Cash  as l i k e l y that  may  flows  project  flow  patterns  to occur be  used  profiles are  37  not  or  i n each  profiles project  to describe  them  associated with  the  considered  the  in  38  discussion  since  Therefore,  this  borrowed  funds  Since project  are  flows  namely  OIL  AND  The  o i l and  flows  3.2.1  gas  the  major  field  for  surface  of  area  geophysical  surveys,  probability  that  this it  time,  seems  wells  are  Drilling of  money  probable drilled of  fields  the  type  where been  mining,  test  production  phases:  i n an  begins  the  and  in each  stage  o i l  in  no  real  of  intensive chosen  for  estate  and  projects  exploration,  operation  of  comprise  them  are  and  economic  disposal.  discussed  The  below.  PHASE  identification  search  chapter.  s i t u a t i o n when  have  gas,  development,  generated  first  o i l and  drilling  EXPLORATION The  a  last  INDUSTRY  following  cash  major  encountered  the  3.2  GAS  to  the  c h a r a c t e r i s t i c of  four  are  industries.  evaluation,  are  evaluated,  process  the  corresponds  in  used.  projects  discussion,  were p r e s e n t e d  analysis  these  being  capital  they  with  that and wells  extraction  preliminary  concerned which  flows  gas  feasible extractable  o i l is  o i l exploration,  o i l and  at  leads  in a a  is  since  the  examination  involves  to  or  really  costs  reserves.  an  less  rise  mapping  and  most  uniform  rapidly  of  single  i t requires  During Once  area,  this  costly  expensive  the  rate.  the at  The the  evaluation  is o i l in  is  on  particular location.  more  there the  and  project  test stage.  operation  drilling  and  39  pumping  equipment  drilling Crew  costs may  Other  costs  seismic them  oil,  money  i s spent  step  payments  and land a  to  depths. patterns.  phase  are  governments,  rental costs.  large  involved  pattern  be  said  up  or  that  down  or abandonment  in  cannot  reservoir  exactly  A l l of that  of  is  finding  defined.  the exploration  uniform  jumps  of t e s t  the event  be  during  i n a more o r l e s s  some  way,  are  phase,  and from  introduced  wells,  At  which  may  time  by  the  create  a  ECONOMIC E V A L U A T I O N During  this  quantified.  necessary project  when  meaningless. this  economic  outside  A  the economic  forecast  to asses  or r e j e c t e d . with  merits  of revenues  the p r o f i t a b i l i t y  compared  consequently,  during  phase,  i s accepted  duration  the  shooting  The  function.  3.2.2  and  drilling  the e x p l o r a t i o n  bonus  until  t h e randomness  i t might  drilling  with  the j o b .  feasible i s defined.  an e x p e n d i t u r e  time,  during  lease  t o happen  best,  are  incurred  t o do  t o complex  transportation  continue  labor  exponentially  according  permits,  commercially  to  vary  crews,  Given  qualified  increase  costs  right-of-way  and  This  phase  the t o t a l  phase  are only  corresponding  evaluation.  the project  there  I t may  following  and  venture  expenses  of the f i e l d ,  a detailed description  In g e n e r a l ,  of the  to the  of the  expenses cost  of  that  the short  project  of the cash  be a s s u m e d  an u n i f o r m  and  has a very  life  is  flow  is  generated performing  money  distribution,  flows or i n  40  two  d i s c r e t e payments  the  end of the phase),  payment  3.2.3  equal  FIELD The  to the total  economic  accepted  is  to design  the  development  Similar  a  of the  phase.  c a n be d o n e  may  to  order  to  be  charge, may  according convened series  to  (discounted similar  the  the next that  are  stage needed  i s the o b j e c t i v e  of  the a c q u i s i t i o n of  evaluation  a very  the  process. phase,  short  period  design of  d i s t r i b u t e d over  the c o n s t r u c t i o n  purchased.  cash  flow  payment,  value  generated  with  or a  conditions  the  payments  former can  t o the time  series of  time,  time,  or  owner  when  the design  physical  development include  of  is  an  this  the land important  transaction  of d i s c r e t e  the  be r e p l a c e d  Following  activities,  Its  commercial the land.  payments agreement  However,  by i t s p r e s e n t  the construction  s i t u a t i o n t o the s i n g l e  development  this  project  payments.  the  with  of  discrete  i f the  to the design  t o be u n i f o r m l y  already  be a s i n g l e  facilities  addition,  during  to start  and t h e  the  economic  are incurred  determine  project;  In  the  s e t of d i s c r e t e  has  i n one  i t i s accepted,  simultaneously  be a s s u m e d  In  simply,  at  of the evaluation.  will  If  and c o n s t r u c t  the operation  and  more  cost  evaluation  or r e j e c t e d .  for  expenses  or even  and the other  DEVELOPMENT  is  land  (one a t t h e b e g i n n i n g  payment  case  begins), is  a  worth and a  obtained.  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 of  casing  the of  field. wells,  The  costs  drilling,  of well  41  equipment,  pumping  water-  or  gas-injection  roads,  buildings,  expenditures  i t with  oil  gas  to  The have  a  flows  flow  and  to  drill  well  form.  mathematical  them  i s given  of  in  of  the  well to  during  section  discrete  the  to  the this  access a l l  the  and  to  well to  the  field  description  of  batteries,  includes  required  functions  some p i e c e s  inclusion  it  complete  head  The  the  acquisition  and  of  tank  electrification,  facilities  bottom the  lines,  general,  generated  bell-shaped  represent  the  the  i t from  cash  In  production  from  transport  gathering systems,  etc.  required  provide and  units,  lift  the  surface  and  terminal.  process  tends  to  of  types  of  used  to  that  the  may  be  3.4.3. A d d i t i o n a l l y ,  c o s t l y equipment payments  may  the  justify  to  represent  these  and  gas  deals  transactions.  3.2.4  with  OPERATION The  operational  the  generation  of  the  sales  of  expenses  of  of  occur  during  operational  non-cash  expenses:  disbursements  treated  here The derived  as  of  the  extracted  capital,  The  stage  the  income crude this  costs,  they  were  of  phase.  taxes,  to  the  o i l and  depreciation, related  o i l  project gas.  They  depletion  discussed  in  are  the of  and  items  the  as  a  result  Different  repayment  financial  field  last  types  working  loans  and  amortization. will  not  be  chapter.  REVENUES revenues from  future  generated  by  the  production  estimates  project by  may  be  multiplying  42  the  saleable  natural be  production  gas v a l u e .  estimated.  employs  Current  prices  liquids..  However,  contracts A in  figure  at  are  also  in  or w e l l  years.  Then,  production  for  years  before  rate the  a  when  project The  production  described  by o n e  of  functions  that  rate  t,  existing  reaching  to use.  of production, q,  rate  begins  rate  known  Q  during  a  is  shown  the  field  as  maximum  a period  to decline  a r e not longer  t  of  exponentially  non-economic  during  of three  relate  happens.  These  constant-percentage  the  natural-gas  of o i l w e l l s  allowable,  production  justified  commonly  and  decline, figure  are  recognized  on  the  the  may  types q  with  production  referred  harmonic 2,  period  of production  the decrement  functions  d e c l i n e . In  functions during  the d e c l i n i n g  the l e v e l  d e p e n d i n g on how  hyperbolic  for  i s abandoned.  be  time  of crude o i l .  f o r the gas p r i c e  stage  the operations  price  should  o i l income  n a t u r a l gas,  pattern  constant  o i l or  factors  [25], future  t h e gas of  production  two  employed  be e x a m i n e d  a  efficient, rate  these  t o Ikoku  1. I n t h e f i r s t  operates  appropriate  the c u r r e n t l y posted  should  typical  the  Therefore,  According  usually  by  to  decline  typical  as and  shape  of is  the  exponential  d e c l i n e phase,  that  the nominal  rate  depicted. It in  c a n be  shown  the production  rate  q,  i s described  by  of d e c l i n e the  D,  equation:  FIGURE 1. P r o d u c t i o n rate of oil  wells  FIGURE 2 . P r o d u c t i o n d e c l i n e c u r v e s  45  D =  1 dq  (3. 1)  q dt  Now,  the production  different 1.  f u n c t i o n s can  characteristic  forms  Constant-percentage The  decline given  most  curve  that  equation wells  constant-percentage their  productive  significantly this  decline  mathematics much  simpler  types  of d e c l i n e Here,  nominal  widely  used  follow  and  the  easier  actually a great  then,-  end of  portion  only  this  a of  deviate  period.  to present  in this  When  time,  i t is  In  addition,  the  type  of  decline  are  the other  two  t o use  than  curves.  i t i s assumed  d e c l i n e r a t e D,  instantaneous  the  and f i e l d s  significant.  and  is  industry,  life,  involved  curve  and most  d e c l i n e over  toward  usually  D.  i n t h e o i l and gas  deviation i s discounted  not  the  of the d e c l i n e r a t e  conservative  many  assuming  decline.  constant-percentage  simplest,  be d e d u c e d  that  the instantaneous  i s a constant  production  rate q.  percentage  or of  Mathematically:  (3. 2)  with the  k being rate-time  a constant. relation  Integrating this  c a n be o b t a i n e d . ' I t  equation, i s :  46  q  =  q e  -Dt  (3. 3)  0  where time  q  i s the  origen  is  the  is  an  production  at  the  production  decline  is also  beginning rate  exponential  known  production  integrating  Eqn.  D  t  0  Q =  at  Harmonic In  the  3.3.  )  harmonic  as  expressed  k  D  0  by  -1 5  being  =  from  zero.  Q  the  Since  q  Eqn.  3.3  be  decline.  The  obtained  by  yields:  q -q 0  =  0  constant-percentage  can  That  taking  d e c l i n e , and  exponential  decline  rate  q  the  t  (3.4)  D  proportionally  =  time  decline.  decline  D  of  time  D  2.  at  f u n c t i o n , the  cumulative  q (l-e"  rate  of  curve,  the  is  not  constant  but  with  the  production  rate.  the  =  type  differential  nominal decreases This  is  equation:  (3.5)  kg  dt  a  kq  constant.  Since  (3. 6)  0  Eqns  3.5  and  3.6  47  -15  D b  q  D  dt  f  (3.  7)  Qo  integrating  Eqn  3.7  and  rearranging  terms:  1+D t 0  that  is  the  cumulative 3.8;  harmonic  function  decline  i s obtained  by  function.  The  integrating  Eqn.  that i s :  Q = JiilnO+Dot) D  decline  estimation.  3.  i t as  under  some  in  thick  gravity  this  is  defined  widely are  been  observed  be  terminal  used  there  by  in  reserve  conditions crude  of e x t r a c t i o n  encroaching  operations  drainage  in  several  the case  o i ldriven  or  In  not  has  would  viscosity  Hyperbolic  is  However,  which  production high  9)  0  Harmonic  under  (3.  such  o i l of  edgewater,  as steam  soak  reservoirs.  decline.  type  of  as:  production  curve,  the decline  rate  48  -beV  D =  where b  c =  Going  q =  and  Q =  i s a number  i n the  and  c is:  0  t h r o u g h the  m a t h e m a t i c s , the  production  rate  time t i s :  q (1+bD t)" 0  the  (3.  ( l / b )  0  cumulative  — (l-b)Do  1-  function  _ 3 q  (  l  _  b  will  decline  constant  equal  (3.13)  o i l production  decline to  0.5.  is a generalization  functions.  obtained  The  w i t h b=0,  harmonic  is:  )  conditions,  drainage  function  12)  0  gravity  the  [0,1]  10)  (3. i i )  Under c e r t a i n  of  interval  _L_ bD  at  (3.  with  by  a  hyperbolic  Also,  the  hyperbolic  the  other  of  exponential whereas a v a l u e  decline.  obtained  decline of  b=1  two can will  types be yield  49  2.4.2  EXPENSES  Working Once for  capital  the f i e l d production,  project, drawn  working  i n order  single  operational  payment phase  i t is  economic  evaluation. costs  Operating  costs  operations  further operating former  plants,  maintenance,  water-injection indirect incurred Items  operating on  considered  overheads, and  behalf  here  and l o c a l  in  the  selling taxes,  storing, They  may  costs  gas  The for  processing gas-  or  stations.  The  those  operation and  expenditures in  expenses,  general.  home  a n d management,  bonuses,  be  direct  costs.  systems,  are plant  administration  development,  insurance  of the  the  incurred  materials  are  of  the  pumping  costs  a  in  operating  workovers,  and  by  item  categories:  disposal  plants  smooth  into  producing,  and  t o be  modeled  i t goes  costs  two  labor  salt-water  is  an o u t - c a s h  and i n d i r e c t  includes  into the  insure  o i l and gas.  into  ready  at the beginning  and a l t h o u g h  and s e l l i n g  i t is  o f money  and  input  extracting,  costs  operation,  reservoir  are a l l those  divided  and  i s injected  located  considered  of  transporting  a  capital  project,  Operating  capital  to f a c i l i t a t e  Working  discrete  developed  t o have  on a s n e e d e d  operations.  the  has been  office research  royalties,  donations,  etc.  50 There between  is  indirect  allocated  to  that  from  vary  practice on  top  to  of  production project. the  and  direct phases  company  express  costs  period  and  proportional  cost by  to  in turn in  to  by  the  the  be  last  a  steady the  multiplying They  gas  one  common  along  output.  using  rules  the  by  o i l and  are  percentage  constant  defined  of  is a  during  production  volume  as  they  simple  It  costs  them  i s determined the  means o f  incurred  can  but  company.  keep  relationship  costs  indirect  direct  cost  presented  straightforward  various  Direct  unit  which  no  are  produced,  of  the  curves  section.  Taxes Taxes  to  which  subjected include  o i l  vary  widely  on  production  volume  municipal, legislation same  the  state  country  generalizations particular  case  and  should  to  establish  are  be  project  their  Depletion  special  and  paid  time  is  to  this  the type  value,  The  time  current and  to tax  within to  topic. according  may  taxes  either  difficult  are  They  excise  governments.  analyzed  and  world.  production  from  it  projects  and  and  regarding  in  These  both,  changes  the  Depreciation,  of  national  of  the  property  or  location order  production  basis  or  itself  gas  throughout  conservation,  calculated  the  and  make Each  to  the  legislation,  value.  Amortization.  expenditures  since  they  do  not  51  imply  actual  flow  of  cash.  considered  in  the  the  is  important,  profit  them  may  during  analysis  reverse the  the  economic  Depreciation, the  means  type is  of  of  the  capitalized years. charge, which  but  depreciable the  sponsor during  to  certain  a  of  income. the  i t s estimated  equipment  and  or  surface  declared  reusable There  determining  are  items  over  noted,  i t is a  from  of  a  several  the  a  In  normally In  of  commonly  used  charges,  acceptable  are  for  project asset  o i l and  gas well  an  item usable  methods  although  government-imposed they  of  time.  certain  States,  the  held  general,  conforms  United  for  include  is  the  base,  i f i t retains a  period  depreciation  the  method  For  tax  depreciable  life.  of  non-cash  obsolescence  enables  equipment.  the  period  the  items  after  a  This  cost  certain  allowance  and  are  expenses  consistent to  made  Depreciation  or  depreciable  value  in  in business  useful  depreciable  be  tear  used  industry,  may  excluding  decision  as  reasonable and  recover  on  amortization  prorating  property  production  impact  dollars.  deductible  wear  their  investment  before-tax  i t is  exhaustion,  and  the  previously  represents  be  evaluation.  of  As . i t was  should  accept-reject  of  cost  they  i n c l u d i n g or  depletion  in  process  because  and  recovering  assets  However,  as  the  long  of any  as  it  limitations. straight-line  52  method, years  the declining  digits  method. found  method  A detailed  elsewhere  that  the method  the  one  for  depreciation not  lead  salvage  value also  ([1]).  the  which  is  that  This method  the project value  project  with  zero  c a n be suggests  should of rule  be a l l does  since  the  lifetime,  of  f o r the sake  early-stage method  [54]  value  a maximum.  time  production  project  present  upon  of the  o f a l l o f them  of a unique  and the  straight-line  of  Valle-Riestra  the  depends  t h e sum  unit  s e l e c t e d i n the  suggest  the  method,  description  to the choice value  during  and  charges  present  author  balance  money. of  the This  simplicity  evaluation,  salvage  value  the  may  be  is  the  used. The  second  depletion charge  as  shrinks  made  a  and  some  is  a  depreciation  the reserves  value  of a  a s some m i n e r a l  of  of  the property  will  idea  resource the  is  mineral  diminishes.  as the crude  the net r e s u l t  like  natural  as d e p l e t i o n charges  the investment  and s o l d ,  charges  of i t s e x t r a c t i o n . The  p r o v i s i o n such  to recover  pumped  It  i s that  sold,  and the  of non-cash  f o r the exhaustion  result  depletion  extracted  Unless  allowance.  t o account  resource behind  type  is  o i l is  be t h e l o s t  of  capital. The either  a  depletion fixed  allowance  percentage  may  basis  be  of a  computed  on  cost-per-unit  53  basis. found  A  description  in Gentry Finally,  capital which time  time of  the  amortization  can  be  the  company,  to  place  where  United  in  the  and  the  for  development  expenses.  The  firm  may  deduct  expenditures  and  thus,  each  from fiscal  expenses expenses,  and  some  year  recover  is  example,  organization  expenditures,  and  to  project  States,  a p p l i e d to  the  be  certain  place  variation  tradename  to  to  to  and  similar  can  expenditures  trademark  manner  a  other  part  them  of  in  a  straight-line depreciation.  DISPOSAL When  declined  the to  the  rate  a value  limit,  equipment  can  These  the  be  of  production  expenses project  o i l and  of  the  well,  i s abandoned.  or  sold  and  At  the  the  analysis  their  with  However,  the  since  the it will  actual  preliminary  land  of  economic  on  this  land that  value  the  field will  known  transaction)  depend  quantity  gas  revenues  revenues  obtained  purposes  the  an  non-operational  revenue  and  when  of  are  in  considerable.  production  scrapped  included  project  of  operating  economic  sold.  applies  from  research  methods  capital  country  In  these  meet  the  undertaken.  of  The  according  two  [16].  amortization  i t applies varies to  these  O'Neil  expenditures.  policy  3.2.5  and  of  just  as  the  time,  the  may  be  also  should  be  (mainly  the  could  be  location  of  s a l e a b l e equipment. evaluation,  has  the  the For  salvage  54 value  of  flowing phase. kinds of  the  project  into In  of  the  cases  modelling  or  when  the  a  PROJECTS  The  phases  in a  oil  and  section.  investment  mining  search  in  the  first  long  end  of  a  of  the  may  and  value,  certain  and  a  set  appropriate  the  same  discussed  then  of  operational  effect  be  payment  for  venture.  are  the  single the  high  economically  place,  a  take  function  an  period  be  might  project  for  to  has  project  is evaluated  relatively  land  value  exploitation  The  conducted  the  the  agreements  salvage  MINING  assumed at  discrete  3.3  gas  be  project  commercial  payments  can  the  mine  as in  those the  ore  profitability i s developed. the  an  previous  extractable  operation,  in  is  of  the  After  project  a is  abandoned. The and  cash  disposal  since  the  execution phases  last  are  kind  of  generated  very  not  activities  be  concerning  section  also  occurring  during  presented  below.  to  and  equal  the  land  exploration,  those the  in  treated  applies the  during  similar  is practically  will  discussion  flows  work  both  in  of  development  The and  o i l  involved cases.  mining  acquisition  here.  an  evaluation project, in  their  Then,  these  projects. presented  likely  type  operation  in  of  phases  The the flows are  55  3.3.1  MINE The  DEVELOPMENT  c o n s t r u c t i o n and  giant  civil  moved  and  engineering  buildings  roads,  railways  costly  handling  be  purchased.  sum  of  The  several  according The  to cash  be  represented  equations  heavy  and  payments  mine in  Gamma  be  mine  or  money  less  i s spent  can  the  be  the  and  as  to the  number  construction  form  that  can  functions  like  the  The  3.2.3. and  Earth while  acquisition  represented axis  These  corresponding  operation  time  have  viewed  their  uniformly.  as  itself.  section  continuous  are  such  functions.  and  a  addition,  type  bell-shaped  in  In  be  during  Weibull  introduced  along  by  i t of  discrete  according  to  a  schedule. sub-projects  are  schedule,  Therefore,  bell-sha.ped  size,  functions  distributed  development  in  the  a  and  expenditure  development  time.  of  have  equipment  These  can  is  earth  equipment,  mine  varying  expensive  procurement  a  several mathematical  i s a more  place,  of  only,  of  constructed.  generated  to  mine  facilities  processing  size  profile  by  will  takes  and  tends  Beta,  construction  sometimes  type  projects  Normal,  are  development  flow  civil  ports  a  amounts  transportation  sub-projects  the  of  movement  and  of  p r o j e c t . Large  and  and  development  phase subflows  the is plus  undertaken and  they  general made  up  following  are  cash of  some d i s c r e t e  usually  flow  the  overlapped  profile  several payments.  general  of  the  overlapped  56 3.3.2  OPERATION  PHASE  Revenues  Estimating and  risky  task.  multiplying the  year  number from but  the  by  of  the  mineral Annual number  the  units units  revenue kind  This  sold  value  to  is also  for  in  times the  in  by  set  of  profitability The since are  most  of  techniques. production optimum  rate  any  the  and  levels,  project  in which  and  i t has  should rate  components  be may  are  valuation  selling  mine  throughout  established  these  any  involved  in  mining  particular characteristics  at  the  beginning  towards the  the  best is  pointed  out  variables  are  in  any  carefully  evaluated.  be  to  easier  its  end  the of  define  issues  that  engineering  at  a  life.  engineers of  optimal  the  variables  mining  of  the  of  variables  operates  most by  been  technical  classical a  from  inventory in  sensitive  using  differ  amount  critical  that  the  small  those  the  output  a  of  of  the  practice,  arithmetic  two  by  during  ignored  production  literature,  and  in  sold  determining  Generally, rate  by  and  trivial,  production  determined  differs  in  difficult  is  highly  its  In  Besides,  measure  annual  the  While  each  the  price.  changes  valid  much m o r e d i f f i c u l t . many  to  is a  is calculated  produced  is generally  revenues  use  units unit  due  commodity.  calculating  of  revenues  revenue  usually  mined  is obtained  of  mine  sales  this difference  studies.  project  constant It  is  depending  project. operation  production  an  rate  Only does due  57  to  adjustments  start-up mineral  of the near  In  and increments mine  be  considered  of  the operation  is  assumed  many  Then,  the  and f i n i s h  preliminary  functional  form  production  linearly  from  zero  logistic  or  will  described  process  of  linearly is  the from  reached  justified. can  be In  for  introduced output  the  start-up  assumed  to  increase  rate  i n a given  time,  special  production  discussed).  i t  the optimal  rate  continued  functions  to  is  the later  happen  t h e economic  operation  of  when  at the  be a s s u m e d  until  the  functions  Similarly,  to decline may  at  During  (these  the  by  limit  no  longer  a p a r a b o l i c or e x p o n e n t i a l  decline  used. figure  a coal  during  be  economic  curves  commences  Otherwise,  stage  this  function like  project,  and  be  may  duration  of exponential  are  production  early  to the production  can  when  industries  saleable stages  Gompertz  function  of s i m p l i c i t y ,  can  to the optimal type  recoverable  the entire  of o p e r a t i o n s .  the  f o l l o w i n g some  during  F o r t h e sake  period,  be  the production  refinements  a  of  during the  of the o r e .  case,  phase.  assigning  or  decrements  t o be c o n s t a n t  in  evaluations.  start  and t o  the exhaustion  the simplest  of p r o d u c t i v i t y  mine  3, a n is  the early  rate  i s obtained,  long  period  hypothetical production  presented.  operation; the  of time;  when  output  then,  A  logistic  curve  the optimal  remains  i t starts  schedule is  used  production  constant to decline  during  a  linearly  -IGURE 3 . E x a m p l e of o u t p u t of a m i n e  Time CJI  00  59 until  the economic The  second  calculation exercise exists.  is  very  adopting  the  estimate  total  more  past  errors.  type  However,  this  be  an  made  use  by  i t to  to  even  techniques prices  weighted,  modelling.  on or  including  A great  in this  are  based  moving  regression  ingredient  is  invariably  can lead  of future  order  revenue i t  and  mathematical  higher  cost  to  other of  in  defined during  projects, o i l and  between  project.  deal  process.  charges  in section  is  those  their  structure  costs  and  also  similar  same i s  depletion  apply flow  i s very  The  and i n d i r e c t  the cash  functioning  projects.  that  very  ongoing,  the normal  amortization  Therefore,  expenses  as  gas  direct  depreciation,  operational  operational presented  incurred  that  taxes,  are  In m i n i n g  differentiation  are  may  price  and e c o n o m e t r i c  costs  t h e mine.  made;  and  of estimation  include  i s a basic  mine  price,  assumption  forecasts  averages,  of  Expenses  recurring  similar  error  Some  They  Operating  of  sales  mineral  revenues.  series  judgement  unit  a high  t o produce  logarithmic  of  component  simplistic  values.  Fourier  major  current  serious  available  i s reached.  the  f o r which A  limit  to  profile  to  the  this of one  60  3.4  REAL  Real  ESTATE  PROJECTS  estate projects  market  are  opportunities.  buildings, comprise  housing  six  analysis  They  phases  followed  absorption,  o p e r a t i o n and  during  of  3.4.1  each  them  FEASIBILITY The  will  study  study  analysis  can  usually the  sponsor  analyses: The the  a  of  the  of i n the  relatively  low  relatively  short  three  following  1.  A  single  2.  Two  to  certain  centers,  office  like.  These  the  design, The  projects  feasibility  construction,  cash  flow  generated  presented.  stage  of  to  out  It  and  figure  the  simple  cash  the  a  this  the  feasibility  Besides,  flow  of  not  the  success  invested  by  evaluation. correspond  the  compared  or  interdependent  phase  analyzing  a  feasibility  capital  financial  produce  with  r e q u i r e s two  d u r a t i o n . Because that  A  d i s c o v e r whether  when  phases.  i s to  investment.  during  of  work  successfully,  r e s e a r c h and incurred  the  r e t u r n on  project.  discrete  discrete  now  intended  other  assumed  response  with  the  proposed  production  in  be  the  collecting  generated  may  be  sufficient  a market  cost  the  disposal.  carried  expenses  required  of  be  meaning  and  starting by  in this  feasibility  project  a  ANALYSIS  objective  i s an  as  include shopping  developments  basic  and  undertaken  to  information report. It  with this  these  two  profile  has  cash phase  is  flows has  reasons, one  of  and  one  a i t the  forms: payment;  payments,  one  at  the  beginning  at  61 the 3.  A  end of t h e phase; or uniform  distribution,  uniformly  during  the  assuming  that  preparation  of  money  the  flows  feasibility  study.  3.4.2 D E S I G N During  the design  the  project  in  its total  mechanical of  are defined.  designing  roads  should  that  construction execution mentioned treated  3.4.3  is  large  required  components  structural, housing  utility  a n d sewage  has a  also  phase, be  in the  are  projects,  of  included  electrical  or  and  the  cost  infrastructure  systems  relatively  relatively  the  cash  expressed previous  as a g l o b a l  and  internal  one  or broken  duration  relation  generated of  s e c t i o n . The  quantity  analyzed  low i n  flow in  short  the  design down  and  to  the  during  i t s  three  ways  cost  may  t o produce  be  a set  independently.  CONSTRUCTION During  considered order  I n some  phase  may  sub-flows  major  specifications  included.  this  i t s cost  Four  as water  be  the p h y s i c a l  architectural,  some  such  Given  of  cost:  design.  facilities  stage,  the t o be  to proceed  acquired.  This  construction  construction integral with  these  task  phase  part  and  is  phase,  a l l the  of the p r o j e c t  activities, really  make  take  facilities  are b u i l t .  the land  has t o  independent place  anytime  of  In be. the  before  62  beginning  of c o n s t r u c t i o n .  land  value  i s represented  the  beginning  reasonable the  land  is  subject  of  on w h i c h  a  involved  specify  a schedule  series the  time  when  the  present  discounting  other are  also  the  logical  i s that  that  construction  beginning  have  and e n d i n g  Thus,  a  discounted  to When  be o b t a i n e d  by  the  that  land  this  the  is  i s subject  are linked  r e l a t i o n s h i p s . Those packages  are  an  schedule.  One  t o have  t o be e x e c u t e d and l e s s  each  a  work  logical  network  characteristic an a g g l o m e r a t i o n  towards  o f them  construction.  a  the middle  towards  a  activities  and f o l l o w i n g in  to  to  (generally,  arranged  i t tends  of  may  with  project  of a c t i v i t i e s )  period,  agreements  be e m p l o y e d .  given  activities  work  they  the  investment.  i n which  construction  a network  activities the  rules,  between  i n the c a l c u l a t i o n of  o f any c i v i l  is a collection  may  i t should  the project,  t o as  a  planned  years.  worth  associated used  is  i s being  several  starts,  used,  rate  of the  to  referred  precedence defines  of  schedule,  according  package  such  value  construction  predefined  is  outflows  component  The  along  at  the a c q u i s i t i o n of  Such  or i t s present  method  This  agreements  negotiation.  the  occurring  phase.  development  the construction  studies,  payment  cases,  contractual  a t t h e same  present  integral  state  of payments  the  acquisition net  real  flows  worth  single  b u t i n some  i n the  of s i n g l e  a  evaluation  construction  to s p e c i a l  parties  most  by  the  assumption,  In  both  that of of of the  63  The  latter  implies  that  during  more  heavily  spent  at the  less  heavily  spent  at the beginning  Also,  due  between be  to the  these  nature  of  two d i f f e r e n t  exponential,  turns  middle  and the  direct  this  patterns  There  only  a r e two  costs  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 assumed  during  to  be  construction,  constant  construction.  management,  overheads,  Mobilization  and  They temporary  and d e m o b i l i z a t i o n  be  payments  of time  greatest  costs  They  was  can  Several  they  component  construction, It  or uniformly  when  of  discussion previously  be  expressed  mathematical  include  are  and they  flow  will  focus  on  mentioned a  Beta,  that  former  distributed  so  incurred may  forth. at  the  be a s s u m e d  during  the  cost  generated  to  short  are  the  during  them. direct  bell-shaped may  indirect  The  and  direct  cash  cost  administration,  utilities  Since  the  major  uniformly  the  functions  the Normal,  to  function  the  costs.  distributed  occur.  by  other  namely  costs  and end of c o n s t r u c t i o n  period  tends  represents  include  beginning single  transition  curve.  incurred  be  the  and  period.  expenditure  items  can  during  is  of the process  of expenditure  of f u n c t i o n  costs.  money  and end of t h i s  construction  type  construction  stages  the networks,  o u t t o be a b e l l - s h a p e d However,  construction,  be u s e d  type  construction of  for this  Gamma, R a y l e i g h  and  curve. purpose. Weibull  functions. 1.  Normal This  density is  the  function well-known  probability  distribution  64  function, the  also  =  _ ^ e x p " ay/2-n  u i s the  where  probability In  (  t  ' 2a  M  order  to  n should  by  will  will  3.14  i s the standard  the  variable  since  result  t  points  actual  mean.  This  figure  4,  as the time  and a as a  a  wider,  in  the value  function may  symmetric than  the  by t h e B e t a some  presented  rule.  at  values  made Also,  and  minus  at the  with  time  respect  using  a r e more  be s e e n  o.  the  may  be  later.  In  normal  of u and  to  i t , since  disadvantage  and t r a n s f o r m e d  for different  of  ends.  when  f u n c t i o n as w i l l  truncated  be  flow.  plus  patterns  This  Eqn  [0,1].  should  cash  i s symmetric  expenditure  whereas  curves.  be t r u n c a t e d  be a r e s t r i c t i o n  parameter.  interval  and  of zero  peak  i e .the values  the  time  the  profiles  transformation of  when  smoother  function,  only  values  narrow  expenditure  shape  c o n s t r u c t i o n commences a n d  normal  overcome  deviation in  construction  t h e f u n c t i o n has t o  The  exception  in  an a p p r o p r i a t e  where  perfectly  standard  yield  normal  are  C ( t ) takes  infinity,  and o t h e  i s obtained  values  obtain  (3.14)  2  be v i e w e d  of a  values  Therefore,  )  represent  high  are  It i s defined  2  mean  expenditures  Small  its  curve.  distribution.  functions,  to  Gaussian  equation:  CU)  of  called  curves  FIGURE 4-- T r u n c a t e d 0.1 0.03 H  Tfm*  normal  curves  66  The  Beta  distribution  The  Beta  distribution  perhaps, flows  t h e most  C(t)  useful  associated  Mathematically,  with  i ttakes  _L_  =  (  a  +  Z-A  defined is  for values  l  )  can  be  equation  t o express  capital  projects  fc  '  A  8  ^  Z-A  and  expenditure  (3.15)  A a n d Z, a n d w h e r e  t h e shape  uniform, or  In f i g u r e  are  shown  The  Gamma  f u n c t i o n has t h e form:  t  )  skewed  bell-shaped of the  combinations  parameters.  function  b  function  exponential,  for different  Gamma  (  extreme  5, s e v e r a l c a s e s  The  b  C(t)  parameters.  o f a and b, t h e Beta  represent  patterns.  general.  t , A and Z a r e t h e  symmetric  distribution  -  in  Z-A  a t time  to  and  continuous  b  of t between  combination  used  triangular  C(t)  function,  of t h e f u n c t i o n and a a n d b a r e shape  a proper  of  +  o f money  With  Beta  b  versatile  the form:  a b  t h e flow  values  i s a very  !  6  X  p  (  -  b  t  (3.16)  )  n!  The flow  value  of t h e parameter  while  noticed  that  b  i s this  n determines  a scaling function i s  parameter. equal  t h e shape It  t o zero  oft h e  should for  be  values  FIGURE 5. Beta  distribution  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  examine. values The It  The  of  n  shape  be  a r e , however,  of  t h e Gamma  i s presented  Rayleigh may  t^O  advantageous  t o use  parameter.  Mathematically,  given  Rayleigh  function i s :  C(t)  —exp a 2  it  a  has  shape The  been  Concluding as  1  =  n  defined shape  this  that  function to  i t  the  of  the  different  enumeration,  alternative  to  represent  contains  expression  f u n c t i o n . In values  only  one  of  the  (3.  17)  figure  7,  to present  t-Ts  (b-1 )  t-Ts  n  the  the  the  function  is  construction  form:  b  (3.  18)  n  for t>T , g  some  the Weibull represent  f u n c t i o n . I t has  factor  presents  6.  function.  this  expenditure  C(t)  different  function  an  b  for  to  2  assigned  this  Weibull  given  2a  i s the parameter  of  interest  function  flows,  where  no  function  in figure  continuous  =  of  and  where T  g  n  is a  examples  of  is a  s c a l e parameter,  location  b  i s the  parameter. Figure  the Weibull  function.  8  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 = 5 c a l « , n = 5 h a p « 0.1 0.09  b*.1 ,n=0  H  +  b = .15 n=1 r  b = .2+,n=3  b = .33,n=6  cn  F I G U R E 0.8  7,  R a y l e i g h  f u n c t i o n  F I G U R E  8.  W e i b u l l  f u n c t i o n  P a r a m « t « r s : b = S h a p « , n = Scal« 6 -i  —  0  :  10  b = 2,n=3  20  +  b = 2.5 n=2 r  30  O  b = 3,n=1.5  40  72  One  of the p r e v i o u s l y  represent  the d i r e c t  necessary  t o make  to  meaningful  obtain  reminded total  that  direct In  a  values  the t o t a l  cost  may  profile,  transformation of time  area  be s e l e c t e d  under  but i t i s  to i t in  a n d money.  to  order  I t should  the curve  equals  be the  costs. to  these  c a n be a d o p t e d ,  that  the c o n t r i b u t i o n  term  combine  shape  functions  construction suitable  addition  distributions  described  but they  have  polynomial  the disadvantage  of t h e c o e f f i c i e n t s and powers  to render  adjustments  distributions,  conceptual  of  each  v i s u a l i z a t i o n of s c a l e  more d i f f i c u l t ,  except  f o r very  low  and  order  polynomials. At  this  generated projects and  during c a n be  are  direct  an  the  follow  of  the cash  construction  costs  uniformly  costs  example  introduced.  demobilization  cost  and  point,  phase  In f i g u r e  9,  are discrete  distributed a Beta  flow  of  real  the  estate  mobilization  payments;  during  profile  indirect  construction  d i s t r i b u t i o n with  and  parameters  a=3  b=3.  3.4.4  ABSORPTION The  absorption  construction During  and  negative  revenues  of the  phase  steady  this period  generate  selling  PHASE  project some  flows. start areas  the  interface  operation  some a c t i v i t i e s cash  or l e a s i n g  state  is  like  But a t being  of  the  project.  marketing  and  t h e same  time,  collected  or units.  between  sales  by means  Absorption  rate  the of is  FIGURE 9. C a s h flow d u r i n g  construction  74  defined  as  the  For  instance,  the  number  facility rate  but  upon  market  negative  at  be  of  the  this  unit  of  presented  cash  when  be  or  rate  month  be  the  this  to  has  the  two  until  the  function  real  is finished,  since sold  i s considered Otherwise The  may  be  or, to  part  operation  depend the  rate  equation.  positive  will  A  expenses,  partial  already  chapter,  the  components.  a  the  line.  the  absorption  start-up and  by  rate,  straight  be  constant.  profile  revenue  sold.  would  the  construction  obtained  exponential in  every  uniform,  absorption  is a  that  Obviously,  the  to  flow  to  If  leased  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  multiplying  later  leased  marketed.  time  This  is  building,  or  revenues  price.  an  project  corresponding  the  function  form  the  the  by  the  i t i s assumed  project.  calculated by  the  assumed  representing  nature  the  portion  may  the  sold  i s completely  Therefore,  of  which  apartment  units  in general  that  at  i n an  of  depends  estate  rate  on  the  income  is  leased be  it will  area  constant, take  logistic  considered  the  curve, for  that  purpose.  3.4.5  OPERATION A  of  real  leasing  premises of  of  estate  in  capital  i s undertaken  or  selling  a  the  project.  The  i n t e r e s t when  only  venture  this  the  case  committed  project  when to  fixed  the  the  useful  analysis is  to  owner  project.  with  of be  area this  leased  still  the  has  objective within  phase  is  since his  the only  it  is  original  75  Conceptually, during  the  the  operation  Revenues  are  the  unit  rent  price.  and  operating  costs.  There  vacancy leased area the  of  in  a  provided.  It  prices  a  at  certain  can  of  cash  flow  two  should the  or  a  first  95%  alternatives  of  a l l  can  be  it is  be  employed.  in  should  be  of  them  would  rent every  yield  would  are  the  If  of  second  a  completely  increment  method  The  assume  analysis  revision  the  i s 5%,  escalation the  in  to  be  dollars.  by  maintenance  rate  p r i c e s might  profile.  This  an  imply  presented  a in  10. costs  fixed  a  at  taxes,  in  those  (utilities unusually  real  given  items  and high.  estate  value,  insurance,  administration.  between  income  consider  area  i s not  vacancy  rent  The  fixed  facility  current  rate,  leasable  simple.  i n t o account  second,  of  time.  function.  of  generated  i s very  i t i s convenient  rent  either  Operating  include and  current  the  almost  the  And  flows  project  take  the  if  or  mechanism  amount  stepwise  be  Thus,  continuous  exponential  to  that  space.  dollars,  Otherwise,  to  calculation  leasable  cash  of  are  First,  means  the  multiplying  Expenses  either constant  constant  figure  type  aspects  time.  i n the  total  this  revenues.  any  used  done  two  rate. This at  of  c a l c u l a t e d by  are  calculation  of  form  in  projects constant  maintenance, is  worthwhile  that  are  dependent  Then,  the  only  when  outflow  be  to on  the  assumed  dollars.  utilities,  It  janitorial)  can  They  janitorial  differentiate the  leased  vacancy  occurring  rate  during  area is this  77  phase  may  be  3.4.6  DISPOSAL When  the  the  useful  facilities  implies land to  represented  can  time  when  studied  valorization adjacent  PROCESS  The  last  are  those  any  proposal  new  or  real  are  single  inflating  an  property  during  the  due  life  of  That  flow.  Also,  benefit  The value  i t  should due  developments  the  end,  is sold.  i t s current  sold.  to  an  to  in  the  project.  INDUSTRIES of  capital  which  project  i n the  will  or  main  ones  The  short,  discrete  investment  facilities. stages:  generated  venture,  The  the  generated  with  They  during  in  which  purchase payment  expenditure  of  and pattern  defined of  can  and  be  broken  can  be be  during is  disposal.  exception  may  for  design,  them  analogous  and  as  cash  a l l of  analysis  money land  the  only  feasibility  review,  feasibility,  during  the  in this  industries,  construction, operation  profiles  phase.  considered  process  require  processing  five  estate  bell-shaped  is  to  discrete  the  the  uniformly.  single  be  come  land  of  cash  rather  by  the  additional  modified  operating  positive  calculated  undertaken  to  a  and  has  there  implementation  a  and  project  if  into  similar  the  distribution.  to  type  The  of  uniform  i t i s intended  areas  3.5  down  be  life  a  demolished  negative  value  the  be  a  are  by  phase  in  being  design  assumed  to  represented implementation,  generated.  are  Given  the phase flow by  a a the  78 nature  of  required  process to  portray  items  during  yield  a positive value  the  land.  These  3.5.1  will  only  sold  revenue  per  cash  the  costly  equipment will  corresponding  the s e l l i n g  already  cash  be  of the p r o j e c t  flow  plus  have  necessary before  or  influences  When  she  more  of  been  flows  to  price  of  discussed  generated  until  the product  moderated.  can  than  during  is different  general  pattern  two  factors  each  of  potential level  the  demand  in figure used  to the  curve  rises  is  saturated i f any, i s  due  cycle,  product,  to  the This  and  of  but  i t s  represent  the  11.  functions that  introduction,  is  a n d due  alternatives.  life  particular  i t  customer  and growth,  product  are  satisfied  sales  from  unit.  existence  purchaser, the  of  i t s  i s a p e r i o d of d e c l i n e  f o r each  a r e two w i d e l y  per  introduced,  t o know  and c o m p e t i t i o n  i s shown  during  If  a given  called  course,  volume  customer  is  number  price  these  product  campaigns,  there  obsolescence  There  industries,  buy.  of the  selling  one p o t e n t i a l  reaches  is  the  the t o t a l  Finally,  process  the product  a new  marketing  exponentially  product  and  for a potential  he  effects  year  is  i n the process  independent.  sales  of  may  be s t u d i e d .  annual  Generally,  whole  concepts  payments  OPERATION  units  and  discrete  of the equipment  Therefore,  The  not  the a c q u i s i t i o n  single  salvage  operation  discrete  c o n s t r u c t i o n . The d i s p o s a l  the  earlier.  industries,  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  Tfm* (months)  80  100  120  80  product.  They  Gompertz  curve  In  y =  a r e the Gompertz  I n A1  limit  equal  during  t o t h e demand parameters.  the  sales  the early  may b e e m p l o y e d .  y  volume  fordifferent  When  a t time  t , A1  i s an  of a s a t u r a t e d market, In f i g u r e  values  trend  years  (3.19)  asymptotic a n d A2  12, T h e G o m p e r t z  and  curve i s  o f A2 a n d A 3 .  is  not  of the l i f e  Mathematically,  expected  cycle,  i t takes  to  be  skewed  the l o g i s t i c the  curve  form:  hi  =  The  - A2exp(-A3*t)  y i s the sales  presented  curves.  has t h e form:  where  A3 a r e s h a p e  and the L o g i s t i c  (  3m  20)  1+A2exp(-A3*t)  The  meaning  for  E q n . 3 . 1 9 . Some  the  influence  figure  3.5.2  of t h e terms  in this  typical  expression  shapes  of the parameters  i s t h e same  of the l o g i s t i c  as  curve and  A2 a n d A3 a r e p r e s e n t e d  in  13.  EXPENSES Cost  incurred  can  also  the  beginning  project.  be d i v i d e d  in  the operating  into  of t h i s  direct  phase,  and i n d i r e c t  working  The r e p r e s e n t a t i o n o f  of process  cash  capital flows  industries  costs.  Also, at  i s added  related  to  to the these  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  •  A3=0.08  +  A3 = 0.12  O  A3 = 0.16  CD  83  items  also In  be  h a s been  Table  used  to  project  1, t h e summary represent  type  IMPLEMENTATION  The  computer  user  to  project 1.  cash  and p r o j e c t  3.6  functions  previously  as b u i l t - i n  phase,  Initial  flow  phase,  patterns,  those  chapter. can  according  to  PROGRAM  of  function  that  flow  that  i s presented.  h a s some  cash  in this  of a l l the functions  ON THE COMPUTER  program  represent  discussed  the previously  described  c a n be s e l e c t e d  profiles.  According  by  the  to  each  functions a r e :  investment  (Land)  and d i s p o s a l :  Single  discrete  payment. 2.  Feasibility discrete  3.  Construction:  flows),  uniform  Operation:  function, number  phase  as  exceed  50.  represented uniform  uniform  function,  as  For by  specified.  example,  fixed Fixed  the  of which  and costs  a r e assumed  curve. t o each  of  flows  do  phase  can  cash  3 a r e Beta  variable  Beta  c a n be a s s i g n e d  construction  an 2 a r e d i s c r e t e  discrete  function,  and Gompertz  number  discrete  (trapezoidal  two  linear  of any type  the t o t a l  12 f l o w s  functions  Also,  flows  two  function.  payment,  function  two  function  and exponential discrete  payment,  payment,  linear  Single  exponential  discrete  function.  discrete  function,  function  of cash long  Single  and uniform  Single  Beta  payments,  Any  Design:  payments  payments,  4.  and  functions,  not be  7 are  payments.  operating to take  costs effect  can  be  a t the end  TABLE 1. Summary o f mathematical f u n c t i o n s used t o express cash flow p r o f i l e s PROJECT TYPE O i l and Gas  Mining  Uniform Step f u n c t i o n Straight line  Uniform Step f u n c t i o n Straight line  Real Estate  Process  Industries  PHASE  Exploration  S i n g l e payment, Two d i s c r e t e payments. U n i f o r m  Feasibility and d e s i g n  One d i s c r e t e: payment  Initial Inves tment  Construction  Set  Operation  Exponential d e c l i n e curves  Disposal  function  o f d i s c r e t e payments, Uniform,  Uniform, s t r a i g h t line, logistic  Beta, Normal, Gamma, R a y l e i g h , W e i b u l l  Uniform  One d i s c r e t e payment  Uniform, E x p o n e n t i a l , Gompertz, L o g i s t i c  85 of  each  year.  production  Variable  costs  output to obtain  are  the t o t a l  multiplied  the  taxable  income. The  operating  repayment  costs,  latter  i s obtained  depreciation  the  costs.  T a x e s a r e t r e a t e d by m u l t i p l y i n g t h e income the  by  and  by. long  tax rate  by  substracting term  debt  f r o m 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 . I n t h e  program,  two d e p r e c i a t i o n  m e t h o d s have been  implemented:  straight  l i n e method and t h e d e c l i n i n g , b a l a n c e method.  the  CHAPTER 4.  S E N S I T I V I T Y ANALYSIS  4.1  INTRODUCTION  The  development of m a t h e m a t i c a l  m o d e l s t o compute  performance measures i n a d e t e r m i n i s t i c  fashion  step  and  in  the  decision  capital projects. considerations of p o r t f o l i o the  making  Along  such as  with  very  etc., these  information  isa  of  qualitative  diversification  models w i l l  for deciding  first  evaluation  important  s o c i a l convenience,  investment,  required  process  economic  generate  between  proceeding  the cash flows  associated  with or r e j e c t i n g a p r o j e c t . As with  seen i n t h e l a s t c h a p t e r ,  the phases of a  according  to  considering a given  the  p r o j e c t have d i f f e r e n t shape and investment  type.  Furthermore,  size when  s i m i l a r t y p e s o f p r o j e c t s , t h e shape and s i z e o f  c a s h f l o w p r o f i l e may c h a n g e a c c o r d i n g  to particular  p r o j e c t c h a r a c t e r i s t i c s a n d / o r management s t r a t e g i e s . One o f t h e evaluation flows  of  most c r i t i c a l  any p r o j e c t  profiles to  involves  calculation  the  definition  tasks of  i n the  the  the evaluation process.  f u n c t i o n a l forms  involved  w h i c h we may  primary v a r i a b l e s  r a t e s , market p r i c e s , l a n d v a l u e 86  call  primary  are inflation  This  values  variables.  and  and c o n s t r u c t i o n  cash  i n the  o f t h e p e r f o r m a n c e m e a s u r e s and a s s i g n i n g  to t h e i r parameters, E x a m p l e s of  i s the  be u s e d i n  selecting  and i m p o r t a n t  taxation duration.  87  4.2  PARAMETER  The  estimation  projects  ESTIMATION and  i s not  environment). estimation thesis. making  forecast  an A  and  easy  task  detailed  however  estimates  about  the  The  use  of  historical  2.  The  use  of  the  is  is  of  beyond are  the  the  three  future,  events  in  i t in almost  discussion  there  1.  future  (nor  forecasting  Briefly,  of  any  other  methods  scope  basic  large  of  of this  approaches  to  according  to  Hull  [24]:  experience  of  one  person;  experience  of  several  data;  judgement  and  and 3.  The  use  of  the  judgement  and  people. Historical and  estimated.  indirectly.  the  The  has  disadvantages,  or  lack  a  to  the  structures  may  be  him  of  be  The found  a  the  of  to  In  the  her  in  and  a  either  of  order  the  different  between  of  a  which or  possible  overcome not  to  the  directly  factors  to  with  asking  situation  disadvantage  and  elsewhere  variables  parallel  individuals  produce  statistical relationships  consists  consideration  project asked  or  and  encountered has  group  variables. may  draw  knowledge.  committed  forecasting  method  to  with  possible  certainty  second  approach  estimator's  primary  with  facing  combination  identify  previously  This  bias  in  to  known  currently  she  personal  used  professional  situation or  be  models  variables  qualified  he  can  econometric  between be  data  outside these  a l l  heavily  different  reward  best  estimate  approaches [24],[40].  to  for  the  group  88  4.3  RISK  MANAGEMENT  Independent estimates be  an  from  about  element  They  are  the  data  only  there  matter  they  are  investment  change,  several  the  arises,  with  such  estimates.  or  and  how  primary  variables,  about  the  reliable  expert  cash  flows,  initial  uncertainty  calculated  values.  Therefore,  evaluation  process  is  in  the  a  This  risk  the  -  such  as  etc.,  it  is  risk  in  an  the the  turn,  uncertainty  gives  estimates. as  is  of  and  then  activity  in  cash  to  the  reduce  is  to the  the  transferred step  rise  Since  functions  further  assess  project.  that  in  flow  computed  to  of  environment,  which  are  the  sources  e s s e n t i a l l y , from  measures  their  economic  the  risks  referred  to  as  management. Two  analytical  been  developed.  will  be  The  known  risk  as  second  performing  probability procedure  The  discussed  chapter.  in  provide inevitably  precise  literature  performance  risk  to  will  based  political  in  project  uncertainty  involved  how  used  there  associated  no  exist  recognized  the  variables,  uncertainty  which  is  are.  technological  about  technique  primary  estimates  Although  widely  the  of  on  forecasters  which  procedures first in  one  detail  one  for  is  quantifying  sensitivity in  the  consists  in  simulation.  Briefly,  Monte  simulation  Carlo  distribution  involves  four  of basic  the  analysis  remainder  carrying  this in  out  technique order  performance  steps:  risk  a)Define  a  to  have and  of what  it  this is  consists find  the  measure.  The  probability  89 distribution  most  suited  random  from  each  value  variable;  c)run  combination d)repeat  of  a  In  values  of  SENSITIVITY the  last  level,  technique  different The measure  et  for  performance  a l . [14], which  measure  technique  from  analysis previous  obtain  the  b)draw  a  i t to  each  using  the  point;  and  probability  measure.  analysis  define  "What  i f the  that  NPV  primary  IRR)  likely  and  then of  At a  the  as  conceptual  deterministic "What value x  if..." of  the  assumes  a  for i t ? "  the  or  a  variable  calculating  on  introduced  answers  would  estimated  or  most  measure  was  - i t as  primarily  involves f i r s t  variables  performance  be  than  (usually  primary  assign  for quantifying risk.  instance,  value  calculated  to  sensitivity  technique  questions,  and  i n the  times  variable;  ANALYSIS  Flanagan  modelling  selected  performance  section,  mathematical  primary  distribution  of  the  each  deterministic  number  distribution  4.4  a  to  basis  "best"  observing  changes  of  a  performance  of  cash  estimates the  effect  those  flows of  the  on  the  most  likely  estimates. The if NPV  the or  basic  change IRR,  depend  to  On  other  the  large  o b j e c t i v e of i n an  then  any  change  hand, in  estimate  the  great  sensitivity has  investment  extent  on  very  analysis little  decision  the  accuracy  if a  change  in  the  performance  the  is  effect  i s not of  simple:  likely  that  estimate measures,  on  the to  estimate.  produces then  a the  90  uncertainty  surrounding  significant  consideration  being  made. T h u s ,  a  of  way  quickly  contribute Using will  a  identifying to  the  this  information, to  between  the  exposure,  and  cost  should  collected  of  will  also  mitigation  strategies  insurances,  etc.  UNIVARIATE  The  most  quantifies primary  the  change  variable  original  values.  only  variable  two  one  different  analysis exact  if  ways  will  analysis.  be  is  regarded  as  of  the  project making  reduces  least The  which  risk  that  equals  result  term  it its  of  the  appropriate  long  a  risk  contracts,  ANALYSIS  approach in  is  meaning  defining  as  decision  variables  that  at  analysis.  such  the  to  and  at  carrying  discussed.  sensitivity  performance the  basically  i s changed of  i t s value  in  a  uncertainty  information,  and  i s changed This  and  be  be  management  information  helpful  SENSITIVITY  generalized  project.  that  only  be  the  risk  of  can  primary  of  well  investment  analysis  the  value  may  those of  c o l l e c t i o n , storage  analysis  4.5  risk  reduce  the  the  sensitivity  trade-off  cost  estimate  when  most  proceed  be  the  a  rest a  time. out  They  measure are  held  In  this  the  when to  univariate  univariate  are  analysis one their  analysis:  section,  the  sensitivity  linear  and  the  91  4.5.1  LINEAR Linear  obtaining  sensitivity an  sensitivity complete  approximate  of  or  each  time  from  called  of  variable. when  the  by  from  benchmark  the  total  linear  Z • i=1  3f 3  of  primary  i s the  function  with  evaluated  at  control  may  PQ  higher. terms  be  linear  and For  are  the  using from  then  the  would  theory is  be  the  in  used  a  highly  sensitivity  obtain  point  or  analysis  linear  fundamental  systems  to  operating  first-order  is  deviations  formula  of  the  calculus:  (4.  performance  measure  variables.  The  respect  the  expanding  point  of  replace  dx.  P  It  of  degree  may  latter  way  1)  X i  where n  and  evaluating  differential  n  the It  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  conducted  by  simplified  quasi 1 i n e a r i z a t i o n  is identified  =  estimate  primary  benchmark  dP  is a  consuming.  technique  engineering these  analysis  (or exact) approach  expensive A  ANALYSIS  point  noticed  the  to  a  function  derivative  primary  of  variable  f  this x^  is  PQ. that  function  neglecting sufficiently  from  partial  each  the  f  which  same  in a the  r e s u l t can  Taylor's  terms  small  n e g l i g i b l e compared  terms,  e x p r e s s e d as  series second  deviations,  with  the  of  the  name  first of  be  the  about  the  order  and  non-linear  order  this  obtained  terms  (or  approach  is  92  taken).  We  deviations issue From  however,  from  the bench  i s the range  by  Taylor's  performance  =  Since  =  3  x  small  i  this  i n the by  analysis  very  important is  approximation  immediate the  an  vicinity  linear closely  terms  valid. can of  PQ,  of  the  the behavior  the  deviations  differentials  dx^  can  may  (4.  2)  case  i s being  t o change,  considered, only  i e . Ax^=0,  the  jth  i * j , then:  (4.  3)  j  the  variable  of  be  A x ^ . T h e r e f o r e , E q n . 4.1  £ £ Ax . X  be  1  i s allowed  first-order  describing  the x^,  coefficient s-;  the l i n e a r  approximates  the u n i v a r i a t e  3  Now,  Thus,  large  Ax.  1  variable  =  value.  of view,  defined  to investigate  as:  I 1  AP  which  wish  3f  n  AP  mark  practice,  by  rewritten  we  measure.  actual  substituted  that  that  plane  expansion  In  be  saying  tangent  the  over  a geometrical point  justified the  note,  partial  performance is  defined  of the v a r i a b l e  mathematically:  derivative  with as x^,  respect the  of  the  to  each  absolute  and w i l l  be  function primary  sensitivity represented  as  93 3f  (4.  However,  this  absolute  changes  performance Using by  Bode  coefficient both  c a n be  in  only  used  the primary  to  variables  4)  quantify and  the  measure. the d e f i n i t i o n  and q u o t e d  percentage  or  performance  in  of Sinha  relative  measure  coefficient  will  be  coefficient  and w i l l  [50],  change  can  be  coefficient  the magnitude  in  a  linked.  This  represented  by  S^.  given of  variable  the  and  a  sensitivity  t o a s t h e relative  referred be  sensitivity  sensitivity  Bode  defines  as:  9(ln  P)  9P  x • l  =  P  (4.  5)  (4.  6)  P  then:  AP P  which  i s the d e s i r e d  same p o i n t 4.3  by  expression. Again,  in a different  P and  then  by  x^,  way: yields:  dividing  we  can a r r i v e  both  sides  of  at the Eqn.  94 AP  .  3x  r  j.  P.x  i  rearranging  (4.  7)  (4.  8)  i  terms:  Ax.  AP  l  P  Equations  4.6  definition be  of  obtained  tabular  S^.  4.8 The  are  a l l the  format.  However,  critical  which  straight  will lines  a  result  passing through graph  percentage  change  i n the  representing  percentage  This  graph  and [24]  an  of  example  is given  measure  under  project.  As  straight  line  is  f o r an  with  as  consideration  In  the  approximation  and  shown  results  the  most  Eqn.  is a  4.8  to  origin.  These  of  the  i n the  example Net  the  holds  or  range  the  are  other  measure. diagram,  extracted the  from  performance Value  over  i s unknown.  of  representing  "star"  Present  or  primary  lines  and  o i l field  this  n  performance  "spider"  a  useful  equations  axis  variables  in  sensitive  the  i s the  previously,  can  of  hypothetical 14.  coefficients  number  one  change  the  same  primary  known  in figure  noted  of  indicates  i n the  single  kind  graph  to  variables  a p p l i c a t i o n of  in a  according  sensitivity  primary  quickly  v a r i a b l e s . The  variables  equivalent  relative  for  presentation  drawn  and  of  the  which  the  95  F I G U R E 14. S e n s i t i v i t y d i a g r a m S o u r c e : P e r r y and Hayes [ 4 0 ] .  4.5.2  LINEAR The  latter  difficulty measure the  ANALYSIS:  when  consideration  C A S E OF  rationale the  is explicit  internal  THE  rate  f o r an  can  function on  o i l field  I M P L I C I T FUNCTIONS be  applied  describing  without  the  performance  t h e p r i m a r y , v a r i a b l e s . However,  of  i s required.  return  is  used,  an  any  when  additional  96 The rate  internal  that  implicit  makes  the  function  derivatives implicit theorem  rate  are  NPV  of  return  equal  the  theorem  the  is defined  to  zero.  primary  calculated  function states  of  variables  to  the  Therefore,  differently. has  as  be  and  In  IRR its  this  used.  discount is  an  partial  case,  the  Briefly,  that  following:  Let:  P=f(X,y),  and  y=g(X)  (4.  in which g(x) i s the i m p l i c i t  function.  !l  and q= !£  =  -E q  3x^  The In  w i t h p= ££ 3x^  application Eqn.  4.9,  zero), the  the  IRR.  absolute 4.10.  Thus,  when  sensitivity  (i,y)  =  the  coefficient  S  (i,y)-J  analysis  the  contains  NPV  the  (4. 10)  will  be  is  straightforward.  (in this  primary  performance  coefficient  coefficient  x. s  sensitivity  X  Then,  3y  represents  vector  This  relative  P  to  9)  case  variables  measure  is  the  is calculated denoted  by  equal  to  and  is  y  IRR,  the  using  Eqn  s^.  The  is:  (4. 11)  97  and  the  r e l a t i v e changes  variable  A  -  y  —  "  A  U,y)  a  percentage  change  in  this  produced  to  /, ( 4  „,  -  I 2 )  i  x  primary  given  i  x  —  y  Using  IRR  i is:  c  s  in  equation,  a  represent  the  variable  when  the  similar  spider  degree IRR  is  of  diagram  can  sensitivity  selected  as  the  be  of  each  performance  measure.  4.6  EXACT  The  ANALYSIS  linear  analysis  described  in  provides  some  insight  into  which  most  the  overall  risk  of  to  sensitivity primary However, exact  coefficients  variables the  linear  to  of  pattern.  exact  An  evaluate  the  relative  change  (ie.  function  of  magnitude  The the  sensitivity  the  idea  primary  is  to  the  of  analysis the  the  are  fixed  increment  (again,  and  z  should  selected  the  project  considers  varied  only  one  can  the  "most  a to  the  follow  performed for  a is  an to  given now  a  change).  performance  between at  be  not  in  measure.  coefficient  relative  according the  does  the  relative  changes  variables  sensitivity of  The  performance  variables  recalculate  variables  be  the  project.  the  section  contribute  percentage  in  sensitivity  previous  variables  the  relate  those  the  -w%  time). what  measure  and  +z%  The  values  the  when  with of  management  pessimistic"  and  a w of  "most  98 optimistic" better  explained  In the of  the  this-  US$1.3 will  are  Thus,  in  this  the  and  that  the  US$1.0 to  most the  copper  increments  or  say,  ten  Note  nonlinear the  that  fashion  sensitivity  as  cents.  and  the  i f the with  curve  an  will  be  per  pound  valuated of  in  copper  characteristics  expected that  price this  This  the  most  respectively.  should  be  US$1  carried  and  may  plotted measure  variable  of  value  US$2.0.  estimate,  changes  results  not  price  than  between  primary  of  estimates  performance  the  one  likely  best  The  development,  future  analysis  price  be  behavior  higher  the  exact  the  terms  or  may  project,  the  i s not  optimistic  of  diagram.  it  concept  dollar  the  defines  case,  percentage  of  reviewing  values  in  constant  life  This  mine  management  than  and  copper  possible  referred  pessimistic  variable.  the  pound,  lower  a  the  considering  per  figures  example.  After  market,  be  an  is  over  dollars. and  each  of  variables  this mineral  prices  for  with  of  evaluation  primary  today's  of  estimates  US$2  out with  be  expressed  in  a  is  spider  linked  being  necessarily  a  in  a  studied, straight  line.  4.7  BIVARIATE  One  limitation  current  some e x t e n t . the  of  analysis The  extension  it  is  the  of  analysis  only  moderates  concept of  ANALYSIS  sensitivity  applications,  sensitivity  is  SENSITIVITY  this  that,  univariate.  A  sensitivity  approach.  In  in  . its  bivariate  l i m i t a t i o n to  bivariate  univariate  is  at  least analysis  this  case,  99  the  impacts  two  variables In  on t h e p e r f o r m a n c e  the  univariate  independence allowed not be  between  to vary  always  be  dependent  the  are allowed  variables  t h e new  contour  diagram,  surface  diagram  order  to  eventual of  variations  second  variable  performance other  of  the salvage  value  can  costs  possible  in  if..."  other type  on  related  ones  change measure  by m e a n s  figure  can  15,  of  a  or  a  order  maintaing  For  each be  to  to offset the o r i g i n a l  identified  deal  the  In with  the  life  required  changes value  variable,  as t h e i r  with  questions  during  t o know  particular  p r o v i d i n g management  of  be a n s w e r e d .  variables  be o f i n t e r e s t i in  types  strategies  i n the primary  may  may  or the t o t a l  shown  is  This  the performance  approach,  j , while  variables  one  o f them  constant.  two  of  16).  variable  mitigation.  each  sensitive  managerial  i t may  measure.  counterparts, risk  the  "What  implement  i n one  two  like  the  change  assumption  and d i s p l a y e d g r a p h i c a l l y  (figure  the project,  Letting  values  the b i v a r i a t e from  remain  highly  an  since  of the land,  when  time.  is  For instance,  two  are quantified  at a  there  others  output.  be c a l c u l a t e d  different  the  on t h e c o s t  or  Using  case,  the case.  simultaneously, can  t o change  the v a r i a b l e s  while  production  measure  in  a  of the one  or  "offsetting"  a valuable  tool  for  1 00  Contour 1 2 3 ' 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20  20  LCC 1 000 2 000 3 000 4 000 5 000 6 000 7 000 8 000 9000 10 000 11 000 12000 13 000 14 000 15 000 16 000 17 000 18 000 19 000 20 000  JO  Project lite (y)  FIGURE 1 5 . Contour diagram (source: Flanagan [ 1 4 ] )  FIGURE 16. S u r f a c e d i a g r a m  (source:  Flanagan [14])  101  4.8  THREE V A R I A T I O N S  Some  variations  sensitivity  of  into  capital  projects.  been  points"  Three  proposed  literature  but  since  functional  literature.  As  i n t h e whole  4.8.1  BREAK-EVEN The  that the  involved  of each  Value  i s the  its  when  the rest  point. the  break-even  This  i f IRR  point  will  Return  the break-even  rate,  herein,  analysis  t h e name  of  has  and have  "extreme  been  found.  treated  in  the  analysis,  simple.  level  yield  t h e NPV  is  project.  When the  variable  reverses the  an  IRR e q u a l  reverses  constant  the  primary  i s the performance  at  break-even  to the  the Internal  f o r the  Net  break-even  that  are held  called  identify  as the performance  Indeed, point  to  that  measure,  of each  i s used  of r e t u r n .  when  the  is  variable  of the v a r i a b l e s  rate  discount  with  two m e t h o d s  analysis  performance  acceptable is  associated  of s e n s i t i v i t y  primary of  the value  estimates.  Similarly,  first  are rather  decision  find  best  more  i s barely  issue  uncertain  will  their  provide  points  other  forms  here  approach sign  no  of break-even  accept-reject  Present  to  univariate  ANALYSIS  objective  level  of  be p r e s e n t e d  extreme The  to  concepts  will  forms.  Sensitivity  the  developed  o f them  analysis,  i n the  is  been  concept  and u n c e r t a i n t i e s  to functional  treated  ANALYSIS  basic  have  the risks  break-even  sensitivity  SENSITIVITY the  analysis  insight  namely  OF  measure, minimum Rate  of  variable  measure.  102  The  break-even  defined a  by  better  idea  uncertain  4.8.2  the  assess  three  different  the  most  assumption  the and  the  carrying  unacceptable  acceptable accepted  ranges  4.8.3  this when  have  SENSITIVITY  performance the  the  associated  interval to  give  with  each  former  point  to In  expect  will  spite  of  any  is  estimates  are  further  analysis to  it the  any  estimates  most  consists  in  a l l  the  their  The  lowest  Conversely,  simultaneously  this,  considering  the  estimates.  take  If  take  still  worth  investment combined,  further.  are  analysis,  is  If  combined, assuming  it  is  it  is  it  is  it  that  can the  estimated.  FUNCTIONAL  due  to  primary  and  combining  optimistic  them  should  uncertain  analysis  measure  variables  accurately  measure  each  is overly-pessimistic.  worth  TO  management  pessimistic  calculation.  without been  most  the  pessimistic  Sensitivity  since  with  estimates  that  for  extreme  optimistic  not  when  the  a l l  time  value.  certain  The  a l l the  same  out  estimates  then  that  highest  almost  risk  previously  performance  overly-optimistic  their  optimistic  potential  likely,  estimates.  pessimistic  at  and  compared  ANALYSIS  mentioned  calculating  be  POINT  was  optimistic  is  the  then  variable.  variable:  value  is  pessimistic about  EXTREME It  point  FORMS  examines  the  variations  in  obviously  a  changes primary  function  of  the  in  a  variables latter.  103  However, depends the  the  NPV,  not only  functional  flows. flow  These  into  IRR  or  on t h e v a l u e  forms  that  functions  or outside  the performance  to  know  how  sensitive  principle  (or  parameters)  is the  study  such  i s defined.  the flow  computed  measure.  that  are selected  selection  as f r o n t -  representation  or back-end of t h i s  a  spider  parameter  are considered.  presented  as a  steps  the  in  simple  capital  projects.  nature,  i t  presented 1.  by P e r r y  and Hayes  that  there  impact is  cash  t o be  on  a range  flow,  a r e used  construction  measure  to a i d  projects.  in  The  be d o n e  changes  in  by one  S E N S I T I V I T Y ANALYSIS  used  analysis a s one  has  of the  quantification  benefits. [40],  Those  of  been first  risk  in  preliminary  benefits,  as  are:  management o f of  to  strategies,  cannot  the  a  forms  likely  i t ss i m p l i c i t y and i t s  important  The p o w e r f u l  OF  and  brings  interest  variations.  management  unless  technique  Despite  thought  sensitivity  evaluation  of  change,  set of f u n c t i o n a l  of a n a l y s i s  diagram,  chapter,  will  and the performance  loaded  4.9 CONCLUSION: T H E B E N E F I T S this  For each  diverse  type  money  i s to such  The r e s u l t s  of  means o f  Throughout  are  a  cash  i t they  be a l s o  on  of the  much  Therefore, I t may  Then,  f o r a l l o f them.  and  a n d how  i s the following.  form  describe  when  measure,  but a l s o  t h e shape  the investment  functional their  describe  the p r o j e c t .  will  performance  of the v a r i a b l e s ,  define  so  The  any o t h e r  possible  the  realization  outcomes  for  the  104  project; 2.  Decision  making  information  is  on  made m o r e  which  realistic  decisions  although  a r e made  becomes  the more  complex; 3.  The r o b u s t n e s s be  4.  The r e l a t i v e  importance  therefore  benefit  from  or  further  4.10  need  t h e computer linear,  ON  exact,  have  absolute  and r e l a t i v e  to  NPV,  different  values  optimistic  estimates  bivariate  of the  analysis  i n the  estimates matrix  range  f o r each  containing to  100 s e t by  of the this  interpolate  as  part  most  uncertainty,  of t h i s  thesis,  sensitivity  analysis,  c o e f f i c i e n t with  f o r each NPV  is  for  the  10 and  break-even  range. by c o m p u t i n g  of points  the pessimistic two v a r i a b l e s  constant  taking  and  being  i s presented. of  variable.  calculated  and  i n that  combinations  selected  the  respect  the pessimistic  i s performed  contours  which  bivariate  variable,  results  immediately  PROGRAM  s e t by  i f i t exists  areas  In t h e l i n e a r  the  t h e range  f o r the r e s u l t i n g  points  made  on  is  or control  and  sensitivity  analysis,  i s calculated The  NPV  developed  implemented.  the exact  those  THE COMPUTER  IRR a n d T C C a r e c o m p u t e d  In  point  can  work.  break-even  analyses  variable  to reduce  development  program  been  of each  highlighting  attempts  IMPLEMENTATION  the  to specific uncertainties  compared; and  apparent,  In  of projects  the 10  optimistic studied.  No a t t e m p t NPV  A is  values.  Similarly,  contours  of  constant  IRR  are  not  identified.  CHAPTER  5.1 A  5. THE COMPUTER  PROGRAM  INTRODUCTION  computer  program  the  main  computer  was  implemented  previous provide any  a star  also  computes  program  ii)calculation  about  language)  treated  in  the model  the  is  the s e n s i t i v i t y  involved  and  are  a period-by-period  cash  projects.  points  analysis  to of  i n the  capital  break-even  is  made  of  Internal  the  Rate  up  of f i v e  The  main  of Return,  cash  flow;  to  flow  patterns;  describe v)the The  cash  plot  of  general  flow  chart  Flow  control  data  input  major  parts  performance  period-by-period  and  of  typical  d-iagram,  o f 49 s u b r o u t i n e s .  Value,  objective  parameters  with  available at  exact  produced.  cash  flow  in  dollars.  The total  of the t o p i c s  information and  compiler  77 p r o g r a m i n g  and b i v a r i a t e s e n s i t i v i t y  program  current  basic  with  associated  univariate The  The  variables  Specifically,  (FORTRAN  i n c l u d i n g most  the user  flows  t h e FORTRANVS  o f UBC  chapters.  of the  using  (Net  construction  built-in  iv)the  with  are: i)data  measures  Total  iii)the  modules  input; Present  costs  functions  sensitivity  a  and used  analysis;  results. architecture  i s depicted routine subroutine  in  of  the program  figure  initiates (step  106  17. A m a i n  the program 1).  Once  and i t s segment  basic called  by c a l l i n g this  process  the is  Flow | controlj  I  I  I.  1  i  3 I Data | j input j  I  I  I I | Menus  i  I  T I  r  Output file  i  i.  11  4|  12  NPV IRR TCC  I  Sensitivity Analysis  .1.  I.  I.  Linear  Built-in | functions j  j 10  Plotting  FIGURE 17. Program  b a s i c flow  I  | I  j  |  Exact  Bivariate |  I  routines  |  chart  o  108  completed, 2)  and  These and  the program  the performance  values  selects  in the  the  type  6) a n d f r o m  recalculated these  (step the  control  file  i n step  a s many  restriction  8)  (step  (step times  5).  analysis  Then,  the exact plotted  i n step  12)  steps  as d e s i r e d .  make  6  use  returns  through  The major  user  are of  sensitivity analyses  10 a n d s e n t  the program  4)  performed  and b i v a r i a t e  11. T h e n , and  the  measures  the  3).  (step  t o be  routines  calculate  (step  (step  routine  the performance  to  results are  routine  repeated  block,  and t o perform  9 ) . These  output  file  routine  calculated  7 ) . The s e n s i t i v i t y  (step  coefficients  are  to the control  sensitivity  this  (step  values  output  of  to the control  measures  are transferred  printed  (step  returns  to  to the 12  are  assumptions and  of the program a r e :  1.  A maximum  o f 50 c a s h  2.  Any c o n s i s t e n t  flows  system  a n d 100 p e r i o d s  of u n i t s  are allowed.  f o r money a n d t i m e  c a n be  used. 3.  Only  one f o r e i g n  4.  The i n p u t  from  construction 5.  Inflation  exchange borrowed  funds  expenditure  and i n t e r e s t  rate  c a n be s p e c i f i e d . follows  the form  of  the  function. rates  are  constant  and  nominal  ones. 6.  Two a r b i t r a r y can  be p r e s c r i b e d .  another 7.  functions One  to  f o r the  for the operating  Negative  flows  values;  positive  describe  flow  construction  patterns phase  and  phase.  (disbursements) flows  cash  are entered  (revenues)  are  as  negative  entered  as  109  positive are  ones,  always  except  entered  fixed as  and v a r i a b l e  positive  but  operating are  costs  treated  as  assigned  to  superimposed  in  disbursements. 8.  There cash  i s no r e s t r i c t i o n flows.  It  means  on  the time  values  that  they  c a n be  different  unit  sale  time. 9.  A s many  as  nine  correspondent 10.  Fixed  inflation  and v a r i a b l e  the  period  when  can  be a t t a c h e d  11 . C o n t i n u o u s The  rates  operating  operation t o each  compounding  five  major  prices  with  their  c a n be s p e c i f i e d . costs  starts)  are constant b u t an  (as  inflation  of rate  o f them. i s used  bodies  of  throughout  the program  the program. are  described  below.  5.2 DATA The  input  namely (cash  begins  project flows  exchange The is  INPUT  the  input  from  occur  for  number  on), discount  rate,  flows foreign  life. loan  those  cases  a  funds  expenditure  the p r o j e c t ,  of cash  the c o n s t r u c t i o n  borrowed  which  initial  about  about  in a period  construction,  information  later  and p r o j e c t  that  construction will  be a d d e d  information  assumed  general  identification,  may  rate  with  when  will  function.  not  i s input  such  follow  loan  by t h e  equal  user.  is  t h e form  The repayment  necessarily  i s next. I t used,  of  the  of the  loan  t o t h e end  of  1 10  Then, is  the general  requested  prices  by t h e p r o g r a m .  c a n be  inflation the  unit  the  operating  they  to  period  revenues  when  that  later  the value  dollar  when  has  (earlier)  to the  of  rate  prices  construction  dollars t o be  operations  been  period,  period  when  are  long  loan  c) the user  term  (including  or  c)  are selected,  rate,  the  b)  period  model when to  period  are  method.  the c h a r a c t e r i s t i c s  case  The  when  is  program no l o n g  taken  an a r b i t r a r y amount  when  any  According  each  interest during  enter  The  the period  for  entered.  may  of  during  follows.  assets,  and  loan  should  are produced.  depreciation  a)the  their  the start  of the a s s e t .  line  with  costs  in effect  charges  tax rate  to the user:  costs  as of  depreciation  financing  b)the  operating  of d e p r e c i a b l e  t h e income  options  interest  from  the s t r a i g h t  term  taken;  current  depreciation  using  long  options  corresponding  a r e s p e c i f i e d . These  s t a r t s and t h e l i f e  values,  Then,  and  its  the  (inflated)  rates  about  the value  depreciation  is  sale  with  If  for a  a r e assumed  Information  three  dollars  in  They  the  commences.  inflation  specified  computed  different unit  to the current  be d e f l a t e d  operations.  these  phase  t o note  the f i x e d and v a r i a b l e  respective  requires  o f them  the operating  start.  Then,  be  phase  about  to nine  important  corresponds  in current  operations  also  It i s  prices  have  Up  s p e c i f i e d , each  rate.  estimated  information  the  user  the loan  is  to  of  offers  term  loan  repay  the  construction); borrowed.  When  specifies  the  taken  the  and  111  type  of  repayment  selected  f u n c t i o n . The  repayment  f u n c t i o n can  be  from:  1.  Uniform  2.  Step  payments.  function  (increments  every  given  number  of  periods  between  two  payments). 3.  Gradient  The  user  also  payments, grace of  period  date  For  the  number first  of  payment  financing strategy)  the  cases  value  of  the  information  of  the  step  first  (which  and  and  payment  the  allows  total  gradient should  a  number  repayment be  entered  well.  done  with  the  appropriate  the  user.  18.  At  The  this  selects  of the  as  flows  the  according  these  to  menus to  program to  the  will  the  cash  p r o j e c t phase  This  request  choices  i s presented  which  the  i s entered.  made  in  flow  by  figure belongs  selected,  the  follows:  and  the  cash  menus a n d  phase  According  its 19.  about  information  Feasibility selected,  of  first  proceeds  figure  aid  point,  specified.  input 1.  the  the  the  is  of  i n the  payments.  Then, is  specifies  the  functions, as  function.  Design:  user type  Then,  When  assigns from the  a  either  a  name  menu  of to  like  parameters  of  these  phases  is and  the  cash  flow  the  one  shown  cash  flow  the  in are  entered. 2.  Initial  Investment  single  discrete  can  l o c a t e d at  be  and  Disposal:  payments any  to  point  The  model  only  describe  these  flows.  in  time.  allows They  1 12  FIGURE  18. Menu  f o r the s e l e c t i o n  of project  PROJECT PHASE 1. F E A S I B I L I T Y 2. D E S I G N 3. I N I T I A L INVESTMENT 4. CONSTRUCTION 5. OPERATION 6. D I S P O S A L  FIGURE  1 9 . Menu f o r t h e s e l e c t i o n o f f l o w ( F e a s i b i l i t y and Design)  SELECT 1. 2. 3.  ONE  OF THE  FOLLOWING:  S I N G L E PAYMENT TWO D I S C R E T E PAYMENTS UNIFORM FLOW  type  phase  113  3.  C o n s t r u c t i o n : For each name a n d s e l e c t s in  Figure  phase  be a n  user  and l i n k e d  This  function  from  arbitrary  the user  a menu flows  subprogram  code  construction  programmed  o f t h e main  should  have  a  t h e o n e shown  of the  function  to the object  like  specifies  by  the  program.  the  following  coding:  FUNCTION  CO(X,F,I)  DIMENSION CO=  i t s type  flow,  2 0 . One o f t h e c a s h  can  FORTRAN  cash  F(50,9)  (Arbitrary  function;  CO=f(x,F,I)  )  RETURN END  The  function  given  row  of  matrix  is  parameters case,  a  user  above,  For  equation  represent ing: b + mx  may  write  i n which  CO=F(I,2)+F(I,3)*X  Funct ion,=  F.  third  are the intercept  the  described  the  maximum  of  s t r u c t u r e of the  as the second,  function  a  have  the internal  specified Ith  may  three  parameters  program.  They  and f o u r t h columns  example, of  a  i f  the  straight  b and t h e slope the  Function  the function  are  of the  arbitrary line,  m.  In  the such  subprogram  i s expressed  as:  FIGURE  20.  Menu f o r t h e s e l e c t i o n  SELECT  ONE OF THE  1. 2. 3. 4. 5. 6. 7.  FIGURE  21.  of flow  type  (Constructi  of flow  type  (Operation)  FOLLOWING:  S I N G L E PAYMENT TWO D I S C R E T E PAYMENTS UNIFORM FLOW TRAPEZOIDAL BETA F U N C T I O N EXPONENTIAL OTHER  Menu f o r t h e s e l e c t i o n  SELECT 1. 2. 3. 4. 5. 6. 7. 8.  ONE OF THE  FOLLOWING:  S I N G L E PAYMENT TWO D I S C R E T E PAYMENTS UNIFORM FLOW • TRAPEZOIDAL BETA F U N C T I O N EXPONENTIAL GOMPERTZ CURVE OTHER  115  4.  The  numerical  value  the  execution  of the program.  Operation: phase 21.  The type  i s selected  Also,  function the  one  these  flow  like  flows  phase.  the  the f u n c t i o n subprogram  of  CO). A f t e r  name  belonging  that  shown be  i s  RE  and t h e  in this  have  been  entered,  unit  sale  price  a p p l i c a b l e t o the revenue  will  n o t be d o n e entire  assumes  that  entered  under  multiplied  Some order.  the  except  under an  a unit  Firstly,  or  that  f o r the  does  In  price,  and  that  the salvage flows  of o p e r a t i o n a l  the  costs  program flows that  does  has  not  to  unit  a  be price  function. parameters be  o f any  value always  are  negative  f o r revenues  the sign  are  This price  the cash  should  assumes  cash  sale  phase  flow  not  (instead  function.  that  positive  the  t h e name  the case  to that  of the flow  of  of the  a dummy  the cash  construction  case  phase.  be a s s i g n e d  or outflows  not assumed  to a l l  to  ask f o r the  case,  profile  sale  the value  The program  will  the operational  output  similar  one u n i t  this  applies  c o n s i d e r a t i o n s about  (it is  positive  In  operating  t o one s h o u l d  disbursements  inflows.  price  the  to by  i s only  project.  entered  correspond  equal  i f there  program  figure  case  parameters  this  arbitrary  i s that  flow  the  the  in  function  difference  during  to  an  i n a manner  arbitrary  The o n l y  i s input  can  by t h e u s e r  for  the  cash  a menu  of  function  flow  from  of  explained  for  for  of each  programmed  construction  in  of the parameters  is  or cash  always  negative)  and repayment  of  1 1 6  the as  long  term  positive  assumed  l o a n . The  values  t o be  current  starts when an  dollars  will  flow rate  be  flow  costs are entered  originated  by t h e m  is  of the cash of  flows  the period  i n the case  applies  to  with  when  flows  happens  i s assumed the  cash  of d i s c r e t e  be flow  and of the  a continuous  respect  to  period  flows. I f  cash  flow,  to the starting  the  period of  flow.  when  any  former  the  Two  be  the basic  included  in  functional  stream.  flow  may  Then,  The program  they  are  o f some  model.  stored  aforementioned  variable  allows  phases  The f i r s t  variables  They  may  also  be  date  x i s specified  refers  associated  but that used  can to  of the  date  be set cash  of a g i v e n  the f i n i s h i n g  cash  of  another  in a vector  called  a s 20 o f t h e s e 20  and  the data  one  not  the parameters  the s t a r t i n g  elements  the  flexibility  concerning  flow,  V. A f t e r  (obviously, That  of any c a s h  a s many  in  vector  primary  period  phase.  considered.  after  the time  different  t h e same  between  x periods  this  latter).  f e a t u r e s of t h e model  F o r example,  occur  about  finishes  the  within  parameters  the  and  superimpose  relationships  flow  flow.  to  be c a r e f u l l y  the existence  with  starts  flows  important  restriction  before  user  cash  should  i s no  flow  should  different  input  there  cash  permits  V.  cash  of continuous  inflated  Thirdly,  to  as  f o r the case  inflation  the  the value  the cash  flow  but the  and v a r i a b l e  negative.  Secondly, in  fixed  variables  through  the information  39  and  of  the  about  the  117  cash  flows  has  user  to  they  exist.  input  primary  the  the  The  to  first  The compiled  by  user  any  the  of  cash  refers  where  variables  and  such  The  i n f o r m a t i o n about  matrix 9  called  columns  first  always  columns  a  Table of  3,  during  the  have  the  f o r the  sale  price.  when  the  single  the  five  flow to  to  the  vector  case  contain  that  general  subroutine  are  not  structure  V.  can  This  of  8.  each  on  follows:  of  a and  flow.  The  function  that  column  will  remaining  the  in  flows)  cash  this  The  specified as  cash  and  between  is stored  40  type  be  works  flows  the  1 and  written  relationships  therefore,  is of  input.  flow,  in  type  of  in each  of  columns flow  as  4.  information,  Column  refer  I  number  data  a  (maximum  information  row  the  same  3 and  The  cash  depending  the  any  to  parameters  between  this  the  2.  rows  I;  request  variables  parameters  refers  will  program  flow.  the  50  flow  in Tables  user  , 1)= 2  I  number  to  F(I  row cash  corresponds  applies  I t has  information  described In  of  the  have  contain  F.  the  in vector  c o n t a i n i n g the  column  describes  variables  of  functional  including basic  by  in Table  feature  primary  elements  specific  second  program  these  20  i s shown  the  of  the  considered  any  vector  entered,  values  variables  associated of  been  stored  presented. the In  cash  The  flow  a l l cases,  ie.  the  foreign  as  of  I  entered  by  the  7,  inflation  for F(I,1)=1 Columns  period  when  the  five first  8  and  rate  r a t e and  contains  occurs.  eight  value  columns  exchange  the  the  and and  9  that  the  unit  period six  for  second  1 18  TABLE 2 Structure Element  of the v e c t o r  V  Description  1  Discount  rate  2  Foreign  3  Fraction funds  of construction  4  Interest  rate  5  Period  6  Not used  7  Fixed  8  Variable  9  Value  exchange  when  rate  on c o n s t r u c t i o n  construcion  operational  loan  with  borrowed  loan i s due  costs  operational  costs  of depreciable when  financed  assets  10  Period  depreciation  11  Life  12  Income  tax rate  13  Amount  of long  14  Interest  15  equal 1 i f t h e long term l o a n i s taken t o repay the c o n s t r u c t i o n loan. E q u a l 0 o t h e r w i s e .  16  Period  when  the long  17  Period  when  operations  18  Inflation  rate  for fixed  19  Inflation  rate  for variable  20-39  Other  of depreciable  rate  primary  term  starts  assets  loan  on l o n g  term  term  variables  loan  loan  i s taken  begin operational  costs  operational  assigned  costs  by t h e u s e r  119  TABLE Matrix Flow  F: D a t a  elements  3  associated with  Type  Column  flow  type  number  1  2  3  4  5  6  7  8  9  1  P  -  -  T  -  -  FE  SP  Two d i s c r e t e payments  2  PI  P2  -  TI  T2  -  FE  SP  Uniform  3  C  -  -  Ti  Tf  IR  FE  SP  Trapezoidal  4  PI  P2  -  Ti  Tf  IR  FE  SP  Beta  5  c  a  b  Ti  Tf  IR  FE  SP  Exponential  6  c  b  -  Ti  Tf  IR  FE  SP  Gompertz  7  Al  A2  A3  Ti  Tf  IR  FE  SP  8  PI  P2  P3  Ti  Tf  IR  FE  SP  Single  payment  function  curve  Arbitrary (CO o r RE)  TABLE Matrix  F(I,1)  F: D a t a  4  elements i n columns to the flow type  F(I,2)  2,  3 and  F(I,3)  1  Value  of  payment  2  Value  of f i r s t  3  Value  of the  4  Starting  5  Amplification  6  Initial  7  Asymptotic  8  Parameter  paym.  value const.  value limit 1  —  Second  payment  value  Parameter  1  Growth  -  Finishing  Shape  according  F(I,4)  —  flow  4  rate parameter  Parameter  2  Parameter  2  Growth  rate  Parameter  3  120  payments  occur,  continuous and  2,  3 and  4  stores  rate  in  its  occupies  VARIA  to  the  the  each  period  SUBROUTINE DIMENSION  of  say of  the  the cash  cash  rate  of  for these  finishing the  flow  periods  information,  unit  10  sale  rows  the  value  prices  (row  of  the  ie.  one  10  cash  4.  is stored  of  Each the  in row  nine  i s reserved  i t s corresponding  5  columns  2 columns. of  are  columns  in Table  prices  and  types  cases,  i s summarized  in  and  mind,  of  flow  for  inflation  2)  VARIA(F,V,P,NC) F(50,9),V(40),P(10,2)  and  VARIA  0.5  5 and  should  between  the  before  the 7  look  a  called  periods  adding  flows  assigns  subroutine  mentioned  3 occurs  cash  subroutine  a  user  relationships  example  flow  the  writes  functional  For  rest  column.  flow  the  date  same,  F(7,7)=F(5,7)  END  column  cash  F(3,5)=F(2,6)+V(20)  RETURN  the  structure  inflation  the  of  types,  second  this  finishing  always  rest  unitary  variables.  starting  8),  i n f o r m a t i o n ) , and  describing  primary  The  and  P containing first  internal  number  The  different  Having  that  starting  f o r a l l flow  called  possible other  through  i n f o r m a t i o n about  matrix  the  the  respectively.  The a  (F(I,1)=3  6 contain  flow  respectively.  (the after  condition should like:  be  121  in  which:  F(3,5)=Starting  period  F(2,6)=Finishing V(20)=0.5;  this  period value  F(5,7)=Inflation  should  F(3,5)=F(2,6)+0.5, quantity  analysis this  chapter,  user  parameter. the  between  t h e way  explained  the  may  detail  this with  2  5  flow  ( r o w 2)  the  have  been  ( r o w 7)  subroutine, written  in vector  way  a  as V  to  sensitivity  as presented  specify  any  variables.  subroutine  ( r o w 5)  7  to perform  the primary  i n which  i n more  flow  in  I n t h e same  user  ( r o w 3)  the program  7) o f c a s h  also  3  flow  but a s s i g n i n g a p o s i t i o n  example,  relationships  from  that  could  enables  on t h i s  brief  (column  flow  6) o f c a s h  7) o f c a s h  noticed  F(3,5)=F(2,6)+V(20),  this  (column  (column  rate  be  5) o f c a s h  i s entered  rate  F (7 , 7) = I n f l a t i o n  It  (column  in  functional  In  the  next  i s written will  t h e a i d o f a more  be  complicated  example.  5.3 The  BUILT-IN-FUNCTIONS second  mathematical model. function  It  main  block  definition is  a n d no  standard special  of  the  of the FORTRAN topics  program  built-in coding  deserve  contains  functions of  t o be  of  the the  mathematical mentioned.  122  5.4  C A L C U L A T I O N OF PERFORMANCE  Once  the data  compute of  as  First, amounts  i s completed,  t h e Net Present  the cash  well  input  flow  the  MEASURES  Value,  stream  the Internal  and the T o t a l  period-by-period  the cash using  flows  the program proceeds of  Return  c o n s t r u c t i o n c o s t s , as  current  are converted  Rate  to  into  dollar  cash  equivalent  flow.  discrete  the equation:  min(i+1,Tf) C  i + 1  C(t).exp(-rt+0(t-Ts))dt  ={;  }* e x p [ r ( i + 1 ) ] ( 5 . 1)  max(i,Ts)  where: C(i+1)=Equivalent time  discrete  i a n d i+1 c o m p u t e d  r=Discount  rate  Ts=Starting  period  Tf=Finishing figure  period  17A,  explained.  The  equivalent  cash  flow  C(t)  between  a t p e r i o d i+1  f o r cash  continuous  discrete  Then,  f o r cash  payments flow  f o r each  computed. 1.  Initial  2.  Feasibility  flow C ( t ) flow C ( t )  the transformation  NPV o f t h e u n i f o r m payments.  of  rate  0=lnflation  In  value  investment. expenses.  cash  done  by e q u a t i o n  flow  i s  5.1  decomposed  a t t h e end of each  period.  i s equal  to the  NPV o f t h e s e t  period,  the following figures  i s in The of are  1 23  Time  4  P3 P2A PI  P4  i  Time  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  3.  Design  4.  Construction  costs  (equity  5.  Construction  costs  (input  6.  Revenues.  7.  Fixed  8.  Variable  9.  Depreciation  10.  Long  5.1  expenses.  operational  1 1 . Taxable  income.  12.  Income t a x .  13.  Salvage  14.  Net c a s h  value flow  costs.  charges.  debt  from  costs.  operational  term  input).  payment.  borrowed  funds).  124  Taxable costs loan  income  minus  variable costs,  amortization.  taxable 12  i s calculated  income  The  plus  cash  NPV  flow  are  quadrature  method.  method mixed by  by  the program.  procedure  using  Newnan  of t r i a l  to perform  [36].  different  general  types  analysis The  model  i s  the types  the  cash  flows,  absolute  type  matrix or  compounding. using  the  i s computed  In case  obtained  The  the  Gauss  using the  project  rate using  is a  i s  a  requested systematic  main  F from  of s e n s i t i v i t y  program  analysis  using  o f t h e NPV  and  projects.  u n i v a r i a t e a n a l y s i s , exact  univariate  points  is carried  the vector  and b i v a r i a t e  o u t by s e l e c t i n g  corresponding  relative  o b j e c t i v e of the  (TCC) o f c a p i t a l  and u s e r - d e f i n e d and  and  period-by-period  f o r the c a l c u l a t i o n  i n c l u d i n g break-even  from  variables  are linear  first  the  reinvestment  and T o t a l c o n s t r u c t i o n c o s t s  Those  1,2,3,4  the  ANALYSIS  is  IRR  minus  and e r r o r .  was m e n t i o n e d b e f o r e ,  fairly  sum o f i t e m s  of Return  an e x t e r n a l  As  a  fixed  i s c a l c u l a t e d as  numerically  The r e s u l t  5.5 S E N S I T I V I T Y  flow  continuous  the I n t e r n a l Rate  investment,  minus  d e p r e c i a t i o n charges  by d i s c o u n t i n g  computed  proposed  revenues  list.  zero  integrals  Then,  net cash  i s obtained to  minus  the a l g e b r a i c  of the p r e v i o u s The  as the  to  any v a r i a b l e  the information  V containing  other  v a r i a b l e s . The model  linear  analysis.  sensitivity  about primary  computes t h e  coefficients  for  125  the  NPV,  IRR  chapter. or  and  The  user  sensitivity  variables both  on  the  The for  a  in  the  chart  by  screen  range  cases  has  i t . In  exact  between  TCC  any and  of  values  their  option  case,  of  any  attached  i s produced  by  assigned  the  to  or  Finally,  the  of  producing  of  analyzed  unit  written  8.  selected  the  the  NPV  variables and  their  point  user  results  the  is  is  given  obtained  in  analysis.  with  The  bivariate  analysis  the  exception  that  the  produced  columns.  Ten  points  i n the  range  each  variable  are  rows and  lower  and  is  higher  of  percentage NPV,  or  result unit value  10  computed  elements  well  to  diagram  be  break-even  trial-and-error.  NPV  will  The  by  10  the  estimate  calculated  this  star  lower  estimate.  plot  a  previous  calculating  or  a  the  of  results  optimistic  option  in  producing  the  file  pessimistic higher  defined  including  in a  analysis  as  the of  NPV  8. of as  explore  of  for  resulting  the  resulting  the  matrix  resulting  both  Finally, any  estimates  calculated  i s sent  is similar  to  the  cash  changing additional  or  the  screen  behaviors  100  and  the  new of  the  exact is a  a  option or  the  used  the  to  file of  the  flows  investment.  of  by  the  and  the  change  The in  original  Again, attached  resetting  primary  cash  matrix set  estimates. to  analysis  combinations.  respect  "best"  parameter  adding  output  with  the  has  the  represent  at  user  flow  NPV  to  the to the  variable,  as  in  to  order  126  5.6  PLOTTING  The  last  OF R E S U L T S  main  part  subroutines.  It  been  using  77  written  programing  used  (with  feature  the program  should  be  so i t  no c h a n g e )  FORTRAN  a t UBC. U s i n g  this  routine,  and c o n v e n t i o n a l  called after  $RUN  Where  star  are produced. in  to unit  which 9 at  for execution. the execution  *QMSPLOT  diagram  hard  when  copy  i s completed  of  this  package  library  of  the  simple  but  self  procedure t o be main  the plot  issuing  and  since  plotting  the  has  plotting  and v a r i a b l e  plots are  the time  A  simple  The p l o t t i n g  the  The  criteria  the  explained  file  t o these  ALGRAF  compiled  machines.  use i n  center  attached  i n other  plotting  o f t h e FORTRAN  easily  public  computing  the  version  be  the  t h e program  the  for  NPV d i a g r a m s  may  that  use of  available  that  standard  are the exception  makes  comprises  mentioned  an a l m o s t  language,  almost  subroutines  of  requires  produced  is  program  is  i s  t h e MTS  versus  obtained  command:  0=Plotfile  Plotfile  i s the  name  of  the f i l e  attached  to  unit  application  of  this  nine. Given plotting graphic given  other  routines software,  great  obtained  the  restriction  graphic  the  to the a v a i l a b i l i t y this  emphasis.  even  in  using  aspect Graphs  of  of the much  microcomputers.  packages  o f an s p e c i f i c program better The  and t h e program  has not  quality  interface should  kind of  can  been be  between  be made  for  127  every  p a r t i c u l a r hardware-software The  A.  complete  program  listing  configuration. can  be  found  in  Appendix  CHAPTER  6. V A L I D A T I O N  6.1  INTRODUCTION  The  objectives  model  developed  First,  model.  performance  linking  measures model  New  figures  o f an a c t u a l  Strait  used  6.2 V A L I D A T I O N  tested  for  accuracy  time  case,  zero,  estimated years.  can  be s o l d  this  t h e model, previously  accuracy  i n which  begins  of  o f an  highly bridge  Island  A l l the  i s acquired and the  across  estimates  90% o f  continuously  solved  i s built at a  total  comprises  f o r $400000  i t was  examples.  i s demonstrated  a facility  The f a c i l i t y  when  economic  the proposed  Edward  the  are hypothetical.  t o be $ 8 . 5 m i l l i o n s , o v e r  1.5  starting  Prince  with  the  analysis  project,  example  using  the land  Construction  t o compute  to  OF T H E MODEL  development  simple  and  in this  the  section,  used  i n order  obtained  i n A t l a n t i c Canada.  During  this  i s  computer  application.  i s solved  and s e n s i t i v i t y  Brunswick  Northumberland  example  the  of i t s  of the r e s u l t s  the program  OF THE MODEL  are to validate  an example  simple  the accuracy  Second,  simplified  chapter  a n d t o show  an e x t r e m e l y  demonstrate  and  of t h i s  AND A P P L I C A T I O N  each  1 28  and then  cost  o f $5  construction  44 a p a r t m e n t a period  has  been  a  very  sold.  At  millions. costs  a construction  during  construction  using  In  are  period  of  suites  that  of one  year  completed.  No  129  financing term  i s taken  debt.  analysis  pretax  basis.  on  the  project the  the  the  following  1.  The  i s to In  cash  was  exercise  construction be  figure as  solved  done 22,  well  by  was  or  as  in constant  the  as  phase  dollars  information  the  results  long  about  obtained  hand.  solved  with  the  program  using  procedure: flows  are  numbered:  1.  Land  2.  Construction costs.  3.  Revenues  The  the  i s summarized,  problem  Then,  2.  fund  The  and  when  a  to  acquisition.  primary  assigned  a  variables position  particular  i n v e c t o r V,  to  this  starting  problem with  the  are 20th  element: V(20)=C V(2l)=x V(22)=Ta 3.  The  subroutine  relationships C  C  VARIA  between  the  describing variables  RELATIONSHIPS  SUBROUTINE  VARIA(F,V,P,NC)  DIMENSION  F(50,9),V(40),P(10,2)  of  the  second  BETWEEN  flow=C/Tc  F(2,2)=V(20)/F(2,6) C  Value  of  the  third  flow=44/Ta  F(3,2)=44/V(22) C  Start  time  of  third  flow=x.Tc  functional  is written.  FUNCTIONAL  Value  the  It i s :  VARIABLES  130  1  Definition  xTc  o f the p r o b l e m  Ta Area=44*S time  Area=C  Tc  Land  Solution  Net P r e s e n t v a l u e = Internal  $183028.0  Rate o f Return=  19.04%  Linear s e n s i t i v i t y c o e f f i c i e n t s Variable L Tc C  X Ta S  (relative)  NPV -27 32 -11 45 -40 75 -16 66 -5 99 69 24  FIGURE 22. D e s c r i p t i o n and manual o f t h e s i m p l e example.  IRR -1.52 -0.659 -2.251 -0.962 -0.345 3.781  solution  MARR-0.18 L=$ 5 m i l l i o n s Tc=1.5 y e a r s 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  131  ECONOMIC PERFORMANCE  MEASURES:  Net p r e s e n t v a l u e = I n t e r n a l Rate o f Return=  Linear  183027.0 19.04%  sensitivity coefficients:  Variable  L  Value  NPV  -5000.0  -27.318  -1.505  1.5  -11.526  -0.635  -40.701  -2.242  Tc C  8500.0  IRR  X  0.9  -16.772  -0.924  Ta  1.0  -6.025  -0.332  S  400.0  69.017  3.802  FIGURE  23. Summary  of results  obtained  with  t h e program.  F(3,5)=V(21)*F(2,6) C  Final  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  respectively. analyses, 23.  After  figures  24  variables  gave  output  t o 34. F i g u r e considered  are years  performing  the program  The c o m p l e t e  units  by  the r e s u l t s  for 24  linear,  this shows  and thousand exact  bivariate in  figure  i s presented  the value  the program.  and  summarized  example  dollars  Figure  of the 25  in  primary  summarizes  SENSITIVITY  AND ECONOMIC ANALYSIS OF PROJECT:  SIMPLE EXAMPLE  PRIMARY DISCOUNT  VARIABLES 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 FIXED  OPERATING C0STS=  VARIABLE C0STS=  0.0  .  0.0  VALUE OF DEPRECIABLE ASSETS=  0.0  PERIOD WHEN ASSETS ARE ACQUIRED= L I F E OF DEPRECIABLE ASSETS= TAX  DUE=  0.0  0.0  RATE=0.0  INFLATION RATE FOR FIXED  C0STS=0.0  INFLATION RATE FOR VARIABLE COSTS=  UNIT SALE PRICES #  PRICE  1  400.0000000  INFLATION  FIGURE 24. Primary v a r i a b l e s  0.0  0.0  0.0  133  the  i n f o r m a t i o n about  economic Total  performance  used  proceeded  by  by a  during  the  the  in  In  cash  is  of  figure  28  period-by-period Figure  29  presents  independent  primary  coefficient  with  in  4.4.  equation  these For  two  the  NPV  in  cash  flow  is  to  the  presented.  and  TCC  defined  The  i s that with by  the  defined  respect  equation  to 4.5.  the  absolute  coefficient  is defined  in  the  relative  coefficient  is defined  in  analysis  (NPV=0  and  for  column  are  case,  Figure  the  be  absolute  is  pessimistic  should  problem.  measures  univariate  of  for  performance  IRR  total  coefficients  coefficient  4.11.  the  the  the  input.  dollars  the  be  example,  results  data  relative  equation  left  to  user  the  each  the  presents  a  the the  should  project,  The  and  presents  of  in current  of  flows  For  the  that  following  The  sensitivity  respect  noted  27  since  during  presents  dollars.  revenues.  variables  4.10  analysis  the  contribution  the  equation  point  Figure  figures,  flow  be  (negative  of  selected  26  negative,  in current  period  cash  Figure  should  sign).  flow  the  It  program  these  units  flows.  are  r e c e i v e d as  reading  system  the  second  $11440000.0 careful  Costs  minus  period-by-period  cash  measures.  Construction  convention  the  10  and  for  variables,  presents variable  IRR=MARR) points  optimistic  bivariate of  30  the  10  S.  output First,  is printed. the  range  estimates  sensitivity  matrix  taking  in  the  present points  of  the  the  break-even  Then,  the  defined  is presented.  analysis.  The  exact  exact  by Figure  top  31  row  and in  the  percentage  changes  in  the  set  range  the  by  the  INFORMATION »  ABOUT  CASH FLOWS  NAME  TYPE  0.0  CURRENCY  UNIFORM /PERIOD)  CONSTRUCTION  0.0  1.50  0.0  DOLLARS  3 REVENUES VALUE= 44.0001THOUS.  UNIFORM /PERIOD)  OPERATION  1.35  2.35  0.0  DOLLARS  $  FIGURE 25. Information about cash flows  0.0  RATE  $  )  0.0  INF.  2 COfJS1nUC TI ON VALUE= •5666.664(THOUS.  $  INV  PER.  )  4 00.00000001THQUS.  INITIAL  . FINAL  $  SALE PRICE=  PA YM.  PEP.  I L A NO VALUE= - 5000.000(THOUS.  UNIT  SINGLE  INIT.  PHASE  DOLLARS  ECONOMIC NET  PERFORMANCE  PRESENT  CONSTANT  INTERESIS TOTAL  183 .027  VALUE  DOLLAR  ESCALATION  CONSTRUCTION  DURING CURING  RATE  •8499.988  COSIS=  0.0  CONSTRUCTIONCONSTRUCTION::  CONSTRUCTION  INTERNAL  MEASURES  0.0  COSTS=  •8499.988  19.040  OF R E T U R N :  FIGURE 26. Economic performance measures  CURRENT DOLLAR CASH FLOW  INITIAL  INVESTMENT  -5000.000  0.0  0.0  FEASIBILITY  0.0  0.0  0.0  DESIGN  0.0  0.0  0.0  CONST.  (EOUITY)  CONST.  LOAN  -5666.660  0.0  -2833.330  0.0  0.0  0.0  REVENUES  0.0  FIXED COSTS  0.0  0.0  0.0  VARIABLE  0.0  0.0  0.0  DEPRECIATION  0.0  0.0  0.0  LONG TERM DEBT  0.0  0.0  0.0  SALVAGE VALUE  0.0  0.0  0.0  GROSS INCOME  0.0  INCOME TAX  0.0  COSTS  NET CASH FLOW  10666.660  11440.000  11440.000  6159.984  6159.984  0.0  0.0  8606.668  6159 .984  FIGURE 27. P e r i o d - b y - p e r i o d cash f l o w i n c u r r e n t d o l l a r s  1  CURRENT DOLLAR CASH FLOWS  1  CASH FLOW LAND  • 5000.000  CONSTRUC11 ON  • 5666.660  REVENUES  0.0  2  3  0.0  0.0  -2833.330 1 1440.000  FIGURE 28. Cash flows i n current d o l l a r s  0  0.0 6159.984  36  LINEAR SENSITIVITY  NPV IRR TCC  ABSOLUTE -1.00000 -0.00006 0.0  LINEAR SENSITIVITY  NPV IRR TCC  NPV IRR TCC  NPV IRR TCC  1.5000000  RELATIVE - 1 1 .52638 -0.63495 0.0  COEFICIENTS FOR VARIABLE x  =  0.9000000  RELATIVE -16.77235 -0.92393 0.0  COEFICIENTS FOR VARIABLE Ta  1.0000000  RELATIVE -6.02544 -0.33192 0.0  COEFICIENTS FOR VARIABLE S  ABSOLUTE 31.58008 0.00181 0.0  FIGURE 29. S e n s i t i v i t y  8500.0000000  COEFICIENTS FOR VARIABLE Tc  ABSOLUTE - 1 102.81982 -0.06320 0.0  LINEAR SENSITIVITY  -5000.0000000  RELATIVE - 4 0 . 7 0 1 10 -2.24207 1.00000  ABSOLUTE -3410.88940 -0.19546 0.0  LINEAR SENSITIVITY  NPV IRR TCC  COEFICIENTS FOR VARIABLE C  ABSOLUTE - 1406.42896 -0.08060 0.0  LINEAR SENSITIVITY  =  RELATIVE -27.31831 -1.50486 0.0  ABSOLUTE -0.87640-0.00005 - 1.00000  LINEAR SENSITIVITY  NPV IRR TCC  COEFICIENTS FOR VARIABLE S  coefficients  RELATIVE 69.01717 3.80190 0.0  400.0000000  138  EXACT UNIVARIATE BREAK  EVEN  POINT=  VARIABLE  ANALYSIS  FOR  VARIABLE  394.1838379 NPV  370.0000000 377.7775879 385.5554199 393.3332520 401.1110840 408.8886719 416.6665039 424.4443359 432.2221680 439.9997559  S  IRR  -764.385 -518.766 -273.137 -27.509 218.113 463.738 709.363 954.988 1200.617 1446.234  FIGURE 30. Exact u n i v a r i a t e  analysis  (%)  13.483 14.968 16.423 17.839 19.235 20.593 21.931 23.239 24 .528 25.778  139  pessimistic numbers both  and o p t i m i s t i c  i n the matrix  variables Figure  program. the  exact  concluded  i t  is  that  between  by  errors  6.3 In  order  functions profiles  noted  those  the  NPV  comparing obtained  provides sets  incurred  in  by  and  the  the from IRR  results  by hand,  accurate  of answers both  allowed of the  an e x a m p l e  by  i t  results.  can The  c a n be e x p l a i n e d  methods,  simple  Although  (trapezoidal  cash  example the  mainly  a=F(2,2):  cash  in  the  in matrix  First  F  parameter  2,  flows  35A, r e s p e c t i v e l y .  flows  the cash a s shown  will  type be  flow in of  entered  by t h e m o d e l . i e . Land  and Revenues  i s cash is  cash  2 a n d 3 a r e a,b a n d c , d  Therefore,  i s as  arbitrary  includes this  as before,  flow  of c a s h  the  modified  the cash  a r e numbered  3. T h e p a r a m e t e r s  quantities  were  functions considered  flows  how  a r e used,  program  flows),  flow  in figure  o f t h e way  the program  1, C o n s t r u c t i o n i s  1.  produced  of the r e s u l t s  to  that  and  flow  these  when  FUNCTIONS  the a r b i t r a r y The  as  diagram  respect  t h e two  to provide  35.A.  profiles as  i n t h e NPV,  solution.  ARBITRARY  figure  The  time.  star  the model  differences  manual  with  by t h e p r o g r a m  rounding  the  variable.  i s presented.  Finally,  be  at a  change  33 a n d 3 4 , t h e p l o t  analysis  respectively  obtained  presents  In f i g u r e s  of each  are percentage  a r e changed  32  estimates  the p o s i t i o n  follows:  (j=2) of c a s h  flow  2 (i=2)  of  BIVARIATE VARIABLE VARIABLE  1: 2:  SENSITIVITY S C  MATRIX  CONSTANT CONSTANT  PERCENTAGE  - PERCENTAGE CHANGE IN  THE NPV  ALONG ROWS ALONG COLUMNS  CHANGE IN VARIABLE C  •5.882  -4.412  -2.041  -1.471  1.471  2.941  4.412  5.882  -7.500  -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  -3.125  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  -33.435  -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  S  0.0  ( %)  FIGURE 31. B i v a r i a t e  analysis  141  FIGURE 32.  S e n s i t i v i t y chart for Lineau analysis  simplified  example  1 42  FIGURE 33.  Plot: of r e s u l t s from the exact a n a l y s i s  (NPV  FIGURE  34  Plot of results  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  3.  c=F(3,2):  First  4.  d=F(3,3):  Second  The  functional  figure  vector  1.  V(20)=C  2.  V(21)=X  3.  V(22)=Ta  and  RE  forms  the  V  has  the  subroutine  for this  parameter of  cash  same  VARIA  example  SUBROUTINE DIMENSION C  parameter  (j=3) (j=2)  of of of  cash  flows  2  and  structure  and  the  as  are:  VARIA(F,V,P,NC) F(50,9),V(40),P(10,2)  b=(2*C)/Ta-a  d=88/Ta-c  Start  time  of  revenues=x.Tc  F(3,5)=V(21)*F(2,6) C  Finish  time  of  revenues=x.Tc+Ta  F(3,6)=F(3,5)+V(22) RETURN END  FUNCTION DIMENSION C  flow flow  2 3  flow 3  are  (i=2) (i=3)  3  (i=3) shown  in  subprograms  CO  CO(X,F,I) F(50,9)  CO=-a-((b-a)/Tc)*t  before:  Function  F(3,3)=88/V(22)-F(3,2) C  cash  (j=3)  F(2,3)=2*V(20)/F(2,6)-F(2,2) C  cash  35A.  The  Then,  parameter  145  CO=-F(2,2)-((F(2,3)-F(2,2))/F(2,6))*X RETURN END  FUNCTION  RE(X,F,I)  DIMENSION C  F(50,9)  RE=c+((d-c)/Ta)*(t-xTc) CO=F(3,2)+((F(3,3)-F(3,2))/(F(3,6)-F(3,5))*(X-F(3,5)) RETURN END  After  running  the  example  in  to  $210137  and  the  goes  be  6.4  EXAMPLE  OF  Although  the  intended  to  the  In  can  show  also  powerful  variables  the  behavior  of  in  capital  as  the  be  use  used  state,  to  the  NPV  results  19.21%.  of  the  the  the  projects.  well  By  almost  f o r the  proposed other  program an  flows  the  for  the  model  any  problem  basically  calculation  investment,  can  of  used  example  economic be and  the  as  in  used  a  which  deleted  insights  of  analyses.  be  added,  can  allocation  is  kinds  important  employed Also,  section  running  cash  gain  allowance as  a  computer  and  can  model  model  of  tool.  reset user  in this  to perform  teaching  contingency  problems  up  presented  coefficients  are  changed,  of  example  i t s present  very  computer,  APPLICATION  sensitivity  model  IRR  the  into  or the  evaluation to  assist  fast-tracking  involving  time  value  146  of  money.  6.4.1  DESCRIPTION The  Edward  project  Island  proposal with  be  after  time  zero  Total  design  duration  time  flows  rates  f o r both  in  terms  phase. shown 1989,  span  The work in figure  estimated  indirect  be  their  start  of  used  for  of the  have  phases, Inflation  For  purposes described  an  indirect facilities,  construction  and d u r a t i o n s as  of A p r i l  construction,  have  are 1, been  5.  in  the  inflation  i t has  to the expected  a l l work  for preliminary  will  site  d o l l a r costs  in Table  equal  c  this  months  initial  and  sequencing  is anticipated,  rate  phase  has been  costs, T  and  5%.  packages  length,  variability  costs  costs,  t o be  a  commences.  distribution.  project  work  35. C o n s t a n t  phase  two  of  Three  t=1.5 y e a r s .  the  the e n t i r e  year).  these  at time  packages,  s t a r t i n g date  and t h i s  uniform  Prince  of the p r o j e c t ,  design  ( a l l management  some  a constant  the  i s the  o f $1.5 m i l l i o n s  period=1  are estimated  and p r e s e n t e d  construction  inflation  a  major  forecast  While  that  three  stage  cost  During  analysis,  category  the  (1  years.  begins  an a p p r o x i m a t e  which  zero  items  of  etc.)  total  example  o f 9 m o n t h s . The  following  Construction  expense  a  a r e $20 m i l l i o n  o f 2.25  of  at  this  first  (0.25 y e a r s ) ,  costs  money  for  In t h e  duration  will  PROJECT  selected  i s prepared  a total  THE  bridge.  phase  a  OF  package  analysis  been average costs,  purposes.  rate  for  suggested rate  of  including  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  3 5 . S e q u e n c i n g a n d d u r a t i o n o f work during construction phase.  TABLE  Estimated constant d o l l a r  packages  5  construction  costs  Symbol  Units  Work P a c k a g e  Cost  Indirect costs  50.0  Coi  $ million/year  F o o t i n g s and P i e r s  120.0  Cof  $ million  Superstructure  200.0  Cos  $ million  Approaches  70.0  Coa  $ million  148  A preferential exchange  for  organization. by  present the the  balance  consortium.  During  drawdown  cash  flow  No  been  construction  plus  6  of  consortium  term  loan  the loan  including used  will  be  interest  to discharge  members.  be  to  10% a n d life  a gradient  expected  t o be  forecasts  the  members  period,  The  of 90%  to that  of with  of  t h e shape  the of the  of the p r o j e c t  interest  interest  the  the  be b o r r o w e d ,  of accrued  set to  will  rate  inflation  to the t o t a l  be  during  rate  during  construction  The l o a n will  will be  with  of the g r a d i e n t  positive.  of i n c r e a s i n g  This  revenue.  fixed over  repayment  first  loan  payment  will  35  costs, be  accrued of  the  interest  rate  years,  the  function equal  be d e r i v e d  repayment  a  size  will  (including  a  repaid  a  The  contribution  have  The  to take  period.  The  loan  the equity  plans  construction  construction.  repay  i t  the project  end of c o n s t r u c t i o n  equal  function  The v a l u e  can  correspond  of t h e p r o j e c t .  million.  and c l o s u r e  of the p r o j e c t ,  from  undertaking  the  consortium  operating  completion  during  and  to  subsidy  percent.  at the  interests)  equal  guarantee  construction. has  long  and a  payments  construction  The  of the p r o j e c t ,  the construction  profile.  during  lending  of a  will  in  the  derived  profile  arranged  by  for construction  being  loan  made  the size  s y s t e m upon  required  has been  participation  government  ferry  funds  for financing  equity  Given  the f e d e r a l  rate  schedule  to  and  will $45 i ti s  reflects  149  Constant of  dollar  the bridge  when  are forecast  operations  begins  construction). 5.5%  annual  They  t o be  and maintenance  $10 m i l l i o n s  (0.25 p e r i o d s  are  expected  costs  as of the date  before  the  to increase  end  at a  of  rate  of  per year. Revenue  will  be g e n e r a t e d  annual  subsidy  exceed  the i n f l a t i o n  the  ferry  First  from  system  operating  adjusted  that  passenger 6000000 a n d  to  be  are  forecast  to  grow a t  both  are forecast increase  subsidy, be  year.  at  to  start  5.5% p e r  $25 m i l l i o n  and  36,  an  i s not  to  and c a p i t a l  costs  i s committed  1.8%  to  year.  The  vehicle  trips  operation  general  They  respectively.  first  year  begins,  Toll  schedule  and  operating  is  to increase  of  run.  a n d $6 r e s p e c t i v e l y  i t i s projected  the  and  3000000 r e s p e c t i v e l y .  a t $3  when  tolls  which  and commercial  1.5% a n d  as of the time  In f i g u r e  operating  year  user  government  the government  forecast  rates  through  the f e d e r a l  are  to  operating  forecast  a t 5%  per  of the p r o j e c t  is  summarized. At  the end of the year  consortium  6.4.2  will  PREPARATION Prior  sets  the  to the  OF  the p r o j e c t  DATA  containing defined.  VARIA) primary Also,  as  period,  t o the government  the  f o r $1.  INPUT  use of the  functional  (subroutine  be  sell  35 o f t h e o p e r a t i n g  program,  relationships well  as the  between structure  variables  specific  the  unit  time  the subroutine the  variables  of the  to the problem  i s defined  that  a s one  vector should year.  o  OPERATION Ts=4.75  Tf=39.75  CONSTRUCTION Ts=l.5  Tf=5.0  DESIGN Ts = 0  25  Tf=2.5  PROPOSAL Ts = 0  T f = 0 . 75  FIGURE 36  General  time  schedule o f Che project;  (years)  15!  Monetary dollars.  quantities Since  analysis, and  we  flow  we  will wish  be  to  expressed  conduct  by  first  particular  to the problem  subroutine  linking  a  i s changed, the t o t a l  measured The V  and  by  them  variables  the  variables  and  the problem. impact  sensitivity  then  In t h a t  of  such  primary  20  variables  as  in  that  that  should  vector  be  included  V(21)=200  (Constant  d o l l a r cost  of  superstructure,  V(22)=0.65  (Variable  x as d e f i n e d  V(23)=2.20  (Variable  T  (Constant  g  d o l l a r cost  y as d e f i n e d  V(26)=1.10  (Variable  T  (Variable  T  p  of w r i t i n g cash  in figure  in figure  as d e f i n e d as d e f i n e d the  flows  in figure  associated  C  Q A  Design.  3.  Indirect  4.  Bridge  5.  Superstructure  construction  footings  and  construction  construction  costs.  )  i s as  the  follows.  project  costs.  piers  )  35)  Proposal.  2.  )  35)  VARIA  with  Q S  Q F  35)  in figure  subroutine  C  C  35)  numbered: 1.  in  35)  of approaches,  (Variable  A  and  in figure  as d e f i n e d  V(25)=0.50  the  vector  piers,  footings  process  in  follows: of  First,  is  starting  d o l l a r cost  The  when  are assigned  (Constant  V(27)=2.0  way,  a  a change  V(20)=120  V(24)=70  writing  the program.  i t sposition  position  with  V,  of  primary  including  in vector  millions  extensive  s e t t h e r e l a t i o n s h i p s between  parameters  variable  in  costs.  are  152  6.  Approaches  7.  Revenue  from  tolls  paid  by  passenger  8.  Revenue  from  tolls  paid  by  commercial  9.  Revenue  from  government  The  salvage  value  Then, They  construction  the  of  the  of  are  shown  The  unit  sale  1.  Toll  rate  for passenger  2.  Toll  rate  for commercial  3.  Dummy p r i c e  The  functional  way  they  1.  Value  are of  are  F(4,2)=value  2.  F  cash  as  of  3.  Starting  are  defined.  as  follows:  vehicles. vehicles. subsidy  (equal the  1.0)  variables  s u b r o u t i n e VARIA,  flow=CQ /duration,  and  are:  i s expressed  F  the  as:  of  the  fourth  cash  flow  (i=4)  previously.  cash  flow  4=Its  initial  period+Tp,  is  as:  F(4,6)=final F  flows  where  defined  F(4,6)=V(27)+1.5,  V(27)=T  the  numbered  i n the  (j=2)  F i n i s h i n g date expressed  of  r e l a t i o n s h i p s between  F(4,2)=-V(20)/V(27),  V(27)=T  is neglected.  each  f o r government  fourth  vehicles.  6.  prices  expressed  vehicles.  subsidy.  project  parameters in Table  costs.  as  where:  period defined  date  of  (j=6)  of  cash  4  (i=4)  previously.  cash  flow  5=x*Tp+Toc,  F(5,5)=V(22)*V(27)+F(3,5),  where  F(5,5)=starting  of  date  flow  (j=5)  cash  flow  i s expressed  5  ( i = 5)  as:  1 53  TABLE 6 Cash flows d e s c r i p t i o n and  ;  Name  Type  Value ( m i l l i o n $)  parameters  Ts (Period)  Tf (Period)  Inflat (%)  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. c o s t s  Uniform  -50.0  Toc=1.5  Tc=5.0  5.0  4 Footings  Uniform  -Cof/Tf  1.5  1.5+Tf  5.0  5 S u p e r s t r u c t u r e 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(22)=variable V(27)=T_  x as d e f i n e d  as d e f i n e d  previously.  previously.  r  F(3,5)=Toc:  4.  Finishing  Starting  date  date  of c a s h  F(5,6)=V(23)*F(5,5), F(5,6)=finishing F(5,5)=  same a s  V(23)=variable  (j=5) of  flow  5=its  cash  flow  starting  3  (i=3)  date  +  T : g  where  date  (j=6) of  cash  flow  5  (i=5)  above T  c  as  defined  previously.  154  Value  of cash  flow  5=C  F(5,2)=-V(21)/V(23), F(5,2)=value V(21)=C  Q S  (j=2) of the c a s h  V(23)=variable  written  /Tg:  where  as d e f i n e d  Similarly,  0 S  T  the  g  flow  5 (i=5)  previously.  as d e f i n e d  previously.  relationships  for  cash  v  flow  6  can  be  as:  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)  The is  i n f l a t i o n rates of cash expressed  3 to 6 are equal.  That  as:  F(4,7)=F(3,7),  where  F ( 4 , 7) = i n f l a t i o n F(3,7)=inflation and  flows  similarly  rate rate  ( j = 7)  of cash  flow  (j=7) of cash  f o r cash  flows  5 and  4  flow  ( i = 4)  3 (i=3)  6:  F(5,7)=F(3,7) F(6,7)=F(3,7)  The  interest  inflation  of  rate  the c o n s t r u c t i o n loan plus  6%.  That  i s expressed  V(4)=F(3,7)+0.06,  where  V( 4) = I n t e r e s t  construction  Vector  on  i s equal  loan  (see  rate  (j=7) of cash  flow  the  as:  structure  V)  F(3,7)=inflation  to  3 (i=3)  of  1  The  revenues  the  end  of  start  being  construction.  period  of  cash  flows  period  of  cash  flow  F(7,5)=starting  That  7,  8  0.25  means  and  3 minus  F(7,5)=F(3,6)-0.25,  and  collected  9  that  is  0.25.  periods  before  the  equal  to  55  starting the  final  Then:  where  period  (j=5)  of  cash  flow  7  has  a  (i=7)  similarly:  F(8,5)=F(3,6)-0.25 F(9,5)=F(3,6)-0.25  The  operational  35  phase  of  the  project  duration  of  years:  F(7,6)=F(7,5)+35  where:  F(7,6)=Finishing  date  F(7,5)=as and  defined  (j=6)  of  cash  flow  7  (i=7)  above.  similarly:  F(8,6).=F(8,5)+35 F(9,6)=F(9,5)+35  .  Finally,  the  inflation This  rate  statement for  is expressed  P(2,2)=P(1,2)  of  both  the  types  problem of  toll  says rates  that is  where rate  ( j = 2)  of  unit  price  2  ( i = 2)  P(1 ,2) = i n f l a t i o n  rate  ( j = 2)  of  unit  price  1  (i=l)  restated  at  equal.  as:  P(2,2) = in,flation  is  the  this  point,  that  in  the  subroutine  VARIA,  1 56  the  matrix  contain  F  refers  primary  assigned  the  unitary  sale  matrix  shown  both  (see P  flows  parameters,  considered  by  the vector the program  s t r u c t u r e of v e c t o r  contains  V  the information  in  V and  chapter  about  the  prices.  Summarizing, one  cash  variables  by t h e u s e r  5) a n d  the  to  the subroutine  in figure  computer,  the  complete  presented  i n Appendix  B.  37. A f t e r results  VARIA  for this  running and  example  the program  output  is  i n the  obtained  are  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  The  theory  cover  a  and  wide  evaluation  additions  range  THEORETICAL  1.  The cash  flows  long  term  be  developed  dealing  is  model.  of  room  Some  made a r e a s  in this  with  analysis  still  of  a more  generated debt  work  the  economic  large  capital  for  improvement,  recommendations  about  follows:  by  detailed the  repayment  description  financial schedules  of  the  structure,  ie.  and  input  from  funds.  Development  of  a  sensitivity  analysis  Development  of  differences  between  systematic to  7.2  THE  MODEL  1.  Inclusion  COMPUTER  o f more  that  the  for large  theory  functional  a model  coefficients  flow  F U T U R E WORK  FRAMEWORK  development  borrowed  3.  there  could  7.1  2.  sensitivity  i n the computer that  model  of a s p e c t s  However,  especially  C O N C L U S I O N S AND  the computer  and  projects.  7.  can  linear  changes  built-in  to  perform  to  quantify  forms. be  and  used exact  sensitivity  i n the primary  functions  variables.  to represent  cash  profiles.  2.  Consideration  3.  Inclusion  4.  Allow  of  o f more  constant  several error  assumed  foreign checking  quantities  158  exchange  rates.  conditions. (inflation,  interest,  1 59  tax  and  foreign  operating to  costs)  exchange to  take  rates,  sales  functional  prices  forms  with  and  respect  time.  Include  a  built-in  selection  for  system  of  units  plus  a  including  a  calendar. Improve bar  the  chart  Include loan  quality  schedule  the  and  of and  option  the a  of  graphic  general  having  output  cash  more  than  and  add  depreciation  scheme,  repayment  functions  depreciation  It  be  would  fairly  assigns  a  primary  variables,  perform  and  simple  probability  risk  analysis  Add  a  sub-system  the  subroutine  construction.  that VARIA  to  add  using allows  the  one  a  improve  term  built-in  subroutine function  Carlo user  long  more  allowing  Monte  diagram.  methods.  distribution  therefore,  and  flow  to  the  that to  user  the to  simulation. edit  and  friendliness  change in  its  BIBLIOGRAPHY  Abdel-Aoal,  H. a n d S c h m e l z l e e ,  engineering,  Abboud,  Macel  Dekker  Samir..(1979).  estate  projects,"  R. Petroleum  and  I n c , 1976.  "An a n a l y t i c a l The  economics  Appraisal  process  Journal,  of  real  V o l . 47, pp  412-426.  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Project  evaluation  in  the  chemical  M c G r a w - H i l l , 1983.  to  chemical  cs , J o h n  Wiley  engineering  process  a n d s o n s , 1984.  APPENDIX  PROGRAM  A  LISTING  1 70  1 71  _  c  C C C C C C  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 OF C A P I T A L P R O J E C T S DAVID  POVEDA  - NOVEMBER  1988  c  C VARIABLE DEFINITION C " CN: VECTOR OF THE CASH FLOWS NAMES C NA: NAME OF A V A R I A B L E C PRONA: P R O J E C T I D E N T I F I C A T I O N C F : MATRIX C O N T A I N I N G THE INFORMATION ABOUT CASH FLOWS C I T : VECTOR C O N T A I N I N G THE P H A S E TO WHICH EACH CASH FLOW BELONGS C C: MATRIX C O N T A I N I N G THE E Q U I V A L E N T DISCRETE CASH FLOWS C C F : VECTOR WITH THE NET CASH FLOW A T THE END OF EACH PERIOD C V : VECTOR OF PRIMARY V A R I A B L E S C P: MATRIX OF U N I T SALE PRICES AND T H E I R INFLATION RATES C B: MATRIX C O N T A I N I N G THE LONG TERM DEBT REPAYMENT SCHEDULE c  CHARACTER*25 CN CHARACTER*10 U N I T CHARACTER*6 NA CHARACTER*40 PRONA EXTERNAL C F 3 , C F 4 , C F 5 , C F 6 , C F 7 , C O , R E , F I N T , F E S C , F I N T 1 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 C  I N I T I A L I Z E VARIABLES  301 300  303 302  304 C C C  DO 300 1=1,20 IT(I)=0. DO 301 J = 1 , 9 F(I,J)=0. CONTINUE CONTINUE DO 3 0 2 I = 1 , 1 3 DO 303 J = 1 , 5 0 C(I,J)=0. CONTINUE CONTINUE A0 = 0. DO 304 1=1,30 V(I)=0. CONTINUE READ P R O J E C T  IDENTIFICATION  1 72  WRITE(6,1) FORMAT(///,'PROJECT I D E N T I F I C A T I O N ' ) READ(5,2)PRONA 2 FORMAT(A40) WRITE(8,3)PRONA 3 FORMAT(1H1,'SENSITIVITY AND ECONOMIC ANALYSIS OF PROJECT: 1 //,A40,//) C C C A L L SUBROUTINE OF DATA I N P U T C CALL I N P U T ( F , V , B , P , C N , I T , N C , I Z , U N I T ) CALL VARIA(F,V,P,NC) C C WRITE THE F O R E I G N EXCHANGE R A T E 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 T H E PERFORMANCE MEASURES AND P R I N T 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 W R I T E ( 8 , 1"38)UNIT,VPV0 WRITE(6,138)UNIT,VPVO 138 FORMAT(1H1,'ECONOMIC PERFORMANCE MEASURES' ,1 OX,' (' ,A 10,' ) ' , / / , 1 'NET P R E S E N T V A L U E ' , T 5 0 , F 1 2 . 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 F O R M A T ( ' E S C A L A T I O N DURING CONSTRUCTION*T50,F12.3,/) WRITE(8,104)XDCO WRITE(6,104)XDC0 104 F O R M A T ( ' I N T E R E S T S DURING CONSTRUCTION=',T50,F12.3,/) WRITE(8,106)TEI0 WRITE(6,106)TEI0 106 F O R M A T ( ' T O T A L CONSTRUCTION COSTS=',T50,F12.3,/) 1  C  173 C COMPUTE THE IRR. CHECK NUMBER OF SIGN CHANGES IN SUBROUTINE C SNSC AND REQUEST THE EXTERNAL RATE I F 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 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) I F ( I 1.EQ.O) GOTO 137  ZERO  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 C  S E L E C T I O N OF 144 145 146 151 152  C C C  T Y P E OF  SENSITIVITY  ANALYSIS  WRI.TE(6, 145) FORMAT(/,'DO S E N S I T I V I T Y A N A L Y S I S ? ( Y E S = 1 , N O = 0 ) ' , / ) READ(5,146)1 1 FORMAT(I 1) I F ( I 1.EQ.O) GOTO 147 WRITE(6,152) F O R M A T ( / / , ' S E L E C T T Y P E OF A N A L Y S I S ' , / / , 1 T 2 , ' 1 . LINEAR UNIVARIATE',/,T2, 2 '2. EXACT U N I V A R I A T E AND B R E A K - E V E N POINTS',/,T2, 3 '3. B I V A R I A T E ' , / , ' 4 . R E S E T A V A R I A B L E ' , / , T 2 , 4 '5. CHANGE A CASH F L O W ' , / , T 2 , ' 6 . ADD A CASH FLOW', 5 / , T 2 , ' 7 . STOP',/) READ(5,146)11 TRANSFER  CONTROL ACCORDING  TO  SELECTION  GOTO(154 , 1 5 5 , 1 5 6 , 1 5 7 , 1 8 0 , 2 0 0 , 1 4 7 ) , 1 1 C C C  LINEAR  UNIVARIATE  ANALYSIS  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 FORMAT(11) I F ( I 1.EQ.O) GOTO 151 W R I T E ( 8 , 1 7 01)NA,VAR WRITE(6,1701)NA,VAR 1701 FORMAT(///,'VARIABLE ',A6,' HAS BEEN RESET TO:',F15.5,/, 1 'THE NEW PERFORMANCE MEASURES A R E : ' ) 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' , / / , 2 0 ( T 2 , 1 2,' . \A25,/),/) READ(5,*)ICASH CALL ADDCAS(F,P,IT,CN,ICASH) WRITE(6,198)CN(ICASH) 198 FORMAT(///,'CASH FLOW ' , A 2 5 , ' 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) W R I T E ( 6 , 1 9 8 1 ) C N ( I CASH) 1981 FORMAT(///,'CASH FLOW ',A2 5,' HAS BEEN CHANGED.',/, 1 'THE NEW PERFORMANCE A R E : ' ) 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 ' , A 2 5 , ' 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 ' , A 2 5 , ' HAS BEEN ADDED.',/, 1 'THE NEW PERFORMANCE A R E : ' ) GOTO 10 C C STOP THE E X E C U T I O N OF THE PROGRAM C 147 STOP END C C SUBROUTINE OF DATA I N P U T C SUBROUTINE I N P U T ( F , V , B , P , C N , I T , N C , I Z , U N I T ) 5  176  CHARACTER*25 CN,NA CHARACTER*10 U N I T DIMENSION F(20,9),V(40),IT(20),P(10,2),CN(20),B(50,7) C C C  INPUT B A S I C  INFORMATION  ABOUT T H E P R O J E C T  WRITE(6,1) FORMAT(////,'NUMBER OF CASH FLOWS ( 1 - 5 0 ) ' , / ) READ(6,*)NC 2 FORMAT(12) P(10,2)=NC WRITE(6,3) 3 FORMAT(/,'DISCOUNT R A T E ( 0 . # # ) ' , / ) READ(5,4)V(1) 4 FORMAT(F4.2) WRITE(6,15) 15 FORMAT(/,'ARE THERE FLOWS EXPRESSED IN F O R E I G N CURRENCY ', 1 ' ( Y E S = 1 , NO=0)',/) READ(5,2)IDE I F (IDE.. EQ.O) GOTO 19WRITE(5,16) 16 F O R M A T ( / , ' F O R E I G N EXCHANGE R A T E ' , / ) READ ( 5 , * ) V ( 2 ) 17 FORMAT(F10.3) 19 WRITE(6,18) 18 F O R M A T ( / , ' E N T E R $ U N I T S (MAX. 10 C H A R A C T E R S ) ' , / ) 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 T H E CONSTRUCTION PHASE C WRITE(6,44) 44 FORMAT(//,'GENERAL INFORMATION ABOUT CONSTRUCTION PHASE',/, 1 'FRACTION F I N A N C E D WITH BORROWED FUNDS ( 0 . # # ) ' , / ) READ(5,4)V(3) I F ( V ( 3 ) . E Q . 0 ) G O T O 220 WRITE(6,46) 46 FORMAT(/,'INTEREST RATE ON CONSTRUCTION LOAN (0.##)',/) READ(5,4)V(4) WRITE(6,47) 47 F O R M A T ( / , ' P E R I O D WHEN T H E LOAN I S DUE*,/) READ(5,*)V(5) 48 FORMAT(F6.3) C C INPUT INFORMATION ABOUT T H E O P E R A T I O N A L PHASE C 220 WRITE(6,215) 1  177  215 FORMAT(//,'GENERAL INFORMATION ABOUT OPERATIONAL PHASE',/) WRITE(6,79) 79 FORMAT(/,'PERIOD WHEN O P E R A T I O N S COMMENCE',/) READ(5,*)V(17) 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 P R I C E ',11,/) READ(5,*)P(I,1) 204 FORMAT(F10.3) WRITE(6,65) 65 F O R M A T ( / , ' I N F L A T I O N RATE ( 0 . # # ) ' , / ) READ(5,4)P(I,2) 210 CONTINUE PRODUCTION COSTS WRITE(6,74) 74 FORMAT(/,'FIXED COSTS',/) READ(5,*)V(7) 64 FORMAT(F10.3) I F ( V ( 7 ) . E Q . O ) GOTO 7 7 9 WRITE(6,65) READ(5,4)V(18 ) 779 WRITE(6,78) 78 FORMAT(/,'UNIT V A R I A B L E COSTS',/) READ(5,*)V(8) I F ( V ( 8 ) . E Q . O ) GOTO 7 99 WRITE(5,65) READ(5,4)V(19) DEPRECIATION 799 WRITE(6,80) 80 FORMAT(//,'IS DEPRECIATION CONSIDERED (YES=1, NO=0)',/) READ(5,7)IDE I F ( l D E . E Q . 0 ) G O T O 90 WRITE(6,81) 81 F O R M A T ( / , ' S E L E C T D E P R E C I A T I O N METHOD',/,T2, 1 '1. STRAIGTH L I N E ' , / , T 2 , ' 2 . DECLINING BALANCE',/) READ(5,*)ID WRITE(6,82) 82 FORMAT('VALUE OF T H E D E P R E C I A B L E A S S E T S ' , / ) READ(5,*)V(9) WRITE(6,83) 83 FORMAT('PERIOD WHEN T H E A S S E T S A R E A Q U I R E D ' , / ) READ(5,*)V(10) WRITE(6,84) 84 F O R M A T C L I F E OF T H E A S S E T S ' , / ) READ(5,*)V(11) c  c  c  U  U  N  I  T  N  I  T  1 78  I F ( I D . E Q . 2 ) THEN V(9)=-V(9) END I F TAX R A T E  c  90 92  WRITE(6,92) FORMAT(//,'TAX READ(5,4)V(12)  RATE ( 0 . # # ) ' , / )  LONG TERM F I N A N C I N G 95 WRITE(6,96) 96 FORMAT(//,'LONG TERM F I N A N C I N G ' , / / , ' S E L E C T ONE OF T H E FOLLOWING' 1 , / , T 2 , ' 1 . NO LONG TERM LOAN I S T A K E N ' , / , T 2 , ' 2 . LOAN TAKEN ' , 2 'TO REPAY CONSTRUCTION LOAN' , / , T 2 , '3 . I N P U T AMOUNT BORROWED',/) READ(5 , 7 ) IB G O T O ( 5 , 1 0 1 , 1 0 2 ) , IB GOTO 95 101 V(15)=1 GOTO 103 102 READ(5,*)V(13) 98 FORMAT(F13.3) I F ( V ( 1 3 ) . E Q . O ) GOTO 5 103 WRITE(6,100) 100 FORMAT(/,'NOMINAL INTEREST RATE BETWEEN PAYMENTS (0.##)',/) READ(5,4)V(14) WRITE(6,106) 106 F O R M A T ( / , ' P E R I O D WHEN T H E LOAN I S T A K E N ' , / ) READ(5,*)V(16) CALL I N F I N ( B ) C C INFORMATION ABOUT CASH FLOWS C 5 ICASH=0 WRITE(6,6) 6 F O R M A T ( / / / , T 1 0 , ' I N F O R M A T I O N ABOUT CASH FLOWS',//) C 35 ICASH=ICASH+1 12 WRITE(6,10)ICASH 10 F O R M A T ( / / , T 2 5 , ' C A S H FLOW NUMBER ' , 1 2 , / / ) S E L E C T I O N OF PHASE C A L L MENU4(K) IT(ICASH)=K C C TRANFER CONTROL ACCORDING TO PHASE S E L E C T E D •C GO T O ( 2 0 , 2 0 , 2 4 , 2 6 , 2 8 , 2 4 ) ,K GOTO 12 F E A S I B I L I T Y AND D E S I G N --. 2.0 C A L L MENU 1 ( F , CN , I CASH ) GOTO 200 C I N I T I A L I N V E S T M E N T AND D I S P O S A L 24 IC=3 c  c  c  C 26 C 28  68 69 691  C 200  CALL FSING(F,CN,ICASH,IC) I F ( I C . E Q . 2 ) GOTO 24 GOTO 200 CONSTRUCTION CALL MENU2(F,CN,ICASH) GOTO 200 OPERATION CALL MENU3(F,CN,ICASH) I F ( N P . E Q . 1 ) THEN F(ICASH,9)=1 GOTO 200 ENDIF WRITE(6,68) FORMAT(/,'SELECT UNIT SALE P R I C E ' , / ) WRITE(6,69)(J,P(J,1),J=1,NP) FORMAT(T2,1 1 , ' . ' , F 1 5 . 7 ) WRITE(6,691) FORMAT(/) READ(5,7)IU F(ICASH,9)=IU NEXT CASH FLOW I F ( I C A S H . N E . N C ) GOTO 35  C  c C C  I N P U T OF OTHER  PRIMARY  VARIABLES  110 WRITE(6,112) 112 FORMAT(//,'INPUT OTHER PRIMARY VARIABLES (YES NO=0)',/) READ(5,7)IN I F ( I N . E Q . O ) GOTO 140 WRITE(6,114) 114 FORMAT(/,'NUMBER OF V A R I A B L E S ( 1 - 2 0 ) ' , / ) READ(5,*)NV DO 120 I=20,20+NV-1 WRITE(6,116)1 116 F O R M A T ( / , ' I N P U T V A R I A B L E ' , 1 2 , ' 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 A D D C A S ( F , P , I T , C N , I CASH) CHARACTER*25 CN DIMENSION F ( 2 0 , 9 ) , I T ( 2 0 ) , C N ( 2 0 ) , P ( 1 0 , 2 ) . C A L L MENU4(K) IT(ICASH)=K G O T O ( 1 0 , 1 0 , 2 0 , 3 0 , 4 0 , 2 0 ) ,K 10 C A L L MENU 1 ( F , C N , I CASH) GOTO 50 C  180  20  IC=3 CALL FSING(F,CN,ICASH,IC) I F ( I C . E Q . 2 ) GOTO 20 GOTO 50  30  C A L L M E N U 2 ( F , C N , I CASH) GOTO 50  40  CALL MENU3(F,CN,ICASH) WRITE(6,45) FORMAT('SELECT UNIT SALE . P R I C E / ) WRITE(6,48)(J,P(J,1),J=1,10) FORMAT(T2,1 1,' . ' F 1 0 . 3 ) READ(5,*)IU F ( I CASH,9)=IU  C  C  45 48  f  C 50  RETURN END  C C SUBROUTINE FOR THE INPUT OF THE LONG TERM DEBT CONDITIONS C SUBROUTINE I N F I N ( B ) DIMENSION B ( 5 0 , 7 ) 1 WRITE(6,10) 10 F O R M A T ( / , ' S E L E C T T Y P E OF REPAYMENT F U N C T I O N ' , / , T 2 , 1 ' 1 . UNIFORM P A Y M E N T S ' , / , T 2 , ' 2 . S T E P F U N C T I O N ' , / , T 2 , 2 ' 3 . GRADIENT F U N C T I O N ' , / ) 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 S T A R T I N G ON P E R I O D ' , / ) READ(5,*)B(1,3) WRITE(6,65) 65 FORMAT (/,' NUMBER OF P E R I O D S BETWEEN PAYMENTS'-,/) READ(5,*)B(1,4) I F ( I T 1 . E Q . 1 ) GOTO 200 WRITE(6,105) 105 F O R M A T ( / , ' V A L U E 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 P R I N T I N G T H E REPAYMENT S C H E D U L E C SUBROUTINE P R R E P ( B , V , U N I T ) CHARACTER*10 U N I T DIMENSION B(.50,7) , V ( 4 0 ) WRITE(8,10)UNIT,V(13),V(14) 10 FORMAT('LONG TERM DEBT REPAYMENT S C H E D U L E ' ,1 OX,' (' ,A10,' )' , / / , 1'AMOUNT BORROWED=',F13.3,//,'INTEREST RATE=',F6.4,///,'PERIOD', 2 T10,'AMOUNT O W E D ' , T 2 9 , ' P A Y M E N T ' , T 4 4 , ' I N T E R E S T S ' , T 5 5 , 3 'PRINCIPAL REPAID',T75,'LOAN BALANCE',//) NP=B(1,2) DO 100 I=2,NP+1 WRITE(8,15)(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 P R I N T I N G T H E GENERAL INFORMATION C ABOUT T H E P R O J E C T C SUBROUTINE O U T P U T ( F , V , P , I T , N C , C N , U N I T ) CHARACTER*7 CU CHARACTER*10 U N I T CHARACTER*25 CN CHARACTER*12 T Y , P H DIMENSION F ( 2 0 , 9 ) DIMENSION V ( 4 0 ) , P ( 1 0 , 2 ) , I T ( 2 0 ) , C N ( 2 0 ) C~PRIMARY V A R I A B L E S WRITE(8,1)(V(I),1=1,5),(V(J),J=7,12) 1 FORMAT(//,'PRIMARY VARIABLES',//, 1 'DISCOUNT RATE=',F6.4,//,'FOREIGN EXCHANGE RATE=',F15.5,//, 2 'FRACTION O F - CONSTRUCTION F I N A N C E D WITH BORROWED FUNDS=',F6.4, 3 / / , ' I N T E R E S T RATE ON C O N S T R U C T I O N LOAN=',F6.4,//, 4 'PERIOD WHEN T H E CONSTRUCTION LOAN I S D U E = ' , F 6 . 2 , / / , 5 'FIXED OPERATING COSTS=',F15.5,//, 6 'VARIABLE COSTS=',F15.5,//,'VALUE OF D E P R E C I A B L E ASSETS=', 7 F 1 5 . 5 , / / , ' P E R I O D WHEN A S S E T S A R E A C Q U I R E D = * , F 6 . 2 , / / , 8 'LIFE OF DEPRECIABLE ASSETS=',F6.2,//,'TAX RATE=',F6.4,/) WRITE(8,4)V(18),V(19) 4 F O R M A T ( ' I N F L A T I O N RATE FOR F I X E D C O S T S = ' , F 6 . 4 , / / , 1 ' I N F L A T I O N RATE FOR V A R I A B L E C O S T S = ' , F 6 . 2 ) UNIT SALE PRICES NP=P(10,1) c  182  WRITE(8,5)UNIT 5 FORMAT(///,'UNIT SALE PRICES',5X,'(',A10,')',//,T2,'#',T10, 1 'PRICE',T25,'INFLATION',//) DO 7 1=1,NP WRITE(8,6)I,(P(I,J),J=1,2) 6 FORMAT(T2,I1,T6,F15.7,T28,F6.4) . 7 CONTINUE __ LOWS W R I T E ( 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 II1=F(I,1) G O T O ( 1 5 , 1 6 , 1 7 , 1 8 , 1 9, 20 , 21 ,22) ,1 1 1 15 T Y = ' S I N G L E 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 I F 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 c  C  A  S  H  F  183  C WRITE(8,50)I,CN(I),TY,PH,F(I,5),F(I,6),F(I,7),CU 50 FORMAT(T2,I2,T8,A25,T34,A12,T47,A 12,T60,F6.2,T75,F6.2,T90,F6.4, 1 T105,A7) G O T O ( 5 5 , 6 0 , 6 5 , 7 0 , 7 5 , 8 0 , 8 5 , 9 0 ) ,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 WRITE(8,61)F(I,2),UNIT,F(I,3),UNIT WRITE(6,61)F(I,2),UNIT,F(I,3),UNIT 61 FORMAT('FIRST PAYMENT=',F13.3,'(',A10,')',/, 1 'SECOND P A Y M E N T = ' , F 1 3 . 3 , ' ( ' , A 1 0 , ' ) ' , / ) 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) WRITE(6,71)F(I,2),F(I,3) 71 FORMAT('INITIAL VALUE=',F13.3,/,'FINAL VALUE=',F13.3,/) GOTO 300 C 75 WRITE(8,76)F(I,2),F(I,3),F(I,4) WRITE(6,76)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 WRITE(8,81)F(I,2),F(I,3) WRITE(6,81)F(I,2),F(I,3) 81 FORMAT('BASE VALUE=',F13.3,/,'GROWTH R A T E = ' , F 5 . 2 , / ) GOTO 3 00 C 85 WRITE(8,86)F(I,2),F(I,3),F(I,4) WRITE(6,86)F(I,2),F(I,3),F(I,4) 86 FORMAT('ASYMPTOTIC LIMIT=',F13.3,/,'SHAPE PARAMETERS,F9.3,/, 1 'GROWTH R A T E = ' , F 5 . 2 , / ) GOTO 300 C 90 WRITE(8,91)F(I,2),F(I,3),F(I,4) WRITE(6,91)F(I,2),F(I,3),F(I,4) 91 FORMAT('PARAMETER 1=',F13.3,/,'PARAMETER 2»',F13.3,/, 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 F O R M A T ( ' U N I T S A L E P R I C E = ' , F 1 5 . 7 , ' (' , A 1 0 , ' ) ' ,/) ENDIF WRITE(8,305) WRITE(6,305) 305 FORMAT (' 1 301  .  .  500  C C C  ',  CONTINUE RETURN END CALCULATION  OF  NPV,  T C C AND  CURRENT  DOLLAR  NET CASH  FLOW  SUBROUTINE NPV(A,F,C,P,CF,V,B,IT,NC,A0,IZ,Y,VPV,TCC,EDC,XDC) EXTERNAL C F 3 , C F 4 , C F 5 , C F 6 , C F 7 , C O , R E , F I N T , F E S C , F I N T 1 DIMENSION F(20,9),IT(NC),C(35,IZ),CF(IZ),V(40),P(10,2),B(50,7) DIMENSION A ( 5 0 ) R E S E T V A R I A B L E S TO ZERO A0 = 0 • TCC=0 EDC=0 XDC = 0 DO 1 J = 1 , I Z 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 A L L THE FLOWS (NC=NUMBER OF FLOWS) C DO 1000 1=1,NC C F I N D OUT T Y P E OF FLOW AND TRANFER CONTROL III=INT(F(I,1)) GO T O ( 1 0 0 , 1 0 0 , 3 0 0 , 3 0 0 , 3 0 0 , 3 0 0 , 3 0 0 , 3 0 0 ) , I I I C FLOW I S A S I N G L E OR TWO D I S C R E T E PAYMENTS 100 IFL=1 PP=F(I,2) -PER=F(I,5) c  j)  1 85  C 102  110  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 M U L T I P L Y BY S A L E P R I C E I F FLOW BELONGS TO O P E R A T I O N A L PHASE I F ( 1 X 1 . E Q . 5 ) THEN IN=F(I,9) PRI=P(IN,1) TEP=P(IN,2) C(5,IX2)=C(5,IX2)+EQUIV*PRI*EXP(((IX2)-V(17))*TEP) 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  C C C  I F ( I T ( I ) . N E . 4 ) GOTO 110 TCC=TCC+PP XDC=XDC+FF*PP*EXP(RIC*(DUE-PER)) I F ( P E R . E Q . O ) THEN A0=A0+PP A(I)=PP GOTO 15 ELSE  REPEAT 15  C C C C C  THE  PROCESS  FOR  THE  SECOND  PAYMENT  I F ( 1 1 1 . E Q . 2 . A N D . I F L . E Q . 1 ) THEN IFL=2 PP=F(I,3) PER=F(I,6) GOTO 102 ENDIF GOTO 1000 UNIFORM FLOW. D E F I N E THE T Y P E AND COMPUTE THE E Q U I V A L E N T D I S C R E T E PAYMENTS AT THE END OF E A C H PERIOD  300  IXL=INT(F(I,5)) IXU=INT(F(I ,6)-.05) DO 900 J = I X L , I X U XL1=J XL=MAX(XL1 , F ( I ,5) ) XU1=J+1 XU=MIN(XU1 , F ( I , 6 ) ) J1=F(l,l)-2 GO T O ( 3 5 0 , 4 0 0 , 4 5 0 , 5 0 0 , 5 5 0 , 6 0 0 ) , J 1 : UNIFORM F U N C T I O N 350 CALL SEQU(F,C,V,P,IT,Y,I,J,FF,DUE,RIC,CF3,XL,XU,TCC,EDC,XDC) GOTO 900 . T R A P E Z O I D A L FLOW 400 CALL SEQU ( F , C , V , P , I T , Y , I - , J , F F , DUE , RI C , CF 4 , XL , XU , T C C , EDC , XDC )  c  c  186  GOTO  900 BETA  FUNCTION 4 50 SEQU(F,C,V,P,IT,Y,I,J,FF,DUE,RIC,CF5,XL,XU,TCC,EDC,XDC) GOTO 900 E X P O N E N T I A L FLOW 500 SEQU(F,C,V,P,IT,Y,I,J,FF,DUE,RIC,CF6,XL,XU,TCC,EDC,XDC) GOTO 900 GOMPERTZ CURVE 550 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  c  CALL  c  CALL  c  CALL  CALL SEQU(F,C,V,P,IT,Y,I,J,FF,DUE,RIC,RE,XL,XU,TCC,EDC,XDC) GOTO 900 A R B I T R A R Y F U N C T I O N , CONSTRUCTION P H A S E 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 F I X E D AND V A R I A B L E C O S T S C DO 1100 1 = 1 , I Z C(13,I)=C(6,I) C(7,I)=C(7,I)*V(8)*EXP(V(19)*(I-V(17))) I F ( C ( 5 , I ) . E Q . 0 ) THEN C(6,I)=0 ELSE C(6,I)=V(7)*EXP(V(18)*(I-V(17))) ENDIF 1100 CONTINUE C C COMPUTE D E P R E C I A T I O N 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 S T R A I G H T L I N E METHOD DEP=V(9)/V(11) DO 1110 I=IDP+1,IDP+IDL C(8,I)=DEPC 114 0 CONTINUE ELSE D E C L I N I N G BALANCE METHOD FAC=-V(9)*2/IDL FI=(IDL-2)/IDL DO 1115 1 = 1 ,IDL DI=FAC*FI**(I-1 )  c  c  187  1115 C C C  COMPUTE LONG 130  135 C C C  TERM  DEBT  REPAYMENT  SCHEDULE  IF(V(13).EQ.O.AND.V(15).EQ.O) 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) I F ( D F F . E Q . O ) THEN  GOTO  140  TAX  FOR  C(9,XPE)=B(J,3) ELSE DT=1-DFF C(9,XPE+1)=B(J,3)*EXP(Y*DT) ENDIF CONTINUE COMPUTE T A X A B L E  140  C C C  C(8,IDP+1)=DI CONTINUE ENDIF  INCOME  AND  INCOME  EACH  PEERIOD  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(12,1)=(C(11,1)-C(8,I)-C(9,I))*V(12) ENDIF COMPUTE NET  T O T A L CASH  FLOW FOR  EACH  PERIOD  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 ) CF(I)=C(14,1 ) 1130 CONTINUE C C COMPUTE NPV D I S C O U N T I N G T H E 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 E Q U I V A L E N T D I S C R E T E FLOW AT T H E C END OF THE P E R I O D . F O R D I S C R E T FLOWS C SUBROUTINE D l S C ( P , P E R , I T F , F E , Y , E Q U I V , I X 1 , 1 X 2 ) D l F = PER-1 N T ( P E R ) IX1=ITF I F ( D I F . E Q . O ) THEN  188  IX2=PER EQUIV=P*FE ELSE IX2 = I N T ( P E R + 1 ) TX=IX2-PER EQUIV=P*EXP(Y*TX)*FE ENDIF RETURN END C C C C C  NUMERICAL I N T E G R A T I O N S U B R O U T I N E (GAUSS DO NOT I N C L U D E E S C A L A T I O N AND I N T E R E S T S CONSTRUCTION  QUADRATURE) DURING  SUBROUTINE I N T E G ( F , X L , X U , F C T , T E , D R , 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 = B 1 * ( Z + . 4444 4 4 4 * F C T ( A , F , I ) * E X P ( ( T D * A ) - T X ) ) RETURN END C C C C  NUMERICAL I N T E G R A T I O N S U B R O U T I N E (GAUSS INCLUDE E S C A L A T I O N AND I N T E R E S T S DURING  QUADRATURE) CONSTRUCTION  SUBROUTINE I N T E 1 ( D U E , F , X L , X U , F C T , T D , R I C , F U N , Z , I ) DIMENSION F ( 2 0 , 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 , T X ) X2=FUN(A-Z,DUE,RIC,TD,TX) Z=.27777778*(Z1*X1+Z2*X2) Z=B*(Z+.44 44 4 4 4 * F C T ( A , F , I ) * F U N ( A , D U E , R I C , T D , T X ) ) RETURN END C C C C  SUBROUTINE TO F I N D OUT FOR THE C A L C U L A T I O N OF  THE THE  NUMBER OF IRR  SUBROUTINE S N S C ( C F , A O , I Z , N S C ) DIMENSION C F ( 5 0 ) , I S I G ( 5 0 ) NSC = 0 DO 10 I = 1 , I Z I F ( C F ( I ) . E Q . O ) THEN  SIGN  CHANGHES  189  10  15  20  C C C  ISIG(I)=0 GOTO 10 ENDIF ISIG(I)=CF(I)/ABS(CF(l)) CONTINUE I F ( A O . E Q . O ) GOTO 15 ISO=A0*ISIG(1)/ABS(A0) I F ( I S O . G T . O ) GOTO 15 NSC=1 DO 20 1=1,IZ-1 IS=ISIG(I)*ISIG(I+1) I F ( I S . G E . O ) GOTO 20 NSC=NSC+1 CONTINUE RETURN END COMPUTATION OF  THE  IRR  FOR  SUBROUTINE  ONE  SIGN  CHANGE  SIRR1(A,F,C,P,CF,V,B,IT,NC,AO,IZ,Y,VPV,YR) DIMENSION F(20,9),C(35,IZ),CF(LZ),IT(NC),V(40),P(10,2),B(50,7) DIMENSION A ( 5 0 ) YR=Y VPVO=VPV I F ( V P V . G T . O ) THEN DEL=.05 ELSE DEL=-.05 ENDIF 10 I F ( V P V O . G T . 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 = V P V 0 * V P V / A B S ( V P V O ) I F ( C H E 1 .GT.0) GOTO 10 I F ( V P V O . G T . 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) I F ( V P V . L T . O ) THEN RS = YR ELSE RI = YR ENDIF DIF=RS-RI IF(DIF.LT.0.0001)GOTO  20  190  20  C C C  YR=(RS+RI)/2 GOTO 100 YR=(RS+Rl)/2 VPV=VPV0 RETURN END COMPUTATION  OF T H E IRR U S I N G NEWNAN  METHOD  SUBROUTINE S I R R 2 (A , F', C , P , CF , V, B , I T , NC , A0 ,1 Z , Y , V P V , E X T , YR) DIMENSION F(20,9),C(35,IZ),CF(IZ),V(40),IT(NC),P(10,2),B(50,7) DIMENSION A ( 5 0 ) PV=VPV VPV0=VPV YR=Y I F ( V P V 0 . G T . 0 ) THEN DEL=.05 ELSE DEL=-.05 ENDIF 5 I F ( V P V O . G T . 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 , I Z I F ( P V . L T . O ) THEN RATE=YR ELSE RATE=EXT ENDIF PV=PV*EXP(RATE)+CF(I) 10 CONTINUE CHE 1 = V P V 0 * P V / A B S ( V P V 0 ) I F ( C H E 1 .GT.0)GOTO 5 I F ( V P V O . G T . O ) THEN RS = YR ELSE RI =YR ENDIF 15 CALL NPV(A,F,C,P,CF,V,B,IT,NC,A0,IZ,YR,VPV,TCC,EDC,XDC) PV=A0 DO 20 1 = 1 I Z I F ( P V . L T . O ) THEN RATE=YR ELSE RATE=EXT r  191  20  100  C C C  ENDIF PV=PV*EXP(RATE)+CF(I) CONTINUE I F ( P V . L T . O ) THEN RS = YR ELSE RI =YR ENDIF DIF=RS-RI I F ( D I F . L T . 0 . 0 0 0 1 ) GOTO YR=(RI+RS)/2 GOTO 15 YR=(RI+RS)/2 VPV=VPV0 RETURN END SUBROUTINE FOR  PRINTING  100  THE  P E R I O D - B Y - P E R I O D CASH  SUBROUTINE P R C A S ( C , I Z , A , A O , C N , N C , U N I T ) CHARACTER*25 CN CHARACTER*10 U N I T 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 ( 1 4 , 1 ) + A ( I ) C ( I + 14,1 ) = C ( I + 14,1 ) + A ( I ) 5 CONTINUE WRITE(8,10)UNIT 10 FORMAT(1H1 CURRENT DOLLAR 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)) WRITE(8,30)(C(3,J),J=LI,LU) 30 FORMAT(//,'INITIAL INVESTMENT',T20,8(F10.3,2X)) W R I T E ( 8 , 3 5 ) ( C ( 1 , J ) , J = L I ,LU) 35 FORMAT(//,'FEASIBILITY',T20,8(F10.3,2X)) W R I T E ( 8 , 4 0 ) ( C ( 2 , J ) , J = L I ,LU) 40 FORMAT(//,'DESIGN',T20,8(F10.3,2X)) WRITE(8,45)(C(4,J),J=LI,LU) 45 FORMAT(//,'CONST. ( E Q U I T Y ) ' , T 2 0 , 8 ( F 1 0 . 3 , 2 X ) ) WRITE(8,70)(C(10,J),J=LI,LU) 70 FORMAT(//,'CONST. LOAN',T20,8(F10.3,2X)) WRITE(8,50)(C(5,J),J=LI,LU) 50 FORMAT(//,'REVENUES',T20,8(F10.3,2X)) WRITE(8,55)(C(6,J),J=LI,LU) 55 FORMAT(//,'FIXED COSTS',T20,8(F10.3,2X)) WRITE(8,60)(C(7,J),J=LI,LU) 60 FORMAT(//,'VARIABLE COSTS',T20,8(F10.3,2X)) WRITE(8,65)(C(8,J),J=LI,LU)  FLOW  CASH  65 68 75 80 85 90 95 100  FORMAT(//,'DEPRECIATION' ,T20,8(F1 0.3,2X)) WRITE(8,68)(C(9,J),J=LI,LU) FORMAT(//,'LONG TERM D E B T ' , T 2 0 , 8 ( F 1 0 . 3 , 2 X ) ) WRITE(8,75)(C(13,J),J=LI,LU) FORMAT(//,'SALVAGE V A L U E ' , T 2 0 , 8 ( F 1 0 . 3 , 2 X ) ) WRITE(8,80)(C(11,J),J=LI,LU) FORMAT(//,'GROSS INCOME',T20,8(F10.3,2X)) WRITE(8,85)(C(12,J),J=LI,LU) FORMAT{//,'!NCOME TAX' , T 2 0 , 8 ( F 1 0 . 3 , 2 X ) ) WRITE(8,90)(C(14,J),J=LI,LU) FORMAT(//,'NET CASH F L O W ' , T 2 0 , 8 ( F 1 0 . 3 , 2 X ) ) WRITE(8,95) FORMAT(1H1) CONTINUE  C 105  110  120 150 200  500  C C C C  WRITE(8,105) 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) FORMAT(//, 'CASH FLOW' , T 4 0 , 1 2 , 7 ( 1 O X , 1 2 ) ) DO 150 11=1,NC WRITE(8, 120)CN(I 1 ) , ( C ( I 1 + 1 4 , J ) , J = L I , L U ) FORMAT(/,A25,T35,8(F10.3,2X)) CONTINUE WRITE(8,95) CONTINUE DO 500 1=1,NC C(3,1)=C(3,1)-A(I) C(14,1)=C(14,1)-A(I) C ( I + 14,1 ) = C ( I + 1 4 , 1 ) - A ( l ) CONTINUE RETURN END SUBROUTINE TO COMPUTE E Q U I V A L E N T D I S C R E T E END OF EACH P E R I O D FOR UNIFORM FLOWS  FLOW AT  THE  SUBROUTINE SEQU(F,C,V,P,IT,Y,I,J,FF,DUE,RIC,FCT,XL,XU,TCC,EDC,XDC) EXTERNAL C F 3 , C F 4 , C F 5 , C F 6 , C F 7 , C O , R E , F I N T , F E S C , F I N T 1 EXTERNAL F C T DIMENSION F ( 2 0 , 9 ) , C ( 3 5 , 5 0 ) , I T ( 2 0 ) , P ( l 0 , 2 ) , V ( 4 0 ) CALL I N T E G ( F , X L , X U , F C T , F ( I , 7 ) , Y , E Q U I V , 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) C A L L I N T E G ( F , X L , X U , F C T , 0 . , 0 . ,RES 1,1) TCC=TCC+RES1 CALL I N T E 1 ( D U E , F , X L , X U , F C T , F ( I , 7 ) , R I C , F E S C , R E S 2 , I ) EDC=EDC+RES2 I F ( F F . E Q . 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) I F ( I X 1 . E Q . 5 ) THEN IN=F(I,9) PRI=P(IN,1) TEP=P(IN,2) ADD=EQUIV*F(l,8)*PRI*EXP(((J+1)-V(17))*TEP) C ( 5 , J+1 ) = C ( 5 , J + 1 ) + A D D C(7,J+1)=C(7,J+1)+EQUIV*F(l,8) C(1+14,J+1)=ADD ELSE C ( I X 1 , J+1 ) = C ( I X 1 ,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 S C H E D U L E  10  100  110  SUBROUTINE R E P A Y ( B , V , P F ) DIMENSION B ( 5 0 , 7 ) , V ( 4 0 ) I T 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 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 G O T O d O O , 1 5 0 , 2 0 0 ) ,IT1 A=OW*(R*RIN/(RIN-1)) DO 110 1=1,NP B(I+1,3)=A CONTINUE GOTO 300  C 150  170  B(2,3)=B(1,5) IS=B(1,7) DO 180 1 = 1 , N P - 1 , I S DO 170 J = 1 , I S - 1 B(I+J+1,3)=B(I+J,3) CONTINUE B(I+IS+1,3)=B(I+IS,3)+B(1,6)  194  180  CONTINUE GOTO 300  200  PA=B(1,5)*((RIN-1)/(R*RIN)) 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) CONTINUE  C  210 C 300  350  C C C  B(2,2)=OW DC 350 I = 2 , N P + 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) CONTINUE RETURN END INPUT CASH  10  11  C C C  FLOW  NAME  SUBROUTINE NAME(CN,I C A S H ) C H A R A C T E R * 2 5 CN DIMENSION C N ( 2 0 ) CHARACTER*25 NA WRITE(6,10)ICASH FORMAT(//,T25,'CASH FLOW NUMBER  2  7 3  ,I 2 , / / , ' I N P U T  1 '(MAX. 25 C H A R A C T E R S ) ' , / ) READ(5,11)NA FORMAT(A25) CN(ICASH)=NA RETURN END INPUT THE PARAMETERS  1  1  OF  A  SINGLE  PAYMENT  SUBROUTINE F S I N G ( F , C N , I C A S H , I C ) C H A R A C T E R * 2 5 CN DIMENSION F ( 2 0 , 9 ) , C N ( 2 0 ) WRITE(6,1) FORMAT(//,'YOU HAVE S E L E C T E D A S I N G L E PAYMENT', 1 / , ' P L E A S E CONFIRM: ( C O R R E C T = 1 , I N C O R R E C T = 2 ) ' , / ) READ(5,2)IC FORMAT(11) I F ( I C . E Q . 2 ) GOTO 10 CALL NAME(CN,ICASH) F(ICASH,1)=1 WRITE(6,3) F O R M A T ( / , ' I N P U T V A L U E OF T H E FLOW',/) READ(5,*)F(ICASH,2)  NAME  195  5 1 0 C C C  INPUT THE PARAMETERS  1  2  3  5  7  10 C C C  2  3  10  OF  TWO  DISCRETE  PAYMENTS-  SUBROUTINE F T W O ( F , I C A S H , I C ) DIMENSION F ( 2 0 , 9 ) WRITE(6,1) FORMAT(//,'YOU HAVE S E L E C T E D TWO PAYMENTS', 1 / , ' P L E A S E CONFIRM: ( C O R R E C T = 1 , I N C O R R E C T = 2 ) ' , / ) READ(5,2)IC FORMAT(11) I F ( I C . E Q . 2 ) GOTO 10 F(ICASH,1)=2 WRITE(6,3) F O R M A T ( / / , ' I N P U T V A L U E OF T H E F I R S T FLOW',/) READ(5,*)F(ICASH,2) WRITE(6,5) FORMAT('PERIOD',/) READ(5,*)F(ICASH,5) WRITE ('6, 7) F O R M A T ( ' I N P U T V A L U E OF THE SECOND FLOW',/) READ(5,*)F(ICASH,3) WRITE(6,5) READ(5,*)F(ICASH,6) RETURN END INPUT THE PARAMETERS  1  C C C  WRITE(6,5) FORMAT(/,'PERIOD',/) READ(5,*)F(ICASH,5) RETURN END  OF  A UNIFORM  FLOW  SUBROUTINE F U N I F ( F , I C A S H , I C ) DIMENSION F ( 2 0 , 9 ) WRITE(6,1) FORMAT(//,'YOU HAVE S E L E C T E D A UNIFORM FLOW', 1 / , ' P L E A S E CONFIRM: ( C O R R E C T = 1 , I N C O R R E C T = 2 ) ' , / ) READ(5,2 ) IC FORMAT(11) I F ( I C . E Q . 2 ) GOTO 10 F(ICASH,1)=3 WRITE(6,3 ) F O R M A T ( / , ' I N P U T V A L U E OF THE FLOW',/) READ(5,*)F(ICASH,2) CALL I TIME(F,ICASH) CALL ININF(F,ICASH) RETURN END INPUT THE PARAMETERS  OF  A TRAPEZOIDAL  SUBROUTINE F T R A P ( F , I C A S H , I C ) DIMENSION F ( 2 0 , 9 )  FLOW  196  1  2  3  5  10 C C C  INPUT  1  2  3  5  7  1 0 C C C  WRITE(6,1) FORMAT(//,'YOU HAVE S E L E C T E D A T R A P E Z O I D A L F L O W , 1 / , ' P L E A S E CONFIRM: (CORRECT=1, INCORRECT=2)',/) READ(5,2)IC FORMAT(I 1 ) I F ( I C . E Q . 2 ) GOTO 10 F(ICASH,1)=4 WRITE(6,3) FORMAT(/,'INPUT I N I T I A L V A L U E OF T H E FLOW',/) READ(5,*)F(ICASH,2) WRITE(6,5) FORMAT('FINAL VALUE',/) READ(5,*)F(ICASH,3) CALL I TIME(F,ICASH) CALL I N I N F ( F , I C A S H ) RETURN END THE PARAMETERS  OF A B E T A  FUNCTION  SUBROUTINE F B E T A ( F , I C A S H , I C ) DIMENSION F(20,9) WRITE(6,1) FORMAT(//,'YOU HAVE S E L E C T E D A BETA D I S T R I B U T I O N ' , 1 / , ' P L E A S E CONFIRM: ( C O R R E C T S , INCORRECT=2)',/) READ(5,2)IC FORMAT(11) I F ( I C . E Q . 2 ) GOTO 10 F(I'CASH,1)=6 WRITE(6,3) F O R M A T ( / / , ' I N P U T A M P L I F I C A T I O N CONSTANT',/) READ(5,*)F(ICASH,2) WRITE(6,5) FORMAT('PARAMETER 1',/) READ(5,*)F(ICASH,3) WRITE(6,7) FORMAT('PARAMETER 2',/) READ(5,*)F(ICASH,4) CALL ITIME(F,ICASH) CALL I N I N F ( F , I C A S H ) RETURN END INPUT  T H E PARAMETERS  OF AN E X P O N E N T I A L  FLOW  SUBROUTINE F E X P O ( F , I C A S H , I C ) DIMENSION F(20,9) WRITE(6,1) 1 FORMAT(//,'YOU HAVE SELECTED AN EXPONENTIAL FUNCTION', 1 / , ' P L E A S E CONFIRM: (CORRECT=1, INCORRECT=2)',/) READ(5,2)IC 2 FORMAT(I 1 ) I F ( I C . E Q . 2 ) GOTO 10  1 97  3  5  1 0  F ( I CASH,1) = 1 1 WRITE(6,3) F O R M A T ( / / , ' I N P U T B A S E PARAMETER',/) READ(5,*)F(ICASH,2) WRITE(6,5) F O R M A T ( ' I N P U T GROWTH R A T E ' , / ) READ(5,*)F(ICASH,3) CALL ITIME(F,ICASH) CALL ININF(F,ICASH) RETURN END  C C INPUT THE PARAMETERS OF A GOMPERTZ CURVE C SUBROUTINE F G O M P ( F , I C A S H , I C ) DIMENSION F ( 2 0 , 9 ) WRITE(6,1) 1 FORMAT(//,'YOU HAVE S E L E C T E D A GOMPERTZ CURVE', 1 / , ' P L E A S E CONFIRM: ( C O R R E C T S , I N C O R R E C T = 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 L I M I T ' , / ) READ(5,*)F(ICASH,2) WRITE(6,5) 5 F O R M A T ( ' I N P U T SHAPE PARAMETER 1',/) READ(5,*)F(ICASH,3) WRITE(6,7) 7 F O R M A T ( ' S H A P E PARAMETER 2',/) READ(5,*)F(ICASH,4) CALL ITIME(F,ICASH) CALL ININF(F,ICASH) 1 0 RETURN END C C INPUT I N F L A T I O N R A T E AND D E F I N E CURRENCY OF THE CASH FLOW C SUBROUTINE I N I N F ( F , I CASH) DIMENSION F ( 2 0 , 9 ) WRITE(6,1) 1 FORMAT(/,'INFLATION RATE',/) READ(5,*)F(ICASH,7) WRITE(6,3) 3 F O R M A T ( / , ' I S T H E FLOW E X P R E S S E D IN F O R E I G N CURRENCY', 1 ' ( Y E S = 1 , NO=0)',/) READ(5,*)F(ICASH,8) RETURN END C C INPUT THE I N I T I A L AND F I N A L PERIODS OF CONTINUOUS FLOWS  198  1  3  C C C C C C  SUBROUTINE I T I M E ( F , I C A S H ) DIMENSION F ( 2 0 , 9 ) WRITE(6,1) FORMAT(/,'INITIAL PERIOD',/) READ(5,*)F(ICASH,5) WRITE(6,3) FORMAT(/,'FINAL PERIOD',/) READ(5,*)F(ICASH,6) RETURN END MENU FOR THE S E L E C T I O N OF FLOW T Y P E DURING F E A S I B I L I T Y AND D E S I G N P H A S E S . ACCORDING TO THE S E L E C T I O N , THE A P P R O P I A T E SUBROUTINE TO I N P U T THE PARAMETERS OF THE FLOW I S C A L L E D  SUBROUTINE M E N U 1 ( F , C N , 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,/, ' S E L E C T ONE OF THE FOLLOWING' 1 ,//,T5,'1. SINGLE PAYMENT',/,T5,'2. TWO DISCRETE PAYMENTS 2 / , T 5 , ' 3 . UNIFORM',/) READ(5,2)1 2 FORMAT(I 1 ) GO T O ( 5 , 1 0 , 1 5 ) , I 5 CALL FSING(F,CN,ICASH,IC) GOTO 20 1 0 CALL FTWO(F,ICASH,IC) GOTO 20 1 5 CALL F U N I F ( F , I CASH,IC) 20 I F ( I C . E Q . 2 ) GOTO 30 RETURN END  c  C MENU FOR THE S E L E C T I O N OF FLOW T Y P E IN CONSTRUCTION PHASE. C SUBROUTINE M E N U 2 ( F , C N , I C A S H ) CHARACTER*25 CN DIMENSION F ( 2 0 , 9 ) , C N ( 2 0 ) . CALL NAME(CN,ICASH) . 5 W R I T E ( 6 , 1 )I CASH 1 FORMAT(//,'CASH FLOW NUMBER ' , 1 2 , / , 1 'SELECT ONE OF THE FOLLOWING:',//,T5,'1. SINGLE PAYMENT',/, 2 T5,'2. TWO DISCRETE PAYMENTS',/,T5,'3. UNIFORM FLOW',/,T5, 3 '4. T R A P E Z O I D A L ' , / , T 5 , ' 5 . BETA F U N C T I O N ' , / , T 5 , 4 '6. E X P O N E N T I A L ' , / , T 5 , ' 7 . OTHER',/) READ(5,3)I  199  3  10 20 30 40 50 60 130 70 4 CO',/)  6 7 90  140 C C C C  FORMAT(11) GO T O ( 1 0 , 2 0 , 3 0 , 4 0 , 5 0 , 6 0 , 7 0 ) , I GOTO 5 CALL F S I N G ( F , I C A S H , I C ) GOTO 130 -CALL FTWO(F,ICASH,IC) GOTO 130 CALL F U N I F ( F , I C A S H , I C ) GOTO 130 CALL FTRAP(F,ICASH,IC) GOTO 130 CALL F B E T A ( F , I C A S H , I C ) GOTO 130 CALL FEXPO(F,ICASH,IC) I F ( I C . E Q . 2 ) GOTO 5 GOTO 140 WRITE(6,4) F O R M A T ( ' T H I S F U N C T I O N SHOULD BE F(ICASH,1)=8 DO 90 1 = 1 , 3 WRITE(6,6)I F O R M A T ( ' I N P U T PARAMETER READ(5,*)F(ICASH,I+1)' FORMAT(F15.4) CONTINUE CALL I TIME(F,ICASH) CALL ININF(F,ICASH) RETURN END  MENU FOR PHASE  THE  SELECTION  OF  S P E C I F I E D AS  FUNCTION  ',11)  FLOW T Y P E  DURING  OPERATIONAL  SUBROUTINE M E N U 3 ( F , C N , I C A S H ) CHARACTER*25 CN DIMENSION F ( 2 0 , 9 ) , C N ( 1 0 ) CALL NAME(CN,ICASH) IC = 0 5 WRITE(6,1)ICASH 1 F O R M A T ( / / / , ' C A S H FLOW NUMBER ' , 1 2 , / , 1 'SELECT ONE OF THE FOLLOWING:',/,T5,'1. SINGLE PAYMENT',/, 2 T5,'2. TWO DISCRETE PAYMENTS',/,T5,'3. UNIFORM FLOW',/,T5, 3 '4. T R A P E Z O I D A L ' , / , T 5 , ' 5 . BETA F U N C T I O N ' , / , T 5 , 4 '6. EXPONENTIAL',/,T5,'7. GOMPERTZ CURVE',/,T5,'8. OTHER',/) READ(5,2)1 GO T O ( 1 0 , 2 0 , 3 0 , 4 0 , 50 , 6 0 , 7 0 , 8 0 ) , I 2 FORMAT(11) GOTO 5 10 CALL FSING(F,CN,ICASH,IC) GOTO 110  200  20 30 40 50 60 70 110 80 3 RE',/)  4 7 90  120 C C C  CALL FTWO(F,ICASH,IC) GOTO 1.1 0 CALL F U N I F ( F , I C A S H , I C ) GOTO 110 CALL F T R A P ( F , I C A S H , I C ) GOTO 110 CALL F B E T A ( F , I C A S H , I C ) GOTO 110 CALL F E X P O ( F , I C A S H , I C ) GOTO 110 CALL FGOMP(F,ICASH,IC) I F ( I C . E Q . 2 ) GOTO 5 GOTO 120 WRITE(6,3) FORMAT('THE F U N C T I O N SHOULD BE S P E C I F I E D F(ICASH,1)=8 DO 90 1=1,3 WRITE(6,4)1 FORMAT(* I N P U T PARAMETER READ(5,*)F(ICASH,I + 1 ) FORMAT(F15.4) CONTINUE CALL I T I M E ( F , I C A S H ) CALL I N I N F ( F , I C A S H ) RETURN END  MENU  IN  FUNCTION  ',11)  FOR T H E S E L E C T I O N OF P R O J E C T  PHASE  SUBROUTINE M E N U 4 ( 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. D E S I G N ' , / , T 5 , ' 3 . I N I T I A L I N V E S T M E N T ' , / , T 5 , 2 '4. C O N S T R U C T I O N ' , / , T 5 , ' 5 . OPERATION*,/,T56. DISPOSAL',/) READ(5,12 ) K 12 FORMAT(11) RETURN END c  C C C C c  c  _  MATHEMATICAL  REPRESENTATION  FLOW  UNIFORM FLOW FUNCTION C F 3 ( X , F , I ) DIMENSION F ( 2 0 , 9 ) CF3=F(I,2) . . RETURN END T R A P E Z O I D A L FLOW FUNCTION C F 4 ( X , F , I ) DIMENSION F ( 2 0 , 9 )  TYPES  (STRAIGHT LINE)  201  c  10  20  30  c  c  C C C C  CF4=F(I,2)+(F(I,3)-F(l,2))*(X-F(I,5))/(F(I,6)-F(I,5)) RETURN END BETA F U N C T I O N FUNCTION C F 5 ( X , F , I ) DIMENSION F ( 2 0 , 9 ) K1 = 1 DO 10 J = 2 , F ( l , 3 ) K1=K1*J CONTINUE K2= 1 DO 20 J = 2 , F ( I , 4 ) K2=K2*J CONTINUE K3=1 K4=F(I,3)+F(I,4)+1 DO 30 J = 2 , K 4 K3=K3*J CONTINUE K5=F(I,6)-F(I,5) K6=K3/(K5*K1*K2) CF5=K6*(((X-F(I,5))/K5)**F(l,3))*((F(I,6)-X)**F(l,4)) RETURN END E X P O N E N T I A L FLOW ' FUNCTION C F 6 ( X , F , I ) DIMENSION F ( 2 0 , 9 ) CF6=F(I,2)*EXP(F(I,3)*X) RETURN END . GOMPERTZ CURVE FUNCTION C F 7 ( X , F , I ) DIMENSION F ( 2 0 , 9 ) CF7=EXP(LOG(F(I,2))-F(I,3)*EXP(-F(l,4)*X)) RETURN END FACTORS TO C A L C U L A T E E S C A L A T I O N AND CONSTRUCTION  I N T E R E S T S DURING  FUNCTION F I N T ( X , D U E , R I C , T D , T X ) FINT=EXP((DUE-X)*RIC)*EXP(TD*X-TX) RETURN END C FUNCTION F E S C ( X , D U E , R I C , T D , T X ) FESC = E X P ( T D * X - T X ) - 1 RETURN END C FUNCTION F I N T 1 ( X , D U E , RI C , TD , T X ) FINT1=(EXP((DUE-X)*RIC)-1)*EXP(TD*X-TX) RETURN END  202  C C SUBROUTINE COEFFICIENTS C  TO  COMPUTE  THE  LINEAR  US(A,F,C,P,CF,V,B,IT,NC,A0,IZ,V1,VPVO,YR,EXT,CN,TEI CHARACTER*6 NAME,NA CHARACTER*25 CN  SENSITIVITY  SUBROUTINE 0)  DIMENSION F(20,9),C(35,IZ),CF(IZ),V(40),IT(NC),B(50,7) 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) I F ( K . E Q . 4 2 ) 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 V A R I A B L E ', 1 A6,'= ',F15.7,//,T20,'ABSOLUTE', 2 T50,'RELATIVE',/,'NPV,T10,F20.5,T40,F20.5,/,'IRR',T10,F20.5, 3. T 4 0 , F 2 0.5,/, ' T C C ,T10,F2 0 . 5 , T 4 0 , F 2 0 . 5 ) WRITE(6,20) 20 FORMAT(/,'DO YOU WANT TO I N C L U D E T H I S V A R I A B L E I N T H E STAR ', 1 'DIAGRAM? ( Y E S = 1 , N O = 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 F O R M A T ( / , ' A N A L Y Z E ANOTHER V A R I A B L E ? (YES=1, NO=0)',/) READ(5,30)11 I F ( I 1.EQ.1) GOTO 5 IN=IN-1 I F ( I N . E Q . O ) GOTO 200 CALL STAR(SN,SI,NAME,IN) 200 VPV0=VPVO0 RETURN END C  203  C C C  COMPUTATION OF T H E P A R T I A L D E R I V A T I V E R E S P E C T TO THE DISCOUNT RATE  OF  NPV  WITH  SUBROUTINE DPVDY(A,F,C,P,CF,V,B,IT,NC,AO,IZ,VPVO,YR,DY) DIMENSION F(20,9),IT(NC),C(35,IZ),CF(IZ),V(40),P(10,2),B(50,7) DIMENSION A ( 5 0 ) 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 P A R T I A L D E R I V A T I V E OF THE NPV WITH C R E S P E C T TO A G I V E N V A R I A B L E C SUBROUTINE DERIV(A,F,C,P,CF,V,B,IT,NC,A0,IZ,VS1,IL,K,IC,DER,DTC) DIMENSION F(20,9),IT(NC),C(35,IZ),CF(IZ),V(40),P(10,2),B(50,7) DIMENSION A ( 5 0 ) V(1)=VS1 CALL VARASS(F,V,P,IC,IL,K,VAR) VAR0=VAR I F ( V A R . E Q . 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 E X A C T S E N S I T I V I T Y A N A L Y S I S 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(20,9),C(35,IZ),CF(IZ),V(40),IT(NC),EXA(10),B(50,7) 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 S E N S I T I V I T Y ANALYSIS',/) CALL MENU5(F,P,B,V,IT,IL,K,IC,NA,CN) I F ( K . E Q . 4 2 ) GOTO 80 WRITEC6,20) 20 F O R M A T ( / , ' E N T E R LOWER E S T I M A T E (PESSIMISTIC)',/) READ(5,*)V1 WRITE(6,40) 40 F O R M A T ( / , ' E N T E R HIGHER E S T I M A T E ( O P T I M I S T I C ) ' , / ) 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 I F ( N S C . E Q . 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 I F ( C H E . L T . 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 , I T , N C , AO , I Z , V ( 1 ) , V L A S T , 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 A N A L Y S I S FOR VARIABLE \A6) I F ( B R E A K . E Q . O ) THEN WRITE(8,50) WRITE(6,50) 50 F O R M A T ( / / , ' T H E R E I S NOT A BREAK-EVEN POINT WITHIN THE RANGE 1 /,'DEFINED BY T H E 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 I F ( C H E 2 . G T . O ) THEN VU=VAR ELSE VL=VAR ENDIF DIF=VU-VL I F ( D I F . L T . C H E 1 ) 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) ( E X A ( I ) , EXAN (I') ,EXAI (I ) ,1 = 1 , 10) WRITE(6,70)(EXA(I),EXAN(I),EXAI(I),I=1,10) 70 FORMAT(F15.7,T20,F15.3,T50,F7.3) VPV0=VPVO0  206 WRITE(6,75) 75 FORMAT(/,'DO YOU WANT A P L O T OF T H E S E R E S U L T S ( Y E S = 1 , NO=0)',/) READ(5,76)11 76 FORMAT(11) I F ( I 1.EQ.0) GOTO 80 CALL PLEXA(EXA,EXAN,EXAI,NA) 80 RETURN END C C SUBROUTINE TO PERFORM 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 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(20 9),C(35,IZ),CF(IZ),V(40),IT(NC),SEN(10,10),A(50) DIMENSION B ( 5 0 , 7 ) , B I V ( 2 , 1 0 ) , P ( 1 0 , 2 ) , C N ( 2 0 ) ,WAR1 ( 1 0 ) , W A R 2 ( 10) WRITE(6,10) 10 FORMAT(//,'BIVARIATE S E N S I T I V I T Y ANALYSIS',/,'SELECT FIRST 1 VARIABLE',/) CALL MENU5(F,P,B,V,IT,IL1,K1,IC1,NA1,CN) I F ( K 1 . E Q . 4 2 ) GOTO 90 WRITE(6,20) 20 FORMAT(/,'ENTER LOWER E S T I M A T E ' , / ) R E A D ( 5 , * ) V1 L WRITE(6,40) 40 FORMAT(/,'ENTER HIGHER E S T I M A T E ' , / ) READ(5,*)V1U WRITE(6,50) 50 F O R M A T ( / , ' S E L E C T SECOND V A R I A B L E ' , / ) CALL MENU5(F,P,B,V,IT,IL2,K2,IC2,NA2,CN) I F ( K 2 . E Q . 4 2 ) GOTO 90 WRITE(6,20) READ(5,*)V2L WRITE(6,40) READ(5,*)V2U WRITE(6,55) 55 FORMAT('ENTER NUMBER OF P O I N T S A N A L Y Z E D IN THE GIVEN RANGES',/, 1 '(9 MAXIMUM)',/) READ(5,*)NUMP NUMM1=NUMP-1 DEL 1 = (V1U-V1L)/NUMM1 DEL2=(V2U-V2L)/NUMM1 C A L L V A R A S S ( F , V , P , I C 1 , I L 1 ,K1 ,VAR1 ) CALL VARASS(F,V,P,IC2,IL2,K2,VAR2) NUMP1=NUMP NUMP2=NUMP r  CALL CALL  S W A R ( W A R 1 , VAR 1 , NUMP 1 , V1 L , D E L 1 ) S W A R ( W A R 2 , VAR2 , NUMP2 , V 2 L , D E L 2 ) .  207  C DO 80 1=1,NUMP1 C A L L A S S V A R ( F , V , P , I C 1 ,1 L 1 , K 1 ,WAR1 ( I ) ) I F ( V A R 1 . E Q . O ) THEN BIV(1,I)=0 ELSE B I V ( 1 ,1 ) = ( W A R 1 (I )/VAR1-1 ) * 1 00 ENDIF C DO 70 J=1,NUMP2 CALL A S S V A R ( F , V , P , I C 2 , I L 2 , K 2 , W A R 2 ( J ) ) I F ( V A R 2 . E Q . 0 ) THEN BIV(2,J)=0 ELSE B I V ( 2 , J ) = ( W A R 2 ( J ) / V A R 2 - 1 ) * 1 00 ENDIF CALL N P V ( A , F , C , P , C F , V , B , I T , N C , A O , I Z , Y , VPV, T C C , EDC , XDC ) SEN(I,J)=(VPV/VPV0-1)*100 70 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 N P V ' , / / , ' V A R I A B L E 1: ',A6,'CONSTANT ALONG ', 2 'ROWS',/,'VARIABLE 2: ',A6,'CONSTANT ALONG COLUMNS',//, 3 / / , T 1 5 , ' P E R C E N T A G E CHANGE IN V A R I A B L E ',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) WRITE(8,65)BIV(1,1),(SEN(I,J),J=1,NUMP2) 65 F0RMAT(F9.3,T15,10(F9.3,2X,/)) 85 ' CONTINUE 90 RETURN END C C SUBROUTINE TO D E F I N E THE V A L U E OF T H E VARIABLES C FOR THE 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 C SUBROUTINE S W A R ( W A R , VAR , NUMP , V L , D E L ) DIMENSION W A R ( 10) W A R ( 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 I F (CHE.EQ.O) THEN FLA = 2 GOTO 15 ENDIF I F ( C H E . G T . O ) THEN W A R ( J)=VAR NUMP=NUMP+1 J = J+1 FLA = 2 ENDIF ENDIF C 15 10  C C C C  W A R ( J)=VX J=J+1 CONTINUE RETURN END ASSIGN THE VALUE VARIABLE  10 20 30 40 50  C C C C  20 30 40 50  "VAR" TO A G I V E N  PRIMARY  SUBROUTINE A S S V A R ( F , V , P , I C , I L , K , V A R ) DIMENSION F ( 2 0 , 9 ) , V ( 4 0 ) , P ( 1 0 , 2 ) G O T O ( 1 0 , 2 0 , 3 0 , 40, 50) , I L V(K)=VAR GOTO 50 F(IC,K)=VAR GOTO 50 P(K,1)=VAR GOTO 50 P(K,2)=VAR CALL VARIA(F,V,P,50) RETURN END ASSIGN THE VALUE V A R I A B L E "VAR"  10  IN V A R I A B L E  OF A G I V E N  PRIMARY V A R I A B L E  SUBROUTINE V A R A S S ( F , V , P , I C , I L , K , V A R ) DIMENSION F(20,9),V(40),P(10,2) GOTO(10,20,30,40,50),IL VAR=V(K) GOTO 50 VAR=F(IC,K) GOTO 50 VAR=P(K,1) GOTO 50 VAR=P(K,2) RETURN END  TO  209  C C C C  MENU TO S E L E C T ONE V A R I A B L E SOME A N A L Y S I S WITH I T  I N ORDER  TO  PERFORM  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 F O R M A T ( / / , ' S E L E C T ONE OF T H E FOLLOWING', 1 / , T 6 , ' 1 . DISCOUNT R A T E ' , / , T 6 , ' 2 . FOREIGN EXCHANGE RATE' /, 2 T6,'3. FRACTION OF CONSTRUCTION FINANCED WITH BORROWED FUNDS', 3 / , T 6 , ' 4 . I N T E R E S T RATE ON C O N S T R U C T I O N L O A N ' , / , T 6 , 4 '5. P E R I O D WHEN THE C O N S T R U C T I O N LOAN I S D U E ' , / , T 6 , 5 '6. U N I T S A L E P R I C E ' , / , T 6 , ' 7 . F I X E D C O S T S ' , / , T 6 , 6 '8. VARIABLE COSTS',/,T6,'9. V A L U E OF DEPRECIABLE ASSETS',/, 7 T 5 , ' 1 0 . 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 ' , / , T 5 , 8 '11. LIFE OF DEPRECIABLE ASSETS',/,T5,'12. TAX RATE',/,T5, 9 '13. AMOUNT OF THE LONG TERM LOAN') WRITE(6,4) 4 F O R M A T ( T 5 , ' 1 4 . I N T E R E S T RATE ON LONG TERM LOAN',/,T5, 1 '15. OTHER LONG TERM D E B T V A R I A B L E S ' , / , T 5 , 2 '16. PERIOD WHEN REPAYMENT OF LONG TERM LOAN STARTS',/, 3 T 5 , ' 1 7 . I N F L A T I O N RATE FOR S A L E S P R I C E ' , / , T 5 , 4 ' 1 8 . I N F L A T I O N RATE FOR F I X E D C O S T S ' , / , T 5 , 5 ' 1 9 . I N F L A T I O N RATE FOR V A R I A B L E COSTS',/, 6 T 2 , ' 2 0 - 4 0 . OTHER PRIMARY V A R I A B L E * , / , T 5 , 7 ' 4 1 . CASH FLOW P A R A M E T E R ' , / , T 5 , ' 4 2 . E X I T ' , / ) 5 READ(5,* ) K 2 FORMAT(12) I F ( K . E Q . 4 2 ) GOTO 200 WRITE(6,6) 6 FORMAT('ASSIGN A NAME TO THE VARIABLE (MAX. 6 CHARACTERS)',/) READ(5,7)NA 7 FORMAT(A6) I F ( K . L E . 4 0 ) THEN I F ( K . E Q . 6 ) THEN IL=3 ENDIF I F ( K . E Q . 1 7 ) 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  8 ',F15.7,/))  WRITE(6,8)(J,P(J,1),J=1,P(10,1)) FORMAT(//,'SELECT THE P R I C E ' , / , 9 ( T 2 , 1 1 ,' .  READ(6,17)K GOTO 200 ENDIF ELSE I L= 1 GOTO 200 ENDIF I F ( K . E Q . 1 5 ) THEN CALL K 1 5 ( B , V , I L ) 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' , / / , 5 0 ( T 2 , 1 2,' . \A25,/)) 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 F O R M A T C C A S H FLOW ' , A 2 5 , ' I S A S I N G L E PAYMENT',/, 1 ' S E L E C T THE P A R A M E T E R ' , / , T 5 , ' 1 . V A L U E 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 ' S E L E C T THE P A R A M E T E R ' , / , T 5 , ' 1 . F I R S T PAYMENT', 2 / , T 5 , ' 2 . SECOND PAYMENT',/,T5, 3 '3. P E R I O D OF F I R S T PAYMENT',/,T5,'4. PERIOD OF SECOND PAYMENT', 4 / , T 5 , ' 5 . INFLATION RATE',/) READ(5,17)11 G O T O ( 2 7 , 2 7 , 2 9 , 2 9 , 2 9 ) ,1 1 27 K=I1+1 GOTO 200 29 K=I1+2 GOTO 200 35 WRITE(6,36)CN(IC) 36 F O R M A T C C A S H FLOW ',A25,' I S A UNIFORM FLOW',/, 1 'SELECT THE PARAMETER',/,T5,'1. VALUE OF THE FLOW',/,T5,  21 1  2 3  '2. I N I T I A L P E R I O D ' , / , T 5 , ' 3 . '4. I N F L A T I O N R A T E ' , / )  FINAL  PERIOD',/,T5,  READ(5,17)11  GOTO(37,38,38,38),11 37 38 45 46  K=2 GOTO 200 K=I1+3 GOTO 200 WRITE(6,46)CN(IC) F O R M A T C C A S H FLOW *,A25,' I S A T R A P E Z O I D A L 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. F I N A L P E R I O D ' , / , T 5 , ' 5 . I N F L A T I O N R A T E * , / )  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 . F O R M A T C C A S H FLOW *,A25,' I S A BETA FUNCTION',/, 1 'SELECT THE PARAMETER',/,T5,'1. AMPLIFICATION CONSTANT',/, 2 T 5 , ' 2 . PARAMETER 1',/,T5.,'3. PARAMETER 2 ' , / , T 5 , 3 '4. I N I T I A L P E R I O D ' , / , T 5 , ' 5 . F I N A L P E R I O D ' , / , T 5 , 4 '6. I N F L A T I O N R A T E ' , / )  READ(5,17)11  K=I1+1 GOTO 200 65 WRITE(6,66)CN(IC) 66 FORMAT('CASH FLOW *,A25,' I S AN EXPONENTIAL FUNCTION',/, 1 'SELECT THE PARAMETER',/,T5,'1. AMPLIFICATION CONSTANT',/, 2 T 5 , ' 2 . GROWTH R A T E ' , / , T 5 , ' 3 . I N I T I A L P E R I O D ' , / , T 5 , 3 '4. F I N A L P E R I O D ' , / , T 5 , ' 5 . I N F L A T I O N R A T E ' , / )  READ(5,17)11  GOTO(67,67,69,69,69),11 K=I1+1 GOTO 2 00 69 K=I1+2 GOTO 200 75 WRITE(6,76)CN(IC) 76 F O R M A T C C A S H FLOW ',A25,' I S A GOMPERTZ CURVE',/, 1 . 'SELECT THE PARAMETER',/,T5,'1. ASYMPTOTIC LIMIT',/,T5, 2 '2. SHAPE P A R A M E T E R ' , / , T 5 , ' 3 . GROWTH R A T E ' , / , T 5 , 3 '4. I N I T I A L P E R I O D ' , / , T 5 , ' 5 . F I N A L P E R I O D ' , / , T 5 , 4 '6. I N F L A T I O N RATE',/) 67  READ(5,17)11  85  K=I1+1 GOTO 2 00 I F ( I T ( ' I C ) .EQ.5) GOTO 95 WRITE(6,86)CN(IC)  212  86 FORMAT('CASH FLOW ',A25,' IS THE ARBITRARY FUNCTION OF THE 1 CONSTRUCTION P H A S E ' , / ) WRITE(6,87) 87 . FORMAT('SELECT THE PARAMETER',/,T5,'1. PARAMETER T,/,T5, 1 '2. PARAMETER 2 ' , / , T 5 , ' 3 . PARAMETER 3',/,T5, 2 '4. I N I T I A L P E R I O D ' , / , T 5 , ' 5 . F I N A L P E R I O D ' , / , T 5 , 3 '6. I N F L A T I O N R A T E ' , / ) READ(5,17)11 K=I1+1 GOTO 200 95 WRITE(6,96)CN(IC) 96 F O R M A T C C A S H FLOW ',A25,' I S THE ARBITRARY FUNCTION OF THE 1 OPERATIONAL PHASE',/) WRITE(6,87) READ(5,17)11 K=I1+1 2 00 RETURN END C C A D D I T I O N TO SUBROUTINE "MENU5". T H I S SUBROUTINE I S C C A L L E D WHEN TO S E L E C T I O N MADE I N "MENU5" I S 15. C SUBROUTINE K 1 5 ( B , V , I L ) DIMENSION B ( 5 0 , 7 ) , V ( 4 0 ) IL=5 WRITE(6,9) 9 F O R M A T ( / / , ' S E L E C T ONE OF THE F O L L O W I N G : ' , / , T 2 , ' 1 . NO LONG', 1 ' TERM LOAN C O N S I D E R E D ' , / , T 2 , ' 2 . UNIFORM REPAYMENT FUNCTION', 2 / , T 2 , ' 3 . S T E P REPAYMENT F U N C T I O N ' , / , T 2 , ' 4 . GRADIENT FUNCTION', 3 /,T2,'5. V A L U E OF THE AMOUNT BORROWED',/,T2,'6. RESET VALUE', 4 ' OF AMOUNT BORROWED',/,T2,'7. RESET NUMBER OF PAYMENTS',/,T2, 5 '8. R E S E T P E R I O D WHEN REPAYMENT S T A R T S ' , / , T 2 , 6 ' 9 . R E S E T NUMBER OF P E R I O D S BETWEEN P A Y M E N T S ' , / , T 2 , 7 ' 1 0 . R E S E T V A L U E OF I N I T I A L P A Y M E N T ' , / , T 2 , 8 ' 1 1 . R E S E T 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  16  161 18 200 C C C  F O R M A T ( / , ' I N P U T NEW VALUE',/) READ(5,*)VALUE IC5=IC-5 GOTO(16,161,161,161,161,18),IC5 V(13)=VALUE V(15)=0 GOTO 200 B( 1 , I C 5 ) = V A L U E GOTO 200 B(1,7)=VLAUE GOTO 200 RETURN END  . SUBROUTINE TO  PRODUCE T H E  STAR  DIAGRAM  SUBROUTINE S T A R ( S N , S I , N A M E , I N ) 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 I N V A R I A B L E ' , 2 0 , ' % CHANGE 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 = A T A N ( S N ( 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) C A L L ALDONE C C C A L L A L S I Z E ( 8 . ,8. ) CALL A L A X I S ( ' % CHANGE IN V A R I A B L E ' , 2 0 , ' % CHANGE IRR',15) C A L L A L S C A L ( - 1 0 0 . , 1 0 0 . , - 1 0 0 . ,100.) DO 60 1 = 1 , I N X(1)=100/SQRT(1+SI(I)**2)  IN  IN  214  60  C C C  X(2)=-X(1) Y(1)=SI(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) 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) C A L L P S Y M ( 6 . 5 , 7 . 0 , 0 . 1 7 , S E N S I T I V I T Y ' ,0 . , 1 1 ) CALL PSYM(6.9,6. 5,0.17, CHART',0.,5) C A L L ALDONE RETURN END SUBROUTINE  TO  PRODUCE A P L O T OF  THE EXACT ANALYSIS  SUBROUTINE P L E X A ( E X A , E X A N , E X A I , N A ) CHARACTER*6 NA DIMENSION E X A ( 1 0 ) , E X A N ( 1 0 ) , E X A I ( 1 0 ) XMIE=EXA(1) XMAE=EXA(1) XMIN=EXAN(1) XMAN=EXAN(1) XMII=EXAI(1) XMAI=EXAI(1) DO 1000 1=2,10 I F ( E X A ( I ) . G T . X M A E ) THEN XMAE=EXA(I) ENDIF I F ( E X A ( I ) . L T . X M I E ) THEN XMIE=EXA(I) ENDIF I F ( E X A N ( I ) . G T . X M A N ) THEN XMAN=EXAN(I) ENDIF I F ( E X A N ( I ) . L T . X M I N ) THEN XMIP=EXAN(I) ENDIF I F ( E X A I ( I ) . G T . X M A I ) 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) C A L L 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) C A L L ALDONE RETURN END  APPENDIX B  COMPUTER OUTPUT  FOR T H E S I M P L E  216  EXAMPLE  S E W I I I'.' I T V AND PRINCE  ECONOMIC ANALYSIS OF PROJECT.:  EDWARD ISLAND  PRIMARY  BRIDGE  VARIABLES  DISCOUNT  R A T E - 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 FIXED  OPERATING C0STS=  VARIABLE C0STS=  10.00000 0.0  VALUE OF DEPRECIABLE ASSETS= PERIOD WHEN ASSETS  0.0  ARE ACQUIRED=  L I F E OF DEPRECIABLE ASSETS= TAX  RATE=0.0 RATE FOR FIXED  INFLATION  RATE FOR VARIABLE COSTS=  UNIT SALE  PRICES  1 2 3  0.0  0.0  INFLATION  #  DUE=  C0STS=0.05G0  (Million  PRICE  0.0000030 0.0000060 1.0000000  $)  INFLATION  0.0550 0.0550 0.0  0.0  5.00  FCONCUIC  PERFORMANCE MEASURES  HE T P R E S E N T CONSTANT  INTERESTS TOTAL  VALUE  DOLLAR  ESCALATION  CONSTRUCTION  DURING DURING  RATE  OF  $) 74.260  COSIS=  CONSTRUCTIONCONSTRUCTION=  CONSTRUCTION  INTERNAL  (Million  C0STS=  RETURN=  -564.999 -35.827 101.199 -702.025  21.114  I N F O R M H I O N  I  ABOUI  CASH  FLOWS  NAME  TYPE.  PHASE  J  UNIFORM /PERIOD)  =  I n d t r e e X c o s Is • SO .OOOIMI I I i o n J  UNIFORM /PEHIOO)  CONSTRUCTION  8.8B9(Mi I I ion  PEn.  FINAL  PER.  INF.  RATE  CURRENCY  FEASIBILITY  l Pronosa1 UNIFORM V4t.IJE = • 7. . O O O I M i I 1 /I o PnE R J IOD"  2 Design VALUE=  INIT.  4' Foot ings VALUE= •60.0001 M i l l ion  UNIFORM /PERIOD)  CONSTRUCTION  t  5 Superstructure VALUE= - 9 0 . 9 0 9 ( M t l I ion  UNIFORM /PERIOO)  CONSTRUCTION  DOLLARS  t  UNIFORM /PERIOD)  CONSTRUCT ION  DOLLARS  UNIFORM /PEHIOO)  OPERATION  6 V»LUE=  Approaches • f>3 6 30 I M i 1 1 i  1 Passenger trips VALUCr 6011(101)0 . O O O I M i r I i o n UNI1  SALE  FRICL~ =  0.0000030IMiI 1 ion  8 Commercial trips VALUC= 3000000.000(Mi I 1 ion UNII  SALE  rnicE---  t  I  J  )  UNIFORM /PERIOO)  O.OOOOOGOIMi I 1 ion  OPERATION  $  3.50  )  3 9 . 75  9 Subsidy VALUE= 25.000(Mi11 Ion S UNIT  SALE  PRICE=  UNIFORM /PERIOD)  1.OOOOOOO(Mi 11 i o n $ )  OPERATION  4.75  39.75  O.OSOO  DOLLARS  9  12  10  13  14  15  16  0.0  0.0  0.0  0.0  0.0  0.0  0.0  FEASIBILITY  0.0  0.0  0.0  0.0  0.0  0.0  0.0  DESIGN  0.0  0.0  0.0  0.0  0.0  0.0  0.0  INITIAL  INVESTMENT  CONST.  (EOUITY)  0.0  0.0  0.0  0.0  0.0  0.0  0.0  CONST.  LOAN  0.0  0.0  0.0  0.0  0.0  0.0  0 . 0  95.001  101.243  107.907  115.021  1 2 2 . 6 18  I5.00B  15.872  16.787  17.754  18.776  FIXED  COSTS  VARIABLE  COSTS  DEPRECIATION  LONG  TERM  SALVAGE  GROSS  INCOME  NET  OEBT  VALUE  INCOME  TAX  CASH  FLOW  12.687  13.418  14.19  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  52.428  0.0  13.428  0.0  13.428  54.904  0.0  15.354  0.0  15.354  57.38  0.0  17.58  0.0  17.58  59.856  0.0  20.137  0.0  20.137  62.332  0.0  23.038  0.0  23.038  64.808  0.0  26.312  0.0  2 6 . 3 12  67.284  0.0  29.984  0.0  29.984  69.760  0.0  34  082  0.0  34.082  21  0.0  0.0  0.0  0.0  0.0  0.0  0.0  FEASIBILIT Y  0.0  0.0  0.0  0.0  O  0.0  0.0  DESIGN  0.0  0  0.0  0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  INITIAL  INVESTMENT  0  CONST.  (E0U1TY)  0.0  0.0  0.0  CONST.  LOAN  0.0  0.0  0.0  130.731  139.395  148.649  19.858  21.001  22.211  REVENUES  FIXED  COSTS  VARIABLE  COSTS  DEPRECIATION  LONG  TERM  SALVAGE  GROSS  INCOME  NET  DEBT  VALUE  INCOME  TAX  C A S H FLOW  0.0  0.0  0.0  0.0  0.0  0.0  72.236  0.0  38.637  0.0  38.637  74.713  0.0  43.681  0.0  43.681  77.189  0.0  49.250  0.0  49.250  0  0  0.0  159.094  26.274  0.0  79.665  e2.141 0.0  0.0  B6.354  55.379  0.0  0.0  55.379  62.  1 10  69.485  7 7.550  86.354  ro ro oo  25  26  27  28  29  30  3 I  32  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  FEASIBILITY  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  DESIGN  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  INITIAL  INVESTMENT  CONST.  (EQUITY)  0.0  0.0  0.0  0.0  0.0  0.0  0.0  O . 0  CONST.  LOAN  0.0  0.0  0.0  0 . 0  0.0  0.0  0.0  0.0  219.076  233.788  249.512  266.320  284.288  303.497  324.036  345.998  31.081  32.871  34.764  36.766  3B.884  4 1.124  43.492  45.997  REVENUES  FIXED  COSTS  VARIABLE  COSTS  DEPRECIATION  LONG  TERM  SALVAGE  GROSS  INCOME  NET  DEBI  VALUE  INCOME  TAX  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  0.0  0.0  0.0  0.0  101 . 9 4 9  104.425  106.901  109.377  92.045  0.0  95.951  0.0  95.951  94.521  96.997  99.473  0.0  0.0  0.0  0.0  0.0  0.0  0.0  106.396  117.751  130.080  143.455  157.948  173.643  190.653  0.0  0.0  0.0  0.0  0.0  0.0  0.0  106.396  117.751  130.000  1 43.455  157.948  17 3 . 6 4 3  190.623  tsj  33  INITIAL  INVESTMENT  0  34  0  35  0.0  0.0  0.0  0.0  0.0  0.0  FEASIBILITY  0.0  0.0  0.0  0.0  0 . 0  0.0  0.0  DESIGN  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  CONST.  (EQUITY)  0.0  0.0  0.0  0.0  0.0  CONST.  LOAN  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  369.4B3  394.599  421.462  450.194  480.929  513.808  548.984  438.G04  48.647  51.449  54.412  57.546  60.861  64.366  68.073  REVENUES  FIXEO  COSTS  VARIABLE  COSTS  DEPRECIATION  LONG  TERM  SALVAGE  cnoss  INCOME  NET  DEBT  VALUE  INCOME  TAX  CASH  FLOW  7 1 .994  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  111.853  114.329  116.805  121.757  124.233  126.709  129.185  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  250.244  273.3G6  298.311  325.209  354.202  237.424  0.0  0.0  0.0  354.202  237.424  200.983  228  821  1 19.281  0.0  0.0  0.0  0.0  0.0  208.983  228.821  250.244  273.308  298.31 I  ro ro  — O O  vn  O O  O  O  O  O O  O  O — ff>  O O  O  tT>  O O  C O  D O  O  CO <J1 CO  co LT \Tt  O  CD  ID  O  (\i v  f f\t  -  fu  — 1*1 S r. iTi - m  co J ^  ro  cn  m  CJ  " W t D  CASH  91  FLOW  10  1 1  12  13  14  15  16 0.0  Propose1  0  0  0. 0  0. 0  0. 0  0 .0  0. 0  0. 0  Des i g n  0. 0  0. 0  0. 0  0 .0  0. 0  0 .0  0 .0  0 . 0  Indirect  0. 0  0. 0  0. 0  0. 0  0. 0  0 .0  0 0  0.0  Foo t 1 ngs  0. 0  0. 0  0 .0  0. 0  0. 0  0. 0  0. 0  0.0  Super 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  Approaches  0. 0  0. 0  0. 0  0. 0  0. 0  0 .0  0. 0  Passanger Commercial S u b s iriy  costs  tr ips trips  31 . 8 2 9  34 . 137  0.0  3G . 6 1 2  39.267  24 . 0 5 6  2 5 . 800  27 . 67 1  2 9 . 677  24 . 328  26 . 17 1  28 . 152  3 0 . 284  3 2 . 578  35 . 0 4 5  37 . 6 9 9  40.554  3 0 . 159  31 . 705  33 . 331  35. 040  3 6 . 836  38 . 725  40 . 7 10  4 2 . 7 98  228  O O  *-  x  a  •-  f  u  34  35  36  37  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  0.0  0.0  0.0  0.0  0.0  0  0  Foo t ings  0 .0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  Superstructure  0. 0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  Approaches  0. 0  0.0  0.0  0.0  0.0  0.0  0.0  129 . 0 7 3  138.432  148.470  159.235  170.781  183.. 164  136  445  157 . 7 2 0  140. 279  150.90 3  162.331  174.624  187.848  202.074  217.377  174.984  100 . 13 1  105.2B5  110.662  116.336  122.300  128.57 I  I 3 5 . 163  105.90 I  CASH  33  FLOW  Propose 1 O e s ig.n Indirect  Passenger Commercial Subs idy  costs  tr ips trips  0.0  231  L 'iG r  TERM  AM<;I>:II  0'  8 .0 9 0  SCHEDULE  ( M i l l i o n  6 4 1.9-12  SI  RATF=0.1000  AMOUNT  6 .0 7  REPAYMENT  BORROWED^  INTEREST  PEniOD  DEBT  OWED  64 .  1 .. 9 4 2  PAYMENT  INTERESTS  PRINCIPAL  REPAID  LOAN  BALANCE  45 .000  6.) . 1 9 4  - 19 . 194  661  66 1 . 136  4 7 .476  66 .114  - 18 .638  579 .773  6"? .773  49 . 952  67 .977  - 18 . 0 2 5  697 . 799  697  52 . 428  69 . 780  -17. . 352  7 15 . 1 5 0  7 1 .515  - 16 . 6 1 1  731 . 76 1  73 . 176  - 15 . 796  747 . 5 5 7 762 .456  . 799  . 136  1 0 .0  7 15 . 1 5 0  54  1 1 .0  73 1 . 7 6 1  57 . 380  1 2 .0  747  55 7  5 9 .. 8 5 6  74 . 7 5 6  - 14 . 8 9 9  1 3 .0  762  456  62  76 .246  - 13 .913  776 . 369  14 ..0  7 7 6 .. 3 6 9  6 4 .. 8 0 8  77 .637  •  7 89 . 198  . 904  . 332  12 .829  1 5 .0  7 89 . 198  67  . 284  78 .920  -11  1 6 .0  800 .833  69 . 760  80 .083  - 1 0 .. 3 2 3  1 7 . .0  811 . 156  72 . 236  8 1 .. 1 1 6  -8. .879  820 .034  1 8 .0  820. 034  7 4 ..7 1 3  82 .003  - 7 .. 2 9 1  827  19  827  77 . 189  82 .733  -5. . 544  832 . 869  .0  . 325  .635  600 .833 811  . 156  . 325  2 0 .0  832 .869  79. . 6 6 5  83 .287  - 3 .. 6 2 2  836 . 49 1  2 1 .0  8 3 6 .49 1  8 2 .. 1 4 1  83 .649  22  - 1 .5 0 8  838 .000  8 3 8 .. 0 0 0  8 4 .. 6 1 7  83 .800  0.  8 3 7 .. 1 8 3  8 7 .. 0 9 3  8 3 . .7 1 8  3 .. 3 7 4  833 .808  833 .808  89 . 569  8 3 .381  .6. . 1 8 8  827 . 6 2 0  827  92  .045  8 2 .. 7 6 2  9 . 283 12. 6 6 7  .0  2 3 .0 2 4 .0 25  .0  .620  817  837  . 183  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  2 7 .0  8 0 5 .. 6 5 0  9 6 :. 9 9 7  8 0 .. 5 6 5  16 . 4 3 2  789 . 218  2 8 .0  739 .218  9 9 .473  78 .922  20. 551  768 . 66 7  2 9 .0  766 . 667  10 1 .949  7 6 .. 8 6 7  25.  3 0 .0  7 4 3 .. 5 8 4  104  74 . 3 5 8  30. 067  713. 518  . 425  082  805. 650  7 4 3 .. 5 8 4  .0  7 1 3 .. 5 1 8  1 0 6 .. 9 0 1  7 1 .. 3 5 2  35.  549  677 . 969  3 2 .0  6 7 7 .9 6 9  109  . 377  67 . 797  4 1 .5 8 0  636 . 3S8  3 3 .0  6 3 6 .. 3 8 8  111  .853  63.  639  48. 214  588 . 174  3 4 .0  5 8 8 .. 1 7 4  1 1 4 .. 3 2 9  5 8 .. 8 1 7  55.  512  532. 662  3 5 . .0  532. 662  1 1 6 .. 8 0 5  53.  266  63.  539  469 . 123  3 5 . .0  469 . 123  1 1 9 .. 2 8 1  4 6 ..9 1 2  72. 369  396. 753  37 . 0  395. 753  12  39 . 675  82 .082  314 . 67 1  3 8 .0  314. 67 1  124 . 2 3 3  3 1 .. 4 6 7  3 9 .0  22 1 . 9 0 5  1 2 6 .. 7 0 9  2 2 ., 1 9  4 0 .0  1 1 7 .. 3 8 6  1 2 9 .. 1 8 5  11.  31  1.. 7 5 7  92. 766  221 . 905  1  104 . 5 1 9  117. 386  739  117. 447  -0.  06 1  232  LINEAR  NPV IRR TCC  ABSOLUTE 193.86804 0 . 44402 - 1 12.44034  LINEAR  NPV IRR TCC  SENSITIVITY  ABSOLUTE -493.68286 -1.13070 - 1 8 7 7 . 4 4 14 1  LINEAR  NPV IRR TCC  SENSITIVITY  A8S0LUTE -1756.40B20 -4.02276 0.0  LINEAR  NPV IRR TCC  SENSITIVITY  ABSOLUTE 4 1404720.00000 94830.50000 0.0  LINEAR  NPV IRR TCC  SENSITIVITY  SENSITIVITY  ABSOLUTE -1.28596 -0.00295 -4.55811  COEFICIENTS FOR VARIABLE  (1-F)  0.9000000  RELATIVE 2.3496 1 1.89266 0.14*15  COEFICIENTS FOR VARIABLE F a r e - P =  0.0000030  RELATIVE 1.67270 1.34739 0.0  COEFICIENTS FOR VARIABLE IRLTL =  0.1000000  RELATIVE -2.36523 -1.90523 0.0  COEFICIENTS FOR VARIABLE I f f l - c o =  0.0500000  RELATIVE -0.33240 -0.26776 0.13372  COEFICIENTS FOR VARIABLE IndCos= RELATIVE -0.86586 -0.69746 0.32464  -50.0000000  232  11NE AR S E N S I T I V I T Y  NPV IRR TCC  ABSOLUTE 193 . 86B04 0 .44402 - 1 12.44034  LINEAR  NPV IRR TCC  ABSOLUTE 4 1404720.00000 94830.50000 0.0  LINEAR  NPV IRR TCC  SENSITIVITY  ABSOLUTE •493.68286 - 1 . 13070 - 1 8 7 7 . 4 4 14 1  LINEAR  NPV IRR TCC  SENSITIVITY  ABSOLUTE - 1 756.40820 -4.02276 0.0  LINEAR  NPV IRR TCC  SENSITIVITY  SENSITIVITY  ABSOLUTE - 1 . 28596 -0.00295 -4 . 5581 1  COEFICIENTS FOR VARIABLE ( 1 - F )  =  0.9000000  COEFICIENTS FOR VARIABLE F a r e - P =  0 . 0 0 0 0 0 30  RELATIVE 2. 3496 1 1 .89266 0. 144 15  RELATIVE 1.67270 1.34739 0.0  COEFICIENTS FOR VARIABLE  IRLTL  0 . 1000000  RELATIVE -2.36523 - 1 .90523 0.0  COEFICIENTS FOR VARIABLE  HR-co=  0.0500000  RELATIVE -0.33240 -0.26776 0 . 1 3372  COEFICIENTS FOR VARIABLE  lndCos=  RELATIVE -0.86586 -0.69746 0 . 32464  -50.0000000  


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