Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Optimum life of production assets in short and medium term timber harvesting projects Oyugi Ogweno, Donald C. 1988

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1988_A6_7 O43.pdf [ 4.63MB ]
Metadata
JSON: 831-1.0097810.json
JSON-LD: 831-1.0097810-ld.json
RDF/XML (Pretty): 831-1.0097810-rdf.xml
RDF/JSON: 831-1.0097810-rdf.json
Turtle: 831-1.0097810-turtle.txt
N-Triples: 831-1.0097810-rdf-ntriples.txt
Original Record: 831-1.0097810-source.json
Full Text
831-1.0097810-fulltext.txt
Citation
831-1.0097810.ris

Full Text

O P T I M U M L I F E O F P R O D U C T I O N A S S E T S IN S H O R T A N D M E D I U M T E R M T I M B E R H A R V E S T I N G P R O J E C T S By Donald C. Oyugi Ogweno B. Sc. Forestry (Hons.) University of Nairobi, 1984 A THESIS SUBMITTED IN PARTIAL F U L F I L L M E N T OF T H E REQUIREMENTS FOR T H E DEGREE OF M A S T E R O F SCIENCE i n T H E FACULTY OF GRADUATE STUDIES HARVESTING AND WOOD SCIENCE We accept this thesis as conforming to the required standard T H E UNIVERSITY OF BRITISH COLUMBIA Apri l 1988 © Donald C. Oyugi Ogweno, 1988 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Harvesting and Wood Science The University of British Columbia 2075 Wesbrook Place Vancouver, Canada V 6 T 1W5 Date: / Abstract An optimal equipment replacement model was developed, that is useful for evaluating machinery replacement proposals. The model is based on discounted cash flow methods, and performs the evaluation by comparing the cash flow profile of the currently owned machine (the "defender") against that of a proposed replacement (the "challenger") over a finite time period. The optimum time to replace the defender is determined as the age which will maximize the net revenues from operating both machines over the planning horizon. Real time data were collected from the operation of similar machines, and used to estimate repair and maintenance costs, machine resale values, and machine operating costs. These costs were then discounted to a base year, and aggregated into cash flow profiles. The cash flow profiles were then converted to annual equivalents, which form the basis of the replacement decision. A method of estimating the rate at which a group of machines accumulate tech-nological obsolescence was developed. These estimates are made as a function of the improved ratio of productivity to fuel consumption of new generations of machines over older ones. The replacement model was encoded into a microcomputer spreadsheet application program, that is useful as a financial planning tool in short and medium term timber harvesting projects. The program is interactive, and can be used to evaluate the sensitivity of the proposed replacement to different economic parameters. Sensitivity analyses was performed on the computer model by varying six of the input variables. From the results, it was concluded that the optimum life was relatively n insensitivity to changes in most of the inputs. The cash flows, however, was highly sensitive to changes in most of the input variables. Changes in the length of the planning horizon had the highest effect on both optimum life and cash flows of the assets. The value added cost of the product had no effect on optimum life, but a very high effect on cash flows. m Table of Contents Abstract ii Acknowledgement ix 1 I N T R O D U C T I O N 1 1.1 Problem Statement 1 1.2 Literature Review 2 2 F O R M U L A T I O N A N D D E V E L O P M E N T O F T H E M O D E L 15 2.1 Introduction 15 2.2 Outline of the method 15 2.2.1 The Defender/Challenger/Descendants concept 16 2.2.2 Treatment of Unequal Lives of Assets: Planning Horizon 19 2.3 The Replacement criteria 20 2.4 Sources of data 23 2.4.1 Repair and maintenance cost data 23 2.4.2 Machine resale value data 25 2.4.3 Technological Obsolescence data 26 2.4.4 Purchase price and cost data 28 2.5 Development of the cash flow profiles 28 2.5.1 Introduction 28 2.5.2 Derivation of costs and revenues 28 2.5.3 The Cash Flow Profiles . 47 iv 2.5.4 The Cash Flow Profiles and the Replacement criteria 50 3 R E S U L T S A N D D I S C U S S I O N 52 3.1 Results of the regression analyses 52 3.1.1 Cumulative use/repair and maintenance costs 52 3.1.2 Machine resale value data 53 3.2 Calculation of Annual Obsolescence rate 54 3.3 Results of Tests performed on the model . 54 3.3.1 Comparison of model to the Classical approach 55 3.3.2 Sensitivity Analysis 58 4 S U M M A R Y A N D C O N C L U S I O N S 65 B ib l i og raphy 68 A The M i c r o c o m p u t e r Spreadsheet M o d e l 73 A . l Project software and hardware 73 A. 2 The E Q U I P R E P Program 74 jp?<*M • B E Q U I P R E P User ' s manual 78 B. l Introduction 78 B.2 System Requirements 78 B.3 Files on the distribution diskette 79 B.4 Setting up the program 80 B.5 Running the program 80 B.5.1 The E Q U I P R E P menu and H E L P facilities 81 B.5.2 Starting a new analysis 81 B.5.3 Inputs in the I/O Window 82 v B.5.4 Other Inputs 83 B.5.5 Viewing Graphical Plots of the Cash Flows 84 B.5.6 Printing The output 84 B.5.7 Saving the current worksheet 84 B.5.8 Exiting the program 85 C Descr ip t ion of the Cost M i n i m i z i n g M o d e l 86 D Resul ts of SHAZAM™ A U T O procedure regressions 89 D . l Caterpillar D8 tractor regressions 89 D . l . l Ordinary Least squares procedure 89 D. l .2 First order autocorrelation procedure 89 D. l .3 Second order autocorrelation procedure 90 D.2 Caterpillar 966/980 F E L regressions 91 D.2.1 Ordinary Least squares procedure 91 D.2.2 First order autocorrelation procedure 91 D.2.3 Second order autocorrelation procedure . 92 E Mach ine age/resale value equations 95 v i List of Tables 2.1 Summary of the repair and maintenance cost data 24 2.2 Summary of the resale value data 26 2.3 C A T D8 series tractor dozing production data (Caterpillar Tractor Co., 1970-1986) 27 3.4 Results of the cumulative use/cumulative repair and maintenance re-gressions 53 3.5 Results of the resale value regression for C A T D8 tractors 53 3.6 Results of the resale value regression for C A T 966 54 3.7 Inputs to the model for the replacement simulation. Equipment:- De-fender: C A T D8K; Challenger: C A T D8L 56 3.8 Inputs to the model for the replacement simulation. Equipment:- De-- fender: Cat 966D; Challenger: C A T 980 57 3.9 Results of the replacement simulations . 57 D.10 C A T D8: Ordinary Least Squares procedure, No regression constant . . 89 D . l l C A T D8: First order autocorrelation proc, No regression constant . . . 90 D.12 C A T D8: Second order autocorrelation proc, No regression constant . . 90 D.13 C A T 966: Ordinary Least Squares proc, No regression constant 91 D.14 C A T 966: First order autocorrelation proc, No regression constant . . . 9T D.15 C A T 966: Second order autocorrelation proc, No regression constant . . 92 D.16 Results of the A l l Combination Regression procedure for repair and maintenance costs of C A T 966 F E L 93 vii D. 17 Results of the A l l Combination Regression procedure for repair and maintenance costs of C A T D8 tractors 94 E. 18 Machine age/Resale value Regression statistics 98 viii Lis t of Figures 1.1 Machine cost/use function showing how the ORT is determined (From Sinclair et al. 1986) 8 2.2 Flow diagram of the replacement evaluation process 17 2.3 The defender/challenger/descendants concept (after Elmaghraby 1958) . 18 2.4 The cash flow profiles of both machines, showing how the optimal re-placement point is determined 22 2.5 Effect of obsolescence on the operating cost function of machines (after Shore 1975) 32 2.6 Typical cumulative use/cumulative repair and maintenance cost pattern (after Sinclair et al.1986) 41 3.7 Sensitivity of E A W to change in purchase price of challenger 59 3.8 Sensitivity of optimum life to change in the planning horizon 59 3.9 Sensitivity of E A W to change in the Planning horizon 60 3.10 Sensitivity of E A W to change in interest rate on financing 60 3.11 Sensitivity of E A W to change in the term of financing 61 3.12 Sensitivity of E A W to change in the V A C of the product 61 A.13 Logical Flow Diagram of the E Q U I P R E P program . . 75 A . 14 Schematic Diagram showing how the program is organized in windows . 7 6 E.15 Resale value/Age scatter plots for C A T D8 tractors 96 E.16 Resale value/Age scatter plots for C A T D966 tractors 97 ix Acknowledgement I wish to express my sincere appreciation to my supervisor, Dr A. F. Howard for his invaluable support and helpful suggestions throughout this study. I also wish to give special thanks to the other members of my academic committee Prof. G. G. Young and Prof. P. Oakley for reviewing the manuscript and for their helpful suggestions. I am very grateful to Messrs Blair Gourley of Finning Tractor Company, Vancouver, and Tony Wong of F E R I C for providing the data used in this study. This study was accomplished with funding from the Ministry of Education, Science and Technology of the Republic of Kenya, and this aid is acknowledged. Finally, this thesis is dedicated to my mother, Mrs E. A . Ogweno, and to the memory of my late father, Mr J. T. Ogweno, without whose constant encouragement and support through the years nothing like this would ever have been possible. x Chap te r 1 I N T R O D U C T I O N 1.1 P r o b l e m Statement Replacement analysis is one of the most common and important types of comparison of economic investment alternatives encountered in the productive use of machines. It is usually conducted to determine when and if an asset currently in service should be replaced by an alternative. The reasons for considering replacement are attributable to deficiencies in the presently owned asset, and to greater capabilities of potential replacements. Various methods have been developed for determining the optimum economic life of an asset. These methods, however, are based on assumptions which in my view, make them inappropriate for analyzing replacements of machines owned by small businesses, and in projects with short and medium term life spans. They also do not give the complete cash flow information required for a field manager to "sell" a replacement proposal in the face of budget restraints. One aim of this study was to formulate and describe a replacement model that would overcome inadequacies observed in previous models. The other was to present the model developed on an easily accessible and usable computer program that can be used as an aid to making replacement decisions. This study is divided into three chapters. It begins with a review of the literature on replacement analysis, which concludes with an outline of the proposed method of 1 Chapter 1. INTRODUCTION 2 determining the optimum economic life of an asset. The second chapter is a discussion of the cash flow replacement model developed in the study, and how the costs and revenues used in the model were formulated and derived. The types of data used in the study, and how they were collected and analyzed is also discussed in this section. Chapter three is a presentation and discussion of results of tests performed on the computer model. The last chapter is a summary of the study, and a discussion of the conclusions reached in the study. 1.2 Literature Review The purchase of any production equipment ("machine", "production asset", or just "asset") is a capital budgeting decision, made with the objective of deriving maximum benefits from the investment. Once in use, a machine exhibits increasing unit pro-duction costs and decreasing unit quality and quantity of output over its service life (Brennan 1964; Murchison and Nautiyal 1971; Dreyfus 1960; Caterpillar Tractor Co. undated; Sinclair et al. 1986; Eilon et al. 1966; Peterson and Milligan 1976; Tufts and Hitt 1983). A critical point is finally reached when the combined effects of these adverse factors outweigh the large initial capital expenditure required for replacement of the existing machine by one with lower total production costs (Dreyfus 1960; Peterson and Milligan 1976). This point represents the machines maximum economic potential, and is the point at which it should be replaced in order to maximize its benefits (Murchison and Nautiyal 1971). This is the optimum economic life of the machine, and methods of defining and determining this point is the optimum replacement problem. The replacement strategy to be used in determining the optimum economic life of any production asset depends on the operating characteristics of that asset. A l l pro-duction assets fall into one of two categories of operating characteristics (ElMaghraby Chapter 1. INTRODUCTION 3 1958; Eilon et al. 1966): 1. Items with no observable deterioration before failure, and; 2. Items with observable gradual deterioration with age before failure. An example of the first type of asset is the light bulb, which shows no visible deterioration in efficiency until failure. The second type of asset is usually composed of several parts of type I items, and shows some observable, gradual deterioration with age before failure. Fetter and Goodman (1957) described these assets as being a "diminishing efficiency" type, which are durable goods whose lifetime can be extended indefinitely if their parts are repaired or replaced as necessary. Replacement of the first kind of asset is concerned with predicting the point in time at which the asset breaks down and ceases to be useful, and it then has to be replaced. A discussion of replacement problems of these types of assets is provided by Elrnaghraby (1958), and is not in the scope of this study. Replacement of items in the second category, however, is concerned with establish-ing the optimum point in time when the machine should be replaced to achieve an economic objective. The machine would then be replaced despite the fact that it can still be used in the production process. "Optimum", in this context, is defined with respect to the economic objectives of the owner, most commonly profit maximization. Replacement before or after the optimum life therefore results in some financial penalty to the owner of the machine. Into this second category of problem fall machinery and plant replacements. As forest harvesting equipment is of the "diminishing efficiency" type, replacement strategies of assets in this category will be the focus of this study. The operation of a production asset involves the expenditure of costs, and receipt of some revenue or service. To determine the economic life of an asset, these costs and revenues are quantified, aggregated, and then evaluated in some way over the Chapter 1. INTRODUCTION 4 assets service life. The optimum economic life is then determined according to prior established criteria. The most significant cost and revenue factors in this decision process are (Caterpillar Tractor Co. undated): 1. Depreciation and Replacement Costs: depreciation charges decrease with machine use, while asset replacement costs increase. These factors favour retention of the machine. 2. Asset investment Costs: includes insurance, interest and taxes. These de-crease with machine age, and favour its retention. 3. Repair and Maintenance Costs: the costs of repairing machinery breakdown increase with machine age. These favour its replacement. 4. Downtime: the cost of lost time due to machinery breakdown increases with machine age. This favours replacement. 5. Obsolescence costs: opportunity costs incurred as a result of introduction into the market of new machines taking advantage of improved technology, and/or due to a drastic change in the services required of the asset. These costs increase with machine age, favouring replacement. 6. Revenues accruing from goods and services provided by the machine: due to increasing downtime and obsolescence, these decrease with machine age, which favours replacement. Many different methods have been used to determine the optimal economic life of production assets. A l l the methods involve the quantification and evaluation of the factors listed above. The major differences between the methods are in the selection of factors considered important in the analysis, and in the criteria used to establish optimal Chapter 1. INTRODUCTION 5 replacement. Three basic methods of determining the economic life of production assets can be distinguished. These methods are: 1. Models in which the economic life of an asset is defined as that service life which will result in minimum average cost of owning and operating the asset. 2. Those in which the economic life is defined as the point at which the cost of impending repairs exceed a predetermined Repair Expenditure Limit (REL). 3. Those in which the economic life is defined as the service life which will result in a maximum of average annual net revenue of operating the asset in a production process. In models that use R E L to determine optimum economic life of assets, a replace-ment evaluation is made every time the machine fails, and before it is repaired. This evaluation is made with the aim of minimizing total machine costs by preventing un-warranted expenditure on repairs. The basic consideration in the evaluation is the difference between the cost of maintaining efficiency of the current machine, against that of acquiring a new one. In this approach, it is assumed that the "normal" replacement age of the machine is known. Normal replacement age refers to the planned life expectancy of machines in a fleet performing a common production function (McPhallen 1975). The R E L is then defined as the maximum expense allowed to repair the current machine failure and restore it back into its normal operating condition. To calculate the R E L , expected future repair and maintenance expenditures up to the machines normal service life are obtained from historical machine data and accu-mulated. To this cost is then added the expected replacement cost of the machine. The R E L is then determined by expressing the sum of these costs on an average annual ba-sis. When evaluating replacement, the expected cost of impending repairs is compared Chapter 1. INTRODUCTION 6 to the R E L . Replacement is recommended if this repair cost is greater than or equal to the R E L . Drinkwater and Hastings (1968), McPhallen (1975), and Logistics Management Institute (LMI) (1968) developed replacement models based on the R E L approach. In all these studies, the R E L was estimated by the procedure described above. Themain differences between the models is in the combination of costs included in the analysis, and in the treatment of asset resale values. McPhallen (1975) included downtime and depreciation payments in the machine cost analysis, and treated the cost elements for the effects of inflation. L M I (1968) included the effects of downtime and obsolescence on the R E L analysis, but assumed that salvage value had no effect on replacement. Drinkwater and Hastings (1968) did not include the effects of downtime or obsolescence on the R E L . They considered the R E L of a machine at any age to be a quantitative estimate of its worth at that age, and no salvage values were included in the model. A l l the R E L replacement models discussed above are based on non- discounted, before-tax cash flows. The most common approach to evaluating the economic life of an asset is based on determining the service life that minimizes the average annual cost of ownership and operation of a machine (Eilon, King and Hutchinson 1966; Clapham 1957; Barlow un-dated; Demirdache, Howell and Fowler 1968; Elmaghraby 1958; Wellwood and Sinclair 1972a,1972b; Sinclair et al. 1986; Helmer and Watts 1981). Elmaghraby (1958) referred to this method as the "classical" approach. In this technique, the economic life of an asset is referred to as the Optimal Replacement Time (ORT). To estimate the ORT, machine cost elements are obtained from historical data collected from the operation of similar machines. These costs are then separated into annual components, combined and then accumulated year by year. Average annual costs are then calculated from the accumulated machine costs for each operating year. The point in the service life of Chapter 1. INTRODUCTION 7 the machine yielding a minimum of average annual costs is then selected as the ORT. Figure 1.1 is a plot of average annual capital, repair, maintenance and total costs for a machine, showing how the ORT is determined using this approach. In Figure 1.1, capital costs decline with machine age, whereas repair and mainte-nance costs increase. Average annual total costs, which is a sum of capital and repair and maintenance costs, decline initially then increase with continued machine use. The ORT is the machine age yielding the minimum average annual cost of owning and operating the machine, and is the lowest point on the total cost curve. A basic assumption in cost minimizing replacement models is that the asset will be replaced by one with an identical cash flow profile, i.e. replacement is with a like asset. The owner is assumed to be in business for an extended period, and replace-ment will be at intervals equal to the ORT. These models can be grouped into classes based on whether or not they include consideration for the effects of income taxes and discounting. In non-discounted, before-tax cash flow models, the costs are combined and evalu-ated with no consideration given to taxes or the time value of money. Clapham (1957) developed a non-discounted, before-tax model based on the cost minimizing method. In this model, ORT was defined as the point in the service life of the asset when the current hourly rate of maintenance payments is equal to the hourly rate of depreciation payments (if salvage is assumed to be zero). The model did not include the effects of downtime and obsolescence on the ORT. Demirdache, Howell and Fowler (1968) de-fined the ORT as the lowest point on the average annual cost curve, when expressed as a function of machine use. These researchers included the effects of depreciation, operating and downtime costs as major factors influencing the ORT. Eilon et al. (1966) discussed two models, one of which was based on non-discounted cash flows, but with Chapter 1. INTRODUCTION 8 i i i r r CUMULATIVE MACHINE USE (hours) —> Figure 1.1: Machine cost/use function showing how the ORT is determined (From Sinclair et al. 1986). Chapter 1. INTRODUCTION 9 consideration given to the effects of taxes on the ORT. In this model, the ORT was defined as the lowest point on the average annual cost curve. This definition is similar to that in the models discussed by Demirdache, Howell and Fowler (1968), and the non- discounted, after tax models discussed by Sinclair et al. (1986) and Wellwood and Sinclair (I972a,1972b). The model by Wellwood and Sinclair (1972a,1972b) differed by including the influence of taxes on ORT. In discounted, after-tax cash flow models, the time value of money and taxes are considered to be major factors influencing the ORT of a machine. Sinclair et al. (1986) determined ORT as the machine age which will result in minimum Uniform Annual Equivalent Costs ( U A E C ) of owning and operating the machine. To compute the U A E C , total annual machine costs are treated for tax effects, discounted to a base year, and then accumulated year by year. The accumulated costs are then converted to uniform annual equivalents by applying a capital recovery factor. This approach is similar to the non-discounted, cash flow model discussed by Eilon et al. (1966) but with'considerations for the effects of discounting, income tax and C C A . Brennan (1964) discussed a discounted, after-tax cost minimizing model similar to that of Eilon et al. (1966), with extensions covering the influences of asset financing through equity and debt money on the solution. In this model, the asset was assumed to be financed through the media of stocks and bonds, and interest on capital is therefore an average cost of equity and debt money. Peterson and Milligan (1976) used minimum equivalent annual cost as the basis of determining ORT. The model is similar to that discussed by Sinclair et al. (1986), but with machinery costing methods specific to the potato farming industry. This model also differed in considering all costs (owning, operating and repair and maintenance) as affecting the ORT, whereas Sinclair et al. (1986) only included the effects of capital and repair and maintenance costs. The last major method of determining optimum economic life of machines is by Chapter 1. INTRODUCTION 10 models which aim to maximize the net revenues earned by the productive use of a machine. In these models, the economic life of the machine is defined as the length of time over which it must be operated to maximize the value of the total assets (Murchison and Nautiyal 1971). The total assets of a machine are defined as the sum of the annual net revenues earned by the machine, and its residual value at replacement. This method is based on the assumption that average annual revenues, net of costs, will reach a maximum at some point in the service life of the machine (Murchison and Nautiyal 1971; Lusztig and Wood undated; Fetter and Goodman 1957). This is because capital costs of a machine decline with age. At the same time, repair, maintenance, and operating costs increases, and productivity of the machine declines. As with the other methods, revenue maximizing models may or may not include the effects of the time value of money and taxes. Murchison and Nautiyal (1971) discussed a discounted, after- tax cash flow model based on the revenue maximizing approach. In the model, the annual net revenues were expressed on a marginal basis, yielding annual Marginal Quasi Rents (MQR) for the machine. The M Q R when summed over the service life of the machine and added to its residual value, yields the value of its Total Assets (TA). The optimum economic life of the machine is then determined as the year yielding the maximum TA. Dreyfus (1960) described two discounted, before-tax cash flow models based on maximizing the Present Worth (PW) of the machine. In these models, the economic life was defined as the age which maximizes the P W of revenues, net of operating and asset replacement costs. The first model was developed under the assumption of no technological change and linear obsolescence. The second was developed with con-sideration for the effects of non linear obsolescence under unpredictable technological change. Fetter and Goodman (1957) presented a discounted cash flow model based on the P W method. In this model, the economic life was defined as that year which yields Chapter 1. INTRODUCTION 11 a P W of revenues equal to "asset investment costs". Asset investment costs refers to the total installed cost of the machine, plus a margin for profit at a given interest rate. The treatment of costs and revenues in this model is similar to that of Murchison and Nautiyal (1971), except that they are not expressed on a marginal basis. The other major difference between the models is in the assumption of replacement by similar assets. Fetter and Goodman (1958) made this assumption implicitly by including an "asset investment cost" in the model they described, as opposed to the "asset replace-ment cost" included in the model described by Murchison and Nautiyal (1971). Asset investment cost refers to the total installed cost of the current asset, whereas asset replacement cost is the expected capital cost of a future replacement. Lusztig and Wood (undated) discussed a revenue maximizing model based on the Net Present Value (NPV) criterion. In this model, cyclical replacement of assets by like ones was assumed. The annual, after-tax net revenues are expressed on a N P V basis, and the optimal economic life determined as the year yielding the maximum N P V . The optimal economic life in the model was assumed to be the length of replacement cycles for the machine. A n implicit assumption made in R E L models is that repair and maintenance costs are the most important factors influencing the optimal economic life of an asset. This is not always the case, especially in the early life of the asset. Schoney and Firmer (1981) estimated that 60-75% of the total cost of owning and operating a machine in productive use is due to capital recovery. The capital recovery costs become even more important if the effects of discounting and taxes are considered. A l l the R E L models discussed here are based on before-tax, non-discounted cash flows. Cost and revenue estimates based on non-discounted, cash flow methods are realistic if the asset life is shorter than one year, in which case the effects of the time value of money are minimal. The exclusion of tax effects is also based on the assumption that these effects Chapter 1. INTRODUCTION 12 are uniformly spread over the service life of the machines (Helmer and Watts 1981). This is not the case. The purchase and use of a production asset is usually a short to medium term (0-20 year) investment. As the asset is commonly financed through the media of equity and short term (less than 5 year) debt, the cost of capital (interest), and income tax effects are important components of the cost analysis. This is especially so during the capital recovery period of the life of the asset. Therefore, cash flow data obtained from models not incorporating these factors, and replacement decisions based on such models will differ considerably from reality (Helmer and Watts 1981). The R E L and classical approaches implicitly assume either that cash inflows remain constant over the operating life of the machine, or that cash inflows for the current machine and that of a proposed replacement are equal. In such a case, production costs determine the level of net revenues, and revenues can therefore be ignored in the analysis. The frequency and duration of downtime increase with machine use (Tufts and Hitt 1983), resulting in reduced productive machine hours (PMH). As a result, the assumption of constant gross revenues does not hold. Consequently, any replacement model based on the cost minimizing method and which does not include considerations for the effects of decreasing cash inflows, will not accurately reflect the true returns to the investor. This shortcoming can be overcome by incorporating the effects of downtime as a cost, but estimating these costs is difficult. Downtime is a loss in availability of the machine, and should therefore be assessed as a reduction in the machines productive time. A l l the R E L , classical, and some of the revenue maximizing models (Fetter and Goodman 1957; Lusztig and Wood undated) discussed above assume replacement of the present asset with one having an identical cash flow profile. In reality, this assumption is rarely valid. This is because older models are phased out by manufacturers and newer, more productive ones introduced. Furthermore, significant changes in the services Chapter 1. INTRODUCTION 13 required of machines may occur. For instance, a logging operator using cable skidders may be considering a change to grapple skidders as the operation moves into cut blocks with smaller trees. The required investment decision can be even more complex if alternative ways of fulfilling the productive function are to be considered. For example, a log stacker at a centralized sorting yard can be replaced by several smaller front end loaders, or an overhead crane. The replacement decision then is not only when to replace, but also whether a shift to a different type of equipment, with completely different cost and production patterns is economically justified. Therefore, if it is desired to replace the existing asset with a different one, then any solution determined by a model in which replacement by like assets is assumed, will not be valid. Models that are based on the assumption of cyclical replacement by like assets (ORT) are useful for replacement decisions involving large fleets of machines perform-ing a common function. They are most useful in non profit organizations, such as public service, government or military organizations. In such institutions, services of a machine, such as an automobile, may be foreseen long into the future. The procedure required then is one that will determine when a deteriorating machine should be taken out of service and replaced by a new, more efficient but functionally similar one. In small commercial organizations, where only a few of any particular line of machines are held, replacement decisions for individual machines should be made based on their service lives. Replacement must also consider the performance of the present machine, against that of alternatives. The required model for performing replacement analysis should therefore have the capability of evaluating the current machine (the "defender") against a specified re-placement machine (the "challenger") based on the defenders service life. The model should have the flexibility required to evaluate replacement with either a similar or a completely different machine. The model should be capable of performing an analysis Chapter 1. INTRODUCTION 14 based on the current age of the defender, and permit evaluation of replacements by either a new or used machine. The model should also incorporate all the major fac-tors that influence the operation and replacement of production assets, and therefore present the investor with realistic cash flow profiles. Chapter 2 F O R M U L A T I O N A N D D E V E L O P M E N T O F T H E M O D E L 2.1 Introduction This section is a detailed discussion of the replacement analysis method developed in this study. It starts with a discussion of how the cash flow profiles of both machines are used to determine the optimal economic life of the presently owned machine (the defender). The data required for developing the cash flows, and how the they were collected and analyzed is then described. The section ends with a discussion of how the different cash flows (revenues and costs) are aggregated into cash flow profiles, which form the basis of the replacement decision. 2.2 Outline of the method In any replacement analysis, there are two alternatives: to maintain and retain the de-fender, or replace it with a challenger. In this study, the scheme of evaluating mutually exclusive investments, described by White et al. (1984) was followed. This approach is outlined below, and a flow diagram of the implementation of procedures 3-6 is shown in Figure 2.2. 1. The set of mutually exclusive investments are defined by identifying the most suitable of currently available challenger(s). 2. A finite planning horizon is defined. 15 Chapter 2. FORMULATION AND DEVELOPMENT OF THE MODEL 16 3. Cash flow profiles for each machine (costs and revenues) are developed and con-verted to annual equivalents using discount and income tax rates appropriate to the investor. 4. The alternatives are compared on the basis of the annual equivalents over the planning horizon. 5. Supplementary analyses, including sensitivity analyses, are performed, and 6. The preferred alternative is selected. In this study, the total cash flow approach, as opposed to the incremental cash flow approach, was followed. In the total cash flow approach, cash flows associated with each alternative are considered individually. In the incremental cash flow approach, alternatives are compared in pairs, and only the incremental (differences in) cash flows are considered in the evaluation. 2.2.1 T h e Defender /Chal lenger /Descendants concept The defender/challenger/descendants method of performing replacement analysis in-volves the comparison of a deteriorating present day defender against an improved later day challenger, and an ever improving line of "descendants" (Elmaghraby 1958; Riggs et al. 1983; White et al. 1984), as shown in Figure 2.3. Line A represents the increasing yearly costs of operating the existing machine. Line B shows the increasing (but at a different rate) yearly cost of operating the present day challenger. Line C represents the declining operating costs of the ever improving line of descendants. Chapter 2. FORMULATION AND DEVELOPMENT OF THE MODEL REAL TIME MACHINE USE AND COST DATA I I I DATA ANALYSES (REGRESSIONS, etc) GENERATE COSTS GENERATE REVENUES TOTAL DEDUCTIBLE COSTS GROSS REVENUES CASH FLOW PRORLES FOR THE MACHINES REPLACEMENT CRrrERIA REPLACEMENT DECISION Figure 2.2: Flow diagram of the replacement evaluation process Chapter 2. FORMULATION AND DEVELOPMENT OF THE MODEL 18 MACH. OPER. COST ($/HR) DESCENDANTS CUMULATIVE MACHINE USE (HOURS) Figure 2.3: The defender/challenger/descendants concept (after Elmaghraby 1958) Chapter 2. FORMULATION AND DEVELOPMENT OF THE MODEL 19 A basic requirement in the financial evaluation of any two projects is that the analy-sis must be made on the basis of equivalent outcomes (Riggs et al. 1983). This require-ment implies that replacement analysis can only be performed between two similar machines. This precondition has led many researchers developing economic replace-ment models to assume that replacement will be by similar assets. This requirement can be met by using the defender/ challenger method to perform the analysis. To perform a replacement analysis between the two machines, the defender is com-pared to the descendants, and the challenger to the descendants, and the two evalua-tions are then compared to each other. It is therefore a dynamic process, in which the defender and challenger are never compared directly to each other, but through a line of ever changing descendants (Elmaghraby 1958; Shore 1975). The challenger can there-fore be quite different from the defender, eliminating the need to assume replacement by like machines. 2.2.2 Treatment of Unequal Lives of Assets: Planning Horizon Replacement analysis between alternative machines must be done on the basis of equiv-alent outcomes (Riggs et al. 1983). Different machines have different expected service lives, which renders results from direct comparison of such machines invalid. In the case where replacement by a like machine is being considered, the defender will have performed some productive function, and its remaining useful life will not be equivalent to that of a new machine. This problem can be overcome either by use of a common life multiple for both alternatives, or by converting the analysis to that of alternatives with equal lives. Common life multiple analysis is most frequently employed in classical and R E L methods of establishing optimum economic life. In these models, replacement by like machines at intervals equivalent to the ORT is assumed. The analysis can be converted Chapter 2. FORMULATION AND DEVELOPMENT OF THE MODEL 20 to that of alternatives with equal lives by confining the evaluation to a planning horizon or study period. The planning horizon provides a "window" through which the cash flow profiles of both alternatives are evaluated. The most common methods of establishing a planning horizon are (Riggs et al. 1983; White et al. 1984; Kulonda 1978): 1. The shortest economic life of all competing alternatives. This protects the investor against technological obsolescence. 2. Known duration of required service. Assumes that the project starts with new assets, and continues with replacements by like assets, which are disposed of at the end of the project. 3. Time before a better replacement become available. Attempts to minimize costs by purposely upgrading machines as new improvements are made. This method introduces the complication of requiring a forecast of when a better replacement will be available. 4. A standard planning horizon established by the owner for evaluating all economic investments. In this study, the analysis was converted to that of alternatives with equal lives by the adoption of a standard planning horizon. This is because a standard planning horizon ensures consistency between different investments in the organization, and makes 2.3 T h e Replacement c r i te r ia In the model developed in this study, the optimum economic life of the defender is determined by simulating all combinations of operating the defender for a number of Chapter 2. FORMULATION AND DEVELOPMENT OF THE MODEL 21 years, and the challenger for the remaining time up to the end of the planning horizon. The cash flow profile developed by this simulation is then converted into an Equivalent Annual Worth. The number of years over which the defender must be operated to maximize the E A W of combined cash flows in the simulation, is then selected as its optimum economic life. Figure 2.4 shows how the combined cash flows are developed, and how the optimum economic life of the defender is determined from the combined cash flows. Equation [2.1] is a functional representation of the replacement model shown in Figure 2.4. It illus-trates how the replacement decision is made with respect to the physical age of the machines and the planning horizon. In equation [2.1], the optimum economic life of the defender is determined as the year (k) that maximizes the E A W of Combined Net Cash Flows (future worth) from operating both machines over the planning horizon. KNCFfwk = £ NCFfw{DEF)0 + £ NCFfw{CHAL)1 (2.1) j=q l=p and EAWk = KNCFfwk * CRF where KNCFfwk - Combined N C F (Future worth) in year k k = number of years into planning horizon n = Planning horizon v = discount rate p = age of proposed challenger, 1 if new q. == current age of defender, 1 if new n = planning horizon, and Chapter 2. FORMULATION AND DEVELOPMENT OF THE MODEL 22 Figure 2.4: The cash flow profiles of both machines, showing how the optimal replace-ment point is determined Chapter 2. FORMULATION AND DEVELOPMENT OF THE MODEL 23 k + r < n Equation [2.1] shows how the replacement decision is made with respect to the current age of both machines, and the length of the planning horizon. It can therefore be used for evaluating replacement of a defender of any age with either a new or used machine. 2.4 Sources of data This study involved the development of a machinery replacement model, based on discounted cash flow methods. For developing and testing the model, machinery costs and revenue data were collected from different sources and analyzed. The costs and revenue data were collected for two groups of machines used in de-veloping and testing the model: Caterpillar D8 (CAT D8) tractors, and Caterpillar 966/988 (CAT 966) Front end loaders. These two machine groups were selected be-cause they are widely used in the British Columbia forest industry, and because of the availability of data required for developing and testing the model. The machine operating cost data collected for the purposes of this study can be divided into several components. These cost components are repair and maintenance, resale value, technological obsolescence, and machine purchase price and debt data. 2.4.1 Repair and maintenance cost data Repair and maintenance cost data for the two machine groups were provided by Wong (1987). These data were collected for a replacement study conducted by the Forest Engineering Research Institute of Canada (FERIC) (Sinclair et al. 1986). The. data were collected from three B C logging divisions of the MacMillan Bloedel Company: Chapter 2. FORMULATION AND DEVELOPMENT OF THE MODEL 24 Table 2.1: Summary of the repair and maintenance cost data Machine Period data Total # Longest Service Available Machines Life (Years) C A T D8 1960-1985 14 8 C A T 966/980 1960-1985 14 12 Chemainus, Kelsey Bay, and Northwest Bay. The data consisted of the annual cost of parts and labour incurred in repair and maintenance as a function of annual use (in hours) for each machine. Labour costs were comprised of the hourly wage rates and fringe benefits, but excluded the costs of overhead (Wong 1987). Table 2.1 is a summary of the number of machines, longest service life, and the length of period over which data were available for both machine groups. These costs were converted to a uniform monetary time base (1986 dollars) by the method described by Sinclair et al. (1986). This calculation is based on increases in the Canadian Consumer Price Index (CPI) for the Vancouver area, and the B C Forest Industry wage rate for certified heavy duty mechanics. Parts costs were transformed to 1986 dollars by weighting each cost by the ratio of the CPI in 1986 and the CPI in the year of expenditure. Labour costs were similarly transformed by weighting each cost by the ratio of hourly wage rates for certified heavy duty mechanics in 1986 and the wage rate in the year of expenditure. The total repair cost for any year is then the sum of parts and labour costs (in 1986 dollars) for that year. Wage rates for certified heavy duty mechanics and the CPI for the period 1960-1986 were obtained from Forest Products Industries (FPI) 1960-1987, and Statistics Canada (1970-1987) respectively. Equation [2.2] shows how the parts and labour cost Chapter 2. FORMULATION AND DEVELOPMENT OF THE MODEL 25 data were transformed to 1986 dollars using the method outlined above. RkMjk = (L]k * WWW,-) + (Pjk * CPse/CP,) (2.2) where R&zMjk = Repair and Maintenance cost in year j (in 1986 dollars) for machine k Ljk = Labour costs incurred on R8zM in year j for machine k Wj,WS6 = Wage rate for heavy duty mechanics in years j and 1986 respectively Pjk = Cost of parts incurred in year j for machine k CPj,CPS6 = Consumer Price Index for years j and 1986 respectively, and; n : CR&Mnk = R&Mj (2.3) where CR&zMnk = Accumulated repair and maintenance costs to year n for machine k. The annual repair and maintenance costs, and cumulative use (hours) for each machine were then accumulated over the service life of the machine according to equa-tion [2.3]. The accumulated machine use and repair and maintenance costs data were used in developing repair and maintenance cost equations. 2.4.2 Machine resale value data Resale values of machines used in this study were estimated by equations developed from data consisting of resale prices as a function of machine age. These data were extracted from the 1986 edition of the International Equipment Exchange (IEE) Last Bid Annuals (IEE 1986). These annuals contain details of prices paid for heavy ma-chines and the their ages, at auctions in heavy machine auction marts across North Chapter 2. FORMULATION AND DEVELOPMENT OF THE MODEL 26 Table 2.2: Summary of the resale value data Machine Machine Age (Years) Size of Oldest Newest Dataset C A T D8 29 3 520 CAT 966 20 1 296 America in the previous year. A l l the prices were in 1985 Canadian (for machines sold in Canada) or United States dollars (for those sold in the US). The auction price data were converted to Canadian dollars by adjusting the prices expressed in US dollars by the 1986 US to Canadian dollar exchange rate (1.333). The resale price data were converted to 1986 Canadian dollars by adjusting the prices by the ratio of the CPI in 1986 to that in 1985. The machine ages (in years) were converted to hours by assuming 1200 hours as an annual usage rate. The machine age (in hours) and sale price (in 1986 Can. dollars) data were then used to develop models for predicting machine resale values as a function of age. Table 2.2 is a summary of the number of machines and the age of the oldest and newest machines in each dataset. 2.4.3 T e c h n o l o g i c a l Obso lescence d a t a The data used in estimating the annual rate of technological obsolescence were ob-tained from Caterpillar Performance handbooks, editions 10-17 (Caterpillar Tractor Co. 1970-1986). Within the machine test groups, data were collected for each genera-tion of machines introduced in the period 1970-1986. The data consisted of: 1. Year of introduction of each machine generation; 2. Hourly fuel consumption, in litres/hour, for each machine generation, and; Chapter 2. FORMULATION AND DEVELOPMENT OF THE MODEL 27 Table 2.3: C A T D8 series tractor dozing production data (Caterpillar Tractor Co., 1970-1986) Year of Model Hourly Fuel Hourly Product. Introd. Con. (L /HR) ( L C M / H R ) 1970 D8H 39.4 400 1975 D8K 40.9 450 1982 DSL 42.5 550 3. Machine unit hourly productivity, in loose Mz/Hour ( L C M / H R ) for CAT D8 tractors and M3/Hour (M3/HR) for C A T 966 F E L . In the sample calculation of annual obsolescence rate given in Chapter 2.5.2, es-timates of the variables were obtained for each generation of C A T D8 tractors. It was assumed that the tractor was used for clearing and subgrade construction in road building. The dozing production data were obtained under the following operating conditions: 1. C A T D8 tractor, equipped with a Universal (U) blade. 2. Average dozing distance of 60 metres 3. Material density 1370 k g / L C M . 4. Fuel consumption at normal load factor. 5. Machine efficiency, 100% (60 minute hour). The dozing production data for C A T D8 bulldozers, working under the operating conditions listed above are summarized in Table 2.3. The data in Table 2.3 are used in the sample calculation of annual obsolescence rate given in Chapter 2.5.2. Chapter 2. FORMULATION AND DEVELOPMENT OF THE MODEL 28 2.4.4 Purchase price and cost data Purchase prices of machines used in testing and developing the model were obtained from Finning Tractor Company, Vancouver (Gourley 1987). The data consisted of the purchase price of machines fully equipped for dozing (CAT D8) and Loading (CAT 966 and 980) production. 2.5 Development of the cash flow profiles 2.5.1 In t roduct ion This section starts with a discussion of methods used for analyzing the data collected as described in Chapter 2.4. Definitions of the different cost and revenue elements used to compile the cash flow profiles, and how they were formulated and derived are also discussed. The last part is a discussion of how the costs and revenues are aggregated into cash flow profiles, which when combined, form the basis of the replacement decision shown by Figure 2.4 and equation [2.1]. 2.5.2 Der iva t ion of costs and revenues Deprec ia t ion Depreciation is a decrease in worth of a production asset due wear and obsolescence. Depreciation charges are made to recover capital spent on purchasing production assets, and to substantiate deductions from income for tax purposes. The charges are most often calculated by some form of accelerated method, which recovers the bulk of the investment in the early part of the life of the asset, and defers tax payments until further in the future. The depreciation method utilized affects the timing of tax payments, which in turn affects the after-tax cash flow of investment projects. Chapter 2. FORMULATION AND DEVELOPMENT OF THE MODEL 29 The only depreciation expense allowed for tax deductions in Canada is the Capital Cost Allowance (CCA) . Every asset must be included in a class and each class has asset. The C C A rate for a Class 10 production asset, which includes timber harvesting equipment, is 30%. In the first year of operation, the depreciation is computed by applying 50% of the C C A rate against the capital cost of the machine (Bellemare 1982). In subsequent years, depreciation is computed by applying the C C A rate to the undepreciated balance. The capital cost of the machine is composed of the purchase price less an Investment Tax Credit (ITC). The ITC is offered by the federal government to corporations as an incentive for investing in capital equipment. To qualify for ITC, the machine purchased must be brand new. The normal ITC rate is 7%, but it may go as high as 20% in areas designated for additional incentives (Bellemare 1982). The depreciation is calculated as shown by equations [2.4] and [2.5] in the first and subsequent years of operation. a specified C C A rate. The C C A rate is applied against the book value (BV) of the (2.4) DCj = BV3 * (d) (2.5) where BV:— Book Value of asset after j years DCj = Depreciation charge (allowance) in year j P = Asset purchase price d = C C A rate (30% for the purposes of this study) ITC Investment tax credit Chapter 2. FORMULATION AND DEVELOPMENT OF THE MODEL 30 The difference between the capital cost and accumulated depreciation of an asset is its book value. If an asset is disposed of, any surplus between its book and resale (or trade-in) values is a capital gain. Capital gains are taxed at a lower rate than income, in recognition of capital investment risks. M a c h i n e Resale values The resale value of an asset is the actual cash flow that would be realized if it were disposed of, and is not usually equal to its book value. Different empirical models have been used to determine the approximate resale value of assets (for instance Sinclair et al. 1986). The best indicator of the current market value of an asset, however, is the average sale price of similar assets in the free market. These can be obtained from dealer (Drinkwater and Hastings 1968; Sinclair et al. 1986) or auction surveys. Different dealers mark-up prices of assets at different rates, however, making determination of the actual asset values difficult. Auction marts, on the other hand, represent a fairly free market, and are therefore a better indicator of the resale values of used assets. In this study, the sale prices of assets were modeled as a function of age, using data obtained from equipment auctions. A ready and accurate source of such information is International Equipment Exchange (IEE) last bid annuals (IEE 1986). These annuals Appendix E shows a scattergram of the sale prices of the assets as a function of age. From the scattergrams and results of the study by Dermidache, Howell and Fowler (1968), it was determined that a declining growth model would be the most appropriate fun In this study, it was assumed that the salvage value of the defender (a positive cash flow) offsets part of the purchase price of the challenger (a negative cash flow). The salvage value of the defender is estimated at replacement, and applied as a decrease in the purchase price of the challenger. The resale value Chapter 2. FORMULATION AND DEVELOPMENT OF THE MODEL 31 A n n u a l Obsolescence Costs Obsolescence is an opportunity cost incurred by not replacing a machine with a newer model incorporating the benefits of improved technology. New models in any line of machinery are introduced once every two to three years (Caterpillar Tractor Co. undated In Figure 2.5, H is the length of the planning horizon and N the age of the defender at replacement. The operating cost function of the defender increases as a result of deterioration, until it is replaced by a challenger at age N (line A) . Over this same period, the defender accumulates obsolescence at some rate (dashed line), but its impact on the operating cost function is not directly felt until it is replaced. Line B shows the level of decrease in experienced operating costs when the defender is replaced, and includes the effects of both accumulated obsolescence and deterioration. C is the operating cost level of the challenger. Obsolescence is caused either by the introduction of new, more productive machines into the market (technological obsolescence), or by a radical change in the services required from the existing machine (functional obsolescence). Introduction of new machines into the market will also commonly reduce the trade-in values of existing machines. Radical changes in the services required from any machine dictate either that it undergo extensive modification, or more often, its replacement. This component of obsolescence was therefore not considered in this study. Technological obsolescence, on the other hand, is a subtle but real cost, that is often ignored when evaluating replacement of machines. This is because it is an imputed rather than an actual cash outflow, whose effects are directly felt only after the machine has been replaced. Technological obsolescence is a function of the following factors common to newer Chapter 2. FORMULATION AND DEVELOPMENT OF THE MODEL 32 Figure 2.5: Effect of obsolescence on the operating cost function of machines (after Shore 1975). Chapter 2. FORMULATION AND DEVELOPMENT OF THE MODEL 33 machines: increased productivity, reduced operating cost, and reduced repair and main-tenance expenditures. Theoretically, imputed costs incurred as a result of reduced re-pair and maintenance expenditure characteristics of newer machines can be estimated by reliability studies of both the defender, and the challenger (Tufts and Hitt 1983). In practice, different operating conditions and lack of historical repair cost data for new machines makes such analyses impossible. Machine productivity and operating cost data can be readily obtained from operat-ing handbooks published by machine manufacturers (for instance, Caterpillar Tractor Co. 1970-86; Komatsu Ltd. 1981). The availability of this information enables estima-tion o the dynamic nature of the defender/challenger/descendant method of comparing machines (Figure 2.3), the following assumptions must be made in order for the analysis to yield valid estimates of accumulated obsolescence (Shore 1975; Elmaghraby 1958)): 1. The defender will accumulate obsolescence at a constant rate, and; 2. The inferiority gradient (obsolescence rate) is constant for both the current chal-lenger and all future challengers ( "descendants"). These assumptions reduce the required comparison to that of the defender against currently available challengers only, thereby eliminating " . . . the need to chart the course of future machines ('descendants') . . . " 1 (Elmaghraby 1958). In this study, the rate of technological obsolescence accumulated as a result of reduced operating costs was estimated as a function of the increased productivity of a group of machines. Increases in the productive potential of machines may involve an i In the method described here, the changes in unit productivity were indexed to changes in the unit fuel consumption of the machines. Fuel consumption was selected 1 italics are mine Chapter 2. FORMULATION AND DEVELOPMENT OF THE MODEL 34 as an index of increased operating cost because data on fuel consumption of different machines are readily available, and it (fuel consumpti 1. A time span is selected over which the analysis is to be made. This period should at a minimum extend from the year the current defender was introduced, to the year of introduction of the current challenger. In the example, the span is 1970-1982, over which CAT D8H (1970), D8K (1975) and DSL (1982) were introduced. 2. Hourly productivity of each generation of new machines is estimated by a method recommended by the manufacturer (Eg. Caterpillar Tractor Co. 1970-1986; Ko-matsu Ltd. 1981). This is done under uniform operating conditions for all gener-ations of machines (Productivity expressed on a unit hourly basis). 3. Fuel consumption, in litres/hour, are obtained for the same operating conditions as in (2) above, for each machine generation. In the absence of such data, fuel costs can be estimated by the method described in the literature ( A S A E 1983). 4. For each new generation of machines, a ratio (fj) of hourly productivity to fuel consumption is computed as shown in equation [2.6]: _ P/hVj L/hrj where; P/hr3 = Hourly productivity for machine generation j L/hr3 = Hourly fuel consumption for machine generation j , and; fj = factor for machine generation j (2.6) Chapter 2. FORMULATION AND DEVELOPMENT OF THE MODEL 35 5. The total obsolescence accumulated by the group of machines over the period is then computed by equation [2.7]. OR=±[^T^/k] (2.7) and AOR = OR/Z * 100 (2.8) where OR = Obsolescence rate AOR — Annual obsolescence rate (%) n = number of years in time span k = number of years between introduction of machine generations (j) and (j — 1) Z = number of generations of machines introduced over time span, and; fj = factors as computed in (4) above. The Annual Obsolescence rate (AOR) is then assessed as an increase in the hourly operating cost (fuel, lubrication, and supplies) of the current machine (defender). Calculation of the rate at which C A T D8 tractors accumulated technological ob-solescence over the period 1970-1982 was performed as shown below. Data for the Chapter 2. FORMULATION AND DEVELOPMENT OF THE MODEL 36 calculation was obtained from Caterpillar Tractor Co. (1970-1986), and is summarized in Table 2.3. Using equation [2.6] to calculate factor (/) for each machine generation based on hourly productivity and fuel consumption: fdBh = 400/39.4 = 10.2 f d 8 k = 450/40.9 = 11.0 f d 8 l = 550/42.5 = 12.9 The (/) factor for the machine generations are used to calculate the total obsoles-cence accumulated by the machine group over the period, according to equation [2.7]: OR =1^/5 + ^ / 7 } OR = 0.04 The Annual Obsolescence rate (AOR) for the group of machines over the period is then computed according to equation [2.8]. AOR = 0.04/2 * 100 = 2% Chapter 2. FORMULATION AND DEVELOPMENT OF THE MODEL 37 Interest Production assets are usually purchased through some combination of equity and short term debt. The only tax deductible cost of purchasing an asset, under the income tax laws of Canada, is interest on debt (Riggs et al. 1983). The debt is normally paid back in installments over a specified term, with interest paid at a rate negotiated with the financier. For the purposes of this study, the debt is assumed to be paid back in Equal Annual Installments (EAI) over a fixed term. This E A I is comprised of an interest component and a debt reducing component. If it is assumed that the principal is equal to the purchase price of the asset less a downpayment and an ITC, then the E A I is calculated by applying a Capital Recovery Factor (CRF) to the principal, as shown in EAI ={P-D- ITC * P) * CRF (2.9) Where P = Purchase price D = Downpayment on the asset ITC = Investment Tax Credit rate, and; i = interest rate on financing, and n — term of financing The E A I calculated by equation [2.9] is in present value terms. The interest com-ponent, of the E A I can be calculated according to equation [2.10]. Chapter 2. FORMULATION AND DEVELOPMENT OF THE MODEL 38 L = EAI - EAI * 1—— (2.10) where j = age of asset (since time of purchase) Ij = Interest component of the E A I in year j n = term of financing The downpayment on the asset at purchase, and the principal reducing (equity) component of the E A I are not tax deductible costs. However, they are negative cash flows that must be included in the cash flow profile of the asset. This is accomplished by assessing the downpayment as a negative cash flow in the first year of the life of the asset. The E A I , less the interest component in any specific year, is then included as a negative cash flow in the first and succeeding years, until the debt is fully repaid. Insurance Paying a premium to an insurer is an investment made to avoid the consequences of a specific disaster. The premium is calculated from rates set by an insurer, and applied as a percentage against the book value of the asset. The book value of the asset is calculated by equation [2.5]. Insurance premiums are a cost of production, and are therefore tax deductible. The insurance premium in year j, Ej, is determined by equation [2.11]. BV1±BVJzl 3 2 (2.11) Chapter 2. FORMULATION AND DEVELOPMENT OF THE MODEL 39 With b as the insurance rate, and BVj and BVj_i the Book value of the asset in years j and (j — 1) respectively. Repair and Maintenance Costs The American Society of Agricultural Engineers (ASAE) defined repair and mainte-nance costs as expenditures required to keep a machine operable due to wear, part failures, accidents, and natural deterioration ( A S A E 1984). Sinclair et al. (1986) defined repair and maintenance costs in a similar manner, but excluded repair costs necessitated by accidents, fire damage and major machine modifications. In this study, repair and maintenance costs are defined as those costs required to maintain a machine in its normal operating condition. This includes both the costs required to maintain the machine on a preventive basis, and to bring it back into normal operating condition after a failure. The definition therefore includes the costs of rebuilding and overhauling a machine, but excludes repair expenditures necessitated by accidents and other natural calamities. Rebuilding and overhauling a machine or its parts is an act of preventive maintenance. This is usually performed either to avoid catastrophic failure of the machines parts, or to restore it back to better operating order, and therefore belongs in this category. Repair costs resulting from accidents are covered by insurance plans, whose costs appear as annual premiums in the total machine cost analyses. Inclusion of such costs with those of repair and maintenance would therefore result in double accounting. Models developed for predicting expected repair and maintenance expenditures are usually derived from historical data for a group of similar machines. Repair and main-tenance costs are commonly modeled as a function of machine use, and expressed either as a proportion of the machine purchase price (Caterpillar tractor Co. undated; A S A E 1977, 1984; Ward et al. 1985), or more commonly as accumulated costs (ASAE 1984; Chapter 2. FORMULATION AND DEVELOPMENT OF THE MODEL 40 Sinclair et al. 1986). Figure 2.6 is a representation of typical cumulative repair and maintenance costs as a function of cumulative machine use. In Figure 2.6, the solid line is the regression curve, and the dashed lines mark the standard deviation of the regression. The regression curve permits use of the model for predicting cumulative repair and maintenance costs. The standard deviation, however, implies that the predicted costs for any individual machine are probabilistic rather than deterministic. In this study, historical repair and maintenance cost data (parts and labour costs as a function of machine use in hours) were obtained for the two groups of test machines, for the period 1960-1986. These costs were converted to a uniform monetary time base according to equation [2.2], and the annual usage and repair costs were then accumulated for each machine. Multiple regression analysis was performed on the accumulated use/accumulated repair and maintenance cost data in order to obtain a model for predicting repair and maintenance costs for each machine group. This was accomplished with the aid of the R S Q U A R E procedure (SAS 1982,1985) in the SAS™ Statistical software package, and the A U T O procedure in the SHAZAM™ 2 Econometrics software package (White and Horsman 1986). The regression analysis involved the fitting of polynomial equations to both sets of data. From the accumulated repair and maintenance cost and machine use data, the following independent variables were generated: • USE = Accumulated machine use (hours) • US2 = USE2 • USS = USE3 2Copyright © K . J . White, Depart, of Econ., U B C Chapter 2. FORMULATION AND DEVELOPMENT OF THE MODEL 41 Figure 2.6: Typical cumulative use/cumulative repair and maintenance cost pattern (after Sinclair et al.1986). Chapter 2. FORMULATION AND DEVELOPMENT OF THE MODEL 42 • Z7S4 = USE4 Accumulated repair and maintenance cost was the dependent variable. Trial fitting of a linear regression with all possible combinations of the independent variables to the data sets was then done with the aid of SAS™ R S Q U A R E procedure. An option available in the R S Q U A R E procedure was used to suppress an intercept parameter from automatically being included in the models. Outputs of the R S Q U A R E procedure showing all combination of the variables, and the coefficient of determination (i? 2) for the models containing each set of the variables are given in Tables D.16 and D.17 in Appendix D for both sets of data. From the R S Q U A R E output, a model was selected for each dataset as being the best predictor of accumulated repair and maintenance cost as a function of accumulated machine use on the basis of significance. As serial correlation of variables was suspected due to the accumulation of the repair cost/use data, regression equations containing the set of selected variables were fit to each dataset with the A U T O procedure in the SHAZAM™ software package. This procedure corrects for serial correlation by estimating the autocorrelation parameter (p) by an iterative Cochrane-Orcutt type procedure (White, Horsman and Wyatt 1986). A summary of estimates of the coefficients and regression statistics for each dataset is given in Table 3.4. Tables D.9-D.14 in Appendices D are SHAZAM™AUTO procedure Analysis of Variance (ANOVA) table outputs for the two datasets. Annual hourly repair and maintenance cost are calculated from the cumulative repair and maintenance costs, obtained by the prediction equations, according to the expression in equation [2.12]. Chapter 2. FORMULATION AND DEVELOPMENT OF THE MODEL 43 where j — machine age (years) Rj = hourly repair and maintenance costs at age j U — equipment annual usage rate CR&iM7 — Cumulative R & M cost in year j Downt ime Downtime is the loss in productive time (out of scheduled machine hours) caused by machine unavailability due to breakdowns and unscheduled maintenance. Incorporation of downtime in cost minimizing models has usually been done by estimating the lost productivity as a cost. The difficulties associated with estimating the cost of downtime has however limited its use in replacement studies (Murchison and Nautiyal 1971, for instance). The best estimate of the cost of downtime is the cost incurred by renting a similar machine to perform the same service over the period the machine is down for repairs. Downtime has usually been modeled as a function of accumulated machine use, based on historical machine operating data. Due to the unavailability of data on actual downtime for the two machine groups used in this study, downtime was estimated by the equation published by A S A E (1983) for diesel engine tractors. This equation was developed for machines with diesel engines in agricultural use. Due to the more robust operating conditions in the forest harvesting environment, this probably gives conservative estimates of the actual downtime experienced. This relationship is given in equation [2.13]. Dj = 0.0003234 * [7 1 - 4 1 7 3 (2.13) ii Chapter 2. FORMULATION AND DEVELOPMENT OF THE MODEL 44 where: U = Accumulated use (hours) to year j, and Dj — Accumulated Downtime (hours) to year j Annual downtime (hours) can be obtained by taking the difference between accu-mulated downtime in one year and the succeeding one. Downtime has also been estimated by correlating it to machine repair and mainte-nance costs (Caterpillar tractor co. undated). However, this method yields erroneous estimates if the exact relationship between repair costs and downtime is not known. In this study, the downtime obtained by equation [2.13] is assessed against the Scheduled Machine Hours (SMH) as lost productive time of the machine, resulting in reduced gross revenues. Operating costs Operating costs for the purposes of this study are defined as those costs dependent on machine usage, but excluding the costs of repair and maintenance. Included in this definition are the costs of operating labour, fuel, lubrication, supervision (overhead), and supplies. These costs are estimated on an hourly basis, and apart from overheads, are a function of productive machine hours (PMH). Operating cost data are usually expressed as a function of Scheduled Machine Hours (SMH), and the S M H basis of costing was therefore used throughout this study. The hourly fuel cost of a machine is a function of the hourly fuel consumption, and the unit cost of fuel ($/Litre). Hourly fuel consumption is a function of the power rating of the machine, and can be obtained from manufacturers production data, such as Caterpillar tractor Co. (1970-1986) and Komatsu Ltd. (1981). In the absence of Chapter 2. FORMULATION AND DEVELOPMENT OF THE MODEL 45 such information, fuel costs can be estimated according to equation [2.14] ( A S A E 1977, 1983). Fuel cost/hr = (0.33) * (kW) * (cost/litre) (2.14) With kW as the machines power rating (in kilowatts). The total annual cost of fuel is then simply the product of hourly fuel costs and the annual usage rate. The cost of lubrication can be estimated as 15% of the total fuel costs ( A S A E 1983). Labour OP3 = (Fuel + Lub. + Supplies) * (1 + d)3 + labour (2.15) OP(chai)j = (Fuel + Lub. + Supplies)* (1 - AOR)m (2.16) Where AOR is the annual obsolescence rate, d is the annual deterioration rate, OPj the total operating cost in year j for the defender, OP( c/ i a() J the operating cost for the challenger in year j, and m is the difference (in years) between introduction of the defender and the challenger. The annual deterioration rate for the purposes of this study was assumed to be zero. This is because the data required to estimate the rate of deterioration was not available. Average hourly operating cost for any year j, OPj/HR, is then the result of dividing the total annual operating costs in that year •4 by the annual usage rate. Chapter 2. FORMULATION AND DEVELOPMENT OF THE MODEL 46 Revenues A production asset may earn three types of revenues: revenues from the use of the asset in a production process; from interest earned on past revenues, and; from sale of the asset. As all past costs and revenues are assumed "sunk" for the purposes of this study, interest earned on past revenues are assumed to have no effect on the replacement decision, and are therefore not included in the analysis. Revenue from sale of the asset accrues once the asset is disposed of, and is evaluated at the time of replacement or at the end of the planning horizon, by the method already outlined. Revenues from the productive use of a machine is a function of the productivity of the asset, the productive machine hours, and the value added cost (VAC) of the product. The productive machine time is determined as the SMH, less total downtime over the period, and less any other unscheduled unavailability (due to weather, labour problems, or any other factors). The best estimate of the V A C of a production process is the unit cost that would be paid to a contractor for provision of the same services. Machinery downtime is estimated by equation [2.13]. Due to lack of data on loss of productive time caused by non mechanical reasons (for instance weather or labour), P M H was estimated by deducting downtime from the expected availability of the machine in the first year (assumed to be 96%). Total revenue from the asset is then calculated according to equation [2.17]. GRVj = Pr*VAC*SMH(Avl-(Dj/SMH)) (2.17) where GRVj = Gross Revenue in year j SMH = Scheduled Machine Hours (Hrs/Year) Chapter 2. FORMULATION AND DEVELOPMENT OF THE MODEL 47 Avl = Machine Availability in year 1 Dj — Downtime in year j VAC = Product Value Added Cost ($/unit) Pr — Machine Hourly Product. (units/Hr) The gross hourly revenue in year j is then obtained by dividing the gross revenue in year j, by the Scheduled Machine Hours. 2.5.3 The Cash F low Profiles In developing the cash flow profiles, the following assumptions have been made: 1. Sunk (unrecoverable past) costs are considered as having no significance on the cash flow profiles of either asset in replacement analysis, except as they affect income taxes. Sunk costs burden the defender, giving an unfair advantage to the challenger (White et al. 1984). 2. A decision to continue with the production process involving the asset has already been made. The required decision is if and when replacement of the currently owned asset (the defender) is most profitable over the planning horizon. 3. Replacement analysis is performed between two mutually exclusive alternatives, the defender and the best available challenger, and only a single replacement is planned over the duration of the planning horizon. 4. End of period accounting is assumed. A l l cash flows are assumed to occur at the end of, rather than over each accounting period. Chapter 2. FORMULATION AND DEVELOPMENT OF THE MODEL 48 5. The cash flows in this study are estimated as the actual amount of money units exchanged at the time of transaction. The cash flow streams are therefore con-sidered to be free of inflation. Cash flow profiles for each asset are obtained by aggregating the cash flows for each machine oyer the planning horizon. Since all evaluations are made on an after tax basis, the cash flows are treated for tax effects before being aggregated. T h e Effect of Taxes Tax affects revenues through tax shelters, investment tax credits (ITC), capital cost allowances, and through the portion of revenues paid to the government(s) as taxes. The investment tax credit is an incentive offered to corporations by the government, and is considered as offsetting part of the purchase price of the asset. This effect of taxes, and that of the capital cost allowance has already been discussed. The tax shelter is the annual allowable tax deductible portion of the total costs. The total deductible costs are calculated according to equation [2.18]. TDC3 = Rj + CCA, + Ij + Ej + OP, (2.18) Where TDCj = Total Deductible costs in year j Rj = Repair and maintenance costs in year j CCAj = Capital cost allowance .in year j Ij = Interest on debt in year j Ej — Insurance costs in year j Chapter 2. FORMULATION AND DEVELOPMENT OF THE MODEL 49 OPj = Total operating costs in year j Income taxes are the portion of gross revenue paid to the government(s) as taxes, and are due from corporations whenever revenues exceed total tax deductions. In Canada, taxes are paid to both the provincial and federal governments. Provincial and federal tax rates are set by the respective governments, and are dependent on the tax class of the organization. This rate is usually applied as an effective rate against the taxable revenue. For calculation of effective tax rates, which represents the total corporate tax liability, see Riggs et al. (1983). The taxable revenue are calculated as the Gross revenue less total deductible costs. This yields the after-tax Net Income (NI), as shown in equation [2.19]. NIj = [GRVj - TDC3] * (1 - t) (2.19) where GRVj = Gross revenue in year j TDCj = Total Deductible costs in year j t = Effective Income tax rate, and; NIj = after tax Net Income in year j The Capital cost allowance is not an actual cash outflow but an imputed cost. It is included in the tax calculations for the purposes of capital recovery and for the computation of income tax deductions. To correctly reflect the actual cash flows due to the asset therefore, the C C A for the specific year must be added back into the after tax Net Income for that year. This yields the annual Net Earnings (NE) (equation [2.20]). Chapter 2. FORMULATION AND DEVELOPMENT OF THE MODEL 50 NEj = NIj + CCAj (2.'20) where NEj = Net Earnings in year j CCAj = Capital cost allowance in year j. 2.5.4 The Cash F low Profiles and the Replacement c r i t e r i a The investment selection criteria employed in the replacement model developed in this study was that of maximizing the Equivalent Annual Worth (EAW) of the asset. The E A W criteria was considered particularly appropriate as it expresses the cash flows on an annual basis. This takes advantage of current methods of collecting and expressing machinery cost and use data, which has traditionally been done on an annual basis. The E A W of a cash flow profile is obtained by applying a capital recovery factor (CRF) to the cash flow profiles of both alternatives. Before this can be done, the cash flows must be converted to a uniform, monetary time base. In this study, the cash flows for each alternative were converted to a Future Value (FV). The F V cash flows were then aggregated into a cash flow profile, which were then converted to an E A W for each asset. In the cash flow model developed above, the Net Earnings (NE) do not include the expense incurred in repaying the debt obtained for purchasing the asset. This must be included in the assets cash flow profile, for the N E to reflect the true equity picture of the organization at the end of the financial year. This is done by subtracting the principal reducing component of the E A I from the Net Earnings. The interest component of the E A I has already been incorporated into the model as part of the total deductible cost, and its further inclusion would result in double accounting. Chapter 2. FORMULATION AND DEVELOPMENT OF THE MODEL 51 The principal reducing component of the E A I is a uniform series of cash flows ex-pressed in present worth terms. A l l the other cash flows are also expressed in present value terms. The cash flow profiles are therefore converted to a future worth (corre-sponding to the end of the planning horizon) by application of a future value factor, as in equation [2.21]. NCFfw0 = [NE0 - (EAIj - I,)} * (1 + v)n (2.21) where NCFfwj = Net cash flow (future worth) in year j NE: = Net Earnings in year j EAI = Equivalent annual Installment in year j (zero if j 2> term of debt) Ij = Interest on debt (principal) in year j (zero if j is greater than term of debt). n = length of planning horizon j — current accounting year v = the discount rate, and; The Net Cash flow (future worth) obtained as shown by equation [2.21] is then used to develop the combined cash flow (future worth) (equation [2.1] and Equivalent annual worth which form the basis of the replacement decision. The replacement analysis model developed in this study was programmed into a microcomputer spreadsheet model (EQUIPREP) that can be used for evaluating re-placement proposals. The spreadsheet model is interactive, with facilities for perform-ing sensitivity analyses. A detailed description of the spreadsheet model, and user documentation for the program are included in appendices A and B respectively. Chapte r 3 R E S U L T S A N D D I S C U S S I O N In this chapter, results from the repair and maintenance costs, and resale value/age regression analyses for the two groups of test machines are presented and discussed. The results obtained from the calculation of annual obsolescence rates are also discussed. Tests were performed on the E Q U I P R E P spreadsheet program, and results of these tests are also presented and discussed. 3.1 Resul ts of the regression analyses 3.1.1 Cumula t ive use/repair and maintenance costs Regression analyses were performed on the cumulative use/cumulative repair and main-tenance cost datasets for each of the machine groups, as described in Chapter 2.5.2. Estimates of coefficients for variables in the model fitted to each dataset, and the re-gression statistics for the datasets are summarized in Table 3.4. Analysis of variance ( A N O V A ) tables for the regressions are in appendix D. From Table 3.4 and Tables D.10-D.15 in appendix D, it was concluded that a significant portion of the variation in cumulative repair and maintenance costs were explained by variations in the cumulative machine use of both machine groups. Both regression '% 52 Chapter 3. RESULTS AND DISCUSSION 53 Table 3.4: Results of the cumulative use/cumulative repair and maintenance regressions Machine Coefficient Estimate Regression statistics R2 F PROB > F P c *-f2/.l,..m C A T 966 USE USE3 2.4361 -1.2938E -7 0.95 579.3 0.0001 0.02 3890.3 C A T D8 USE USE2 USE4 3.8257 0.6845E-3 -1.1622E -11 0.84 523.1 0.0001 0.01 16072 Table 3.5: Results of the resale value regression for CAT D8 tractors Source SS DF MS F c •-'y.x Regression 58611 1 58611 520.3 0.395 Error 80.95 520 0.15568 Total 58692 521 112.65 3.1.2 M a c h i n e resale value data. Regression analysis was performed on the resale value/age dataset of the test machine groups. This was done as described in Chapter 2.5.2, and results of the analyses are summarized in Tables 3.5, 3.6 and Appendix E . From the regression statistics in Tables 3.5 and 3.6 and Table E.18 in appendix E , it was concluded that a significant portion of the variation in resale values of the machines are explained by variation in their ages. Both regressions were significant a Chapter 3. RESULTS AND DISCUSSION 54 Table 3.6: Results of the resale value regression for C A T 966 Source SS D F MS F Regression 34885 2 17442 271267 0.23420 Error 18.84 293 0.0643 Total 34904 295 118.32 3.2 Calcu la t ion of A n n u a l Obsolescence rate The annual obsolescence rate (2%) obtained in the example (Chapter 2.5.2) for Caterpil-lar D8 tractors is lower than the figure (5%) given by Caterpillar Tractor Co. (undated). This is probably due to the narrow definition of obsolescence employed in this study. Obsolescence was considered to be a function of increased productivity and reduced fuel consumption of new generation machines over older ones. The effects of functional obsolescence and reduced repair and maintenance expenditures of newer machines were not included. The inclusion of the effects of these two factors would probably yield an-nual rates closer to the estimates by Caterpillar Tractor Co. (undated). The method described however is an objective procedure for estimating this hidden cost, whichhas commonly been ignored when evaluating machine operating expenses. 3.3 Resul ts of Tests performed on the mode l There were two main objectives in testing the model developed in this study. One was to determine how optimum economic life and cash flows generated by the model compared to those determined by a cost minimizing approach. The other was to determine the sensitivity of optimum economic life "and cash flows generated by the model to changes Chapter 3. RESULTS AND DISCUSSION 55 in selected cash flow variables of the assets. 3.3.1 Compar i son of model to the Classical approach Results from the E Q U I P R E P model were compared to those obtained by a cost mini-mizing model. The cost minimizing approach used in the comparison is a discounted, after-tax cash flow model described by Sinclair et al. (1986), Edge and Irvine (1981), and Ogweno (1986). In the model, the ORT is determined as the machine age that yields the lowest total costs of owning, repairing, and maintaining the asset, when expressed as Uniform Annual Equivalent Costs (UAEC) . A detailed description of the cost minimizing model can be found in Appendix C. Due to differences in the major as-sumptions on which the models are based, results from the two models are not directly comparable. Optimal economic lives and cash flows were generated by simulating replacement analysis for the two groups of test machines with both the E Q U I P R E P and classical models. Inputs to the models and the resulting outputs are given in Tables 3.6, 3.7 and 3.8 respectively. Inputs to the cost minimizing model were set equal to those for the defender in the E Q U I P R E P model for each simulation. This is because replacement by like assets is assumed in the cost minimizing method. The machinery purchase cost data used as inputs to the simulation were obtained from Gourley (1987) as described in Chapter 2.4. From Table 3.8, the optimum economic life obtained for CAT D8 tractors by the E Q U I P R E P model is shorter (by one year) than that obtained from the classical model. This difference maybe a result of differences in the assumptions and methods on which the two models are based. The model developed in this study is based on the planning horizon and challenger/defender methods of analysis. This differs considerably from Chapter 3. RESULTS AND DISCUSSION 56 Table 3.7: Inputs to the model for the replacement simulation. Equipment:- Defender: C A T D8K; Challenger: C A T DSL. Variable Defender Challenger Purchase Price($) 380,000 425,000 Downpayment 76,000 85,000 Equipment age 0 0 Interest On Fin. 7% 7% Oper. Cost($/Hr) Prod. (LM3/Er) 40 41 45 55 Term of financing 5 5 Insurance rate 3% 3% Discount Rate 15% 15% Plan. Horiz.(Yrs) 15 15 V A C ($) 6 : 6 C C A rate 30% 30% Corp. Tax Rate 45% 45% Capital Gains tax 17% 17% Chapter 3. RESULTS AND DISCUSSION 57 Table 3.8: Inputs to the model for the replacement simulation. Equipment:- Defender: Cat 966D; Challenger: C A T 980. Variable Defender Challenger Purchase Price($) 280,000 320,000 Downpayment 52,000 64,000 Equipment age 0 0 Interest On Fin. 7% 7% Oper. Cost($/Hr) Prod. ( M 3 / H r ) 32 33 90 95 Term of financing 5 5 Insurance rate 3% 3% Discount Rate 15% 15% Plan. Horiz.(Yrs) VAC ( $ / M 3 ) 15 15 1.24 1.24 C C A rate 30% 30% Corp. Tax Rate 45% 45% Capital Gains tax 17% 17% Table 3.9: Results of the replacement simulations R E P L A C E M E N T AGE(YRS) E A W / U A E C ($/HR) E Q U I P M E N T E Q U I P R E P C L A S S I C A L . E Q U I P R E P C L A S S I C A L C A T D8 7 ,. 8 30 . 11.8 C A T 966 8 8 20 " 7.5 Chapter 3. RESULTS AND DISCUSSION 58 the assumption of replacement by like asset's at intervals equal to the ORT made in the cost minimizing model. Furthermore, the effects of downtime and obsolescence were included in the model developed in this study but not in the cost minimizing model. These factors both favour early replacement, and may explain the earlier recommended replacement time obtained by the model. The optimal replacement time determined by the classical approach is a range rather than a precise point in time (Brennan 1964; Eilon et al. 1966). This is because of statis-tical variations in the data on which the regression equations used for estimating repair and maintenance costs, and asset resale values were based. As the model developed in this study is susceptible to these same statistical variations, optimal economic life generated by the model described here should be treated in this same manner. 3.3.2 Sensi t ivi ty Analys i s Six input variables were examined to see how sensitive the solutions were to' their variation. Each of the selected input variables were set at various levels above and below the reference case. For each change in a selected variable, all other variables were held constant and the replacement age and Equivalent Annual Worth noted. The base or reference case was the input variables as described in Table 3.6 for CAT D8 Tractors. Results of the analyses are shown in figures 3.7 through 3.12 inclusive. Effect of Change i n Purchase Pr ice of Chal lenger The E A W is highly sensitive to changes in the purchase price of the challenger, while the optimum economic life is not. This effect on the E A W is in agreement with results obtained by Rotz, Black, and Savoie (1981) who noted that uniform annual equivalent costs were highly sensitive to changes in the purchase price of farm machinery. Chapter 3. RESULTS AND DISCUSSION Figure 3.8: Sensitivity of optimum life to change in the planning horizon Chapter 3. RESULTS AND DISCUSSION 60 Figure 3.10: Sensitivity of E A W to change in interest rate on financing Chapter 3. RESULTS AND DISCUSSION 61 Figure 3.12: Sensitivity of E A W to change in the V A C of the product Chapter 3. RESULTS AND DISCUSSION 62 Effect of Changes in the planning horizon Both the E A W and the optimum economic life of the defender are highly sensitive to changes in the planning horizon. This underscores the need for objective selection of a planning horizon, and demonstrates how models based on this concept can be useful in replacement analysis for one time investments. In projects with lifespans longer than the combined life expectancy of both ma-chines, realistic results are obtained by using planning horizons equivalent to the least common multiple of lives of the machines. This is because the model assumes a, single replacement over the planning horizon. In projects with very long lifespans, more than a single replacement may be most economical. The model developed in this study how-ever selects only the optimum combination of using the two machines over this period. This observation is supported by data from the sensitivity analysis. As the planning horizon gets longer, the E A W decreases substantially. A seven year increase in the planning horizon results in a reduction of E A W by up to 131%. This indicates that over such long horizons, more than one replacement should be considered. White et al. (1984) noted the pitfalls of selecting very long and very short planning horizons over which to evaluate economic alternatives. Selecting very short planning horizons commonly results in exclusion of alternatives whose major benefits are realized in the late stages of their service lives. When using very long planning horizons, cash flows developed on the basis of prevailing economic conditions may be invalidated as economic factors change with time. The analyses is better divided into periods of shorter planning horizons, over which economic variables would be relatively more uniform. Chapter 3. RESULTS AND DISCUSSION 63 Effect of Debt Arrangements The interest rate on debt incurred when purchasing the challenger has no effect on the economic life of the defender, and only a moderate effect on the E A W . The term of the debt, however, has a large effect on the E A W but a small effect on the optimum economic life of the defender. The effect of the term of the financing on the E A W can be explained in terms of its effect on interest payments. Short debt terms places greater demands on the equity of the owner of the asset, but results in a lower total interest payment. This may explain the initial increase in E A W with decreasing length of the debt term. With very long debt terms, however, the effects of total interest payments are outweighed by the low demands placed on equity by the debt. Effect of Value Added Cost of product The V A C of the product has no effect on the optimum economic life of the defender, but a very large effect on the E A W . This is expected as the V A C of the product determines revenues, while it has no effects at all on costs. The V A C will determine the profitability of the production process, but will not affect the replacement decision. The sensitivity of the variables examined in this analysis may differ significantly if they were set at levels different from the base case. This effect has been described by Fetter and Goodman (1957) and Rotz, Black, and Savoie (1981). Fetter and Goodman (1981) observed that at discount rates above 10%, estimated machine total costs were relatively insensitive to increases in it (the discount rate). Rotz, Black, and Savoie (1981) observed that sensitivity of costs to changes in the downpayment on an asset at purchase was very low, unless the interest rate on debt was equivalent to the discount rate. Chapter 3. RESULTS AND DISCUSSION 64 This analysis illustrates how the model can be used to determine the relative sen-sitivity of any of the cash flow variables to any particular replacement scenario. Chapte r 4 S U M M A R Y A N D C O N C L U S I O N S In this study, a discounted, after-tax cash flow replacement analysis model, which is suitable as a planning tool in projects with short and medium term lives, was developed. The model was then encoded and presented on a microcomputer spreadsheet. The spreadsheet program is interactive and can be used for evaluating replacement decisions by the defender/challenger method. It includes facilities for performing sensitivity analysis on any of the variables that affect cash flows of assets. A new method of estimating the annual rate at which machines accumulate technological obsolescence was developed and discussed. Methods of estimating other machine costs were also presented and discussed. The importance of optimal replacement of machines as a means of maximizing revenues in a production process has been extensively discussed (White et al. 1984; Riggs et al. 1983). This study attempted to develop a complete cash flow replacement model. The model takes into account the effects of discounting, taxes, and total machine costs. The model is useful for evaluating replacement proposals in projects with short to medium lives. The defender/challenger method of comparing investment alternatives was used in the model. This method permits comparison of machines with completely different cash flow profiles. This allows the investor to explore the feasibility of different replacement scenarios. For instance, the investor can study the feasibility of replacing the current machine with a similar one', or with another used machine, or with a completely different 65 Chapter 4. SUMMARY AND CONCLUSIONS 66 method of accomplishing the production function. This flexibility is a big advantage over classical replacement approaches, that only allow an investor to analyze when to replace the current machine with a similar one. A new method of estimating the rate at which machines accumulate technological obsolescence was developed in the study. The method bases the calculation on the fuel consumption and productivity of succeeding generations of machines. The method does not give an estimate of obsolescence due to reduced repair and maintenance ex-penditures of new machines, or of functional obsolescence. However the procedure is an objective one, that yields valid estimates of reduced operating costs resulting from reduced fuel consumption and increased productivity of new machines. Equations for estimating repair and maintenance costs were developed from histor-ical machine cost data. This method is similar to that used by Sinclair et al. (1986). The method requires a sufficient database of accurate cost records in order to yield accurate cost estimates. The accuracy of this method relies on the definition of repair and maintenance costs used when recording the costs. This inadequacy can be elim-inated by using a uniform definition of repair and maintenance costs when collecting data for the analysis. Resale value of machines used in this study were estimated by equations developed from data collected from machine auctions. Auction marts represent a more objective indicator of resale values than dealer quotes. This is because dealers mark up sale prices of used machines at different rates. Drinkwater and Hastings (1968) developed similar equations, but with data based on dealer surveys. Sinclair et al. (1986) developed an empirical method for estimating'machine resale values, based on data collected by a method similar to that of Drinkwater and Hastings (1968). The resale value/age equations developed in this study should be a better predictor of machine resale values than the methods developed by Sinclair et al. (1986) and Drinkwater and Hastings Chapter 4. SUMMARY AND CONCLUSIONS 67 (1968) because of the inconsistencies in data collected from dealers. Microcomputers and electronic spreadsheets have become popular tools for per-forming financial analysis in homes, educational institutions, and businesses. With the increasing availability and accessibility of personal computers and spreadsheet software, spreadsheet based programs will increasingly be used for financial evaluations. It was for this reason that the model developed in this study was encoded and presented on an electronic spreadsheet. This should increase its accessibility and use for evaluating replacement proposals at all levels. Bib l iog raphy [1] American Association of Agricultural Engineers (ASAE) , 1977. Machinery Man-agement data. A S A E , St Joseph, M I 49085 [2] American Association of Agricultural Engineers, 1983. A S A E Yearbook of Stan-dards and Technology 80's. A S A E , St Joseph, MI 49085.:196-209. [3] Barlow, Richard E . , undated. Planned Replacement. In. Studies in applied problem and management science. :63-87. [4] Bellemare, M . , 1982. Machine ownership cost. In. Pulp and paper Canada. 83(4):34-37. [5] Brennan, J . F. 1964. Optimum life of fleet automobiles. Journal of industrial en-gineering 15(6):297-301. [6] Caterpillar Tractor Co. , undated. Equipment Economics. Market Development Division, Caterpillar Tractor Co., Peoria, 111. 13pp. [7] Caterpillar Tractor Co., 1970-1986. Caterpillar Performance Handbooks, Editions 10-17. Caterpillar Tractor Co., Peoria, 111. [8] Clapham, J. C. R. 1957. Economic life of equipment. Operational Research Quar-terly 8(4):181-190. . [9] Demirdache, A. R., A. B. Howell, and T. R. Fowler'1968. Mathematical mod-els for motor vehicle replacement policies in the federal government. Canadian Operational Research Society. Journal 6(1):1-18. 68 Bibliography 69 [10] Dreyfus, S. E . 1960. A Generalized Equipment Replacement Study. Indus. Appl. Math. (3):425-435. [11] Drinkwater, R. W., and N . A . J. Hastings, 1968. An Economic Replacement Model. Operational Research Quarterly 18(2): 121-139 [12] Edge, C. G, and Irvine, V . B. , 1981. A practical approach to the appraisal of cap-ital expenditures. The Society of Management Accountants of Canada, Toronto, Ontario. [13] Eilon, S., J . R. King, and D. E . Hutchinson 1966. Study in equipment replacement. Operational research quarterly 17(l):59-71. [14] Elmaghraby, Salah A. , 1958. Probabilistic considerations in equipment replace-ment studies. The Engineering Economist 4:31pp. [15] Fetter, R. B. , and T. P. Goodman, 1957. An Equipment Investment Analog. Op-erations Research 5:657 - 669 [16] Forest Products Industries (FPI), 1960-1986. Master Agreement, Forest Products Industries Coast Region British Columbia. FPI , Vancouver, B .C. [17] Gourley, B. , 1987. Personal Communication. [18] Helmer, G. A . , and N . J . Watts, 1981. The Effect of inflation and Income tax on Machinery costs and optimum replacement. A S A E paper No. 81-1514. A S A E , St Joseph, MI 49085 12pp. , [19] International Equipment Exchange (IEE), 1986. The Last Bid. Construction equip-ment annual 1986. Vol. 20. International Equipment Exchange Ltd. 1580 pp [20] Komatsu L T D , 1981. Komatsu *Sales Mates. Komatsu Limited, Tokyo, Japan. Bi bliography 70 [21] Kozak, A . , 1966. Multiple Correlation Coefficient Tables up to 100 Independent variables. Research Notes, Faculty of Forestry, U . B . C . 2pp. [22] Kulonda, D. J . , 1978. Replacement analysis with unequal lives - The study period method. The Engineering economist, 23(3):171-180. [23] Logistics Management Institute (LMI), 1968. Guidelines for making repair expen-diture decisions. LMI . Task 68-6. L M I . , 4701 Sangamore Road, Washington D. C. 20016. 34pp. [24] Lusztig, P. A . , and W. F. J . Wood, undated. Financial Considerations, in the Optimal Equipment Replacement Policy. Faculty Of Commerce, U B C . 6pp. [25] McPhallen, J . C. 1975. Repair Expenditure Limits. Paper Submitted in Partial Fulfillment For Forestry 555. Faculty Of Forestry, U .B .C . 11pp. [26] Murchison, H . Gary, and J .C. Nautiyal 1971. When to replace a vehicle. Forestry chronicle 47(4 ):205-209. [27] Ogweno, D. C. O, 1986. A n Equipment Replacement Model in P A S C A L . Paper Submitted in partial Fulfillment for F R S T 532, Faculty of Forestry, U . B . C . 32p. [28] Peterson, C. L . , and J . H . Milligan, 1976. Economic Life Analysis for machinery replacement decisions. Transactions of the A S A E 19(5):819-822,826. [29] Riggs, J . L . , W. F. Rentz, and A. L. Kahl, 1983. Essentials of engineering eco-nomics. McGraw-Hill Ryerson Ltd., Toronto. 574 pp. [30] Rotz, C. Alan, J. R. Black, and P. Savoie. 1981. A Machinery cost model which deals with inflation. A S A E paper No. 81-1513. A S A E , St. Joseph, M I 49085-9659. Bibliography 71 [31] SAS Institute, 1982. SAS Users Guide: Statistics. SAS Institute Inc., Cary, N . C . 27511. :584pp. [32] SAS Institue, 1985. SAS Users Guide: Statistics. SAS Institute Inc., Cary, N.C. 27511. 600pp. [33] Schoney, R. A. , M . and F. Finner, 1981. The impact of inflation on used machine values. Transactions of the A S A E 24(2):292-295. [34] Shore, B. , 1975. Replacement Decisions under capital budgeting constraints. The Engineering economist, 20(4):243-256. [35] Sinclair, A . W. J . , M . L . Clark, and T. B . Wong, 1986. Two Replacement models for B . C . Coastal Logging Equipment. Forest Engineering Research Institute Of Canada. Technical Report No. T R 68, 34pp. [36] Statistics Canada, 1970-1987. The Consumer Price Index. Minister of Supply and Services, Ottawa. Stats. Can. Reports No. 62-001 (38)1 to (65)4. : • [37] Tufts, R. A. , and J . A . Hitt, 1983. Failure Cause, Frequency and Repair for Forest Harvesting Equipment. Transactions of The A S A E 26(6):1673-1677. [38] Ward, S. M . , P. B. McNulty, and M . B . Cunney. 1985. Repair costs of Two and Four Wheel Drive Tractors. Transactions of the A S A E 28(4):1074-1076. [39] Wellwood, E.W., and Sinclair, A . W . , 1972a. Save:- A Brief overview of the Save program. C A N F O R Co., Van. . • . ' ^ [40] Wellwood, E.W., and Sinclair, A . W . , 1972b. Save:- Englewood Replacement Guide - 1973. C A N F O R Co. Van. l l p p Bibliography 72 [41] White, J. A . , M . H. Agee, and K . E. Case, 1984. Principles of engineering economic analysis, 2nd Ed. John Wiley & sons, N . Y . 546pp. [42] White, K . J., Horsman, N . G., 1986. S H A Z A M - The Econometrics Computer pro-gram. User's Reference Manual Version 5.1. Dept. Of Econ., University of British Columbia, Vancouver. 291pp [43] White, K . J. , Horsman, N . G., Wyatt, J . B. , 1986. S H A Z A M - Computer Hand-book for Econometrics. Dept. of Econ., University of British Columbia, Vancouver. 182pp [44] Wong, Tony B. , 1987. Personal Communication. A p p e n d i x A The M i c r o c o m p u t e r Spreadsheet M o d e l A . l Pro jec t software and hardware The replacement analysis model developed in this study was incorporated into a mi-crocomputer spreadsheet that can be used for analyzing replacement decisions. The microcomputer was an I B M 1 personal computer, which is based on the I N T E L 2 8088 microprocessor. It was equipped with 640K of Random Access Memory (RAM) , and was operating under the Microsoft Disk Operating System (MS-DOS) 3 version 2.10. This microcomputer and disk operating system is currently in widespread use, which should make the program readily portable and accessible as an aid to making replace-ment decisions. The spreadsheet program used in this study was Lotus S Y M P H O N Y 4 . It is a close but more powerful relative of Lotus 1-2-3 5 , with sophisticated windowing, database, graphics, communications, spreadsheet and programming functions 6 . It has a 8192 row by 256 column spreadsheet, which can be viewed through user defined windows. It is equipped with a powerful command language (macros) which can be programmed into applications with pull down menus and graphics routines. The spreadsheet, command language (macros), and graphics functions available in Symphony were used to program 1Copyright ©International Business Machines Corp, Lexington, KY 2Copyright ©Intel Corp., Santa Clara, CA. 3Copyright ©Microsoft Corp., Bellevue, WA 4Copyright ©Lotus Development Corp., Cambridge, MA 5Copyright ©Lotus Development Corp, Cambridge, MA 6Cobb, D., 1985. Mastering Symphony. Sybex Computer books, Berkely, CA 73 Appendix A. The Microcomputer Spreadsheet Model 74 a replacement analysis program " E Q U I P R E P " , based on the cash flow model developed in this study. A .2 The E Q U I P R E P P r o g r a m The cash flow analysis model developed in this study was programmed in the Symphony command language (macros) into an interactive spreadsheet program, that can be used for analyzing machine replacement proposals. Figure A.13 shows the flow of logic of the E Q U I P R E P program, and Figure A. 14 is a schematic representation of how the program is organized in windows. The program is organized in nine windows: an Input/Output (I/O) window, a macro (MACROS) window, a work ( W O R K ) window, a utility macros (UTILMACS) window, a variables (VARS) window, two introduction windows (INIT and INTRO), a Graph ( G R A P H ) window, and a H E L P window. Most inputs to and outputs from the program are done in the Input/Output inter-face of the I /O window. The data variables for both the defender and the challenger are entered and modified in this window. Once any variable is entered or modified in the I /O window, all modules in the other windows dependent on it are automatically modified and updated. The program outputs to the user the Equivalent Annual Worth of the optimum combination of operating the defender and challenger over the planning horizon, and recommends the optimum age at which the defender should be replaced. Sensitivity analysis can be performed on the data by entering and altering values of the required variables or parameter in the I/O window. A l l the revenues, costs and other* required cash flow information are computed in the W O R K window. The costs and revenues are generated and organized in look-up tables in this ( W O R K ) window. The use of look-up tables was considered particular Appendix A. The Microcomputer Spreadsheet Model 75 I/O WINDOW DISC./ INTER. RATES PURCH. COST AND DEBT DATA INPUT / OUTPUT INTERFACE REPLACEMNT. DECISION TOTAL COST LOOK-UP TABLES TOTAL DEDUCTIBLE COSTS UEV AFTER-TAX CASH-FLOW TAXABLE REVENUE GROSS REV. LOOK-UP TABLES WORK WINDOW Figure A . 13: Logical Flow Diagram of the E Q U I P R E P program Appendix A. The Microcomputer Spreadsheet Model 76 I/O WINDOW A1 .. H22 INTRO WINDOW A30 .. H60 INIT WINDOW A61 .. H82 VARS WINDOW A100 .. H124 HELP WINDOW A125... H150 MACROS WINDOW A151 .. M229 ' UT1LMACS WINDOW A230 .. H250 PRINTER WINDOW A251 .. A400 WORK WINDOW 11 . . CZ75 Figure A. 14: Schematic Diagram showing how the program is organized in windows Appendix A. The Microcomputer Spreadsheet Model 77 appropriate because of Symphonys excellent look- up functions, and because they hide the computations from the user, making the program much friendlier and easier to use. The look-up tables however have the disadvantage of making the code difficult to develop and maintain. The V A R S window contains the cells used by E Q U I P R E P as temporary storage for variables required in the computation of costs and revenues, but which would only clut-ter the I /O and W O R K windows. The U T I L M A C S window contains macros for moving around, organizing and editing the spreadsheet, while the M A C R O S window contains the main E Q U I P R E P driver program and subroutines. When using the model, a user interacts only with the Input/Output interface in the I/O window. A l l computations and look-ups are done and hidden way from the user in the W O R K and V A R S win-dows. The G R A P H window is attached to the worksheet, and displays a graphical plot of the cash flows. The INIT and INTRO windows contain messages which introduces the program to the user every time a new analysis session is commenced. The H E L P window contain help messages which can be called up from any part of the program. The E Q U I P R E P user's manual is included in Appendix B. A p p e n d i x B E Q U I P R E P User 's manual B . l In t roduc t ion E Q U I P R E P is a program for analyzing equipment replacement proposals. It is designed for use in analyzing the feasibility of replacing a currently owned machine (the defender) with another (the challenger) with the aim of maximizing net revenues over a specific period. The program was developed on Lotus Symphony1 microcomputer spreadsheet, and is based on the cash flow model developed in this study. The program is an interactive and self documenting one, with multi windows and menus. This manual is intended as a reference on how to run the E Q U I P R E P program. For definitions of the cost and revenues used in the program, and how they can be derived and estimated, the user is referred.to the main text of the study. Symphony spreadsheet functions and operations are sufficiently described in the Symphony Reference Manual and other user documentation, and are not covered here. B.2 Sys tem Requirements The E Q U I P R E P program was developed on Lotus Symphony integrated software pack-age, running on an I B M personal computer2. The program will run on any I B M P C or truly compatible machine. The following, are the minimum system configuration required to run the program. 1Copyright ©Lotus Development Corp., Cambridge M A 2Trade Mark, International Business Machines, Lensington, K Y 78 Appendix B. EQUIPREP User's manual 79 1. I B M P C , X T , A T , PS2 or true Compatibles, with; • 640K minimum of Random Access Memory, of which at least 512K is avail-able for application programs ; • Monochrome, color, or black and white monitor with graphics capability, and; • Two floppy disk drives or one floppy and one fixed disk drive. 2. Lotus Symphony integrated software package, Release 1.00 and above, and; 3. M S / P C Disk Operating System (DOS) Version 2.1 and above In addition to the hardware and software requirements, a basic knowledge of mi-crocomputer spreadsheet operation, especially of Lotus Symphony, is required and assumed. A basic knowledge of machine cost analysis and replacement theory is also assumed. In addition, a basic understanding of regression analysis is also required. Access to a statistical software package, with capabilities for performing multiple re-gression analysis will be an advantage for processing the data required as inputs to the program. B . 3 Files on the d i s t r ibu t ion diskette The distribution diskette contains two files necessary for running the E Q U I P R E P pro-gram. These files are: E Q U I P R E P . W R K This is the main program worksheet file, and; T E M P L A T E . N E W This is a template for the analysis of new replacement propos-als. Appendix B. EQUIPREP User's manual 80 Only one of the two files is required to run the E Q U I P R E P program at any one time. B . 4 Setting up the program The E Q U I P R E P program is set up by copying both files on the distribution diskette to the default directory as installed in the Symphony configuration file ( S Y M P H O N Y . C N F ) . This should be a subdirectory on a hard disk drive, or the second drive on a two drive system. This is the directory that contains your Symphony * . W R K files. B.5 Running the program The E Q U I P R E P program is run in the S H E E T environment within Symphony. To run the program, Symphony must first be loaded from the DOS command prompt. Once in the Symphony S H E E T environment, load E Q U I P R E P by selecting E Q U I P R E P . W R K as the file option in the [Services-File-Load]3 command. Once the program is loaded, the user is presented with two start-up screens, which describes the major functions of the program and some of its features. When [Return] is pressed, the start-up screens are replaced with the I/O window. This is the window that the user mainly interacts with when running the program. The window will currently be displaying the cash flow and replacement information of the last replacement analysis session. It should be noted the cash flow information displayed from any analysis is specific to the machines evaluated in that analysis. Using such data for a different set of machines will lead to erroneous results. Once the file is loaded and the user is in the I /O window, the analysis can be started. 3In this manual, Symphony and EQUIPREP commands will be shown enclosed, and separated by hyphens [in-this-manner] Appendix B. EQUIPREP User's manual 81 B.5 .1 The E Q U I P R E P menu and H E L P facilities The E Q U I P R E P program has a multilevel menu structure. The main menu calls sub menus which in turn call other sub menus as necessitated by the selected menu option. The menu options are displayed in the first line of the Symphony control panel, and functions of the highlighted option are explained in the second line of the control panel. Menu choice selections is done in the same way as in the Symphony SHEET environment. To exit from any menu level, press [Escape]. Note however that aborting a menu action with this key sequence may cause the program to make a window that is undesired the active one. In such a case, the [alt-I] key sequence will make the I/O window the active one. E Q U I P R E P has a help facility, which provides directions on how to move between windows, exit, and on how to invoke the menu. The help facility can be invoked from any window by pressing the [alt-H] key combination. B .5 .2 S ta r t ing a new analysis A new replacement analysis can be started in two different ways, with the same result: 1. By loading the main E Q U I P R E P file, and then selecting the N E W option in the main menu of the E Q U I P R E P environment, or: 2. By loading the file T E M P L A T E . N E W from the Symphony environments [Services-File-Load] command. In either case a new E Q U I P R E P template file will be loaded, and the user is ready to commence a new analysis. The I/O window will be displaying the required cash flow information, with the appropriate sections (to the right of the Variable descrip-tions/name) blank. T=h«_xepia^emen^-~a^e-a*dH^ Note that Appendix B. EQUIPREP User's manual 82 when loading a template, the file T E M P L A T E . N E W must be in the default directory. B.5.3 Inputs i n the I / O W i n d o w When E Q U I P R E P is loaded, the I/O window will display the cash flow information from the last replacement analysis session. When a new template is loaded, however, the cash flow information specific to individual machines is left blank. The user can enter any of the necessary information in the appropriate spaces. This is done by entering the values in the allocated space, and then using the cursor pad direction keys to move to the next variable. To modify any of the information in the window, move to the applicable cell and overtype the previous data. A l l variables have been formatted to reflect the units of measure (%, $, etc.). As a result, the information must be entered in specific formats, as described below. Purchase price Entered in dollars, with no commas. For example, the price $320,000 is entered as 320000 Discount / In te res t and Tax rates Discount, Interest, C C A , Tax and Insurance rates are all entered in decimals. The C C A rate displayed as 30% is entered as 0.30. Costs and Revenues A l l costs and revenues displayed in formatted form as dollars are entered as values without the ($) sign or commas, as is done for asset purchase price. Equ ipmen t age This refers to the age of the defender (in years) at the time the replacement analysis is performed, and to the age of the challenger at the time it is purchased. 0 (zero) is the age of a brand new machine. Appendix B. EQUIPREP User's manual 83 B.5.4 Other Inputs The only inputs which are entered in the W O R K window are: • Repair and maintenance regression coefficients, • resale value regression coefficients, • The annual obsolescence rate, and; • The Investment Tax Credit rate These inputs are entered in the W O R K window within the E Q U I P R E P environ-ment. This is done by calling the main E Q U I P R E P menu and then selecting the [Inputs] option. The program will then make the W O R K window the active one, and move the cursor to the section of the W O R K window containing cells with the required variables. The values can then be modified by moving over to the applicable cell and overtyping the previous data. In the program, it is assumed that the coefficients for predicting repair and main-tenance costs and for machine resale values represent the estimates for variables in the functional forms described in Chapter 2.5.2. Once the required variables have been entered or modified in the W O R K or I /O windows, the user must initiate recalculation of the worksheet by pressing Symphonys ( R E C A L C ) key, [F8]. This is because auto recalculation of the E Q U I P R E P worksheet is always set to [OFF]. Auto recalculation of the worksheet was set to off to minimize the time between entry/change of each required variables, which can be up to two minutes on slower machines when automatic recalculation is on. The ( R E C A L C ) key will recalculate the worksheet and display the new cash flow and replacement information. Appendix B. EQUIPREP User's manual 84 B.5.5 V iewing Graphical Plots of the Cash Flows Graphical plots of the combined cash flow profiles of both machines are automatically-plotted once any variable is entered or modified. The graphs are attached to a graph window, which can be viewed by invoking the E Q U I P R E P menu, and then selecting the [Graph] option. This command will make the G R A P H window active. To print the graph on an external device, however, the file must be saved and then printed with the P R I N T G R A P H program. For details of how to use the P R I N T G R A P H program, reference is made to the Symphony Reference manual 4. To exit from the G R A P H window and return to the I/O window, press [alt-I]. The G R A P H window can also be made active from anywhere in the E Q U I P R E P environment with the [alt-G] key combination. B.5.6 Pr int ing The output The program output can be printed by selecting the [PRINT] option in the menu. This action will cause the program to print all the variables and the output displayed in the I /O window. Printed graphical outputs of the cash flow must be made with the P R I N T G R A P H program supplied with Symphony. B.5.7 Saving the current worksheet The worksheet can be saved with the [File-Save] option in the E Q U I P R E P menu. This option saves files by invoking Symphonys [Services-File-Save] command. Care has to be taken when saving files opened by the E Q U I P R E P [New] option. This is because Symphony will make the input file the default when saving, and may lead to overwriting of the template file. 4 Lotus Development Corporation, 1984. Symphony Reference Manual. 101 First Str. Cambridge, M A 02142 Appendix B. EQUIPREP User's manual ,85 B . 5 . 8 Ex i t ing the program There are two menu choices for exiting the program. The [Quit] option will cause the program to exit out of the E Q U I P R E P environment and out of Symphony. The [To-Symphony] option quits E Q U I P R E P and opens a new worksheet file in the Symphony S H E E T environment. At any point in the program, the user can exit by pressing [alt-Q]. Appendix C Description of the Cost Minimiz ing Model The cost minimizing model used to develop the results which were compared to those from the model developed in this study is described by Edge and Irvine (1981), Ogweno (1986) and Sinclair et al. (1986). In this model, the combined cost of owning and operating an asset are obtained in the following manner. Repair and maintenance costs are calculated from cumulative repair and mainte-nance regression equations developed in this study. The costs are then treated for tax effects, and discounted as shown by equation [C.22]. ^ = ( 1 - C ) * E ( ^ - W * 7 j ^ j 7 (C.22) where '•• R y = Cumulative RSzM cost to year y C =-Income Tax rate r = discount rate Ownership costs are considered to be comprised of depreciation, interest and in-surance charges. Depreciation charges were obtained from the resale value regression equations, then converted to after tax present value costs according to the equation [C.23] below. 86 Appendix C. Description of the Cost Minimizing Model 87 Dy = P- . M \ * CTF (C.23) (i + r)y where Dy = cumulative after tax depreciation charge in year y P — Equipment purchase price My = Market value of equipment at age y CTF = Capital Tax factor, calculated as: CTF = 1 — 1^^+^) Insurance costs is a component of the annual ownership cost of the equipment, and is calculated for each year (y) according to equation [C.24]. jr{ 2 V J (1 + r)' V • where Iy = Cumulative after tax cost of insurance up to year y i = annual insurance rate C = income tax rate Mj,Mj_! = resale value of asset in years j and (j — 1) respectively The cumulative after tax present value combined cost of repair and ownership for each year is then the sum of annual repair and maintenance, insurance, and depreciation costs (equation [C.25]). Cy=Ry + Dy + Iy (C.25) Applying a capital recovery factor to the combined costs yields the Uniform Annual Equivalent Costs (UAE) according to equation [C.26]. Appendix C. Description of the Cost Minimizing Model 88 UAEy = Cy * CRF (C.26) where The optimal replacement Time is then the year yielding the minimum Uniform Annual Equivalent Cost. A p p e n d i x D Resul ts of SHAZAM™ A U T O procedure regressions D .1 Ca te rp i l l a r D8 t ractor regressions D . l . l O r d i n a r y Least squares procedure Results of the Ordinary Least Square (OLS) procedure are in Table D.10. Other statistics are as follows: • Durbin-Watson Statistic = 0.77 • Rho (p) = 0.62 Conclusion: There exists a positive Autocorrelation between the variables. D.1 .2 F i r s t order autocorrela t ion procedure Results of the first order autocorrelation procedure are shown in Table D . l l . Further relevant regression statistics are: Table D.10: C A T D8: Ordinary Least Squares procedure, No regression constant Source of Error SS D F MS R2 Regression 0.45510E+12 2 0.22755E+12 0.719 Error 0.64819E+11 149 0.43503E+09 Total 0.51992E+12 151 0.34432E+10 89 Appendix D. Results of SHAZAM™ AUTO procedure regressions 90 Table D . H : C A T D8: First order autocorrelation proc, No regression constant Source of Error SS D F MS R2 Regression Error Total 0.48055E+12 0.39376E+11 0.51992E+12 2 149 151 0.24027E+12 0.26427E+09 0.34432E+10 0.8294 2: C A T D8: Second order autocorrelation proc, No regression Source of Error SS D F MS R2 Regression Error Total 0.18492E+12 0.38490E+11 0.22341E+12 2 149 151 0.92462E+11 0.25833E+09 0.14796E+10 0.833 • Durbin-Watson statistic = 1.80 • Rho (p) = 0.10 D.l.3 Second order autocorrelation procedure The second order autocorrelation regression was performed by an iterative Cochrane-Orcutt type procedure. The regression statistics are given in Table D.12 and further relevant statistics are included below: • Durbin-Watson statistic = 2.01 • Rho (p) = -0.01 Conclusion: The positive autocorrelation has been effectively removed by the second order AUTO procedure. Appendix D. Results of SH AZ AM™ AUTO procedure regressions 91 Table D.13: C A T 966: Ordinary Least Squares proc, No regression constant Source of Error SS D F MS R2 Regression 0.31591E+11 2 0.15795E+11 0.90 Error 0.14166E+10 52 0.27242E+08 Total 0.33007E+11 54 0.61125E+09 Table D.14: C A T 966: First order autocorrelation proc, No regression constant Source of Error SS D F MS R2 Regression 0.32171E+11 2 0.16086E+11 0.8294 Error 0.83625E+09 52 0.16082E+08 Total 0.33007E+11 54 . 0.61125E+10 D . 2 Ca te rp i l l a r 966/980 F E L regressions D.2.1 O r d i n a r y Least squares procedure Table of results of the Ordinary Least Square (OLS) procedure are in Table D.13. Other statistics are as follows: • Durbin-Watson Statistic = .73 • Rho (p) = 0.65 Conclusion: There exists a positive Autocorrelation between the variables. D.2 .2 F i r s t order autocorrelat ion procedure Results of the first order autocorrelation procedure are shown in Table D.14. Further regression statistics are: • Durbin-Watson statistic =1.66 Appendix D. Results of SHAZAM™ AUTO procedure regressions 92 Table D.15: C A T 966: Second order autocorrelation proc, No regression constant Source of Error SS D F MS R2 Regression 0.11790E+H 2 0.58952E+10 0.95 Error 0.78699E+11 52 0.15134E+08 Total 0.12577E+11 52 0.23291E+09 • Rho (p) = 0.16 D.2.3 Second order autocorrelation procedure The second order autocorrelation regression was performed by the Cochrane- Orcutt type procedure. The regression statistics are in Table D.15 and further statistics are included below: • Durbin-Watson statistic = 1.95 • Rho (p) = -0.02 Conclusion: The positive autocorrelation has been effectively removed by the pro-cedure. Appendix D. Results of SR AZ AM™ AUTO procedure regressions 93 Table D.16: Results of the A l l Combination Regression procedure for repair and main-tenance costs of C A T 966 F E L N U M B E R IN R - S Q U A R E V A R I A B L E S IN M O D E L M O D E L 1 0.6981 USE5 1 0.7987 USE4 1 0.8985 USE3 1 0.9121 USE 1 0.9619 USE2 2 0.9457 USE USE5 2 0.9481 USE4 USE5 2 0.9509 USE USE4 2 0.9571 USE USE3 2 0.9621 USE3 USE5 2 0.9635 USE USE2 2 0.9655 USE3 USE4 2 0.9657 USE2 USE3 2 0.9662 USE2 USE4 2 0.9664 USE2 USE5 3 0.9633 USE USE4 USE5 3 0.9656 USE USE3 USE5 3 0.9665 USE2 USE4 USE5 3 0.9665 USE USE3 USE4 3 0.9666 USE2 USE3 USE5 3 0.9669 USE2 USE3 USE4 3 0.9670 USE. USE2 USE5 3 0.9672 USE USE2 USE4 3 0.9673 USE USE2 USE3 3 . 0.9682 USE3 ' USE4 USE5 4 0.9673 * USE USE2 USE3 USE4 4 0.9673 USE USE2 USE3 USE5 4 0.9676 USE USE2 USE4 USE5 4 0.9676 USE USE3 USE4 • USE5 4 0.9691 USE2 USE3 USE4 USE5 5 0.9704 USE USE2 USE3 USE4 . USE4 Appendix D. Results of SHAZAM™ AUTO procedure regressions 94 Table D.17: Results of the A l l Combination Regression procedure for repair and main-tenance costs of C A T D8 tractors N U M B E R IN R - S Q U A R E V A R I A B L E S IN M O D E L M O D E L 1 0.4609 USE5 1 0.5661 USE4 1 0.6962 USE3 1 0.8276 USE2 1 0.8685 USE 2 0.7739 USE4 USE5 2 0.8188 USE3 USE5 2 0.8356 USE3 USE4 2 0.8612 USE2 USE5 2 0.8658 USE2 USE4 2 0.8707 USE2 USE3 2 0.8736 USE USE5 2 0.8744 USE USE4 2 0.8753 USE USE3 2 0.8764 USE USE2 3 0.8672 USE3 USE4 USE5 3 0.8744 USE2 USE4 USE5 3 0.8753 USE2 USE3 USE5 3 0.8756 USE2 USE3 USE4 3 0.8758 USE USE4 USE5 3 0.8763 USE USE3 USE5 3 0.8765 USE USE3 USE4 3 0.8767 USE USE2 USE5 3 0.8768 USE USE2 USE4 3 0.8768 USE USE2 USE3 4 0.8759 USE2 USE3 USE4 USE5 4 0.8769 ! * USE USE2 USE3 USE4 4 0.8769 USE USE2 USE3 USE5 4 0.8770 USE USE2 USE4 USE5 4 0.8772 USE USE3 USE4 USE5 5 0.8774 USE USE2 USE3 USE4 USE4 A p p e n d i x E Machine age/resale value equations V -In this study, the resale value of machines was estimated by equations obtained from regression analyses. The regression analyses were performed as described in Section 2.5.2, and A N O V A tables of the regressions are in tables 3.5 and 3.6. The coefficients of variables in the linear model and the relevant regression statistics are in Table E.18 95 Appendix E. Machine age/resale value equations 96 12.318 12.236 12.154 12.072 11.990 11.908 11.826 11.744 11 .662 579 11 11 1 1 1 1 1 1 1 1 497 415 333 251 169 11.087 11.005 10.923 10.841 10.759 10.677 10.595 10.513 10.431 10.349 10.267 10.185 10.103 10.021 9.9385 .8564 . 7744 .6923 .6103 .5282 9.4462 9.3641 9.2821 9.2000 M M * M * M M M M M M M M M M M M M M M M M M M M M M • M M M M M * M M M M M * « * » M * M M M M M • M M M * M M M M M M M * * * * * * M M M M * M * M * • * * * * * M • M 0.0 3.000 6.000 9.000 12.000 15.000 18.000 21.000 AGE Figure E.15: Resale value/Age scatter plots for C A T D8 tractors Appendix E. Machine age/resale value equations 97 0.23385E+0B 0.22769E+06 0.22154E+06 0.21538E+06 0.20923E+06 0.20308E+06 0.19692E+06 0.19077E+06 0.18462E+06 0.17846E+06 0.17231E+06 0.16615E+06 0.16000E+06 0.15385E+06 0.14769E+06 0.14154E+06 0.13538E+06 0.12923E+06 0.12308E+06 0.11B92E+06 0.11077E+06 0.10462E+06 98462. 92308. 86154. 80000. 73846 . 67692. 61538. 55385. 49231 .. 43077. 36923. 30769. 24615. 18462. 12308. 6153.8 -0.57298E-10 M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M * M M M M M M M M M M M M * * * M * M * M * * 0.0 3.000 6.000 9.000 12.000 15.000 18.000 21.000 AGE Figure E.16: Resale value/Age scatter plots for C A T D966 tractors Appendix E. Machine age/resale value equations 98 Table E.18: Machine age/Resale value Regression statistics Machine Variable Name Estimated Coefficient Standard Error C A T D8 Age Constant -0.16571 12.960 0.011805 0.0 C A T 966 Age Constant -0.092383 11.810 0.03232 0.036161 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0097810/manifest

Comment

Related Items