Economic Evaluation and Investment Decision Methods

Economic Evaluation and Investment Decision Methods Tenth Edition

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FRANKLIN J. STERMOLE PRopEssoR EuERrrus,

Colonaoo Scsoor_ op MrNrs CHarRrrtnN, INvnsrnr ENr EveLuarroNs CoRpoRetrorv JOHN M. STERIVIOLE

IxslirucroR. ColoRaoo Scuoor_ or. N{rNas AoruNcr [,Ror,ESSon, UrurvERsny op DeNvER

Col_lecr op Law

PRnsroeNt INvEsrlrpNr EvaluertoNs CoRpoRartoN

INVESTMETTIT EVALUATIONS CORPORATION 3070 South Newcombe Way Lakewood, Colorado 90227

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Franklin J. Stermole,8.S., M.S., Ph.D., Chemical Engineering, Iowa State University, is Professor Emeritus of Mineral Economics and Chemical and Petroleum Refining at Colorado School of Mines where he has taught since 1963. Frank also serves as Chairman of Investment Evaluations Corporation. He has taught economic evaluation techniques for over 30 years tri undergraduate and graduate students and has done economic evaluation consulting for numerous mineral and non-mineral companies. Since 1970 when the first short course was prcsented, Frank has taught more than 650 "Economic Evaluation" short courses to over 16,000 persons from mineral and nonmineral industry companies and govemment agencies. In addition to the United States these courses have been presented in Armenia, Australia, Canada, Colombia, Egypt, France, Germany, Great Britain, Guyana, Indonesia, Kazakhstan, Kuwait, Mexico,

Norway, Philippines, Saudi Arabia, S-outh Africa, Trinidad and Venezuela. This domestic and foreign industrial consulting and teaching experience has had a direct eft'ect on the applications-oriented content and organization of the text. John N{. Stermole, B.S.B.A., Finarce, University of Denver, and M.S., Mineral Economics, Colorado School of Mines, is President of Investment Evaluations Corporation. Since 1988 John has taught as an Instructor at Colorado School of Mines for the Departments of Mineral Economics, Chemical And Petroleum Refining Engineering and Environmental Sciences. John has also served as a Fellow to the Institute for Globai Resources Policy at Colorado School of Mines, and was co-author in the 1st Edition of the Global Mining Taxation Comparative Study. Since 1997 John has also taught as an Adjunct Professor at The University of Denver, College of Law in the Natural Resources and Environmental Law Program. John has presented more than 250 "Economic Evaluation" short courses for mineral, petroleum and non-mineral companies and govemment agencies. In addition to the United States, these courses have been presented in AustrrLlia, Canada, Chile, Colombia, Indonesia, South Africa, Srvitzerland and the United Arab Emirates. Prior to joining Investment Evaluations Corporation on a full tirne basis, John gained three years of industry experience with

Loq,dermilk Construction of Englewood, Colorado, applying economic evaluation techniques to heavy construction projects related to mine site development and highwiiy construction, and in replacement analysis.

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This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold with the understantling that neither the authors nor the publisirer is engaged in rendering legal, accounting, tax, futures/securities tnding, or other professional services. If legal advice or other expert assistance is required, the services of a competent professional person should be sought.

From a Declaration of Principles jointly adopted by a Committee of tlte American Bar Association and a Committee of Publishers.

Trademarks:

Microsoft Excel is a registered trademark of Microsoft Corporation. I{Pl0B, HP12C, HPITBII are registered trademarks of Hewlett Packard Company. E\A is a registered trademark of G. Bennett Stewan IIL

Copyright @ 2000 by Investment Evaluations Corporation 3070 South Newcombe Way, Lakewood, CO 80227 USA Ph: 303-984-9954 Fx: 303-984-9895 Web site: www.sterrnole.com Earlier Editions Copydght @ 1996,1993,1990,1987, 1984,1982,1980, 1977 md 1974

By Investment Evaluations Corporation

All rights reserved. No Part of This Text May be Reproduced in Any Form Without Permission in Writing from Investment Evaluations Corporation ISBN r-878740-09-1 Library of Congress Control Number 00-134613 Printed in the United States of America

TABLE OF CONTENTS

t Page

CHAPTER 1: INVESTMENT DECISION MAKING

l.l 1.2 1.3 1.4 1.5 .6 1.7 1

Introduction to Investment Analysis "Engineering Economy" and "Economic Evaluation" Making Decisions Definition of Discounted Cash FIow Analysis Example of Discounted Cash Flow Minimum Rate of Return/Opportunity Cost of CapitallDiscount Rate InvestmentAnalysis

I 3

4 6 9

t2 t3

CHAPTER 2: COMPOUND INTEREST FORMULAS

2.1 2.2 2.3

2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.1

1

Introduction to Equivalence Compound Interest Formula Derivations and Illustrations Nominal, Period and Effective Interest Rates Based on Discrete Compounding of Interest Nominal, Period and Effective Interest Rates Based on Continuous Compounding of Interest Applications of Compound Interest Formulas 'Add-On" or "Flat" Interest (Applied to the Rule of 78) "Loan Points" and Buying Down Interest Arithmetic Gradient Series Alternative Time Line Diagrarn and the Concept of Cash Flow Introduction to Rate of Return Analysis Summary

15 L6

26 29 36

4t 44 46 49

5l 52

CHAPTER 3: PRESENT, ANNUAL, AND FUTURE VALUE, RATE OF RETURN AND BREAK-EVEN ANALYSIS

3.1 3.2 3.3 3.4

3.5 :1.6 3.7 3.8 3.9

3.10 3.I

I

lntroduction

62

Break-even and Rate of Return (ROR) Calculations Using Present, Annual and Future Worth Equations Rate of Return and Cumulative Cash Position Alternative Methods to Obtain Annual Value From Initial Cost, C

63 72

and Salvage, L Rate of Return on Bond Investments Rate of Return Related to T-Bill Discount Rates Financial Cost of Capital vs Opportunity Cost of Capital Rate of Return and the Revenue Reinvestment Question Growth Rate of Return Net Present Value, Net Annual Value, and Net Future Value lMethods of Analysis Benefit-Cost Ratio and Present Value Ratio

3.12 Etfect of Income Producing Project Life on Project Economics 3.13 Mineral and Petroleum Project Analysis 3.14 ROR, NPV and PVR Analysis of Service-Producing Investments 3. I

5

3.1

6

With Equal Lives Present, Annual and Future Cost Analysis of Service-Producing Investments With Equal Lives Comparison of Unequal Life Alternatives that Provide the Same Service tv

80 82 86 8'7

93 98

r03 112 122 124

r32 t36

t39

117 i.18

Comparison of Service-Producing Alternatives that Provide Diflerent Service Summary

CHAPTER 4: NIUTUAI-L\. EXCLUSIVE AND NON.MLiT{;ALLY EXCLUSIVE PROJECT ANALYSIS

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i

1? :t.-3

t

Anall sis lvlutuaiiy Exclusive Irrct,nre pr.or]gci1g Aftcrnatiyes 'ri Using Rrle oi Return. Net Value antj Ratios

Life Nlutuarly Excrusive rncome-protJucing Arternative Analysis r\lutually Excrusive Inr.esrment Analysis using Gr.ivth n^i. nrir." erid Fulure \\brth profit Methods "r Llnequal

.+.-i Changing rhe Minimum Rare of Return With Time -i 5 Diftbrences Between Net Value Analysis and Cost Analysis .1.6 Efl'ect of Evaluation Lit'e on Economic Analt sis Results Investment Analysis When lncome or Savings precedes Cost 11 Alternating Investmenr, Income, Investrnent: The problem 1I 1.9 Alternating Income, Investment, Income SituationsDuar Rate of Return

4.10

4.ll

144 148

Evaluation of Non-lVlutually Exclusive Investments Summary of Mutually Exciusive and Non_Mutually Exclusive

,\lternativc Anall sis

164 170

t82 185 189 193

t94 201 219

221 234

CHAP,IER 5: ESCAL,\IED AND CONSTANT DOLLARS

5.1 1? 5.3

Inflation and Escalariou in Econornic Anulvsis Exchange Rate Et{ecrs on Escalarion and iash Flow Analysis Summary

246 271 276

CHAPTER 6: UNCERTAINTY AT{D RISK ANALYSIS

I Introduction Anail sis to Analyze Efl'ects ol.Uncerrainty I : Scnsiriviry n I ]hg Ralrre Approach to Sensiriviry AnalS.sis 5.,1 Prob:rbilisricScnsitivityAnalvsis 6 5, Expected \hlue Analyiis (Economic Risk Analysis) Expecred NPV, Expected pVR, and Expected ROR 99 6-7 Probability of Survival (Financial RiskAnalysis) Analysis 6.8 Risk Due to Natural Disaster 6.9 Option Pricing Theory Related to ENpV 6.

6.10

Summary

282 284 287 288

296 299 311

Jl-1 315

320

CHAPTER 7: DEPRECIAIION, DEPLETION, AMORTIZATION AND CASH FLOW

7.1 7.2 7.3 7.,1 75

Introduction

After-Tax Cash Flow in Equation Form Business Costs That May be Expensed Depreciation L)epreciation N{ethotls 7.5a Straight Line Depreciation 7.5b Declining Balance Depreciation !2, S-witching liom Declining Balance to Straight Line Depreciation 7 .5d Units of Production Depriciation 7'-5e Modified Accelerated cosr Recoverv System (ACRS) Depreciation Election to Expense Limired Depreciabie Costs 79 7.7 Depletion Methods 7.7a Cost Depletion 7.7h PercenrageDepletion

326 328

330 335 337

340 a^1

343 344 350 3s0 351

352

.8 '.9 '.10

'.ll

Amortization

357

Royalties, Production Payments, Severance and Property Taxes Four Investor Financial Situatlons'That Affept Caqh Flow Calculatig.ns

361

Introduction Forms of Business Organizations and Tax Considerations Corporate and Individual Federal Income Tax Rates Corporate and Individual Capital Gains Tax Treatment Tax Treatment of Investment Terminal (Salvage) Value Alternative Minimum Tax Effective Tax Rates for Combined State and Federal Income Tax

8.10 8.1

I

8.12

Tax Credits Discounted Cash Flow Rate of Return (DCFROR), Net Present Value, (NPV) and Ratio AnalYsis Working Capital Intemational Project Evaluation Considerations Mining and Petroleum Project After-Tax Analysis

CHAPTER 9: AFTER-TAX INVESTMENT DECISION METHOT'S AND APPLICATIONS

9.1 9.2 9.3 9.4 9.5 9.6 9.1

Introduction Payback Perioo Analysis Savings are Analogous to Income Sunk Costs and Opportunity Costs in Evaluations

Break-evenAnalysis Three Methods of Investment Valuation NPV Use For Break-even Acquisition Cost Valuation 9;7a NPV Use for Break-even Sale Value Analysis 9.8 Valuation of Pubtic Projects and Investments 9.9 Tax Analysis Versus Financial (Shareholder Report) Analysis 9.10 Net Income Analysis Cornpared to Cash Flow Analysis 9.10a "Economic Value Added" Net Income Analysis 9. l1 "Regulated" Company Investment Analysis

CHAPTER 10: AFTER-TAX SERVICE ANALYSIS

10.1 10.2 10.3

lO.4 10.5

l0-6

General ReplacementPhilosophy Leasing Compared to Purchasing Sunk Costs and Opportunity Costs Related to Replacement Evaluation of Alternatives That Provide Different Service Unequal Life Service-Producing Alternatives Optimum Replacement Life for Equipment

CHAPIER 11: EVALUAIIONS INVOLVING BORROWED MONEY I

lI

366

Summary

IH.{PTER 8: INCOME TAX, CASH FLOW WORKING CAPTIAL AND DISCOUNTED CASH FLOW ANALYSIS

i. I 1.2 t.3 1.4 1.5 3.6 3.1 3.8 8.9

359

Introduction ofLeverage Applications

I I .l a Joint Venture Analysis Considerations ll.2 Considerations Related to Leveraged Investment Analysis' vt

? 378

379 380 383 384

391 394 395 398

106 415 419

436 437 443 445 451

460 462 467

469

4't0 478 483 490

505

513 529

534 540 543

553

562 567

1.3 Current U.S. Tax Lau, Regarding Interest Deductions 1.4 Minimum Rate of Return and Leverage 1.5 Capitalization of Interest in Certain I_'everaged Investments 1.6 Leveraged Purchase Versus Lease Analvsis1.7 Summary r

s69 573 576 578

584

CHAPTER 12: PERSONAL INVESTMENTS AND HEDGING

12.l

Itrroducrion

12.2 12.3

Common Stock lnr.estments Put and Call Option Investmenrs 12.3a Writing Put and Call Option Conrracts 12.3b Index Options 12.-jc Foreign Currency and Debt Options 12.1 Futures Contract Transactions I 3.-1a Options on Furures 12.5 Net Wbrth, Stock Equity, Bonds and Debentures l?9 Placing o'ders to Buy or Seil stocks, Bonds, Debenrures, options and Fulures 12.7 Comparison of Alternative personal Investments I2.7a Life Insurance Aiternatives 12.7b Home Purchase Versus Renting I 2.7c Personal Auto purchase u".suiLeasc I1.8 Summary of Selected Investment Terminology

,_i89

:r)3 600 604 607

609 611

614

6r6 625 627 633 635

bJv 642

APPENDIX A: Discrete Inrerest, Discrete lhlue Facrors

649

APPENDIX B: Continuous Interest, Discrete Value Factors

6'10

APPENDIX C: continuous Interest, continuous Flowing value APPENDIX D: Production Cost Variations and Break_even APPENDIX E: Arithrnetic Gradient Series Facror Equivalence and Conversion

Information

SELECTED REFERENCES

Factors

Analysis

Development

6E2

696 7O"l

709 710

INDEX

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PREFACE

This textbook represents the ongoing efforts and interests of a father and son who have worked together at various times and in varying amounts for over twenty years. The original versions of this text were the sole efforts of Frank Stermole. John began making some contributions as early as the Fourth Edition, but more significant contributions began with the Sixth Edition. While some might view writing a book as a difficult task, we have

truly enjoyed the opportunity to work together and try to improve our understanding of economic evaluation concepts through the textbook and its examples and problems. This text is an introduction to the concepts of the time value of money and the application of time value of mbney decision criteria to the beforetax and after-tax evaluation of virtually all types of investment situations. We would like to emphasize that the concepts to be developed throughout the text are used by investors in all investment situations. Other than the obvious engineering differences, whether you are considering development or expansion of an existing ore body, coal deposit, oil and gas field, or considering refining projects or a real estate investment, the same economic

evaluation tools are utilized. From an economic evaluation viewpoint, the primary difference between oil and gas, refining, mining and real estate

evalnations

will relate to the relevant tax considerations which

are

addressed in this textbook beginning in Chapter Seven. The {irst six chapters present decision criteria on a before-tax basis to sim-

plify the understanding in developing each of the criteria such as rate of return, net present value and ratios and how they are applied in different investment situations. Chapters Seven through Eleven address the same issues on an after-tax basis. This involves developing an understanding of cash flow, and other subtle aspects of proper after-tax evaluations. Chapter Twelve addresses personal investment considerations which can also be tied directly to any other type of project evaluation. For example, investing in futures is discussed in the final chapter. The use of futures, options, options on futures, etc., are all known mechanisms to reduce the level of uncertainty in some economic evaluation project parameters early on in the project evaluation life. vill

Ti;e material covered in the text is applicable for students in all engineering drsciplines, geology, geophysics, business, accounting, finance, management,

operations research, and anvone interested in economic er.aluation issue

ihis tcxtbook

s.

iras been designed tor use in threp basic ways. First, it SrriYcS as a university textbook for unilergraduate or graduaie students. on thc Coloi-atlo School of Mines campus ,,i.e have used the textbook for a one

seilester course in which all the material from chapters one throush

Twelve is addressed. In a quarterry s1,stem. you might pief'er to break it irrto two components with one quarter on a before-tax basis addressing chapters one through six and a second addressing after-tax applications in cnapters Seven through Eleven. chapter Twelve addresses perional investment considerations and could be addressed in either or both courses. Second, we make extensive use of the text in continuing education courses for industry and government personnel with interests and backgrounds in the aforemen-

tioned categories. The examples and problems throughout the text are

designed with this in mind as they address specific e'aluation consideratiols ibr a variety of industry applications. Third, the text may also be used for self-study to teach one's self economic evaluation techniques and their proper application. To suppiement this later use, we have also written a "Self reaching Manual" for this textbook which specifically addresses in a more step-by-step process, the material in chapters one through Four of the textbook. If you find yourself stru_sgling with the firsr three oitbu, chapters you might seriously consider this g0 page manual as supplemental reading. w'e mzrke use of the Self reaching I\{anual as pre-course ieading when presenting the textbook material in a one week short course format. As you go through the textbook, you'll find we have a common theme centered on "consistency" throughout the evaluation process. Expanding on this simply implies that evaluators must compare projects and alternatives on the same basis. This means making a proper analysis for the evaluation situation and being consistent in terms of discount rates, timing, the type of

doliars irvolved, whether borrowed money is being consiJered and of

course, properly considering the relevant tax issues. You'll also find that evaluation work is onlv as good as the information provided for the analysis. The old saying "garbage in, garbage out,' could not be more accurate than for economic evaluation work. one big advantage with personal computers today is the ability to consider a wide range of sen-

sitivity analyses to uncertainty concerning input parameters. This helps immeasurably in establishing the most sensitive criteria which then can be emphasized through the engineering or cost esrimating process. tx

In most investment decision making situations, you will find that proper application of the concepts and techniques presented in the text together with a little common sense and good management judgment will enable you to do a better job of economic. investment dec,ision-making"than you can achieve without using these methods. Finally, we would like to offer our thanks to Pattie Stermole (John's wife) for her eftbrts in research and editing for this latest edition of the textbook. Frank Stermole and John Stermole

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CHAPTER

1

INVESTMENT DECISION MAKING

1.I

Introduction to Inyestment Analysis

Economic evaruation of investment alternatives rerates to systematicaily e,aluating the rerative profit potenrial of i,r,estment utt.*utir"r. If sy:,tematic, quantitative methods arg not used to compare the econcrnic considera_ tions of investment alternatives, it seems evident that in cedain investment decision making situations the wrong choices may be made frcrn an economic viewpoint. For example, in thJanalysis of investment alternatives for a given investment situation, the artematives under consideration may have differences with respec.r to costs and profits or savings unJ irr" timing of costs and profits or savings. Differences may also exisi in project lives, tax considerations, and the effects of escalation and inflation on projected costs and revenues. If a systematic approach is not used to quantify the economic effects of these factors, it is very difficult to correctry assess which arterna_ tives have the best economic potential. Since the days of the writings of economist Adam smith it has been rec_ ognized that capital accumuration has been the primary investment objective of capitalistic individuars, companies and societies to enable them to improve their standard of.riving. it rs emptrasized Iater in this chapter that factors other than economic consideration, into most i,vestment decisio,s, but from an economic viewpoint it is"n,". assumed that maximizing capi_ tal accumulation (or the value of aisets that courd be converted to capital) is During.rhe ren year period between the late r9g0,s and rate ll"^39;".rt'e' 1990's, it is estimated that **. .upitul investment dolars wil be spent in the united states than were spent cumulatively in the past 200years of u.S. history' The importance of proper evaluation techniques in deter_ ".onorni. mining the most economicaily effective way to spend this money seems evi_

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Economic Evaluation and lnvestment Decision Methods

dent whether you analyze it from an individual, corporate, or government viewpoint. This text presents the development and applicatiofl of economic"evaluation techniques that can be used to enhance your ability to make correct investment decisions from an economic viewpoint. Note thafit is not purported that the use of these techniques will enable you to make correct economic decisions all the time. Because of the effects of risk and uncertainty, including escalation and inflation of costs and revenues, it is not possible to develop evaluation techniques that guarantee investment decision making ,u.."ri. However, by using one or more of the economic evaluation techniques presented and recommended in this text, you should be able to do a consistintly better job of economic decision making than you can do without using these techniques. Obviously a given analysis is only as good as the inpui cost and revenue data that go into it. Risk and uncertainty effects make it impossible to know for certain that a given set of data for a proposed investment situation is correct. This, of course, means we cannot be rertain of the economic analysis results based on the data. Even when probirhilities c'rf success and failure are incorporated into the analyses, aS is introduced in Chapter 6, we clo not have analysis results that aIe certain for any given investment situation. However, even under evaluation conditions of great uncertainty, the use of the evaluation techniques presented in this text *itt giu" the decision maker a much better feeling for the relative risks and uncertainties between alternatives. This information together with the numerical economic evaluation results usually will put the decision maker in a better position to make a correct decision than he would be in if systematic evaluation procedures were not used. Evaluation of investment alternatives to select project investments that per dollar invested is a key goal of every successful corporate manager or individual investor. To fully achieve this goal, manageis or individuals should be familiar with the principles of economic evaluation and investment decision methods which provide the basis for quar'tified economic evaluation of alternative engineering projects and general

will maximize profit

investment opportunities. Most business decisions are made by choosing what is believed to be the best alternative out of several courses of action. Problems in this area are therefore called alternative choice problems. In many business situations, decisions are made intuitively because systematic, quantified decision making methods are not available to weigh the alternatives. This should not be the case for weighing the economic consideratiom related to most invest-

Chaoter 1: lnvestment Decision Makin.:

ment decisions. systematic erronomic decision methods are available for evaluating individual investment projects and for comparing alternative investment projects. The "u,hims of management" should not be the basis for reaching decisions concerning economic dift'erenceg between inr.estment alternatives. In this age of increasingll, complex iinestmeill situatii::rs, to be successful over the long run it is imperative that a primary economil evaluirtion criterion be selected and applied to compare alternative inr,cstmont choices. This text presents economic evaluation criteria which are brrsed tt;: the premise that profit maximization is the investment objective; that is, maximization of the future worth of available investment dollars. Ir{ethorls are developed and illustrated in this text to enable a person to determine the courses of action that will make best economic use of lirnited resources. In general, this involves answering the question, "Is it better to invest cash in a given investment situation or will the cash earn more if it is invested in an alternative situ ation?"

1.2 "Engineering Economy" and,,Bconomic Evaluation,, Engineering and science technology in one way or another provide the basis for most of the investment opportunities iir this world today. Even the economic desirability of investrnents in land often relates to engineering technology that may make the Iand more valuable several years fiom now for apartrnents, a park or some in,Justrial plant utilization. In a capitalistic society it is imperative that engineering proposals as well as all other types of investment proposals be evaluated in terms of worth and cost before they are undertaken. Even in public activitres, benefits must be greater than costs before expenditures normally are approved. Thus, the term "engineering economy" which is used widely in literature and texts applies in general to the economic evaluation of all types of investment situations. The terms "economic ev?rluation" arrd "engineering economy" are considered to have the same meaning in this text. A perscln does not need to be an engineer to be proficient in the application of engineering economy principres to evaluate investment alternatives. The well known prerequisite of successful engineering ventures is economic feasibility. This prerequisite applies to both engineering and non-engineering investment situations, so the terms "economic evaluation" and "engineering economy" have valid meaning and importance not only to engineers, but also to bankers, accountants, business managers and other personnel in a wide variety of job descriptions where

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Economic Evaluation and lnvestment Decision Methods

they are concerned with economic evaluation of investment alternatives. This text is written for peop[with th3s-1krnd; of backqrounds or in1e1est,

,

1.3 Making

Decisions

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Peter Drucker, in his management texts, has stated that decision making has five distinct phases:

1. Defining the problem the problem 3. Developing alternate solutions 4. Deciding upon the best solution 5. Converting the decision into effective action

2. Analyzing

:

These decision making phases apply to economic evaluation decision making as well as general managerial decision making. Defining economic evaluation problems clearly is as important in economic analysis as any other situation that requires a decision. In any situation requiring decision making it is necessary to ask the right questions before one can expect to get the answers that are needed. Analysis of the problem or questions is the next step in the decision making process for economic analysis as well as general managerial decisions. This leads to the third phase of decision making concerning whether alternative approaches or investments might not be better. Analysis of these alternative investments then leaves us in a position to decide upon thti best economic choice and to take action to implement the best choice. This text, and the concept of economic decision making, is primarily con-

cerned with the three middle phases defined by Drucker. Again, this includes presenting and illustrating methods that can be used to analyze correctly various investment situations, develop alternative solutions and the economic analysis of these solutions. Emphasis is directed toward the fact that econornic analysis always involves comparison of alternatives, and determining the best way to invest available capital. From an economic viewpoint this means we want to maximize the future profit that can be accumulated from the available investment dollars. Economic evaluation decision making relates to two basic classifications of projects or investments: 1. Revenue producing investments 2. Service producing investments

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Sometimes people think a third investment classification might be "savings producing projects," but it will be illustrated in Chapter 3 that looking at differences between the costs of providing a service by alternative methods gives the savrngs that incremental investments in the more costly iniriai investment alternatir.es will generate. Analvsis of thes6 savings and incremental costs is just one of severai valid ways oi evaluating generai service producing projects. Ir4anv analvsis techniques are presented and iliustrated in this text. However, emphasis is placed on compound interest rarc of return analysis and net present value analysis, properly applied on an after tax basis. A large rnajority of individuals, companies and government organizations that use tormal evaluation techniques use rate of return analysis as their primary decision making criterion with net present value the second most used technique. There are other correct techniques for evaluating various investment situations including future and annual value, and several ratios. These techniques are presented in the text. It is necessary in economic evaluation work to be familiar with many dift'erent approaches to economic analysis because eventually you will interact with people that have a wide variety of evaluation backgrounds who use or advocate widely varying economic evaluation techniques. Familiarity with different evaluation techniques enhances communication with these people. Also, it will be shown in Chapter 4 that in ceriain evaluation situations, methods such as net present value have significant advantages over rate of return analysis. To communicate effectively u,ith diff-erent evaluation people you must be farniliar with the principles and advantages or disadvantages associated with different evaluation techniques. Also, beware that when you discuss rate of return analysis with different people the chances are that the term, "rate of return", may mean something very different to the other person than it does to you. Many different rates of return are defined in the literature, some of which follow: return on initial investment (ROI), which may be defined as being based on initial investment, average investment or solne other investment; return on assets (ROA), which is also called accounting rate of return and generally is based on the non-depreciated asset value, return on equity (ROE), which refers to return on individual or stockholder equity capital as the basis of the calculation; return on sales (ROS), which is not an investment rate of return at all; and the compound interest rate of return (ROR), or discounted cash flow rate of return on an after-tax basis (DCFROR) which is analogous to a bank account or mortgage interest rate and is the interest rate that makes project costs and revenues equivalent at a given point in time. Only this lat-

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Economic Evaluation and lnvestment Decision Methods

ter rate of return, DCFROR, is valid consistently for anaiyzing alternative investments. The other rates of return may have use in certain analysis or accoirnting'sitUations but they should not, in general, be used to evaluate the relative economic merits of alternative investments becaule they do not account for the time value of money properly over the project evaluation iife. In general these other rates of return look at project rate of return at a specific point in time, or for some kind of average profit and cost considerations.

that the time value of money be handled correctly in all valid economic evaluation methods. Also, Since taxes are a cost relevant to most evaluation situations, economic analyses must be done after-tax. To omit a major project cost such as taxes may be more important than omitting operating costs and few people would think we should leave operating costs out of an analysis. In certain government project evaluations where tares do not apply. it is of course proper to neglect taxes. Irt general you -should think in terms of doing all analyses after tax, omitting tax considerations only when appropriate. [n Chapters 2 through 6 of the text, evaluation techniques and illustrations are presented primarily on a before tax basis to avoid confusing the reader with significant tax considerations, at the same time various evaluation techniques and the time value of money are being introduced. Starting in Chapter 7 everything is presented on an after-tax analysis basis and this is the way all evaluations should be done for decision making purposes.

It is imperative

1.4 Definition of Discounted Cash Flow Analysis In all industries, tvhether for corporations or individuals, economic analysis of potential investment projects is done to select the investment project or projects that will give maximum value from the investment of available capital. Investors usually use economic anal1'sis techniques based on either rate of return, present value, annual value, future value, or various breakeven analyses to reach economic analysis decisions. When the techniques just mentioned are based on handling the time value of money with a compound interest rate, these techniques are all referred to as "Discounted Cash Flow Anal-vsis Techniques". Understanding this concept requires definition of terms "discounted" and "cash flow". The term "discount" is generally considered to be synonvmous tt'ith "present v,orth" in econonic evaluation work. ln handling the time I'alue of money, investors want to account for the fact that a dollar in hand todav has

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Cnapter 1: lnvestment Decision Making

greater value than a doiiar at some future tin-ie because a doliar in hand trrday can be put to work now in a bank account or other investments to accrue interest, or refurn on investment. Compound interest is the generally iicccpted approach today for calcuiaring accrucd interest, or returil on il".'ritment. in time ."'alue of money calculatiors. TIle fut'-:re value thal is prolected to be accrued trom the investurent of dollars toei:r1' at a speciiied compounci interest rate is equal to the sum of the accrued interest and the initial doilars lprincipal.l invested. The concept oi present worth is just the o1-''posite of compounding. The present worth of a future value is the sum of rironey that invested today, at a specified compound interest rate, would grow to the given future value. when you are working with positive interest rates, present values are always less than future values. Since the term "discounting" implies reducing the value of something, the use of the terms "discounting" and "present worth" have equivalent meaning because they botli relate to reducing the value of assets or dollars. The term "cct,.rh flovv" is used to re.fer to the net inflow or outflow of zlstne), that occtrrs durirry a specified csyserating Ttcriod such as a month or r"C0r.

Gross Revenue or Savings

- Operating Expenses - Tax Costs - Capital Costs = Cash

Flow

1-t

Inflows of money from revenues and savings, minus outflows of money for expenditures such as operating costs, income taxes and capital expenditures, equal the project cash flow for a given period. If outflows exceed inflows of money, then cash flow is negative for that period. Of course, it follows that if inflows of money exceed outflows, then cash flow will be positive. Sometimes investors look at project evaluations on a before-tax basis, so they omit income iax costs and savings from economic analyses and define cash flow on a before tax basis. Generally, it is undesirable to evaluate investments on a before-tax basis, uniess the investor is not subject to income taxation. As previously mentioned, Chapters 2 through 6 do not directly address "after-tax" cash flow calculations. The reader can use Equation l-1 to help visualize the after-tax cash flow values that are illustrated in more detail in Chapter 7 through 12 examples.

The term "discounted cash flow" evolved from the fact that investors most often handle the time value of money uging present value calculations

,Dli

'.iiil,: i':ill:]}

.ri

ti rt

.r,;:,iiijl::1fi.

rllti:r:i|Njiiiljilliilfi$S$'.

,l.,,iti.:ii..l,i.lii:ililll{

ilirriti{iiirf

Economic Evaluation and lnvestment Decision Methods

so they "present worth" or "discount" positive and negative "cash flow" anticipated from an investment to evaluate the project economic potential. Discounted cash flow analysis forces an investor to think systematically and quantitatively about all the relevant economic factors that may affect the economic poiential of investments. In the past, successfuT entrepreneurs ''intuitively" took into account investment economic analysis factors such as the magnitude and relative timing of investment costs and revenues, the effects that inflation and escalation may have on costs and revenues, the risk of failure involved with the overall investment, the uncertainty associated with projection of specific investment analysis parameters, the tax effects relevant to a proper after-tax evaluation for the financial situation of the investor, and finally, how to assimilate these considerations in a manner that enabled fair, consistent comparison of alternative investments. As investors have become more diversified, it has become more difJicult to use entrepreneurial judgments consistently and corectly in analyzing the economic potential of different investments. Discounted cash flow analysis has provided a systematic approach to quantitatively take into account the fac-

tors that are relevant in all industries for the proper economic analysis of investments. Examples of the use of discounted cash flow analysis today are innumerable. Income and service producing project investments of all types are analyzed using discounted cash flow analysis. Investors in minerals, petroleum, timber, real estate, manufacturing, leasing, etc., use discounted cash flow

analysis to determine the upper"limit that they could be willing to pay for mineral rights, land or assets to generate projected negative and positive cash flows over future years that yield a specified return on invested capital. Major companies use discounted cash flow analysis to evaluate the economic value of other companies. In a simplified form, by evaluating the value of individual properties and businesses that make up a company, the overall company value may be considered to be the cumulative sum of the value of individual properties or businesses that make up the cornpany. The acquisition bids for companies in recent years are situations where discounted cash flow analysis by major investors has indicated the value of companies to be considerably different than the value common stock shareholders had been placing on the companies utilizing net income approaches. Sometimes the discounted cash flow analysis will give a higher indicated value of a project or company than other evaluation approaches might give. Sometimes the discounted cash flow value may be less. The advantage of discounted cash flow analysis is that in all cases the assumptions on which

Chapter 1: lnvestment Decision Making

the analysis is based can be explicitly stated and understood by all. If you do not like the input assumptions they can be changed to what you consider more realistic. The non-discounted chsh flow, older econornic analysis methods have various implicit assumptions built in may or may not be (orrect in different analysis situations and, therefore,$at often lead to inccrr:ct economic evaluations. In particular, the older evaluation techniqr.:es d: not properly account for the time value of money. This is the single most inipor_ t:int consideration that has caused companies and investors in most in,Justries to shift to discounted cash flow analysis since the mid 1960,s. The real utiiity of discounted cash flow analysis is that it puts all invest_ rnents on a common evaluation basis of handling the time value of money with compound interest rate of return. In all industries, we are concerned rvith analyzing inflows of money (such as revenues and savings) and outflows of money (such as operating costs, capital expenditures and income tax costs). Discounted cash flow analysis enables investors to fairly and properly account for the magnitude and timing of these dollar value consid_ erations regardless of the type of investmeirt.

1.5 Example of Discounted Cash Flow Remembering that investment cash flow in any year represents the net difference between inflows of money from all sources, *lro, investrnent outflows of money from ari sources, consider the cash flow diagram preserited in thousanCs of dollars: Year Revenue

-

Operating Cost Capital

Cosrs -200 -100

Thx Costs

Project cash

23456 170 200 230 260 290 -40 -50 -60 _70 _80 -30

Flow -20a -100 +100

_40

+l

-50

-60

-70

l0 +120 +130 +140

The negative cash flows incurred during years 0 and 1 will be paid off by the positive cash flows in years 2 through 6, very much like loans of $200 and $100 thousand today and one year from today respectively, would be paid off by mortgage payments in amounts equal to the positive cash flow in years 2 through 6. what after-tax discounted cash flow rate of return (DCFROR) would an investor be receiving if he incurs the negative cash flows in years 0 and 1 to generate the positive cash flow from revenue in

,rui

rii;lHlirii}ilhif,

10

Economic Evaluation and lnvestment Decision Methods

years 2 through 6? The compound interest rate that makes the present worth positive cash flow plus the present worth negative cash flow equal to zero.is the desired rate of return, compound interest rate, or DCFROR. using those terms interchangeably. This value is 20.8Vo for this stream;of positive and negative cash flows. Net present value (NPV), is the cumulative present worth of positive and negative investment cash flow using a specified discount rate to handle the time value of money. In general, the discount rate represents the minimum acceptable investment DCFROR. For this example a discount rate of l57a is used. Positive net present value represents the present worth positive cash flow that is above what is needed to cover the present worth negative cash

flow for the discount rate used. In other words, positive NPV represents additional costs that could be incurred in the year NPV is calculated, and allow the project to still have a DCFROR equal to the discount rate. Remember that rate of return (or DCFROR) is the discr:unt rate that makes NPV equal to zero. For the l5Vo discount rate. the NPV for the above values is +$54.75 thousand. This represents the additional negative cash flow that could be incurred in year 0 (in addition to the -$200 thousand cash flow in year zero) and have the project yield a 157o DCFROR. Sensitivity analyses can be made to see how the acquisition cost of $54.75 thousand is affected by changing the relative timing of when the costs and revenues are to be incurred. First, instead of incurring the cumulative positive investment cash flow of $600 thousand over years 2 through 6, assume the same cumulative positive cash flow will be realized over years 2 and 3 with +$280 thousand in year 2 and +$320 rhousand in year 3. Project Cash Flow

-200 -100 +280

+320

Year

For this case the DCFROR will increase to 37.1% and rhe NPV grows to +$135.2 thousand. Accounting for the rime value of money, and realizing positive cash flow much quicker, enhances the economics of a project significantly. Second, if we slow down the receipt of positive cumulative cash flow of $600 thousand so that the cash flow is realized more slowly over years 2 through 9 with +$55, +$60, +$65, +$70, +$75, +$85, +$90, and +$100 thousand per year respecrively, what is the effect on the project economics?

Project Cash

Flow -200 -100 +55 +60 +65 +70 +75 +85 +90 +100

t2

l-

4'56789

Chapter 1: lnvestment Decision Making

11

Def'erring positive cash flow into the future drops the Npv to -$11.7

thousand and the DCFROR to l4vo. Both values indicate that the project is

unsatisfactory compared to other opportunities thought to exist at a 15vo

rate of return and, in f'act, ttie Npv inclicates that we would have to be paid s11.7 thorrsancl to takr this project ancl receive a fsq, return on invested

ciipihl.

Suinmary of Findings lnvestment Life

3 Years

6 Years

9 Years

DCFROR

37Vo ZtVa I4Vo +$135.2 +$ 54.7 _$ 11.7 Cumulative +CF, Thousands $600.0 $600.0 $600.0 Cumulative -CF,'Ihousands $300.0 $300.0 $300.0 Project

ProjectNPV @ 157o

In this example we have looked at three different evaluations o1. the same cumulative negative cash flow (investment dollars) of $j00 thousand and cumulative positive cash flow of $600 thousand. If we neglect rhe tin.)e value of money, we would consistently determine that the project yieliis $300 thousand in profits. Yet the economic conclusions that aicount fbr the tiine value of money indicate a rarlge of Npv's for these three cases ftom -S11.7 thousand to +$135.2 thousand. Obviously, project economics properly accounting for the time value of money can be very sensitive to the relative timing of investment capital costs and revenues over the expected proj-

ect 1ife.

The discount rate selected can arso have a very significant effect on economic evaluation results. To illustrate this concept we will analyze the Npv of the six year life analysis for discount rates of l0 and 20 perbent, as well as l5 percent. The results are presented below: Discount Rate

NPV

107o

+$1 I 6.1

157o

207o

+$

54.8

+$

6.8

NPV results vary by a factor of l7 from +$l16.1 to +$6.g thousand as the discount rate is increased by a factor of two from 10 to 20 percent. In the following section, discussion is related to determining the appropriate dis-

count rate.

Economic Evaluation and lnvestment Decision Methods

12

1.6 Minimum Rate of Return/Opportunity Cost of CapitaMDiscount Rate

It is widely

accepted in industry and government practigq for private government organizations, and regulated utilities alike that the i"=1S7o, so satisfactory

166

Economic Evaluation and lnvestment Decision Methods

The RoR resurts can arso be obtained by dividing annuar savings by initial cost and multiplying by 100, since initial cost-equals satvagJ. Many people think in terms of the project with the raigest rate of return on total investment as aiways being economicatlyiest, but in fact, the largest rate of return prolect is not atways tf;e best economic choice. ln this case, although ,,A,, has a totai investment iaie of return of 100%, which is twice is large as the,,B,,rate of return,

the investments differ in magnitude by a factor of ten. A smaller RoR on a bigger investment often is economicaily better than ger ROR on a smalrer investment. rncremental analysis a bigmust be made to determine if the extra, (or incrementar) ga50,000 that will be invested in "B" over the required "A" investment, wili be generat-

ing more or less profit (or savings), than the $4S0,000 would earn if invested elsewhere at the minimum rate of return ol 1s%. The incremental analysis is made for the bigger project ,,8', minus the smaller

project "A" so that incremental ibst'is ioitowed by incremental income giving:

B_A) C=450

0

l=200

l=200

1...........5

L=450

PW Eq. 0 = -450 + 200(p/A;,5) + 450(p/F;,5) ;

= RORB-

A=

44.4"/"

It should be clear from an economic viewpoint that if $500,000 is available to invest, we would be better off with all of it invested pro_ ject "8". our incrementar anarysis has broken project ,,B,, in into two components, one of which is like project ,,A," and the other is like the incremental project. Selecting proleit ,,8', effectively is equivalent to having $50,000 of the capital invested in project ,,A; earning a 1oo"/" RoR and $450,000 incrementar investment earning a 44.4./" RoR. s-u1ely_selecting "8" is better than selecting ,,A', which wourd give a 100% ROR on the 950,000 capital invested in ,,A,, and require invest_ ing the remaining $450,000 elsewhere at the 15% minimum ROR. lncreme.ntal analysis is required to come to this correct conclusion and notice that it requires rejecting atternative ,,A,, with the largest ROR of 100% on total investment.

chapter 4:

r"4utuarry Excrusive

and Ncn-r\4ri,:aily Excrusrve pr-o.iect Anary"ris

Evaluation of mutually exciusive multiple investment alternatives (the situation where only one alternative may be selected from more than one investment choice) oy rate of return analysrs requires both tctal investment and incremenial investment r-atu of return analysis. T'he rate of reiurn analysis cancept for muttaity exclusive alternafi'ves is baseci on testrng to sce that each satisia-ctori,, level of invest_ ment meets two requirements as foliows: lr) The iate of return an total individual project investment must be greater than or equat to the minimum raie of return, "i"; (2) The rate of return on incremental investment compared to the last satisfactory level of investment must be greater than or equal to the minimum ion, ,'i"". The largest tevel of investment that satisfies both criteria is the economic choice.Anal_ ysis of total investment rate of return alone will not always lead to the correct economic choice because the project with the largest total investment rate of return is not always best. lt is assumed fl-rat money not invested in a particular project can be invested elsewhere at the minimum rate of return, "i*". Therefore, it is often preferable lo invest a large amount of money at a moderate rate of ieturn rather than a small amount at a large return with the remainder having to be invested elsewhere at a specified minimum rare of return. These evaluation rules and concepts appty to grow,th rate of return anatysis as well as regular rate of return analysis, since growth rate of return is just a special type of regular return.

NetValue Analysis (present, Annual, Future) of Mutually Exclusive Alternatives ,.A,, and ,iB,' To illustrate the application of NpV NAV and NFV to evatuate mutually exclusive investment alternatives these techniques will now be applied to evaruate alternatives "A" and "B" for the previously stated 15orl, minimum RCR.

atC=$50 0 B) C = $500

l=$50

l=$50

I = $250

| = $250

1...........s

1...........5

L=$50

L = $500

't

68

B

Economic Evaluation and lnvestment Decision Methods

-

A) c-=

$$q

I = $2oo

| = $2oo

1...........5

L = $450

.4922

L

3.352

NPV4 = 50(P/At S./",5) + 50(P/F15 "/",5) NPV3 = 250(P/At S"/",5) + S00(P/F1

-

S"/",5)

.14832

NAV4 = 50 + 50(A/F1

So/o,S)

-

S0 = +g1+ZISO

-

500 = +$5g6.60

.29832 50(A/p1S%,S) = +$42.50

NAVg = 250 + 500(A/F1 S"/",5) - SOO(A/PI5%,S) = +$175.00 6.742 2.011 NFV4 = 50(F/At5%,S) + 50 - S0(F/p15%,S) +$286.50 = NFV3 = 250(F/At S./",5) + 500 - 500(F/p1 S/",5) = +$1,1g0.00 we see that all the net value results are positive which consistenily indicates that both aiternatives "A" and ,,B,,are satisfactory since they generate sufficient revenle to more than pay off the invLstments at the minimum RoR of 15"/". To determine which alternative is best we must make incremental net value analysis just as we did for RoR analysis. we can get the incremental net value results either by looking at the differences between the total investment net values for the bigger investment minus the smailer, which is "B-A,, in this case, or by working with the incremental costs, savings, and salvage.'Exactly the same incremental net values are obtained either way.

NPV6-4 = NPVB

-

NPVA = 586.6

-

3.352 .4972 or = 2Qg1p I Al S"t",S) + 450(P lF 1 S"/",5) directly from the incremental data:

142.5= +$444.10

-

4S0 = +$444. 1 0

NAVB-4 = NAVB - NAV4 = 175.0 42.5= +$132.50 NFVB-4 = NFVB - NFV4 = 1,180.0 - 286.5 +$893.50 = ln each case the incremental net value results are positive, indicating a satisfactory incremental investment. The reason it is satisfactory can be shown by looking at the net value that would be received the $450,000 incremental capital elsewhere at ilo1_ilvesting i = 15"/".

cnapier 4: Mutually Excrusive and Nor,'-Mutuaily Excrusive project

c = $450 at i.= 15%'

.F

1.........5

Anarysis

169

,E^t-tn \ a^^ . ^= 450(F/P I St",S) = +$904.95

0.4972 IJPV = 9C4.95(P/F15%.5)- 450 = $0 Similarll,, NAV

-

$0 anij NFV = $0.

fu1oney invested at the minimum RoR, "i*", arways has a zero net value. obviously the positive incremental net vatue results for,,B-A,, are better than the zero net value that would be obtained by iinvesting the money elsewhere at "i*"

ln summary, the net value analysis concept for evaluating mutuatty exclusive alternatives is based on two testsi 1t1the net vatie on to,tit individual project investment must be positive; (2) the incremental net value obtained in comparing the totat investment net value to the net vaiue of the last smaller satisfactory investment level must be positive. The largest level of investment that satisfies both criteria is the economic choice. This is always the alternative with the targest positive net value. This means, if you have a dozen mutually exclu-sive alternatives and calculate NpV, or NAV or NFV for each, the economic choice wili always be the alternative with the lar.gest net value. when you select the mutually exclusive investment alternative with the largest net value as the economic choice, ycu are not omitting incremental anaiysrs. Experience shows that incremenial analysis-always leads to selection of the project with the biggest net value on total investment as the economic choice. you can mathematically convert between NPV, NAV and NFV and therefore you must get the same economic conclusion using any of these techniques NPV = NAV(P/A;-,n) = NFV(p/Fi",n)

Ratio Analysis of Mutually Exclusive Atternatives ,,A,,and ,,8,,

n) c

=l!Q 0

B) C = $500

I

t

l=$50

l=$50

1...........5 I = $250

I = $250

1...........5

L=$50 L = $500

170

Economic Evaluation and lnvestment Decision Methods

PVR4 = NPVA / PW cost = 142.srso 2.g5 > 0, so satisfactory = PVRB = NPVB / PW Cost = 5g6.6/500 1.17 > 0, so satisfactory = Project "A" has the bigger total investmenl ratio byt the smaller project "8" ratio relates to ten times larger investment iatue. Getting smaller dollars of Npv per present worth cost dollar invested on larger investment often is a better mutually exclusive investment

choice. Incremental analysis is the optimization analysis that

answers the question concerning which of mutually exclusive alter_ natives "A" and "8" is the better investment. This ii true with ratios the same as was illustrated earlier for RoR and net value analysis.

B_A) C = $450

o

I = $200

I = $200

1...........5

L = $450

PVRB-4 = NPVB-A / PW lnvestment = 444/450 = 0.99 > 0 satisfactory pro. Accepting the incrementa! "B-A" investment indicates accepting ject "8" over'4", even though the total investment ratio on ,,8,, is less than "A". As with RoR anatysis, the mutualty exclusive alternative with bigger RoR, PVR or Benefit cost Ratio on totar individuar project investment often is not the better mutualty exclusive investment. lncremental analysis along with totat individual project investment analysis

is the key to correct anarysis of mutuaily excrusive choices. since benefit cost ratio equals pVFi plus one, it should be evident to the reader that either pVR or Benefii cost Ratio analysis give the same conclusions, as long as the correct break-even ,itio. of zero for PVR and one for Benefit Cost Ratio are used.

4.2 unequal Life Mutually

Exclusive Income-producing Alternatives and The Handling of Opportunity Costs in Evaluatlons As discussed in Chapter 3, it is important to recognize that when using RoR' NAV or NFV techniques to anaryze unequar life service-producing alternatives that generate revenue, you must use a common evaluation life for all alternatives, normally the life of the longest life alternative. The only exception to this rule involves the evaluation of alternatives that do not have the opportunity to have revenue allocated to them, such as remediation work' Analysis of unequal life income-producing ahernatives is not a prob-

chapter 4: Mutually Excrusive and Non-Mutuaily Excrusive project Anarysis

171

leni rvith NPV or ratio analvsis because time zero is a common point in time for calculating Npv or ratios ot either equal or unequal life altematives. If you have unequal lives for different alremati,res, the tirne value of molle)' consideratiofis are difi-erent in rate oi return. annual value and future vaiLie calcuiirtiolts and you may chocrse the wrong aile5nslir. as being best if lt-ru do not get a coir.lulon evaluation lii'e. This merely meaus that 1-ou inu51 calculate NFV at tlie same future point in tirne for aij alrematil,es. or you inust calculate NAV by s;.readilig costs anci revenues over the same nurnber of years for all alternadves. hr RoR, tret value or ratio anctbsis of Lm.:quol life income-producirtg altenntit,rs, treat all projects as hat,irig equ"al lives whk:h are equal to the longest life project with net reyenues and cosrs of zero in the later rears of shorter life projects. Note that this is not the same technique presented in chapter 3 to convert unequal life sen,iceproducing alternatives that have revenues associated with thim, to equal life aiternatives using either Method 1,2 or 3. when projects have different stalting dates, net present value must be calculated at the same point in time tbr all proiects tbr the results to be comparable.

opportunity cost is the current market cash value assigned to assets alreadl' owned which will be used in a project instead of being sold. passing up the opportunit-v to sell the assets in order to keep and use thenr creates an opportunity cost equal to the foregone market cash salc value. If an asser is not saleatrle, the oppor-tunity cost effectively is zero. Actions taken b1 ma,agement to deiay expenditures mav create a nega-

tire opporiunity cost, or actually add value to the property. An exampie ir.ri'.i'es invcsti*g adtlitio*al capital in a negative profit general business unit (or an off.shore petroleum platform or mining operation) in order to delay abandonment or reclamation costs. As long as the net present value of

the altematives calling for additional investment to defer abandonment has greater value than the net present viilue of abandonment no$,, deferring abandonment would be preferred from an economic vie.,vpoint.

Finally. in analyzing either equar lif'e or unequal life income-producin_: or ser'ice-producing alternatives, c.hangirtg, the mirtimtun discount rate Lnay chartge tlw ec'ottontic choir:e. You cannot use net y,alue or ratio results t:ulculaled at a giv,en discount rate such as l2ch to reach valid economic decisions for a dffirent minimum discount rate such as 25To. you m.ust use net value and ratio results cctlculated using a discount rate representative of the opportunitl, cost of capital for consistent economic decision making. The follorving examples illustrate these considerations.

172

Economic Evaluation and lnvestment Decision Methods

EXAMPLE 4-2 Anatysis of Unequal Life Mutuafly Exclusive lncome Producing Alternatives and Opportunity Costs Analyze whether it is economically desirable to sefthe development rights to a new process or property for a $150,000 cash offer at time zero, or, to keep the rights and develop them using one of two development scenarios. The project net before-tax cash flows for each alternative are presented on the following time diagrams. Use NPV, RoR and PVR analysis techniques to make this economic decision for a minimum rate of return of 15.0%. Then, consider the sensitivity of changing the discount rate to 2o.o%. All dollar values are in thousands. (A) Develop

(B) Develop

(C) Sell

-200:gl_100j00

150. . . . . . 150

23

10

-300 -400 200 2ao

200..

...200

150 10

Solution for i* =

15.07o:

since much confusion exists regarding the applicability of different criteria to different investment situations, this solution looks at each of the decision criteria independent of another to show the overall equivalence of each. (A) Develop

-z!q:35qjll too 150...... 150 3

NPV4 = -200

-

4........8

350(P/F1S,1) + 100(P/A1S,2XplF15,1)

+'t 50(P/A1 5,5)(p/F1 5,3) = -32.37 < 0, so, reject A.

I

10

chapter 4: Mutuaily Excrusive and Non-Mutuaily Excrusive project

ROR4

Anarysis

17g

= 13.1g%

is the compound interest rate that makes NPV = 0. 18.ig"/o

<

15.O"A, so, reject A.

t

PVR4 = -32.87 t[2AO + 350(prF1S,1)] = -0.064 < 0, so reject

A.

All criteria indicate that Alternative ,,A,, is not economically ccnpeti_ ive with rnvesting money elsewher.e at i* 1S.0%. This leaves only = "8" and "C" for further consideration.

(B)

Develop

NPVB = -300

{9100 J00_!00 01 -

2oo.

.

. . . 200

400(P/F15,1) + 200(p/A15,9)(p/F15,1)

= +182.0 > 0, so, B is acceptable.

RORB

=

21.62o/" is the compound interest rate that makes NPV = 0.

21.62"k > 15.0"/", so, B is acceptable.

PVRg

= 182.0/

[3OO +

400(piF15.r)] = +0.2809 > 0,

so, B is acceptable

All criteria indicate that Alternative ,'8,, is economically acceptable compared to investing money elsewhere with equivalent risk at i" = 15.07". (C)

Sell

150 0

-

NPV6 = +150.0 > 0, so, C is acceptable. HOR6 = *o/o > 15.O/", So, C iS aCCeptable. PVH6 = - since your denominator is zero > 0, so c is acceptabre. All criteria indicate that Alternative ,,c,, is also economically acceptable.

174

Economic Evaluation and lnvestment Decision Methods

Proper economic analysis of mutually exclusive alternatives requires incremental analysis to determine the optimum choice. However, as previously illustrated in Example 4-1, a proper incremental analysis will always lead to selecting the alterqgtive with the largest individual NPV. Applying this concept here, Aiternative ,,8,, with a maximum NPV of $182.0 is the economic choice. However, note that "B" does not have the largest individual ROR or pVR. With any type of compound interest rate of return or ratio analysis, you must make a proper incremental analysis when evaluating mutually exclusive alternatives. As just shown, of the three alternatives only "8" and "C" are preferable to investing elsewhere at i* = 1s.o/", so incremental analysis is provided between "B" and "C".

-450

(B-C) Dev - Sell

0

The concept of opportunity cost is formally introduced in chapter g, section 9.3, on an after-tax basis, but notice here that the Alternative "B-c" incremental analysis automatically converts the sale cash flow of +$150 to an incremental opportunity cost of -$150. lf an investor passes up the opportunity to sell for +9150 in order to keep and develop, an opportunity cost equal to the forgone sale cash flow must be built into the economic analysis of the alternatives. lncremental analysis of mutually exclusive alternatives will always properly account for opportunity cost considerations as in this Develop minus Sell analysis where the time zero incremental cash flow of -$450 results from a -$150 opportunity cost and a -$300 development cost. To prove that selecting the largest individual NpV is best consider first the incremental NPV analysis which can be solved for with two different approaches:

NPVg-g = -450

-

400(P/F15,1) + 200(P/A15,9)(P/F15,1)

= +32.0 > 0, the incremental investment

is satisfactory,

accept B. or,

=

NPVB

-

NPVC = 182.0

-

150.0 = +32.0 > 0, accept B.

chapter 4: Mutua,y Excrusive and Ncn-Mutuary Excrusive project Anarysis

175

To support the Npv conciusion that Arternative ,,8,, generates the most economic varue, an incrernentat anarysis is reqiired for both RoR and PVR anarysis. RoRg-6 is the compcurrd interesi rate that makes NPV3_6 = 0. t

HORg-g

=

15.g8% by calculator > i*

=

15.A"/o, so,

accept B.

Note that Alternative "c" (selling), with an infinite incividual RoR is not the economic choice. By serecting "8", the additionar capitar

invested i! "8" is generating a oigger rate of return than if that money were earning the minimum rate of return. i" 1S.07o. That translates = into more value \,vith "8", as was refrected in the Npv anaiysis.

PVRB-6 = +32.0 /{4SO

+ a00(p/F15,t)J= +0.04 > 0, so, accept B.

Analysis of changing the Minimum Discount Rate to Za.ao/o: Frorn the individual economic analyses jrst compreted, cr"iy A[ter.natives B and c have rates of return competitive wiih investing else_ where at i* = 20.011. since the rargest NpV is arways the eccnonrjc choice when evaruating mutuariy exilusive alternatives, onry NFV will be iliustrated here for i* = 20%. NPV4 @ 20"/o = -104.8 < O, so, reject A. NPV3 @ 20"/" = + 3g.5 > 0, so, B is acceptable compared to investing @ i*= ZO.O"/". NPVg @ 20% = + 150.0 > 0, so, C is the maximum NpV select

C.

.. Tl" maximum project NpV is the Arternative c, which indicates the investor shourd sell today and invest the g150 in other opportunities where it could earn a 2o.o% RoR and maximize the investor,s economic value. This same sensitivity to discount rates can be expanded to a graphical format, for a range of i* values. This is often referred to as an Npv profire and is iilustratbd in Figure 4-1.

176

Economic Evaluation and lnvestment Decision Methods

$1,200

br,ooo o 5

G

co o o

$8oo

\.- .'.

$6oo

. :.,.\]

$400

o-

zo)

$200 $o

10%;

($eool

Discount Rate, i* lntersection points between the projects indicate the "i." values that make the prgjects a break-even. They also indicate the incremental rates of return between the respective alternatives. For example, RoRa-c is equal to 1s.gg% as previously calcula.ted- Since selling is a time zero value, its NpV is unatfected by the discount rate, with NPV remaining constant at $150 for all disccunr rates.

Figure 4-1 NPV Profile for Example 4-2, Alternatives A, B and C.

A variation of the analysis in Example 4-2 is presented to show when mutually exclusive projects have different starting dates, you must calculate NPV for different alternatives at the same point in time for results to be comparable.

EXAMPLE 4-3 Analysis of Mutually Excrusive Arternatives with Different Starting Dates With NpV, ROR and pVR.

Re-analyze mutually exclusive alternatives ,,8', and ,,C,, as described in Example 4-2 using Npv, RoR and pVR analyses for i. = 15.0"/", assuming the "8" development project starts at the end of year two, instead of time zero. All values are still in thousands.

-300-400

(B) Develop 0

200..

...200

crrapter 4: Mutually Exciusive and Non-ly'utuallv trxclucive project Analysis

177

150

{C) Sell

1 2 3 Solution for i* = 15.0o/o: NPVg = -300(P/Fr

S.e)

-

4...

...12 +

400(p/F15,3) + ZAOptA15,9)(p/F15,3)

= +137.6 > 0, so, ,,8', is acceptable. NPVg = +150 > 0, so, "C" is acceptable and largest

NpV.

selecting the maximum Npv project "c" (or selling) is the economic choice. This is a different economic decision than was reached for the project timing described in Example 4-2 where ,,8,, Deveiop started at time zero with NpV of +192.0.

lncremental Hate of Heturn Analysis

(B-C)Dev-Sell -150 - -300-400 200

o 1 2T.-:z

PW EQ: 0 = -'150

-

.....200

300(PtFi,z) -a00(ptF;,3) + 200(p/A;,9)(p/F;,3)

By calculator, FOR, i = 14.56"io < 15.0% so, reject Develop, accept Sell

lncremental PVR Analysis

PVRg-g = lncremental

= =

NPV

/ lncremental PW Costs

(137.6 - 150 ) / {1S0 + 300(p/F1 5,2) + 400(p/F15,3)} -12.4 / 639"83 = -0.0194 < 0

so, reject Develop, accept Sell

When properly applied, NpV, ROR, GROR, pVR and B/C Ratio criteria will lead to the same economic conclusion in the evaluation of mutually exclusive alternatives. lf projects have different starting dates, for valid NPV analysis of mutuaily exclusive alternatives, project NPV's must be calculated at the same point in time before proper interpretation of the results can be ma'de.

178

Economic Evaluation and lnvestment Decision Methods

EXAMPLE 4-4 Mutually Exclusive Proiect Analysis Case Study

An existing production facility must-be shut,down unless an environmental capital cost of $1so mittion is incurred now at year 0. This improvement will enable production to continue ano @herhte estimated profits of $60 million per year for each of the next g years when salvage value of the facility is projected to be zero. An alternative under consideration would combine process improvement and expansion with an environmental cost change for a cost of $200 million now at year 0, plus $150 million cost at year 1 to generate estimated project profits of $00 million in year 1 and $120 million profit per year in each of years 2 through 8. The minimum ROR is 12ol". Evaluate which of these alternatives is better using ROR, NpV and PVR analysis. Then, change the minimum ROR lo 2S/o and analyze the alternatives using the same techniques.

Solution, allvalues in millions of dollars:

61C=150 l=60

01

B)

I=60 l=60 l=60 l=60 2 4 ......8

l=60 C=200 C-150 l=120

l=120 l=120

l=120 .8

ROR Analysis

A) PW Eq: 150 = 60(P/Ai,g), i = ROR4 = 36.7"/o > i* =

12o/o

B) PW Eq: 200 = -90(P/Fi,r) + t 20(PlAi,)(P/F;,1) i = RORB = 28.60/o > i* =

12o/o

Both projects have acceptable economics, but incremental rate of return analysis is required to determine if the extra incremental investment in "B" generates sufficient incremental revenues to justify the additional $50 million cost at time zero and the additional g150 million cost at year one.

chapter 4: Mutua,y Excrusive and Non-Mutualry Excrusive project Anarysis

B-A) C=50 C=150 l=60

l=60

B

l=60

3

0

-A ) PW Eq: 50 = -'150(p/F;,1) i = RORB-

179

l=60

4......8

+ 60(p/A

A= 2jo/o > i* =

i,Jyprci1 12o/o

So select "8".

Note that once again, the project with biggest RoR on totar investment is not the economic choice. NPV Analysis 4.968

NPV4 = 60(P/At 2y",8)

- 150 = +$148.1 4.564 '0.8929

0.8929

NPVg = 12a(PtAt2.7",)(ptF1zoh,1) _ 90(plf;;. _ZCO ,ry = +$208.7 lncrementar anarysis verifies the serection of the project with the largest total investment NpV which is ,,8,,. NPVB-4

-

NPVB

-

NPV4 =ZOg.7

-

14g.1= 60.6 > 0, so select,,B,,.

lncrementar anarysis.of mutuaily excrusive arternatives arways leads to selection of the investment project with rargesi rvpv on totar investment. often this.is not the project with tre tarjest Rbn or pvR on total investment. However, incrementar anarysil gives tne same economic conclusion with all techniques " of analysis. PVR Analysis

PVRn=r+h=#=o.ee>o PVR.L'=

NPVB

PW Costg

208.7 200 + 90(P/F1 2/o,i)

=0.74>0

180

Economic Evaluation and lnvestment Decision Methods

Which alternative is better, "A" or "8"? "A't is not necessarily preferred just because it has the largest ratio on total investment. As with ROR and NPV incremental analysis must be made and Present Worth Cost "B-A" is taken from incremental "B-A" time $iagram and does not equal Present Worth Cost B minus Present Worth Cost A because of the effect of year 1 income on the year 1 total and incremental investment net costs.

NPVg-4 208.7 - 148.1 PVR3-4 = PW Costg-4 50 + 150(P/F12/"J) = o'33 >

t'

;L'*''ff1'ffi;",.::fitent

with the

See the incremental "B-A' time diagram for verification that the incremental costs are 50 in year 0 and 150 in year 1 . Benefit cost ratio analysis gives the same conclusions following the PVR analysis procedure. Remember that benefit cost ratio equals PVR plus one, and one is the break-even ratio with benefit cost ratio analysis while zero is the break-even ratio with PVR analysis. Change i* lo zso/o: ROR Analysis

A) RORA = 36.7"h > i* = 25"/o B) RORg =28.6/o>i* =25"/o Project ROR for each alternative is greater than the new minimum ROR, indicating acceptable economics for both. lncremental analysis is the optimization analysis that tells whether "A" or "B" is the better economic choice.

B-A) RORB -A=21o/o 0 31.46

PWC"ttB=2@='25>o

PVRe-4=

pwc"ffi=ffiNPVg-4

31.46

49.74

,,8,' = -.'1 0 < 0, so reject

NPV and incremental RoR and pVR indicate that alternative ,,A,, is the correct investment choice when the minimum rate of return is2s"/". Note that NPV and PVR must be recalculated at the appropriate minimum RoR in order to make correct economic decisions. ln this example, NPV and PVR at i* 12/o cannot be used to evaluate = the alternatives when the minimum rate of return has changedro 25%.

&

182

Economic Evaluation and lnvestment Decision Methods

4.3 Mutually

Exclusive rnvestment Anal.ysis using Growth Rate of Return and Future Worth profit Methods

'

It

was mentioned in the summary of the Example 4.1 Res. analysis that Grorvth RoR analysis is applied to evaluate mutually excluiive alternatives in the same way regular RoR analysis is applied. This means calculating

Growth RoR on both total investments and incremental investments to verify that both are greater than the minimum ROR, ,,i*,,.

Looking at future worth profit for decision purposes is just a variation of the Growth RoR or Net Future value evaluation techniqu"i. Th, objective of all investments from an economic viewpoint is to maximize the profit that can be accumrilated at any specified future point in time. from a giien amount of startirtg capital. Instead of using analysis methods such as RoR, Growth RoR, NPV NAV NFV or PVR to achieve that investment objective, another ralid evaluation approach is to directly calculate the futuie worth profit (future value) that can be generated by investing a given amount of capital in difl'erent*'uvays and assuming the prohts can be reinvested at the minimum RoR, "i""', when the profits are received. The investment choice that gives the maximum future worth profit is the same choice we would get using RoR, Growth RoR, NPV NAV NFV or pvR analyses. The following ple illustrates the Growth RoR and future worth profit techniques. "ruo,-

EXAMPLE 4-5 Growth RoR and Future worth profit Analysis Use Growth RoR analysis for a nrinimum rate of return of 15% to determine which of the following mutually exclusive alternatives, ,,A,, or "B", is best. Verify the result with future worth profit analysis and NPV analysis. All Values in T'housands of Dollars, A)

C=200

c

= cost, I = lncome, L = salvage

l=80

l=80

0

B)

C=300

l=150

L=140

Declining Gradient

L=200

L=0

chapter 4: Mutuary Excrusive and Non-N4utuary Excrusive project Anarvsis

183

Solution: Both Growth

FroR and Future worth profit anarysis, as weil as Fii'}v, NAV I\JFV and reguiar RoFi anarysi. ur.qEn" ttiaiiesiouar cap_

itai nct invested in one.of the projects and iircomes as they are leceiygd can be invested ersewhere at the minimum RoR, which is i =15"/" for this anaiysis. This gives the foilowing orowtn RoR and future worth income (profit)

.r,.ilrtion.,

Growth Bate of Return Analysis

Alternative "A,,i

A) C =-?e9

l=80

0.1

Reinvest "l" and ,,L,at i"

=

l=80

L=200

1S"h

C=200 C=80 .8

C=80

F = 1,298

where F = B0(F/A 1b"/",g) + 200 = +1,29g A + Reinvestment of lncome

C=200 F = 1,298

Growth ROR4 pW Eq: 200 1,29g(p/F1,6) = Growth ROR4 i = 26.Syo > i" .157o, so satisfactory =

Alternative "8,':

B) C=-300 l=150

0

l=140

declininggradient,'L=0

- 15"/o _____9= 1s0 C = 140 declining gradient O l----,.......8

Reinvest lncome ali*

where F =

['t S0

-

1

O(A/G1 S1l^,g)]F/ nlSy",e) = 1,627

F=1,677

184

Economic Evaluation and lnvestment Decision Methods

B + Reinvestment of lncome C

=_t99_

F = 1,677

0

Growth RORg PW Eq: 300 = 1,627(plFi,g) Growth RORg, i = 24.1o/o > i* = 1]5/o, so satisfactory

lncremental Growth ROR Analysis (.,8-A',) (B_A) C = 100

F=379

Growth ROR3_4 PW Eq: 100 = 379(p/F;,g) Growth ROR3-4 = i = 1 8.4/o >i* = 157o, indicating Select,,B,, Project "B" does not have the largest GroMh RoR on total investment but incremental analysis indicates that "B" is the economic choice.

Future Worth Profit Analysis Future worth profit analysis uses the future worth profit calculations from the Growth ROR analyses. lf $300 thousand is available to invest, putting.$200 thousand of it into alternative "A" and reinvesting the profits at = 15% will generate a future value of g.l,2gg thousand in I years. lnvesting elsewhere the $100 thousand of our g300 thousand that is not needed if we choose ,,A,,gives:

i

(B-n; c =

3.059

100

1...........8

F

= 100(F/P1S%.8) = $305.90

Therefore, the total future value g years from now of $200 thou_ sand invested in project "A" and 9100 thousand elsewhere is g'1,2gg thousand + $30S.9 thousand or g,|,604 thousand. This is not as great as the future worth of "8" calculated to be g1,677 thousand, so select "8". This is the same conclusion reached with Growth RoR analysis. NPV analysis indicates select,,B,, as'follows:

chapter 4: Mutuarry Excrusive and Non-rJutualry Excrusive project

Npv4

=

-200

Anarysis

1g5

. sop,/ll:;,g + eoo(#i33rlr, = +$zz4

NPVg = -800 + [1S0

-

2.781

4.4t7

10(A/c1s%,g)Xp/ArSZ.e) = +$248

ordinary compound interest RoR anarysis cannot be used on this problem and many similar problems because of difiiculties eflclr.;r_ tered with the incrementar RoR anarysis. Evaruation of ordinary com_ pound interest RoR on totar investment shows that the rates of return on projects ,'A,'and ,,8,, are satisfactory. tncre*entrt gives the following time diagram:

,;;;;

(B.A)

C=

100 l-70 1

l=60.....1=0 2........8

L=

-200

This time diagram has inbrementar cost foilowed by incrementar income followed by negative incrementar sarvage vatue which is the same as incremental cost. This is the type of inalysis situation that generates the duar RCR probrem discussed rater in this chapter. Regular RoR anarysis cannot be used in this situation for reasons that will be given iater. This is why it is important to be familiar witn other techniques of anarysis src-h as Growth RoR, Fr-,ture worth Profit, NPV NAV l',jFV or pVR.

.

4.{

Changing the }Iinirnum Rate of Return with Time The minimum rate of return (opportunity cost of capital or hurdle rate) represents the rate of return that we think we could get by investing our rTl(,r'Iey elservhere, both now ancl in the future f,rr the p"iioa of tlln. coverecl by the project evaluation life. There is little reason to expect that our other ,pportunities rvill remain uniformly the same over a long period of tirne. while other opportunities for the irwesrmenr of capital ,o* -oy i" *"I'= lAcic, we may expect a major project with a proiectid 207c RoR to be deveroped starting three years from norv which could absorb all of our available capital and raise "i*" t-o-zoEo. For anaryses with minimum rates oJ return that change with time, Npv NFV pvR a-nd Future worth profi:.t anarysis are recontmended as the best and reail1' the onry usa.ble analysis methods. Regu_

lar RoR and Growth RoR are not always consistent

o"i.i",

"riteria

if

you

186

Economic Evaluation and lnvestment Decision Methods

do not have a single minimum RoR to which you can compare them. Similarly, you cannot calculate NAV,with different,minimum rate of return values at different points in time. For analysis simplification reasorls, most investors including major companies assume theii minimum Rofr is uniform and equal over project evaluation lives. However, changing the minimum rate of return is illustrated in the following example to demonstrate proper economic analysis techniques for this situation.

EXAMPLE 4-6 Effect of changing the Minimum Rate of Return With Time

compare the economic potential of mutually exclusive investments "A" and "8" using NpV and rate of return anaiysis. Assume the minimum rate of return is 30.0% in years one and two, changing to 12.a"/o in years three through ten. Then re-evaluate the investments using a 12.0% minimum rate of return over the entire ten year project life and then again using a 30.0% minimum rate of return over the entire ten year project life. comparison of these results emphasizes the importance of the minimum rate of return in investment decisionmaking from an economic viewpoint. A)

B)

C=20 l=10 l=10 C=30 l=12 l=12

l=10

l=10

3.

.10

l=12

l=12

L=20 L=30

Solution, All Values in Thousands of Dollars: Net Present Value, Changing i* From 30olo in years 1 &2 to 12o/" Over Years 3 to 10 NPV4 = -20 + 10(P/A3g,2) + 10(p/A1 2,e)(p/fr1,r1 + 2O(P/F 12,6)(P/F3g = +22.ZB ,2)

N

PVg = -30 + 1 2(P l Agg,2) + 1 2(p t A1 2,g) (p /F gg,2) + 30(PiF12,8)(P/FA0,2) = +28.78

These results indicate virtual break-even economics between ,,A,, and "8" with a very slight one thousand dollar present value advan_

chapter 4: Mutuaily Excrusive and Non-Mutuaily Exclusive project

Anarysis

1g7

tage to "8." However, if we consider the minimum rate of return to be uniform and equar over time at either 12.0% or 30.070, as most investors usually do, we get different results. Net Present Value, i*

=

1i2o/oover

the entireirolect Life

NPV4 = -20 + 10(p/A1 2,10) + 2O(P/F12JA) = +42.94 l{PVg = -30 + 1Z(plA1Z,td +30(p/F12.tO) = +42.46 Select B v;ith Largest NpV Net Present Value, i* 30% Over the Entire project = Life NPV4 = -20 + 10(piA3g,1g) + 20(piF3O,1 0) = +12.17 Select A with Largest NpV l.JPVg = -30

+ 12(p/Agg,1g) + 30(piF3O,10) = +9.27.

Assuming uniformry equar discount rates of 12.0% or 30.0% has . given different economic conclusions than the break-even economic conclusion reached by changing the discount rate with time in the ini_ tial analysis. Most companies oL not want to get involved in the addiiional level of confusion invorved with changin-g ilre oiscount rate with respect to time. Therefore, even thougn a Joripanv Lno* they have other opportuniti". investing .rpit"t at a reraiiv"ry nigr, rare of J?f return such as 30.0% for the next'severar years, tottoweo by an assumed rower rate-such as 12-o"/o, tl"y simprify the anarysis by using a 12.0% rate of 'return over the entire evaluation life. This exam_ ple shows that such a simprifying assumption, with respect to the evaluation discount rate, can nivJan effect on economic investment decision-making. Rate of Return Analysis

I,v_Eq.A 0 = -20 + 1l(lfi,r6) + 20(p/F;,16) By Trial and Error. i = RORA lbO.OV; > i*'="C0.07o

or

12.0o/o,

so satisfactory

lW_Eq B 0 = -30 + 12(pifi,ro) + 30(p/F;,1s) By Trial and Error, i = RORfi'J 1O.OU > i*'-50.0% or 12.Ooh, ' so satisfactory

Economic Evaluation and lnvestment Decision Methods

lncremental rate of return analysis is needed now to determine the optimum qhqice .since both "A' and "8" have satisfactory.total invest ment rates of return compared with investing money elsewhere at either i" = 30.07" oI i* = +

12.O"/".

B-A)c19

l=2

0

l=2

!=2.-.'.-,-.-,-.-.'

E

3...........10

t=lo

PW Eq B-A 0 = -10 + Z(PlAi,1O) + t0(P/F;,19) By Trial and Error,

i=

RORB-A =20'0"/o < i* = 30'07o but > 12'0%

The investor cannot tell with rate of return analysis whether the incremental "B-A" investment is satisfactory or not relative to investing elsewhere at 30.0% over the next two years and at 12.O% over the following eight years. The fact that rate of return analysis of projects often breaks down and cannot be used when discount rates that vary with tirne possibly is one of the main reasons that changing the discount rate with time is not more commonly applied in industry practice. A large majority o{ companies emphasize rate of return analysis over the other techniques of analysis and that cannot be done if discount rates are changed with time. Notice that for a uniform minimum discount rate of either Q.A"/o or 30.0% over all ten years, incremental rate of return analysis gives economic conclusions consistent with NPV analysis conclusions. Select "B" if i* = 12.0o/", select "A" if i* = 30.0%. Finally, if firms are utilizing a discount rate based on financial cost of capital, that number is very likely to be changing over project lives the same as opportunity cost of capital changes. once again however, rather than trying to forecast those future changes, most companies use a financial cost of capital calculated today, aS reflecting the average financial cost of capital over the project life. We do not advocate the use of financial cost of capital unless unlimited financing is assumed to exist so that financial cost of capital equals opportunity cost of capital. Remember that it is always opportunity cost of capital that is relevant for valid discounted cash flow analysis of investments.

Chapter 4: Mutually Exclusive and Non-Mutr;ally fy11r.;u" prcjeci Analysis

139

4.5 Differences Between Net varue Anarysis and cost Anarysis Thcre is a tcndency for pe,lpre to get confused c.ncernin-e the .iifference between Present worth (pw), Annual worth (Aw), or Euture *onr, (FW) cost aral-vsis of sei'rice-producrng alterniilives an.i Ner pre-sent Value (Npv), Net A-rmual \alue (NAv) and Net Furure Value iNFV) an*l1,sis of income-producing

aitei-;;atives or dirferences betrveen senice-p;,;d,rcing allernatives. 11ey are simi_

lai'b.rt very difi.'rent because of sigri uoniinirr;n dir.r.rences. co.sr nm!.ysis is

u'seti ro evaius.le ser,-ice-producittg inve:rmerti.t. lvhen L.cst., can1. a positive sign and any revenlies or s,lvag,e a:'e negatiu'e, the net c.ost lpicsen.t, annuar or l,arues discounted

at

.futurc,

"i"')

is a positi,e nurnber wirh this ,ign rorrr"ntionfor minimunt cost option is

Lrnau-Zing altemcfiy,e wa\'s of prcv,idbry a serv,ice, the selected- Net vcilue analysis, horvet,e4 i.s used to asses.i

i*orte-protrucing

"hhu projects or incrcmental differences betw,een seruice-producing pt-ojects usirtg corn'entional cctslt flow' anarysis sigti ctstweniitrt t'herc ,rrt, i,i negadte and t?t'i.turcs are positive, so the altenntit.e yielding nu:xilnrun net v-altts is selecud. To uiliize cost e*ralysis in rhe e'aluation of sirvicetroarcing altematives, you work with the given or estimated costs for each individual alteriative way of pro_ viding a service. To utilize net value anaiysis in service evaluations, you must work with incremental savings that incremental costs will generate. Net v'iue analysis is just a short-cut form of rate of rerurn anelysis. Foinet or rate of tetLlm attalyses, )'ou must look at the incremental 'alue differences betwecn altemative rt ays of providing a se^,ice. The foliowing exarnple illustrates these techniques. EXAMPLE 4-Z A Comparison of present Worth Cost and Net present Value Analysis Criteria

Economic anarysis of the optimum thickness of insuration for a steam line needs to be made for an investor with a minimum rate of return, i. = 12.0"/". Engineering has arrived at the following estimates for installed insulation costs and the annual heat loss resulting for tlre different amounts of insulation. This data is summarized "o.t, in the following table: lnsulation Thickness

0" 1"

2" 3"

Cost of Annual Heat Loss (Per Year

$o

$ 60,000 $ 85,000 $1 18,000

$40,000 $20,000 $10,000 $ 6,000

190

Economic Evaluation and lnvestment Decision Methods

Assume the insulation and project life are eight years with zero salvage, valuq,,and.bgse your analysis resutts on.both present wsrth cost analysis and net present value analysis. The 0"'option represents the current situation, so in calculating net presnt value, compare the current situation with the other amounts of insulation.

Solution: Present Worth Cost Analysis

0" lnsulation

40,000(P/A12,g)

= g1gg,704

1" lnsulation 20,000(PlA12,g) + 60,000 = g1Sg,g52 2" lnsulation 10,000(PlA12,g) + g5,000 = g134,676* Minimum Cost 3" lnsulation 6,000(PlA12,g) +11g,000 = g147,g0s " Selecting two inches of insulation will minimize the present worth cost. This is illustrated in Figure 4-2.

200,000

o 150,000

oo o

100,000

= o a o

o-

50,000

0

0 lnches

1

lnch

2 lnches

lnches of lnsulation Figure 4-2 Present Worth Coit Analysis

3 lnches

Chaprer 4: Mutually Exclusive and Non-MutLrally Erclusive project AnalVSis

191

Net Present Value (lncremental Analysis) For NPV analysis, carcurate the incrementar savings for one, two and three inches of insulation compared to the currenisituation of no insulation. ln other r/,;ords, if $00,000 is spent Today for one inch of ir:suiation, the investor can s.i.,,/e $20,000 in annuai heat loss costs -20,C00 - (-40,C00) = +20,000 savings

1"--0"

2"-0" 3"-0"

20,000(P/A 12,8) 30,000(P/A12,S) 34,000(PiA12,B)

=$c - 60,000 = $3g,352 - 85,000 = $64,028 * Maximum NpV - 118,000 = $S0,ggg

* seleciing two inches of insulation now maximizes the net present vaiue obtainable from these investment alternatives. This is illustraied in Figure 4-3. 70,000 60,000

o

: ;o

(E

o

50.000 40,000

E

30,0c0

i

zo,aoo

o.

10,0c0 0

0lnches

1 lnch

2 lnches

lncremental lnches of lnsulation

3 lnches

Figure 4-3 lncremental Net present Value Analysis

lncremental Analysis (lnch by Inch) lnstead of comparing each alternative with the current scenario of zero inches, each additional one-inch of insulation investment could be

thought of as representing mutuaily excrusivery income producing (savings) alternatives. These alternaiives rangs from doing nothing (0,, option) to spending the money tor 3" of inJulation. whei the alterna_

192

€conomic Evaluation and lnvestment Decision Methods

tives are compared with the current "do nothing,,scenario, the individual economics were determined. Next, the inih-by-inch incremental analysis for each of these mutually excniriv" Oras;;;:'

1o4'

20,000(P/A1e;A)

-

"it"iriiiiv.r'is ,, ---

60,000'E $39;B5Z

b

As discussed in previous examples in chapter 4, the incremental NPV of $39,352 teils us that 1" is better than doing nothing. Therefore, the next level of initial capital investment is coripared to the last satisfactory level, as follows:

2'-1'

10,000(P/A12,g)

-

25,OOO =

g24,676

5a,2" add value over the 1,, option. Note aiso that the NpV2,

- NpV 1,, gives the same result:

$gg,os2 = g24,676 comparing the next level of investment to the last satisfactory level gives: $64,028

-

3'-2'

4,000(P/A1 2,g)

- 93,000 = -$1g,1 29

select the largest level of investment for which incremental economics are satisfactory. This is two inches of insulation as deter-

mined by the earlier incremental NpV analysis. The inch by inch incremental process would be more essential had rate of return analysis been asked for in this problem as investors can't expect individual total investment rates of return to consistenfly determine which alternative is best. ln this example, the results would be the same by relying on individual RoR criieria, but this is not always the case.

Alternative

Rate of Return

1',-0"

29"/"

2"-0' 3',-j',

31"/"

2',-1" 3',-2',

23% 37% -17o

2" is preferred to 1" 2" is pretened to S"

9o, 2" is the largest level of investment satisfying both the individual and incremental economic criteria and is the-ec6nomic choice.

criapter 4: Mutuarly Excrusive and Non-Mutuaily Excrusive project Anarysis

4'6 Effect of Evaruation Life It

193

on Economic Anarysis Resu.rts

n'as illustrared in chapter 3 Example 3-24 thatproject Iife has little

eti'ect on analysrs results when you get biyond 10 orrl5 years, depending on

tite p.oiitabiiity ,ri the projects being evaluated. However, for shorter life pr.;jects ri irh er.'aluation lives under 10 years, the evaluation life used can atiict tiie economic choice significantry. For example, sometimes the life o\cr \\lrich u'e choose to evaluate a process improvement is very *uit*riiy chosen due ro the uncertainty assocLted with irojecting savings in certain prodess analyses. The following illustration shows how evaluation life can affect economic results in this relatively short evaluation life situation.

EXAIIPLE 4-B Effect of Evaruation Life on comparison of rwo Alternatives Evaluate two different levels of improvernent being considerec for an existing process. The new equipment costs anc f,rojected annuar savings in labor and materials are as fcllcurs:

Equipment

projected Annual Savings

.--qg$_ Level 1 $200,000 Level 2 $350,000

$125,000 $18O,0OO

For a minimum RoR of 2oo/o evaruate Levers 1 and.2 using NpV analysis assuming zero sarvage varue for (A) a 3 year evaruati6n rife, and (B) a 5 year evaruation life. (c) For what evaluation rife would there be no economic differences beiween the arternatives?

Sclution, All Vatues in Thousands of Dollars: A) 3 Year Life 2.106

NPVI = 125(P1AZO"/"5)

-

ZOO

= +$63.25 Select Maximum NpV

2.1 06 NPV2 = 1 9O(P/ AZA%,3)- 3S0 +$29.08. =

Economic Evaluation and lnvestment Decision Methods

194

B) 5 Year Life

lncreasing the evaluation life enhances the economics of both alternatives. However, the economics of bigger initial cost alternatives are always enhanced relatively mo!'e rapidly thantmaller initial cost alternatives by lengthening evaluation life (or lowering the minimum discount rate). ln this case the economic choice switches to selecting Level 2 for a 5 year life whereets Level 1 was preferred for a 3 year life. 2.991

NPVI = 125(P|AZO"/",5) -200 = +$173.88 2.991 NPV2 = 180(P/Az O/",s)

-

350 = +$188.38 Setect Maximum NPV

C) Break-even Life "n" When there are no economic differences between the alternatives, NPVl will equal NPV2. lf we write an equation setting NPVl=NPV2 for an unknown life "n", we can solve for the break-even life "n". 125(P / A21o/o,n)

-

200 = 1 80(P/A2g7",n)

-

350

or, 150 = 55(p/A2g7",n) (PlA2g"1",n) = 150/55

=2.727

By interpolation in the P/A1,n factor column of the 20% tables we get o = 4.34 years. Select Level 2 for an evaluation life greater than 4.34 years. Select Level 1 for an evaluation life less than 4.34 years.

4.7 Investment Analysis When Income or Savings Precedes

Costs

\\''hen income or savings precedes cost, ROR analysis leads to the calculation of "i" values that have rate of reinvestment requirement meaning instead of rate of return meaning. These results must be used very differently than ROR results since "rate of reinvestment requirement" results greater than the minimum ROR are unsatisfactory (instead of satisfactory with regular ROR). This is illustrated in Examples 4-9 and 4-10.

Chapter 4: Mutually Exclusive and Non-Mutually Exclusive Proiect Analysis

195

EXAMPLE 4-9 Analysis of Mutually Exclusive Alternatives When lncome Precedes Cost Consider the foilowing problem. Evaluate the. follorving two mutuGrov;thhOR, Future \l/orth Profit, NPV and PVR. The minimum rate of return i* = 107o.

all;v exclusive aliernatives using ROR,

A)

c = $100,000

B)

c

= $100,000

1............5 I = 941,060

L = $305,200

I = $41.060 --='

L = $0

Rate of Return Analysis A) PW Eq: 0 = -100,000 + 305,200(P/F;,5), i = ROF1A =25"/" B) PW Eq: 0 = -100,000 + 41,060(P/A1,5), i = RORB = 30"/o Since the initial costs of projects "A" and "8" are equal, many people conclude there are no incremental differences in the orojects, so, "8" is the choice, since "8" has the larger ROR on total investment. This is incorrect! Looking at "A-8" so incremental cost is followed by incremental revenue we get the following: (remember negaiive incremental income is equivalent to cost) A_B)

C=$0

0

c

= 941,060

c

= $41,060

1............5

L = $305,200

A-B) PW Eq: 0 = -41,060(P1A1,5) + 305,200(P/F;,5) ROR4-3, i = ZO.O"k > 10.0% so, accept "A" Even though project "8" has the largest ROR on total investment, project "A" is the economic choice from incremental analysis. Differences in the distribuiion of revenues to be realized cause incremental differences in the projects that must be analyzed. The year one through five incremental costs of $41,060 per year are referred to as "opportunity costs" by many people since they result from the following rationale. Selecting project "A" causes the investor to forgo realizing the project "B" revenues each year. Revenues or savings foregone are lost opportunities or "opportunity costs", so selecting "A" causes opportunity costs of $41,060 in each of years one through five.

I'

196

Economic Evaluation and lnvestment Decision Methods

lf you look at "B-A", you get incremental income followed by incremental cost so the following rationale-applies:,.,. ;i. ;;

B-A)

C=0

0

l-$41,060 l=$41,060 + c = 9305,200 1............5

B-A) PW Eq: 0 = 41,060(P/A1,S) i = 20.A/"

-

305,200(P/F;,5)

> 10.0% so, reject

,'B,'

(This B-A "i" value does not have rate or return meaning. lnstead, it represents the rate at which funds must be reinvested to cover the year five future cost of 9005,200. See the foltowing discussion)

The incremental numbers and trial and error "i" value obtained, are the same for "A-B". However, note that on the "B-A" time diagram incremental income is followed by cost. tt is physicaily impossible to calculate rate of return when income is fottowed by cost. You must have money invested (cost) foilowed by revenue or savings to calculate rate of return. when income is foilowed by cost you calculate an "i" value that has "rate of reinvestment requiretnent,' meaning. The "B-A" incremental "i" value of 20"/" means the investor would be required to reinvest the year one through five incremental incomes al20"h to accrue enough money to cover the year five cost of $305,200. lf the minimum ROR of 1Oo/o @presents investment and reinvestment opportunities thought to exist over the project life, as it should, then a reinvestment requirement of 2a% is unsatisfactory compared to reinvestment opportunities of 107", so reject ,,8,, and select "A". This is the same conclusion that the "A-8,, ROR analysis gave. Summarizing several important considerations about the RoR analysis for this problem, for the incremental RoR analysis of alternatives "A" and "8" we discussed the need to subtract alternative ,,B,,from alternative "A" so that we had incremental costs followed by incremental revenues. Then we discussed what happens if you incorrectly subtract alternative "A" from "B" as follows: B_A)

C=$0

| = 941,060

1=941 060

c

= g3o5,2oo

chapter 4: Mutuaily Excrusive and Non-Mutuaily Excrusive project Anarysis

1S7

lncrementar "B-A" incomes of $41,060 each year precede the $305,200 incrementar "B-A" cost at the end ot'yeaitive. when income precedes cost, the "i" that we carcurate is the interest rate tnat must be obtained through the reinvestmeet of the income each period, for the finar value ot ine cumuiative incomes and compound irrterest to equal the cost at that time. A required reinvestment rate greater than the minimum RoR is unsatisfactory, whereas an RoB gi-eater than the minimum RoR is sairsfactory. rigure 4-i shows lhe cumulative cash position diagram for this situaion. Note that the cumulative cash position in this example is positive durin! the entire project life. whenever the cumularive cash position is jositive, no investment is invorved and the interest rate ,,i,, means the rate at rvhich money must be reinvested and not the rate of return on investment.

sbo,ooo

"B-A"

264,492

CUMULATIVE

CASH

200,000

POSITION tor i = 20"k

100,000

345 Figure 4-4 cumurative cash position for rncome preceding cost

Given that

the minimum RoR is 10%, do we accept arternative "A" or "B" for the exampre just discussed? As previously mentioned,

if investment preceded income, we wourd accept ariernative ,,A,, because an increm entar 20"/" RoR is better than investing else-

198

Economic Evaluation and lnvestment Decision Methods

where at a 10% ROR. However, if "B-A, incremental income precedes cost, we would be rejecting projec! ,,B',, becausE the "B-A" rate of reinvestment required al2o"/" exceeds the other opportunities we have to invest capital.which is assumed to be @o/o. , Future Worth Protit Anatysis from 9100,000 tnitial lnvestment A) FW Profit = $305,200 6.1 05

B) FW Profit = $41,060(F/A10%,5) = 9250,671 Select Project "A" to maximize future profit. Since the $100,000 initial investment is the same for both ,,A,,and "8", maximum future profit (value) on total investment is desired.

GroMh Rate of Return Analysis A) Growth ROR4 is equal to the regular ROR4, = 2ilyo B) Growth ROR3, PW Eq: 0 = -100,000 + 2SO,6Z1(p/F;,5) GROR3 =i=20.2/o

since the same $100,000 inilial investment is involved with both "A" and "8", we want the alternative with the largest Growth ROR, "A". lncremental analysis gives the same conclusion. A-B) GROR PW Eq: O = 54,529(P/F;.5) GROR4-g = i = o/o > 10.0% SO,' SeleCt "A" OVer "8" Net Present Value (NPV) Analysis 0.6209 NPV4 = 305,200(P/F:o"7",$

-

100,000 = +$89,500 0, acbeptable $8.66 =

200

Economic Evaluation and lnvestment Decision Methods

This analysis has income preceding costs, so the meaning of the calculated "i" value that makes Npv eq-ual zero is rate of reinvestment req ui rement, not rate'of i.eturn. Therefoie, a req'uired,rnua-strl.i: r"i" that is less than our minimum rate of ret nu"ri* nt o p'p oiii, n ti e s) s acce ptanr Ji'x' ;[Et] " ment greater than i* = 15.0% wourd be an unacceptabre project. PW EQ: 0 = 7.0 + 21(ptFi,1) - 4.0(p/Ai,9)(p/F1,1) i

i

#?;?y:i ili?'l*f

i

Rate of Reinvestment = i 5.06% < 15.0"/o, acceptable. =

q,

= 810

oq o

1o

zo

'llk 15k

2Ao/o

ZS/, ZO/o g1o/o

(s)

A}a/a 43% S07o

(10)

Discount Rate

Figure 4-5 Npv'vs i. with Rate of Reinvestment Meaning

As illustrated in Figure 4-s, when NpV increases with a corre_ spondingly higher discount rate it is generally the result of income preceding costs and the presence of rate of reinvestment meaning associated with each i* varue. This situation courd be thought of in two different ways; First, rarger discount rates arways diminish the present vafue of future cash flows more rapidty than imailer discount

rates. second, as other opportunities for ine Lse or iipitut increase, the money received up front at time zero and year one can generate more future value creating more profit relative to the estimated down stream cosfs. once again note that the "i" carcurated when investment precedes income has compretery different meaning than when income preoedes investment. Difficurty arises if these two types of projects are mixed in incremental analysis because the interest ,,i,,has two differ-

chapter 4: Mutualry Excrusive and Non-filutuaily Excrusive project Anarysis

ent meanings in the same equation. Techniques for analyzing this type of investment project situation are presented in the foll6wing

section. lt will be shown that the cumulative cash position diagram is a useful tool in the evaluation of this type of prublem.

4.8 Alternating Investment, Income, Investrnent: The Dual Rate of Return Situation In the last section, examples 4-9 and 4-10 illustrated situations where income preceded costs. Discttssion then focused on how the meaning of the calculated "i" r'a]ue was not rate of return, but the rate at which the rev"enues (or positive cash l1orv.t tlust be reinvested to ilssure sufficient revenues exist to cover future costs. When this occurs, thc resulting rates of reinvestntt:nt that are less than the investor's minimum rate of retum are considered economically satisfactory. Extending this concept, when a time dia,qram contairs cash flows with an

initial investment, foilowed by income and then more investment(s), the related present w'orth equation will yield muitipie ..i', values. Thcse ,.i,, will airval's contain a combination of meariing related to both rare of 'alues retJill on the iriitill irtveslntcnt as weli as rilte of reinvestment requirement relarod to ectrnomicallv corering rl:e cost(s) in the tuture years. These,,i,, vaiucs are olren rei'erred to as "Duai Rates of Return,,and generally speak_ ir.ls. iire nor signilicant in assessing the econornic potential o1a project. This is due to the fact that despite the label, "Dual Rate of Return,,, neither solu_ tio, has pure "rate of return" meaning. Instead, as mentioned previously, the results contain a combination of rate of return and rate of reinvestment meaning, which may be good part of the time, but unsatisfactory part of the time. This forces investors to consider other criteria such as Npv or a modified forr, of rate of return ilrustrated in the foilowine examples. Cash flows containing in'estment-income-investment timing may occur in a variety of investment situations. One such case involves the incremental analysis of mutualll, exclusive alternatives that have different project lives. This is often defined as an acceleration probrem and is to oil and gas as well as mining investments. In depleting a finite, "o,rr*on resource, the decision to accelerate the production rate through immediate capital expenditure(s) will shorten the life of the project. The incremental analysis of these alternatives creates the crassic in'estment-incorire-investment siiuation.

202

Economic Evaluation and lnvestment Decision Methods

Alternating investment, income, investment analysis situations occur in a variety of situations. The most cornmon, which is illustrated in the next example, occurs from looking at incremental differences between uneqdal life alternatives where the bigger investment alternative has bigger period;revenues.and sltorter project life. This is the classical acceleration problem nientioned previously cofirmon to mineral and petroleum development type projects where a given mineral or petroleum reserve can be depleted more rapidly by making a bigger initial investment. This evaluation situation also commonly occurs with acceleration type investments in many different types of general industry situations. Other examples of cost, income, cost include (1) An investment in a building or project that generates income for several years after which the building or project must be razed or restored to different condition; (2) Mining projects that generate income followed by significant reclamation costs; (3) Forest planting investments followed by clear-cutting which generates income but must be followed by forest replanting costs where environmental laws or company policy require it; (4) Offshore platform development fbr petroleum production that must be followed by significant platform ree lltmation costs.

EXAMPLE 4-11 Analysis of Mutually Exclusive Unequal Life Acceleration Type Projects lnvestments "A" and "B" are mutually exclusive ways of developing a project. Which is best if the investor desires a minimum rate of return of 20%? Make a valid ROR analysis using either Growth ROR or one of two present worth cost modifications known as the "Escrow Approach" or "Year by Year Approach." Verify those conclusions with NPV.

Solution, All Values in Thousands of Dollars: I = Revenue, L

A) C = 182

-

Salvage Value, C = Cost

l=

0

B)

C=250

100

l=

184

l=

100

2

1

l=

100

l=

184

Get equal life alternatives by assuming the lile of "B' is 3 years with net revenue and cost of zero at year 3.

chapter 4: Mutually Exclusive and Non-Murually Exclusive prolect Anaiysis

203

Rate of Return Analysis, (ROR) By trial and error the RORA = 3Oo/o and RORB 3Oo/o both of which = exceed the 20% minimum rate of return requirel for the inr,,estment of capiial. The investments and project live.s are ufiequal so it is difficult to teii intuitively if "A" or "B'' is best for i' = ZO"/o. projects with equal

toial investment rates of return are not necessariiy economicaily equivalent. lncrernental analysis gives: B_A)

C=68

l=84

l=84

ROR PW Eq: 68 + 100(P/Fi,3) = B4(p/A;,2) or, in NPV format: B4(P/Ai,2) - 100(p/F;,3)

C = 100

-

6g = 0

i = 0"/" : 84(2.000) i = 10"/": 84(1.736)

- 100(1.0000) -68 = 0 - 100(0.7513) - 08 = +2.69 i = 15"/": 84(1 .626) - 100(0.6575) 08 i.2.89 - = i = 20"/": 84(1.528) - 100(0.5787) OS +2.48 - = i = 307" : 84(1 .361) - 100(0.4552) 68 = +0.80 i = 40"/": 84(1 .224) - 100(0.3044) 6S - = -1 .62

i=0% and i=33"3% are duar rates of return by triar and error.

+

--t--F+-_]%

50%

100%

rL

++ --f-

-r

rt + -T Figure 4-6 NPV vs Discount Rate For Cost, lncome, Cost

204

Economic Evaluation and lnvestment Decision Methods

100

Cumulative

Cash

50

Position in

Thousands for

i=0% i=

33.3%

0.0

-50 -68 -1 00

Figurc 4-7 Cumulative Cash position Diagram and The Meaning of Dual "i" Values A graph of NPV versus the discount rate "i" as illustrated in Figure 4-6 emphasizes the parabolic variation in NpV with the discount rate changes for this cost, income, cost situation. This is very different from the declining exponential variation for NpV versus "i" when cost is followed by income as illustrated earlier in chapter 3, Example 3-21. However, the term "dual rates of return" is really a misnomer because neither "i" value means rate of return. Both "i" values have a combination rate of return, rate of reinvestment meaning as the Figure 4-7 cumulative cash position diagram shows. Note that a oo/o rate of return is bad compared to = 20/o percent whereas a reinvestment rate o'f 0/o is good compared lo 20/" reinvestment opportunities. Similarly, a 3o"/o rate of return is good but a 33% rate of reinvestment requirement is bad. Both dual ROR values are good part of tne time and bad part of the time.

i

Looking at Figure 4-7, whenever you are in a negative cumulative cash position, the meaning of "i" is rate of return. On the other hand, whenever you are in a positive cumulative cash position, the meaning of "i" is rate of reinvestment requirement. Using the cumulative cash position diagram, it becomes evident that the dual ,,i,, values have different meaning at different points in time. Therefore, an analysis method other than regular rate of return should be utilized. lf

ihapter 4: Mutuaily Excrusive and Non-Mutuaily Excrusive project Anarysis

the investment decision must be based on a compound interest rate of return measure, severar modifications qan oe'rnaJe to eriminate the cost-income-cost sequence in the tro*.. wili be introduced and incrude Growth RoR, upe iscrow Approach and the Year-by-year Approach. The rast two ippror"nus are some_ times referred to as "present worth cost Modiiications.,, r.rpv .*uv aiso be utilized if an alternative to RoR analysis is acclptable. The net varue techniques are varid arternative anarysis tecrrniques inai avoid the "dual ROR,'problem.

i;;." ilffi;;

.*n

Net Present Vatue Anatysis, (NpV) For i* = 20"/o,lime zero is a common time for all projects. 2.1 06 NPV4 = 100(P/AZO%,3)

-

182= +$28.6

1.528 NPVB = 184(?lAZA"k,Z) -.ZSO +$31..1 +_ Select ,,8,,, = Largest NpV

Growth Rate of Return Anatysis There is no need to carcurate Growth RoR for the ,,A,, dnd ,,g, total investments. we arready know that ,,A,, and ,,B,, are satisfac_ tory from totar investment RoR anarysis, so we onty neeo to Growth RoR anarysis to the incrementar investments. "il[ the Growtn RoR reinvestment step eriminates tne Note that art"rnliin"g* investment, income, investment siiuation and gets us back to incrementar investment foilowed by incrementar revenue, the RoR analysis situation. B-ur.;c = $68

01

l=$84

l=$84

C = $1oo

23

Reinvesting incremental year 1 and 2 incomes ati" =20"k:

C=$84

C=$84

F = +$221.8

2.200

1.200 where F = 84(F / A2g"/",2)ff /p 2O%,1) = +$221

.B

206

Economic Evaluation and lnvestment Decision Methods

B-A + Reinvesting incremental income: B:A) C=$68

F l-== +$121.8 3 +,:

PW Eq: 68 = 121.8(PlFi,g), i = Growth RORB-4=21.4/o > 2O/" Select "B" ROR Using the Escrow Approach

Another modification for ROR analysis that many individuals and companies use to eliminate the alternating investment, income, investment situation is a present worth modification of the final cost. By discounting the final cost at the minimum ROR, you convert the problem to a regular cost followed by income type of evaluation. Working with the incremental "B-A" diagram, discount the final year 3 cost of 9100 thousand at i* = 20%, giviig the following modified iime diagram: 0.5787-

l=$84

01 Modified PW Eq: 0 = -125.87 + 84(PlA1,2) i = 21.6/o > 2Oo/o, Select "B" NPV

Figure 4-8 NPV vs. Discount Rate For Modified PW Cost Analysis

chapter 4: Mutually Excrusive and Non-Mutuailv Excrusive project Anarysis

Explanation of the Escrow Approach This present worth cost modified RoR analysis really involves adding

an outside investment earning at the minimum discouni rate to the initial cost, income, cosi project. By seiecting the nra$nitude of the outside investment so it wiil generate income in the later years equai to costs foliowing income in the initiai prolect, cost following income is eliminated.

C=$68

B-A)

l=$84

l=$84

6 = 9100 3

+

An Outside lnvestment C = $57.g7 at i = 29"1o

= Total

c

| = 9100

23

0.5787 where "C" at time 0 = 57.87= 100(P/F;.= 20"/o3) l=$84 l=$84 = $125.87

_

Modifiect Present Worth Equation: i = 21.6"/" PW Cost Modified ROR ROR Using the Year-by-year Modification

0=-125.BZ +84(p/Ai,2)

it is not necessary to present worth costs following income all the way to time 0 to eliminate costs following income. lt iJonly necessary

to bring costs following revenue back one year at a time until they are offset by income, as the following illustrates. B_A)

C=$68

l=$84

+

An Outside lnvestment at i* = 20"/o

C=$68

0 Modified PW Eq.: 0 =

i

c

= 9100

2

3

C = $83.3

I = 9100

23

whereCatyear2= = Total

l=$84

0.8333 1 OO(P lF 2g"/", t ) = $83.3e

l=$84

I = $0.7

-68 + 84(PlFi.1) +.0.7(PlFi.2) = 24.4/o PW Cost Modified HOR

3

208

Economic Evaluation and lnvestment Decision Methods

Adding an outside investment of 83.9 at year 2 to the uB-A" project does not .weight,the PW',Modified RoR,as. lsw^as.adding,the investment of 57.87 at time zero. However, note that the zq.4y" modified RoR result relates to very different unamortized invesment values each year than the time zero 21.6% pw Modified RoR relates to. Both results are economically equivalent even though different in magnitude. The modification that eliminates cost following revenue and modifies the analysis as little as possible is felt by many people to be the most desirable modification to use, so the latter year 2 modification often finds use in industry practice.

All of the analysis methods utilized for this example, other than regular ROR, have selected alternative "B" consistenfly. Any of these techniques can and should be used in place of regular rate or return analysis when the investment, income, investment type of analysis is encountered. The combination rate of return, rate of reinvestment meaning associated with cost, income, cost dual rates of return is what makes the dual RoR results useless for valid economic decisir:ns. The existence of dual rates is algebraically caused by the sign changes in cost, income, cost equations. This can be illustrated for incremental "B-A" analysis in this example.

B-n; c

:igq

l=$84

l=$84

C = $100

PW Eq: 0 = -68 + 84(PlFi,1) + 84(p/F i,2) - 100(p/F;,3) Mathematically: 0 = -68 +

Bailt(+i)) + 8a(1/(1+i))2

-

100(1/(1+i))3

Substirute X = (1/(1+i)): 0 = -68 + 84X +84X2

-

100X3

This is a "third order polynomial equation" as a function of X. Alge-

braic rules indicate that polynomial equations may have as many

chapter 4: Mutuaily Excrusive and Non-Mutuaily Excrusive project Anarysis

positive roots as sign changes, two in this case. sorving for X: X = 1, and_X = 314 gives i = O7o and i = g3.A%. These are tf,e same dual ROR results obtained earlier by trial and erroi..

t

EXAMPLE 4-12 Recramation costs can cause the Duar RoR problem

. An investment project requires the initiar investment of g70,000 to generate a projected stream of positive g40,oo0 per year cash flows in^each of years one througi'r tive. However, a reclamation cost of $140,000 is expected to be required at year 6 (the year 6 reclamation cost could relate to restoration of srrface land to origi_ nal contours for an open pit mining operation, recramation of an offshore platform for an offshore pitroreum production project, or reciamation costs for land cleanup from chemical contanrination, to name several possibilities). The minimum RoR is 2c7". Analyze iire econornic potential of this project using both Npv and RoR analysis.

Solution, All Values in Thousands of Doltars: C =7O

l=40

l=40

l=40

l=40

l=40

C=140

when cost foilows revenue, correct RoR anarysis requires use of one of the modified noR analysis techniques intioduced in Example 4-11 (Escrow Approach, year-by-year Approach, or Growth Rate of Return). ln this exampre, the sum of ine posiiive cash frows is $200 while the negative cash frows totar $21d. crea;ry,;ome of the early cash flows will be utilized to pay off the initiii investment, providing a return on that investment, while the remaining positive cash flows will have to be reinvesied at an interest rate if enough cash is to be generated to cover the future obrigation. This iilustrates the rate of return and rate of reinvestment-meaning associ_ ated with all dual "i" values.

210

Economic Evaluation and lnvestment Decision Methods

ROR Analysis Using an NPV Type of Equation

PW Eq: 40(P/A;,5)- 140(P/Fi,6) i = O"/" i = 5"/" i = 8"/"

-

70 = 0

40(5.000) - 140(1 .0000) 40(4.329) -140Q.7462) 40(3.993) - 140(0.6302) i = 15/" 40(3.352) -140(0.4323) i = 20o/" 40(2.991) -140(0.3349)i = 25"/" 40(2.689) -140(0.2621) i=30% 40(2.436) - 140(0.2072) -

+.

70 = -10.0 70 -1 .3 70 +1.5 70 +3.0 70= +2.7 70 +0.9 70 -1 .6

= = =

= =

Note that due to the "parabolic variation" of the NpV type equation results versus "i", by interpolation, Npv = 0 fgr the dual rates of return of 6.40oh and 26.780/, Each of these rates makes the cumulative cash position zero at the end of project-life. Both rates involve a combination meaning of rate of return on investment in early project life and rate of reinvestment rate in the later project years. These dual rates cannot be used direcily for decision making pur poses as ROR results. However, the dual rates do provide some useful information because they bracket the range of minimum rate of return values for.which project net present value is positive. This tells the range of 'ri " for which the project is satisfactory. whenever dual rates exist, it is easiest to rely on NpV analysis for decision purposes. However, going to Growth RoR analysis or present worth cost modified RoR analy.sis is equally valid, but generally more work. NPV calculated at "i^" always leads to correct economic decision in this situation, whereas the dual rates problem makes RoR analysis more confusing. 2.991 N

PV @ i* =2O/" =

qA(P I AZOo/o,S)

-

0.3349 ltr;O(P lF 2g/",d

-

70 = +$2.754 > 0

The NPV analysis is quick and simple to make and the positive NPV result tells us the project investment is satisfactory, although the NPV of +2.754 is only slightly greater than zero compared to the magnitude of costs that generated it, so project economics effectively are a break-even with investing elsewhere al2O"/o.

chapter 4: Mutuaily Excrusive and Non-Mutuaily Excrusive project Anarysis

211

-t

-60 Figure 4-g NpV vs Discount Rate for Cost, lncome, Cost |

Now before getting into the detairs of the modified RoR anarysis, note that Npv at i = 0."/o is negative for this exampre, whln has duar positive rate values of 6.4% ind 26.7g%. whenever the NpV at i = 0% is negative for an investment, income, investment situation, due to the paraboric variation of NpV with changes in ,,i,,, ouat positive ,,i,,varues exist if any real interest rate solutions exist for the Npv equation. lf NPV at i = 97 is positive, duar rate varues exist with one being negative and the other positive. This test of NpV at i = 0% tells an investor where to rook for the dual rates if it is deemed desirable to determine them. Beforg presenting the modified RoR anarysis carcurations, note that in calculating the duar rates at the beginning of this sorution that as ,,i,, increased from 0% to 15% that NpV i-n"r"rr". rather than decreases. This is a unique resurt of cost foilowing revenue in the cost, income, cost analysis situation. whenever you firid Npv increa.ing-*itn increas_ ing interest rates (rather than de'creasing as it always does for cost, income analyses) it is the author's expeiience tnat ihis is caused by cost following revenue in the analysis.

.

--r&..

212

Economic Evaluation and lnvestment Decision Methods

ROR Using the Escrow Approach To eliminate this investment, income, investment situation, present worth the finai cost or costs at the minimum RoR to an equivalent t present value, giving the following diagram:

0.3349

6 = $70 * $1a0(P/FZO*,O)

0

|

1............5

6

PW Cost Modified ROR PW Eq: 116.88 = 40(P/Ai,5) Modified ROR = i = 21.1"/" > 2oo/o, so satisfactory. since this modified RoR result is based solely on income following cost, it is valid for economic decision-making purposes as a rate of return result. Dis: counting the year 6 cost modifies the magnitude of our RoR result but not its validity for comparison to i* = 20"/o for the economic decision.

Growth ROR

combine reinvestment of revenue at "i*" with the initial project to eliminate cost following revenue as follows:

lnitial Project

C=$70 0

l=940 l=940 1..........5

C=9140 6

Reinvest Flevenues @ i*=2Oo/o

_ 0

c=940 c=940 1..........5 7.442 1.200

6

F=$357.20

where, F = 40(FiA 2O%,5)(F /P 21o/o,1) = $3SZ.Z

Combine lnitial + Reinvestment Revenues

C=$70 o

-

C=9140"-

Growth ROR PW Eq: 70 = ZlZ.2(PlFi,A) Growth ROR = i = 20.9"/" > 2oo/o, so satisfactory.

F=$357'2

chapter 4: Mutuaily Excrusive and Non-Mutuaily Excrusive project Ana,ysis

213

Both the present worth cost modified RoR analysis and Growth RoR condulion, which is in this case and in general always consistent with Npv analysis eccnomic conclusions. The key, to correct RoR analysis of cost, income, cost anaiysis situations is to modity tne analysis to eiinrinate cost following revenue before making ihe HoR anaiysis. The present worth cost ani Growth RoR nrcciifications ai.e the turc basic approaches used to elimi_ nate cost following revenues. Hcwever, there are several variatiorrs in the v'ray different people apply these modifications. one in particular is worth noting. - ln applying the escrow approach it is not necessary to bring costs following revenue all the way to year'0. lt realry is only n*""r.rry to pre_ sent worth costs following revenue year by yea, until those costs are ar-ialysis have given the same economic

offset by project revenue. This gives the foilowing modification referred to as the "year by year Modification.,,

HOR Using the Year-by-year Modification

.

Discount the year 6 cost year by year until offset by project

income.

C=19.90 I=40.00

Net l=20.1 0

3'

\

Dttr

C=63.88\

C-110.66\

\ l= 4o.oo t"ro,\"=ro9 20,1. - \Net +4!!A e)rro.., \Net c= C=23 88 76.66

56

4

New Modified Diagram

c=70 l=40 l=40

I

= 20.1

PW Eq: 0 = -70 + 4O(p/Ai,2) + 20.1(p/F;,3) i = l,{odified ROR

= 22.75% > i* =

ZO"k so satisfactory

This modified RoR result is several percent bigger than the initial present worth cost modified result. This is oecause the two modified RoR results relate to very different initial year 0 investments. The results are really equivalent and give the same economic conclusion when compared to the 20% minimum RoR. Remember that you cannot and should not look at the magnitude of RoR results and think

214

Economic Evaluation and lnvestment Decision Methods

big is best' A projggt with a big RoR that rerates to a given invesr ment an d stream ingome m.ay. not .be,a.s..desi rable qs project.with 9f , a smarrer noR that'r"ritei dirrerent stream of b

income.

EXAMPLE

i t, biffiffi;Ji;"r",;;

"

4-rs A petroteum tnfifi Driiling Accereration probrem lnvolving Dual Rates of Return

A producing oil field has wells drilled on 160 acre centers. lt is proposed to infill drill wells on g0 acre centers to accelerate petroleum production and give more efficient drainage of the petroleum reservoir. Present and proposed costs and net revenues are shown on the following time diagrams with varues in thousands of doilars:

Present C

0129456

o

Accelerate C=

0129456

For a minimum RoR of 12yo, use rate of return anarysis to determine if the acceleration drilling program investment is satisfactory from an economic viewpoint.

Solution: The-"present" producing project is crearry satisfactory since costs for deveropment.have arready been incurred (so they are sunk). For no additionar costs to be lncurred, the ,,present,, project revenues are projected to be generated. This relates to an infinite percent return on zero dollars invested in the present project, an economically satisfactory project. The accererated plolect total investment RoR is 2oo%. However, this RoR does not need to be calculated because knowing the present project is satisfactory, we can go to incremental analysis to determine if incremental invest_ ment dollars spent on the accererated production infiil driiling pro_ gram are justified economically by incremental revenues. The incremental diagram involves cost, income, cost as follows because the negative incrementar incomes in years 4, 5 and 6 are

effectively costs as follows:

chapter 4: Mutuary Excrusive and Non-t\,.lutuary Excrusive project

Anarysis

215

lncremental Rate of Return Analysis Accelerated C= *Present o

1

2

s

,4

5

O

6

lf you i,vrite a conventionar present worth eqtration for the incre_

nrental diagranr values, you get dual rates as follows: PIV Eq: 0 = -735 + 850(p/F;,1) + a50{F iFi,2} +50(ptF;,3)

-

310(p/F;,4)_ 280(p/Fi,5) _ 1S0(p/F;,6) . rrial and error, duar "i" varues of 12"/, and 2so/o resurt. An investor that treats either of these resurts as rate of return co*pareo with the minirnuin RoR of 12/, wourd concrude that the incrementar project economics are satisfactory. This turns out to be an incorrect conclusion. Both of the duar rates of 17% and 25"/" have rate of reinvest_ rnent meaning as weil as rate of return rneaning at different pc:nts in time..Required rates of revenue reinvestment of 1 Zo/" and 25"k compared with 120,L reinvestment opporiuniiles inoratei oy trre mini_ mum ROR indicate a very unsatisfactory incrementar investment whereas rates of return of izx and 25"/. compared to the 120n minimum RoR rook satisfactory. The unsatisfactory rate of reinvestment meaning is stronger than the rate of return melning as t!:e foilowing NPV and Escrow ROR analysis results show. Net Present Value Anatysis

NPV= -7OS + 850(p/F1 2"/",1) + 450(p/F1 2y.,2) + S0(p/F1 2%,g)

-

310(P/F1 2/o,4)

-

12y",5) - 150(p/F1 2/.,6) = -13.6 < 0, so slighfly unsatisfactory. 2BO(P/F

Escrow Approach ROR Analysis tulod. Yr 0 Cost

=735 + 3i0(p/F1 2"k,4) + ZgO(p/F12o/o,S) + 150(P/F12%,6) - $1,166.90

Mod. PW Eq: 0 = -'t

,1

66.9 + 850(p/Fi,1) + 4S0(p /Fi,2) + 50(p/F1,3)

Trial and error: i = Modified ROR

=

11"/o



0,

so accept,,A,,, reject "B"

To compiete oui'discussion of the investment, income, investment siiuations, it is inrportant to point out and emphasize that if income fciiows the second investment, a duat RoR situation may not exist. This means that investment, income, investment, income analysis situations may not give the duat RoR prablem but investment, income, investment always does. Look'at the project cumulative cash position diagram for the positive ,'i,, value calculated to test whether combination rate of return, rate of reinvestment meaning is associated with the "i" value at different points in time. Remember, if the cumuiative cash position does not go positive at any time, rate of reinvestment meaning does not exist aid ihe meaning of ,,i,, is rate of return for the entire project evaluation life. The foll6wing example illustrates this important analysis consideration.

EXAMPLE 4-15 An lnvestment, lncome, lnvestment, lncome Situation Where Conventional ROR Anatysis is Vatid Diagram values in thousands of dollars.

C=50

l=30

C=100

l=30

l=60

l=60

l=60

A development project will require investments of g50,000 at time zero and $100,000 the end of year 2 as shown on the time diagram, 9f with incomes of 930,000 at the end of years 1 and 2, and $60,0-00 ai

Eoonomic Evaluation and lnvestment Decision Methods

tggnd of years 3, 4 and 5. For a minimum

rate of return of 2070, use RoR. analysis to, evatuate. the economi'.desirabirity..i tni. oroject. rs the "i" value that you calculate meaningful for economic decision mak_ ing as RoR? Does NpV anarysis verify'your conctusioni--

Solution, All Values in Thousands of Do[ars: NPV Eq: 30(P/A;,2) + 60(p/A;,3)@/Fi,2) _ 100(p/F;,2) _ 50

-

0

Since the NPV at i = O"/o is positive, only one positive ,,i,, exists that will make NPV = 0. By trial and error, i 22.46"/" makes NpV = g. 1s = this "i" value of 27.46o/o a rate of return result or is ii onl of a pair of "dual rates of return" that have combination rate of-rrirrn, iate of reinvestment requirement meaning at difierent points in time? lf a companion dual rate. of return exisG, it would be'negative. However, it is possible to avoid the search for the possinte-iompanion ouat Rpn-lv testing to see if rate of reinvestment meaning is associated wilh 27.46"/" "i" value at any point in rime. Dual rates if return arways have combined rate of return, rate of reinvestment meaning at different point in time. lf rate of reinvestment meaning does not exist at anv time, then dual rates of return do not exi$ f6r this probtem and the 27.46% "i" varue can be treated as RoR for decision'pirpo,i'"1'"

Project years

Figure 4-10 cumurative cash position Diagram of a cost, lncome, Cost, lncome Rate'of Return Analysis

chapter 4: Mutua,y Excrusive anri Non-Mutuariy Exclusive project Anarysis

219

Evaluation of the cumrrrative cash position diagram for this project. at the project "i" varue of 22,46/" does show thatih; cumurative cash position never goes above zero at any ti*" Jriirgiie prolect tife. Therefore, the "i" of 27.460k means*rate of Eturn,,over rhe entire project life and never means rate of reinvestment. onry ,/.,ien ::e cumulative cash position goes positive does ,,i,, nave tne rate of re_ investment meaning.

{.9

Alternating Income, Investment, Income Situations For the situation when you have alternating income, in'estment, income on the time diagram, dual rates of return occur for the opposite conditions rlescribed in the previous section for the inr.,estment, income, investment situittion. For income, in'esiment, income situations, duAl ..i,, varues that are hr;th positive wiii exist if Npv ar i = O,ra is p 0, accept the project

Escalated $ ROR = 42.5/oi this is the ,,i,,value that makes escalated dollar NpV = 0. 42.5% > i" = 157o, accept the project

260

Economic Evaluation and lnvestment Decision Methods

B) Constant Dollar Analysis The escalated dollar costs and net revenues from part (A) are the basis for the constant dollar calculations.

t

Constant Dollar Vatues

.9434 .8900 .8396 Ct =42.8(P /F 6y",1) RZ=57.86(P/F Rg=G2.3(p IF 6y",2) A11^.g)

^ CO-20___:j9fB

=51.49 '

-

=S2.AO"'"'"'

0

constant dollar values are obtained by discounting escalated dollars at the rate of inflation of 6% per year. For constant dollar NpV analysis we must convert the 15% escalated dollar minimum RoR to the equivalent constant dollar minimum RoFl for the assumed 6% per year inflation rate. use Equation s-1 for this calculation as follows: 1l

i

= [(1 + i)/(1

+f)]- 1 = (1.1S/1.06)-

Constant $ NPV = -20

-

1

=0.C849or8.49yo

.9217 .8496 40.98(P/Fg.4go/o,1) + 51 .4g(plFg.49o/o,Z) .7831

+ 52.30(P/Fg.qgy.p) = +27.48 > 0, so accept Constant $ NPV =-20-4O.gB(1t1.08+S11 + 51.49(111.0A+S;2 + 52.30(1/1 .08+S;3 = +27.48 > 0, so accept

Note that the constant dollar NpV is identical to the escalated dollar NPV within round-off error calculation accuracy. constant dollar NPV equations are mathematically equivalent to escalated dollar NPV equations, so of course give the same results. The mathematical equivalency follows: Escalated $ Calculatiohs = Constant $ Calculations (Escalated $ Val ue) ( P/F;*, 6) = ( Escalated $ Value) ( p/F1, since P/F;.,n = (P/F1,n)(p/F;.,,n)

p)

(p/F;.,, n)

as discussed earlier in the development of Fquation 5-1. For this analysis in year Z:

Chapter 5: Escalated and Constant Dcilars

P /F

1

S"/",2 = 0.7561 = (p lF 6"7o,2)

261

p

/F

a.qg6,Z)

= (0.8900X0.8496) = 0.7561

constant $ RoR = 34.41a; this is the "i" var0e that makes constant cjoliar net present value equal to zero. g4.4"'o > i* 8.49o/o, aqgepi the prOject =

C) Today's Dollar Anatysis

Using today's doilars as the basis for evaruation carcurations .involves one of two

different assumptions. Eithei yo, that today's doilars equar escarated doriar vaiues "rrrre that o,, you assume today's dollars equar constant dofiar varues (see Ex. 5-1a and s-1b), Today's Dollars Equal Escatated Doltars Assuming that'today's coilars equar escarated doilars expricitry assumes that costs and revenues in the future will be the same ai tiiey wouid be ioday. This implicifly involves tne assumption that cc_cts and revenues wiil escaiate at oi/" per year over the evaruation rife. This is an escalated doiiar assumption simiiar to, but different fr-orn the pai't "A" assumptions, so an escaraterj doila: minimum RoR must i:e used in NPV carcurations and for RoR anarysis decisions. The

"today's doliar varues equar escarated doilar varues,, ,nrrvai, foilows: I'JPV

= -20

-

4O(,PlF1S"/",1) +

= +15.9 > 0 accept

'

SO(p/FlS,t",2)+ S0(p/F1 S"/"5)

ROR = 32.2% > i" = 157o, accept Note these escalated dollar NpV and RoR results are significanily different frorn the part "A" escalated dollar analysis results. There are an unlimited number of different ways that esiarateci costs and rev_ enues can be projected. Assuming today's doilars are equar to escaiated dollars is just one specific eslalation assumption. lt is to understand specific escaration assumptions used in important anaryses because they v,,ill affect evaluation results. A variation of the today's doilar equar escarated doilars assumption is to escalate ail capitar costs (such as acquisition and deveropment costs) at specified rates and to assume that the escalated dollar net revenues or profits in the income generating years wiil equar today,s dollar net revenues or profits. rnis is often cailed ,,the

washout

262

Economic Evaluation and lnvestment Decision Methods

assumption" since it assumes that any escalation of operating costs each year will be offset (washed out) by the saqe dolfar escalition of revenue. Note there are no revenues in the development years, so costs must be escalated in pre-revenue years. The warhout assumption only applies to revenues and operating costs in the revenue generating years.

Today's Dollars Equal Constant Doilars since constant dollar values are obtained by discounting escalated dollars at the rate ol_ inflation, the only way today's dollars can equal constant dollars is if all today's dollar values escalate each yeai at the rate of inflation. Escalating each cost and revenue at the rate of inflation and then discounting the resulting escalated dollars at the rate of inflation to get constant dollars brings the dollar values back to the starting today's doilar values. This is constant dollar analysis assumption, so a constant dollar minimum RoFl (g.4g"/" for this analysis) must be used in the constant dollar Npv calculations and for the economic decision with constant dollar RoR results. The today,s dollars equal constant dollars Npv and RoR results follow:

i

NPV = -20

- 40(PlFg.ag"/",1)

+ S0(P/F8.49 o/",2) + 50(p/Fg.497.,3)

= +24.8.> 0, so accept ROR = g2.2%, i*'= 8.4g"/o,So accept

Note the today's dollars equal escalated dollars NpV result is significantly different from the today's dollars equal constant dollars NPV result. Although the RoR results are 32.2/o for both cases, different minimum rates of return are used for the economic decision with RoR in the two cases. These two today's dollar analysis cases are very differeht and can lead to different investment decisions. obviously, understanding the escalated dollar or constant dollar inflation and escalation assumptions being made is very important for correct economic decision making.

Chapter 5: Escalated and Constant Dollars

263

EXAMPLE 5-3 Escalated and Constant Dollar Cost Analysis of Service Producing Alternatives Compare tvuo alternatives that provide a service using escalated and constant dollar analysis. Consider alternati'.re "A" to be capital intensive, requiring the expenditure of $100,000 at time zero and no operating costs in years one or tr.ro to provi,Ce a -service for two ye.l!"s while alternative "8" is labor intensive, requiring end-of-yeai"one ard two escalated dollar operating costs of $60,000 and $72,000 respectively. Salvage is zero in both cases. Make present worth cost analysis for an escalated dollar minimum rate of return of 30%, then for i* = 20"h, then for i* = 107o. Assume inflation at 20% per year for all ccnstant dollar calculations. Verify the present rvorth cost results with incremental NPV analysis.

Solution, All Values in Thousands of Dollars: Escalated Dollar Diagranrs

(A)c--too 012

CC =

(B)

Soiution:

60

aC =72

-

Escalated Dollar PW Cost Analysis 1) for i* = 307o, remembering P/F1.,n = (1/1+i.)n PW4 = 'lQg PWB = 60(1/1 .3) + 72(111.3)2 = 88.75, Select "8"

2) tor i" = 20"h

Ptll4 =

1gg PWB = 60(1/1 .2) +72(111.2)2

=

1OO

Results indicate break-even economics.

3) for i* = 10"h PW4 = 100, select smaller Present Worth Cost, "A" PWB = 60(1/1 .1) + 72(111.1)2 = 114

Economic Evaluation and lnvestment Decision Methods

Constant Dollar Diagrams for lnflation Rate, t =

(A) c

2}o/o

=.

012t OC

(B) -

= AOP|IZOW,|

=50

OC

= Z2(PlFZot =50

,Z')

Constant Dollar PW Cost Analysis: 1) for an escalated dollar minimum RO*,R, i* = 307o, the corresponding constant dollar minimum ROR, i*' is 8.93% PS/4 = 'lQQ PWg = 5O(1/1.0833) + 50(1/1.08eS12 = 88.75, Select Smatter, "B" 2) for f - zC,/o, constant dollar i*'is 0 PW4 = 100 Break-even PWg = 50(1/1.0) + 50(111.0)2 = 100 Results indicate break-even economics

3) for i* =

10o/o,

constant dollar i"'is -g.33%

PW4 = 100, Select Smaller, "A" PWg = 50(1/.9166) + 50(1/.9166)2 = 114 Note that not only do escalated and constant dollar analysis give the same conclusion, but those conclusions are based upon identical present worth costs. If we look at the incremental difference between "A" and "8", we can show that incremental NpV analysis gives the same result for escalated or constant dollar analysis.

lncremental Escalated Dollar Diagram

(A-B)

100 012

C=

Savings

60

72

Escalated Dollar lncremental NPV Analysis i*

=3}o/o, NPV4-B = 60(1/1 .3) + t2(1 11.g)2 -1.00 = -1'1 .2S < 0,

select "B"

Ji

Cnaprer 5: Escalated and Consiant Doiiars

265

i*-ZO%, NPV4-g = 60(1 11.2) + 72(111.2)2

- 100 = 0, break-even i* =1}o/o, NPV44 = 60(1 /1 .1) + Z2(1 11 .\2 - 00 = +1 4.0 > 0, 1

select "A"

lncremental Constant Dollar Diagram

A-B) c =

,00

Savings

50

50

Constant Dollar lncremental NpV Analysls For i* = 30% and t=20o/o, equivalent

i*'=

NPV44 = 50(1/1.0833) + 50(1/1.08SS;2 = -11.25, select "B', For i* = 2O/o and f=2Oo/o, equivalent i"'

NPV4-B = 50(1/1.0) + 50(1/1.0)2

-

=

8.387o

- 100 Oo/o

100 = 0, break-even

For i" = 10% and t=20"/o, equivalent i*' = -8.337o NPV44 = 50(11.9166) + 50(1/.9166)2 - 100 = 14.0, select "A"

Note the identical incremental Npv results for both escalated and constant doliar analysis, so of course the same economic decision resulis either way. Now that we have established that either escalated or constant dollar analysis properly handled gives the same economic analysis conclusions, are there reasons for preferring one method over the other? In general it takes two present worth calculations in constant dollar analysis to achieve the same result that can be obtained with one present worth calculation in escalated dollar analysis. r.;ewer calcrrlations means fewer chances for math elrors. a point in favor of escalated dollar analysis. To make proper after-tax anaiysis, tax calcuiations must always be made in escalated dollars as must borrorved money principal and interest payments. For constant dollar analysis. this requires careful diligence to avoid improper mixing of escalated and constant dollars. with escalated dollar analysis all values are in escalated dollars so this is not a problem, another point in favor of escalated dollar analysis. From a practical and ease of calcuiation viewpoint, there is little to be said for constant dollar analysis that cannot be said more favorably

266

Economic Evaluation and lnvestment Decision Methods

for escalated dollar analysis. However, for those evaluation people who .want to make constant dollar analysis rather than escalated dollar analysis, .i the following steps should be fbllo*ed:

1) Determine the escalated dollar values for all project costs &rd revenues. 2) Convert all escalated dollar values to the corresponding constant dollar

3)

values for the assumed inflation rates each year. Convert the escalated dollar minimum ROR, "i*", to the corresponding constant dollar value, "i*"', if the minimurnROR is initially expressed in terms of escalated dollars.

4) Calculate constant dollar NfV using i*', or calculate constant dollar ROR, "i"', and compare to i* for the economic decision. One situation that can give constant dollar analysis a potential intangible advantage over escalated dollar analysis is in evaluation of a project to determine and negotiate the break-even selling price that a purchaser may be u'illing to pay for a product. Since in inflationary times a given constant dollar minimum rate of return is always less than the equivalent escalated dollar minimum rate of return. it may be easier to convince a buyer to accept paying the price needed for you to ger a l57o constant dollar ROR than a higher but equivalent escalated dollar ROR for a given rate of inflatiorr. This is a potential marketing or negotiation advantage rather than an economic analysis advantage. The following example shows that breakeven analysis economic calculations (such as break-even selling price) will be exactly the same with either rscalated dollar analysis or constant dollar analysis.

EXAMPLE 5-4 Break-even Selling Price Analysis in Escalated and Constant Dollars. The investment of $3C,000 today is estimated to produce 100 prod-

uct units each year for the next two years when the product is expected to become obsolete. Year 2 salvage value is expected to be zero. Today's dollar operating costs for years 1 and 2 are estimated to be $8,000 per year. lnflation is expected lo be 7.0"/" per year for each of the next two years. lf product selling price is projected to escalate 8o/" per year and operating costs escalate 10% per year, calculate the year 1 and 2 escalated dollar seliing price that will give the investor a desired 157o constant dollar ROR on invested dollars.

Chapter 5: Escalated and Constant Dollars

257

Solution, All Values in Dollars: Let X = Today's Dollar Selling price per Unit Year Escalated $ Escalated $

---

Year 2

Saies Xl199lt.1tA"/o,t) = 1OB.0X

oC

EscalatedSFrofit Constant $

1

Profit

X(100XF/ps

"/",2) = 116.6X

a99o(rie1oz,r) = 8,800 B0J0(F/P101;,2) = 9,6a0

108.0X-8800

(108.0X

116.6X_g,OS0

- S,800XP/F7%,1) (1i5.6X

-g,6g1)(ptF7%,2)

As shown, today's dollar revenues and operating costs are converted to escalated dollar values using the selling price and operating cost escalation rates of B% and 162 respecti-vely. lf you want to work in escalated dollars you use the resultant escalated dollar profrts shown, which are a function of the unknown today's dollar selling price per unit, X. lf you prefer to work in constant dollars you present rvcrth escalated dollar profit at the 7"k per year rate of inflation to convert escalated dollars to constant dollars. Escalated Dollar Present Worth Equation Catculations To write an escalated dollar present worth equation we mu*qt use escalated dollar values and handle the time value of mcney at the escalated dollar minimum RoR that is equivalent to the desired 15% cor,'stant doliar minimum RoR for assumed 7./" per year inflation. Usirg Equaticn 5-1:

i'= (1 +f)(1 +i"') -

1 = (1.07X1.1S)

-

1=.2305 or23.O5"h

.81268 30,000 = (108.0X

- 8,800XP/FZ3.OS,t)

.66045 + (t 1G.6X

-

9,68OXp/FZS.AS,Z)

Solving for X = g164.26lunits = Today,s Dollar Selling price 264.26(FlPgg/o,1) = $285.40/unit = Year 1 Escalated $ Selling price

264.26(F/P8"/o,Z) = $808.24lunit = year 2 Escalated $ Selling price

Constant Dollar Present Worth Equation Using Constant Dollar Profits Handle the time value of money using the 15% constant dollar minimum ROR:

Economic Evaluati6n and lnvestment Decision Methods

30,000 =

(1

08.0X

+

(1

1

-

6.6X

8,800XP lFT"/o,1)(P lF

-

6y",1

9,680XP 1F7"7",21(P lF 1 S"/o,Z)

solving for X = $264.26lunits = Today's Dollar Selling Price 264.26(FlPg%,1)= $285.40/unit = Year 1 Escalated g Selling Price 264.26(FlPg,/o,Z) = $308.24luoit = Year 2 Escalated g Selling Price

The same break-even selling prices result from either escalated or constant dollar analysis. To conclude the inflation and escalation discussion, a few words should be said about forecasting escalation rates for different commodities or segments of industry. The past often is a good indicator of the future, so analysis of past cost trends for a particular commodity or asset is one way to get an indication of what the future might hold. This approach was very poor in the 1973-1980 period due.to the significant increase in energy costs around the world, but no method of analysis is going to predict consistently the effects of that kind of upset to the world economy. The U.S. Bureau of Labor Statistics publishes 70 or more price indices for commodities and materials, 5 or more indices or wage rates and an index of engineering costs which can be obtained to give past trends. "Chemical Engineering" consolidates these

Bureau of Labor Statistics into the CE Plant Cost Index published on a bimonthly basis as a measure of the cost of typical chemical plants. "Chemical Engineering" also presents the Marshall and Swift equipment cost index bimonthly. No one has a crystal ball to forecast the future accurately, but the use of available indices can be helpful in determining cost and price trends and rates of change of these trends needed to forecast meaningful escalation rates for costs and revenues needed for investment analyses.

In summary, proper evaluation of investments in various escalated dollar or constant dollar analyses requires understanding how to apply the following three different kinds of rates: 1. Escalation Rates: used to convert today's dollar values to escalated dollar values. 2. Inflation Rates: used to convert escalated dollar values to constant dollar values. 3. Time Value of Money Rates: used to account for the time valug of money using "i" oa "i*i' in escalated dollar analyses, and "i"' oa "i*"' in constant dollar analyses.

Chapter 5: Escalated and Constant Dclars

These rates are

all usetl in the foilowing example illustrating general

escalated and constant dollar analysis calculations involving different escaiation rates a:,d infla: ioil ratcs each y:i:r. +

EXAMPLE 5-5 RoR and Npv Anatysis with changing Escatation and lnflation Rates Each year

A cost of $100,000 today is projected to generate today,s dollar incomes of $75,000 per year at the end of eaoh of years 1, e and 3 with today's dollar operating costs of $25,000 per year at years 1, 2 and 3. saivage value is zero at year 3. lncomes and operating costs are projected to escalate 10% in year 1 , 1z/o in year 2, and 1s"1" in year 3, so net income minus operating cost escalates at the same given rate each year. calculate the prolect escalated dollar RoR and NPV assuming the minimum RoR for each of the 3 years is 15% in escalated doilars. Then assume inflation rates will be 10% in year 1, 8'A in year 2 and 6% in year 3, and calculate constant dollar RoR and NPV. Solution: Today's Doliar Values (ln Thousands of Doltars)

C=100

Netll=gQ

Net

12

=

$Q

Net

13

= $Q

Escalated Dollar Values

C=100 Netll=gg 01

Net

12

= 61.6

Net

13

= 70.84

where, 1 .100 Net l1 = 50(F/Pt O"/"J) = 55.0

1

Net

12

Net

13

.100

= 50(F/Pt

1

.120

g"/",iF|P12./",i

.100

.120

= 61.60

1 1 1 .150 = 50(F/Pt g"7"1)f /P12.7"1)fflP11"/b,i =70.84

270

Ecbnomic Evaluation and lnvestment Decision Methods

Escalated Dollar Present Worth Equation for ROR Analysis 100 = 55(P/Fi,1)+ 61.6(P/F1,2) + 70.84(P/F;,3) i = Escalated Dollar ROR = 37.4o/" by trial and error

i

.

37.4% > 15"/o, so satisfactory

Escalated Dollar Net Present Value

.8696

.7561

.6575 NPV = -100 + 55(P/F1 S/o1) + 61 .6(P/F 15"/o,2) + 7A.84(PlFt SZ,g) = +$41.0 > O, so satisfactory

Constant Dollar Vatues C = 100 Net 11 =

50

Net

12

= 51

85

Net

13

= 56.25

where escalated dollars discounted at the annual inflation rates give the following constant dollar net incomes: .9091

Net l1 = 55(P/Ft O"/"J) = 50.0 .9259 Net l2 = 61 .6(P/F 10"/o,1)(P/Fg/.,1) = 51.85

.9091

.9091

Net

13

.9259 .9434 70.84(PlFlOo/",1)(PlF67",1l!lF6"y",1) = = 56.2S

Constant Dollar Present Worth Equation for ROR Analysis 100 = 50(P/F;,,1)+ 51 .85(P/Fy,2) + 56.25(P/F;,,3)

i'= Constant Dcllar ROR = 26.3%

> i*'values shown in next section, so satisfactory.

Constant Dollar Net Present Value Analysis For constant dollar NPV analysis we must calculate the constant dollar minimum ROR each year that is equivalent to the 15% escalated dollar minimum FiOR for the assumed inflation rates of 1O"h in year 1, 87o in year 2 and 6% in year 3 using a.rearranged version of Equation 5-1.

Chapter 5: Escalated and Constant Dollars

271

i" ={(1 +i.)/(1 +f)}-1 Year 1, i*' = (1 .15/1.10) - 1 = 4.54o/o Year 2, i*' = (1 .15/1 .08) - 1 = 6.48o/o 1, 'r€3r 3, i*'= (1.15/1.06) - 1 = 8.4g,/o .9566 .9s66 .9391 NPV = -100 + 50(P/F4.54 + 51 .BS(P/F4 .S4o/o,1)p/F6.agh,i "/o,1)

+ 56.25

.9566 .9391 4"/", 1) (P 6. a6"7", i (P

(P / F 4.S

/F

.9217 /F

g.qg"t,i

= +$41.0 > 0, so satisfactory

Note the equivalence of constant dollar NpV and escalated dollar NPV results. Even with different escalation and inflation rates each year, correct analysis gives the same escalated and constant dollar NPV results, so of course the same economic conclusions from eithei' analysis. similarly, with RoR analysis results in either escalated or constant dollars, as long as you compare project RoR to the minimum RoR expressed in the same kind of dollais (escalated or constant), you get the same economic conclusions from either escalated or constant dollar ROR analy'sis. 5.2 Exchange Rate Effects on Escalation and cash Florv Analysis

lr'henever project costs and revenues involve more than one currency, e

\ciran-qe rates must be projected fbr each evaltration period to perrnit analysis

of the project in terms of one currency. Economic analysis reiults tend to be

very sensitive to exchange rate projections. In general, exchange rate changes often reflect current changes (or perceived tuture changes) in relative inflation rates between countries. However, this is not always the case. Differences in country interest rates and balance of pal,nrent deficits can be major factors that affect exchanse rares. In 1995 the U.S. clollar declined l57o to z\vo against btrth the Jnp:rnese yen anrJ the Cennun mark alrhough U.S. inflation rvas relatively lorv at 3Lh per year or less. usnally however, devaluation of a country cuffency a!,ainst the U.S. dollar, Japenese yen, or European currencies is caused by current or projected future inflation rate differences between the countries. Therelbre, exchange rate projections often implicitly account for future inllation effects on escalated dollar analysis. The following example illustrates the mechanics of handling exchange rates in cash flow analysis as rvell as the sensitivity of evaluation results to exchange rate effects.

272

Economic Evaluation and lnvestment Decision Methods

EXAMPLE 5-6 Exchange Rate Analysis Variations

A company is considering investing,$1,000 in Country'12" whose time zero (now) currency exchange rate is lOOZ Units per$1.00 U.S. The following time diagram. giveis the relevant cost, ptoduction, selling price and exchange rate data, with valdes in today's U.S. dollars. Production = 10,000 units in years one and two Selling Price = $0.06/unit in years one and two Operating Costs = $0.01/unit in years one and two Cost

=

$1,000

$600 Flevenue $600 Revenue $100 Op. Costs $100 Op. Costs Salvags = $400

2

Analyze the following evaluation cases: Case

A)

Evaluate the project ROR and NPV @ i* = 10% using a U.S. dollar analysis assuming zero percent escalation olall values per year.

CaSeB) Evaluate the project ROR and NPV @ i* = 10% using

Country Z currency analysis assuming zero percent escalation of all values per year. Case C) Change the Case B analysis to reflect projected 50% per year devaluation of Country Z currency against the U.S. dollar. Assume all project costs, revenues, and salvage values are incurred or realized in U.S. dollars, but do the analysis in terms of Z units. (This could be a Country Z mining or petroleum project where product is sold internationally in U.S. dollars.) Case D) Re-work Case C assuming sales revenue is realized by selling product (such as electric power) in country Z at the uniform selling price of 6.0 Z units {(1002/$1.00) x ($0.00/Unit)) per product unit each year. ln other words, product is being sold to the country Z general population and the economy of the country will not permit passing inflation effects through currency devaluation on to the consumer. For simplicity, also assume salvage value is unaffected by exchange rate changes. However, operating costs are assumed to be affected by exchahge rate changes.

Chapter 5: Escalated and Constant Doilars

case

E)

Re-anaryze case B using u.s. doilar financiar borrowed assuming $g00 U.S. (g,OO0 2 units) are borrowed at year 0 at 107. annuar interesi to be repaid with year 1 Z mortgage payments of $200 U.S. ban principar prus accrued interest prus a barioon (rump sum) roan principar payment of $400 ar the end of year 2tl pay off the loan when the project is sold.. Sales in 'Corntr, Z currency units are converted tc U.S. dclars to pay oft tf,e toan. Re-anaryze,case D using the reveraged borrowed money conditions described in Case E.

, money leverage

*l

case

F)

Solutions: Case

A) U.S. Doltars Analysis

$600 revenue/yr 19,990 uniisiyr ($0.06iunit) -10,000 unitsiyr ($0.0ilunit) = _$.t00 operatlng cosVyr Before-Tax Cash Flow/yr $500 + = $400 Salvage atyear

=

-$1,000

$500

2

$500+$400 Satv.

ROR = 23.11"/" NPV @ 10"/" = $198.05 U.S.

Case

B) Country Z Currency Analysis

-100,0002

50,0002

ROR = 23.11"/" NPV@ 10%- lg,Bg5ZUnits

Case

C)

-Country Z Currency Analysis With Exchange Rate Changes

Year 0 100 Z Units = $1.0 U.S. Year 1 150 Z Units = $1.0 u.s. Year 2 Z2S Z Units $1.0 U.S. = Z Currency Unit Cash Flow:

(100 Z Units $1.0 U.S.) = 50,0002 + 40,0002 Salv.

274

Economic Evaluation and lnvestment Decision Methods

012

Year

Revenue Operating Costs Capital Costs

-

Cash Flow

.

-100,000 -100,000

90,000* +75,00O

225,0a0

+202,500

$600 U.S.(1502 Units / $1.00 U.S.) = 90,0002 Units **-$100 U.S.(1502 Units / $1.00 U.S.) = -15,0002 Units ROR = 84.667" NPV @ 1Oo/o = 135,537 Z Units

The devaluation effects have worked for the investor and given better economic results for the assumption that revenue escalates proportional to devaluation. This would relate to an export project such as mining or oil and gas production project where product is sold internationally in U.S. dollar prices. Often it is very difficult or impossible to pass on to dornestic consumers price escalation due to currency devaluation effects. The domestic consumer may not have the

financial means to pay higher prices. Case D shows that this assumption gives very different economic results. Case

D) Z Gurrency Unit Cash Flow Analysis as in Case

C, No

Revenue Escalation Year

0

Revenue - Operating Costs - Capital

-100,000

-

-100,000

Costs

Cash Flow

12 60,000

-ru,ooo 45,000

100,000

-22,500 77,500

ROR = 13.36% NPV @ look =+4,958 Z Units

These results are economically less desirable than the "no devaluation" Case B results, because devaluation is assumed to negatively affect operating costs but to have no off-setting positive effect on revenue. When leveraged money is involved, currency devaluation can have much greater effects as the following two cases show.These cases relate to borrowed money analysis considerations introduced

Chapter 5: Escalated and Constant Dollars

in chapter 11, but applied here to illustrate the significant impact of exchange rate changes on leveraged evaluations. Refer to chapter 1 1 , Example 11-1 if the handling of borrowed money (leverage) in ',lris analysis is not clear.

E)

Case

Z Currency Analysis With Borrowed U.S. Doilars, No Exchange Rate Changes

012

Y'ear

Revenue - Operating Costs - lnterest - Loan Principal - Balloon Principal + Borrowed Dollars - Capitai Costs Le,reraged CF

60,000 -10,000 -9,000

-i33;333

:

-20,000 +22,000

100,000 _10,000

-6,000

-4oooo +24,000

Le'reraged BOR = 77.58% Leveraged NPV @ 10o/" = 1g,Bg5 Z Units

This leveraged RoR result is much betier than the 29.11% RoR tor cash investment case B. However, note the NpV for case B is ti:re same as for case E because the cost of borrowed money which is the 10% interest rate is the same as the 10% opportunity cost of capital minimum discount rate. Case

F)

Z Currency Analysis With Borrowed U.S. Dollars, Exchange Rate Changes Affect Operating Costs, Loan Principal and lnterest, Not Revenue

'/ear

0

Revenue - Operating Costs - lnterest - Loan Principal + Borrowed Dollars +80,000 - Capital -100,000

12 60,000 -15,000 -12,000 -u.:..

100,000

-22,500 -13,500 -135,000

Costs

Leveraged CF

-20,000

+3,000

-71,000

Economic Evaluation and lnvestment Decision Methods

276

Since the cumulative negative cash of 91,000 exceeds the 3,000 positive cash flow, it is evident that the leveraged FIOR for this Case is negative. Leveraged ROR = negative infinity Leveraged NPV @ 1Q"/o = -75,950 Z Units The effects of devaluation of currency can be devastating economically on a leveraged project using a U.S. dollar loan (or another hard currency loan) to be repaid with the devalued currency. Unless revenue in terms of the devalued currency escalates at a rate proportional to the currency devaluation rate, the economics of leveraged investments deteriorate. 5.3 Summary Escalated values are also defined as actual, current, then current or nominal dollars. They are always inclusive of the effects of inflation and other parameters including technological, environmental, market and related issues. Constant values are escalated values that have had the effects of inflation discounted from them to a base period in time which typically is time zero, but it could be any point. Constant doliars are also referred to as real or deflated dollars. The only difference between escalated and constant values is the inflation rate each year related to the host currency. Previous variables introduced in Chapters 2 and 3 are now defined more explicitly to reflect the proper handling of inflation, they include: e = escalation rate

f = inflation rate

i* = escalated $ discount rate i*' = constant $ discount rate i = escalated $ rate of return i'= constant $ rate of return Escalated dollar and constant dollar project rates of return and minimum rates of return can be explicitly related for any uniform annual inflation rate using Equation 5-1, which was developed in Example 5-1. Eq 5-1:

lai

Rearranged'

=

(l+l)(1+i')

i'=

{(1+i)/(1+0}

-

1

A commonly used approximation to Equation 5-l is the following:

7'=i-f

Chapaer 5: Escalateci and Constant Doilars

277

PROBLEMS

5-1

Consider the following ,,today,s dollar,, cash flows

C=I00

C=200

For cases A, B, rate of return is

A)

c

Rer,-600 OC=100

and D below, assume the escalated dollar minimum

LS.OVo and:

c^alculate the project escalated dolrar Npv if revenue escarates at -10.lVo per year, and all costs escalate at 6.TLoper year.

B) using

the escarated dolrar results from case A, calculate the project constant dolrar Npv if inflation is 5.\vo per year and escalation of costs and revenues is the same as i, caie A. For evaruation con-

:rrslency' adjust the escalated dolrar minimum discount rate of 15,,vo using text Equation 5-r to calculate the equivaleri.onrtunt dollar minimum discount rate for use in this constant

analysis.

c)

D)

xpv

Calcuiate the projecr escarated do,ar Npv assuming today,s dolrar values equal escalated dollar values. State the explicit cost and

enue escalation assumption built into this analysis.

I

aotta,

rev_

Calculate the project constant dolrar Npv assuming today,s clolrar values equal constant dolrar values. State the explicit cosiand

enue escalation assumption built into this analysis.

reu-

5-2 In I988,

the U.S...gross domesric producr (GDp) increased to $4.90 tril_ lion at year end. from the l9g7 yiar end level of $4.54 trillion in acrual

escalated dolrar varues.-In

the same year, the consumer price index rose approximatery 4vo. what was the escalated lcurrentj dolrar percent increase in GDp? what was the constant (real) dolrar p".""niincrease in GDP?

Economic Evaluation and lnvestment Decision Methods

5-3

An investment related to developing a new product is estimated to have the following costs and revenues in "today's" or "time zero" dollars.

I=$200,000 Co=$5o,ooo

o

I=$200,000

C1=$150,000 OC=$100,000 OC=$100,000

1

2............5

A)

Evaluate the project escalated dollar RoR if both capital cosrs and operating costs are estimated to escalate at l|vo per year from time zero with income escalating at l\Vo per year.

B)

Make constant dollar RoR Analysis of case 'A" assuming the rate of inflation for the next 5 years will be t\Vo per year.

c)

use escalated dollar RoR Analysis to analyze the investment assuming a washout of escalation of income and operating costs with a l\Vo escalation of capital costs in year one.

5-4 A product that sells today for $100 per unit is expected to escalate in price by 6vo in year one, 8vo in year two and,lovoln y"a. three. calcuiate the escalated dollar year three product selling price. If inflation is expected to be 5vo in year one, gvo in year two and 12vo in year three, determine the year three constant dollar product selling price. 5-5

An investor has an opportunity to buy a parcel of land for $100,000. He plans to sell it in two years. what will the sale price have to be for the investor to get a 25vo constant dollar before-tax RoR with inflation averaging 1\vo annually? what escalated dollar annual rate of increase in land value will give the needed sale price?

5-6 Determine the break-even escarated dolrar selling price per unit required in each of years one and two to achieve a 15% constant dollar project RoR, assumtng a 12vo per year inflation rate. AI clor;"r varues are today's dollar values.

C=$10081

Sales=$1116661 Sales=$X(1000)

___99=$50,000

OC=$50,000

Selling price escalation is l\va per year from time zero when selling price is $X per unit. operating cost (oc) escalation is r5vo per lear from time 0. 1,000 units are to be produced artd sold each year.

It

Chapter 5: Escalated and Constant Dollars

279

5-7 what can be paid now (today)

ro acquire a property that will be developed 2 years from now and which engineeri .rii-ut" wilr have today,s dollar costs and revenues shown on th. forlowing time diagram. All values are in thousands of today,s dollars. C

C=$200

0inow)

Rer,=5159

Rev=$ 1 59

Rev=$ I 50

OC=$50

OC=$50

OC=$50

2

Starting from now, it is projected that inflation will beTvo per yea*. The escalated dollar minimum RoR is l5vo. Evaluate the acquisiiion cost that can be paid now to acquire this property for the foilowin! five cases:

case 1. Make the analysis using today's dolrar cc-rsts and revenues assuming they are a reasonable projection of escalated dollar capital costs, operating costs and revenues to be incurred (this assumption effectively assumes zero percent escalation of all costs and revenues each year or lhat escalation of all capital costs and operating costs will be offset by escalation of rev_ enues so that escalation of costs and revenues will have zero eft'ect on economic analysis results).

Case

2.

Make the anarysis using the today's dollar costs and revenues assuming they represent consrant dollar values. (This assump_

tion is valid if you assume that all capitai costs, operating costs and revenues will escalate at the same rate of inflation each year. Discounting these escalated dollar values at the same rate of inflation to get constant dollar values gives the original today's dollar values for this assumption.) case

3. use escalared

doilar anarysis assuming capital cost (c) escaration will be rzvo per year, operating cost (oc) escararion wi, be 10Vo per year and revenue (Rev) escalation

Case

will be lOTcper

year.

4. Make constant dolar analysis for trre Case 3 escaiation assumption assuming 7Vo inflation as given.

case

5.

use the escarated dolrar analysis assuming capital costs escalate at l2%o per year and escalation oioperating costs is exactly offset by a like-dollar escalation of reveiues each year which gives uniform profit margins each year. This com_ monly is called.,the washout assumption,,.

Economic Evaluaticin and lnvestment Decision Methods

5-8

An investor has paid $100,000 for a machine that is estimated to produce 5000 product units pe1 year for each of the next three years when the machine is estimated to be obsolete with a zero salvage value. The product price is the 'unknown' to be calculated; so it is estimated to be $x per unit in year one escalated dollars and to increase l}Vo per year in year two and 67o inyear three. Total operating costs are estimated to be $8000 in year one escalated dollars and to increase l5%o in year two andS%o rn year three. The annual inflation rate is estimated tobe77o. What must be the year one, two and three escalated dollar product selling price if the investor is to receive a L2Vo annually compounded constant dollar ROR on invested dollars?

5-9

Reclamation costs on a project are expected to be incurred over a 30 year period from 27 to 56 years in the future from now. Reclamation. costs are estimated to escalate 5.07o per year in the future. Using a 5.l%o anntal discount rate as representative of annual reclamation Cost escalation, the year 0 piesent worth of the 27 to 56 year future reclamation costs is estimated to be $1.0 million. It is assumed that money today and in the future over the 56 year life of this analysis can be invested in U.S. Treasury Bonds paying 9.lVo interest per year. Determine the magnitude of year 0 investment that an investor needs to make in U.S. Treasury Bonds paying 9.07o anuJal interest to cover the year 27 through 56 future reclamation costs.

5-10 The following time diagram before-tax cash flows are today's dollar values. The investor has a constant dollar minimum rate of return of 1.0.0Vo and annual inflation is forecasted to be 3.0Vo over the project life beginning in year 1. All values are in millions.

-r00

-200

r50

150

150

150

A) Assuming the rate of escalation for all cash flows is equal to the inflation rate, calculate the escalated dollar project NPV and ROR. B) Based on your calculations in part A, determine the constant dollar equivalent cash flows and resulting constant dollar NPV and ROR.

Cirapter 5: Escalated and Constant Dollars

c)

Neglecting A and B, if the rate of escalation was forecasted to be ,Vo per yeir over the project life, calculate the conespoJi"i lated dollar NpV and RbR. tnRution "r"u_ is still forecasr to be 3.0Va

per year.

D) Again

neglecting A anij B, if the rate of escaration was forecasred to be }vo per year over the project life, bur inflation is stiil forecast at 3',vo per year, carculate the corresponding

and ROR,

:

I

I I

t

)

I

I ,

t

constant doilar

Npv

CHAPTER 6

UNCERTAINTY AND RISK ANALYSIS

6.1 Introduction In this age of advancing technology, successful managers must make informed investment decisions that determine the future success of their companies by drawing systematically on the specialized knowledge, accumulated information, experience and skills of many people. In evaluating projects and making choices between investment alternatives, every manager is painfully aware that he cannot and will not always be right. Management pressure is increased by the knowledge that a company's future depends on the ability to choose with a high degree of consistency those investment and market opportunities that have a high probability of success even though the characteristics of future events are seldom precisely known. In the previous chapters in the text investment analyses all were considered to be made under "no-risk" conditions. That is, the probability of success was considered to be 1.0 for each investment evaluated. This means that by expressing risk and uncertainty quantitatively in terms of numerical probabilities or likelihood of occurrence, where probabilities are decimal fractions in the range of zero to 1.0, we implicitly considered that the probability of achieving projected profits or savings was 1.0 for investment situations evaluated. We are all aware that due to risk and uncertainty from innumerable sources, the probability of success for many investments is significantly different than 1.0. When faced with decision choices under uncertain conditions, a manager can use informal analysis of the risk and uncertainty associated with the investment or he can analyze the elements of risk and uncertainty in a quantitative manner. Informal analysis relies on the decision makers experience, intuition, judgement, hunches and luck to determine whether or not a particular investment should be made. The quan282

Chapter 6: Uncertainty and Risk Analysis

.

283

titative analysis approach is based on analyzing the effects that risk and uncertainty can haveon an investment situation by,using a logical and con_ sistent decision strategy that incorporates the effects or iist< and uncertainty

into the analysis results. use of the quantitative analysis approach should aot be considered to imply that the iriformal analyiis considerations of experience, intuition and judgement are not needed. on the contrary, the purpose of quantitative analysis of risk and uncertainty is to provide the decision maker with as much quantitative information as possible concerning the risks and uncertainties associated with a particular investment situation, so that the decision maker has the best possible information on which to apply experience, intuition and good judgment in reaching the final deci_ sion. The objective of investment decision making from an Jconomic view_ point under conditions of uncertainty is to invest available capital where we have the highest probability of generating the maximum possible future profit. The use of quantitative approaches to incorporate risk and uncertainty into analysis results may help us be more successful in achieving this

objective over the long run. No matter how comprehensive or sophisticated an investment evaruation may be, uncertainty still remains a factor in the evaluation. F,ven though rate of return or some other economic evaluation criterion may be calculated for a project with several significant figures of accuracy usinj the best available cost and income data, the decision maker may still feei uneasy about the economic decision indicated because he or she knows the assumptions on which the calculations are based are uncertain. If the economic evaluation method used does not reflect this uncertainty then every assumption built into an economic analysis is a "best guess', and the final economic result is a consolidation of these values. Making decisions on the basis of such ,,best guess" calculations alone can be hazardous. Consider a manager who may select investment alternative 'A" with a 20vo RoR over inv-estment ..B,,

which has a 157o RoR based on the "best guess" RoR calculation approach. would this decision be justifiable if the probability of success of alternative 'A" was 50va (or one chance in two) compared with probabila ity of success of alternative "B" of 90va? It is evident that the manager needs some measure of the "risk" involved in each alternative in addition to

the "best guess" or most likely rate of return results.

Tlrcre ore seve ral different approaches that can be used to quantitatively ittcorporate risk and uncertainty into analyses. These inctuie sensitivity analysis or probabilis_tic sensitivity analysis to account for uncertainty associated with possible variation in project paramercr;, and expected

284

Economic Evaluation and lnvestment Decision Methods

value or expected net present value or rate of return analysis to account for risk associated with finite prubabiility of failure., The,use of, sensitivity anatysis is advocated for most economic analyses and the use of expected value analysis is advisable if finite probability of projectfailure exists. Sensitivity

analysis is described in the first half of this chapter and expected value analysis is described in the second half. Sensitivity analysis is a means of evaluating the fficts of uncertairul,^ on investment by determining how investment profitability varies as the parameters are varied that affect economic evaluation results. Sensitivity analysis is a means of identifying those critical variables that, if changed, could considerably affect the profrtability measure. In carrying out a sensitivity analysis, individual variables are changed and the effect of such a change on the expected rate of return (or some other decision method) is computed. Once all of the strategic variables have been identified, they can be given special attention by the decision maker. Some of the typical investment parameters that often are allowed to vary for sensitivity analysis include initial investment, selling price, operating cost, project life, and salvage value. If probabilities of occurrence are associated with the various levels of each investment parameter, sensitivity analysis becomes probabilistic sensitivity analysis. It may now be evident to the reader that the term "uncertainty" as used in

this text refers to possible variation in parameters that affect investment evaluation. "Risk" refers to the evaluation of an investment using a known ntechanism that incorporates the probabilities cf occurrence for success and failure and/or of dffirent values of each investment parameter. Botll uncertainty and risk influence almost all types of investment decision, but especially investment involving research and development for any industry and exploration for minerals and oil or gas.

6.2 Sensitivity Analysis to Analyze Effects of Uncertainty

As described in the previous section, sensitivity analysis refers to analysis

of how investment profitability is affected by variation in the parameters that affect overall profitability. For a case where rate of return is the economic criterion used to measure profitability, sensitivity analysis involves evaluation of how rate of return varies with parameters such as initial investment, profit per year, project life, and salvage value. It is frequently

Chapter 6: Uncertainty and Risk Analysis

2As

used to determine how much change in a variable would be necessary to reverse the decision based on average-value or best-guess estimates. It usually does not taiie into consideration the likelihood of variation. The rate of

change in the total outcome relative to the rate of change in the variahle being considered u'ill indicate the significance of this variable in the overall evaluation.

Example 6-1 will introduce a single variable sensitivity analvsis. tri is important for the reader to keep in mind that in this analysis, no dor.r'nstream effects are considered relevant to the evaluation. In other words, each parameter is independent of the other so changing the magnitude of the capital investment will have no impact on any other operations or the magnitude of project operating costs, etc. To further illustrate, when the years of income are reduced, there is no adjustment in the residual value of the assets. Such numbers may increase or decrease but again, are neglected here to simplify the introduction of this evaluation procedure.

EXAMPLE 6-1 Single Variable Sensitivity Anatysis Annual profits of $67,000 are shown on the time diagram for ihis

$240,000 investment case with an expected salvage value of $70,000 after five years. Evaluate the sensitivity of project RoR to plus or minus 2o'h and 4oo/" varialions in initial investment, annual profit, project life and salvage value.

Profits

C=$2a0,000 $67,000 $67,00Q $67,000 $67,000

$O7,OOO

L=$70,000

Solution: Using the most expected cost and revenue parameters gives:

PW Eq: 240,000 = 67,000(P/A;,5) + 70,000(p/F;,5) The "most expected" project ROR is 18%. How will this ,,most expected" 18% ROR vary as parameters are changed?

286

Economic Evaluation and lnvestment Decision Methods

A) lnitial lnvestment Sensitivity Analysis lnitial 'Change in Percent Change ih 18.0% investment Prediction ROR ROR Prediction 144,000 192,000 240,000 288,000 336,000

-40 -20 0

+20 +40

42.0 27.5 18.0 11.2 5.8

133.3 52.9 0

-37.9 -67.7

The percent variations in the ROR from changes in initial investment costs are very significant. ln general, changes in parameters close to time zero (such as initial investment and annual profit) have a much more significant effect on investment ROR than changes in parameters many Vears in the future from time Zero (such as salvage value). B) Project Life Sensitivity Analysis Project Life

Change in Prediction

3

-40 -20

4

ROR 5.6

5

0

13.4 18.0

6

+20 +40

20.9 22.9

7

Percent Change in 18.0% ROR Prediction

-68.8 -25.5 0 16.3 27.1

Note that this sensitivity analysis really involves changes in total cash flow as well as project life. lf project life was longer (say 10 years or more), changes in life would have a less sensitive effect on ROR. C) Annual Profit Sensitivity Analysis Annual Profit

Change in Prediction

40,200 53,600 67,000 80,400 93,900

-40 -20 0 +20 +40

ROR

3.6 11.0 18.0 24.8 31.5

Percent Change in 18.0% ROR Prediction

-80.2 -39.0 0 37.9 74.8

Chaorer 6: Unce(ainty and Risk Analysis

287

Percent variations in ROR due to changes in annual profit are very significant beciuse the changes start occurring close to time zero. lndividual parameters such as selling price. production rates and ope;ating costs affect profit.

D) Salvage Value Sensitivity Anaiysis Salvage Value

42,004 56,000 70,000 84,000 98,000

Change in

Prediction -40 -20 0

+20 +40

ROR

Percent Change in 18.0% ROR Prediction

15.9 16.9 18.0 19.0

20.0

-11.9

-

6.0 0 5.4 10.8

Sensitivity analysis shows that accuracy of salvage value is the Ieast important of all the parameters that go into this ROR analysis because salvage value occurs far in the future from ti,-r:e zero. Also, in this case, cumulative salvage doliar value is small compared to cumulative profit. ln some evaiuatjons this is not the case and sali,age value has a much more sensitive effect.

6.3 The Range Approach to Sensitivity Analysis The range approach involves estimating the most optimistic and most pessimistic vzrlues (or the best and worst) tor each thctor in addition to estimating most expected values. This approach will make investmcnt decision ruraking easier fbr the cases where (1) a project appeats desirable even when pessimistic values are used and therefore obviously should be adopted from an economic viewpoint, (2) when a project appears to be undesirable even when optimistic values are used and therefore rejection is dictated on economic grounds. When a project looks good with optirnistic values but bad with pessimistic values further study of the project and the risk and uncertainty surounding the project should be made. Application of this method is shown in Example 6-2.

288

Economic Evaluation and lnvestment Decision Methods

EXAMPLE 6-2 Range Approach Sensitivity Analysis Use the range approach to evaluate the investment described in Example 6-1 for best and worst case sensitivity analysis using the plrrs or minus 2Oo/" parameter variations with a five year life and a minimum rate of return of 15"h.

Solution: Best Case

Expected Case

Worst Case

240,000 67,000 70,000

288,000 53,600 56,000

5

5 3.7

lnvestment 192,000 Annual Profit 80,400 Salvage 84,000 Project Life in yrs. 5 ROR, % 36.4

18.0

The results indicate that the project is satisfactory for the best and most expected conditions but unsatisfactory for the worst conditions. More information is needed on the expected probability of occurrence of the worst case conditions to reach a valid and meaningful decision. The best, worst and most expe-cted sensitivity analysis results give very useful information that bracket the range of project ROR results that can reasonably be expected. This is the type of information that managers need to reach investment decisions. It is very important to recognize that although a project ROR greater than the minimum rate of return is predicted for the most expected parameters, the result is based on parameters which are subject to variation. This variation should be analyzed over the full range of possible results utilizing the best engineering and management judgments of people involved with a project.

6.4 Probabilistic Sensitivity Analysis The application of probability distributions to relate sales volume and prices, operating costs and other parameters to probability of occurrence

Chaoter 6: Uncertainty and Bisk Analysis

289

permits "probabilistic analysis" by the Monte Carlo simulation technique. A brief description of the method follows, then the method will be illustrated.

A weakness of traditional tecirniques for the evaluation of projects is an inabilitv to combine ilfcrmation fron-, a number of sources into a straightforivard and reliable profitability indicator. The major factor in this problern is the large number of variables that must be consi.dered. Ai: additic,nal facior is that it is not possible to obLain accurate single-valued estirnates of n:anr oi the r,ariable:. Probability theory is the study of the uncertainty of events. A basic tool of probability theory is the use of a range of values to describe variables that cannot adequately be quantified by single value estimates. For example, the determination of the least, greatest and most likely values of a variable will more accurately quantify the variable than will the average value. The distribution and relative possibilities of values assigned to a given variable will remain characteristic of that varjable if factors affecting the variable remain constant. Figure 6-l illustratejs three possible distributions of values. The values are plotted on the horizontal axis and the respective probabilities of their occurrence on the vertical axis. Analysis of the three examples indicates that the uncertainty of the parameter described in Example 3 is much greater than that in Example 2. The uncertainty of Example 3 is indicated by the w'ide range of vllues. A m:{ority of the parameters in ieal evaluations otien give an intermeciiate ranse of parameter values as illustrated by Example l. Ideally we would like to have a very smirll range tor all piuameters as illustrated by Example 2. In practice we get a combination of small, intermediate and large ranges of parameter value variation for different parameters in actual evaluation situations.

The drstributions in Figure 6-1 all have their values symmetrically distributed around the most likely value (the familiar bell-shaped curve is an example of this distribution). A distribution of this type is called the normal distribuiion. If the most likely value is shifted to either side of the center of the distribution, then it is refered to as a skewed distribution. The nonnal distributiotr and the skewed distribution are botlt special types of a general cLass of cttrves known as densitl, functions. In rhe remainder of this discr,tssion normal distributions will be referred to as such and the terru density function will be used to describe probability distributions that are not normal. The shape of the distributions will be determined by the nature of the variables they describe.

Economic Evaluation and lnvestment Decision Methods

290

trl

uJ

o zu

O

zul

(f cE f

- MEAN

,r'

tr (r :)

o o o IL o

() u-

tJ

F

co

co

)d]

=

o E

o cc

(L

INTERMEDIATE RANGE EXAMPLE 1

tl UL

o-

LL

SMALL RANGE EXAMPLE 2

uJ

o

zul 0c

c(

f

o o IL o F

-)

6

c0

o (r (L

PARAMETER VALUES, LARGE RANGE EXAMPLE 3

Figure 6-1 Frequency Distribution Graphs lllustrated (LL = Lower Limits; UL = Upper Limits) In principle, a relative frequency distribution graph is converted to the

equivilent cumulative frequency distribution graph by moving from the left .nO of the distribution to the right end and computing the total area that is less than or equal to corresponding values of the parameter within the range evaluated. The cumulative area to the left of a given parameter value divided by the total area under the curve is the cumulative probability that a random parameter value ivill be less than or equal to the given parameter value. Figure 6-2 illustrates typical cumulative frequency distribution graphs that would result from converting the relative frequency graphs shown in Figure 6-1 to the corresponding plots. Note that Example 3 with a large range of parameter values has a much flatter cumulative probability curve than Example 2 which has a small range of parameter values. Example 2

Chapter 6: Uncertainty and F{isk Analysis

has a much higher percentage of the parameter values in a given range of curnulative probabitity of occurrence compared to Example 3.1.0

1.0

no

i ,!

0.9

,_a

0.8

0.7

0.7

0.6

0.6

0.5

0.5

,:1

:C

o-! oi >x

=* E

f O

Pa:a;'le'er Values lnt€rinei;ate fiange Example

o.4

0.4

0.3

0.3

4.2

0.2

0.

0.1

1

0.0

i-:

1

Para;rete:- ', a jues tJL Small Range Example 2

0.0

'1.0

0.9

io' 4.7

=

.c.6

oI .>;

0.5

6LJ

E= tr

0.4

= O

0.3 0.2 0.

LL

Values

parameter Large Range Example 3

1

0.0 UL

Figure 6-2 Cumulative Frequency Distribution (LL = Lower Limit, UL = gppsr Limit) Now to describe the probabilistic sensitivity analysis approach, consider that we are about to evaluate a new development project. we migtrt be interested in the effect on our economic evaluation criterion of changes in prolect

parameters such as initial investment, product selling price per unit, priaucdon rate or

292

Economic Evaluation and lnvestment Decision Methods

sales projections, operating costs, project life and salvage value. For each of these variables and/or other variables to be investigated, a frequeney distribu-

tion plot of probability of occurrence versus para=meter vatue similar ,o tr," 6-l is prepared by the person or persons most familiar with and capable of projecting future values of the parameter involved. These frequency distribution data are then converted to cumulative probability of occurrence versus parameter value graphs similar to the examples in Figure 6-2. when these graphs are available for each parameter that is considered to vary, the use of Monte carlo simulation is applied. This generally involves curve-fitting a mathematical expression to describe each cumulative probability of occrurence versus parameter value so that picking a random number between 0.0 and 1.0 analogous to the cumulative probability of occurrence will automatically fix the parameter at the corresponding value. Different random numbers are selected to fix each of the different parameters being varied. Then using the randomly selected parameter values, the economic analysis criterion such as rate of return is calculated. Then you iterate and do the same thing over again picking a new set of random numbers to determine a new set of parameters used to calculate rate of retum. This is done over and over again for somewhere between 100 and 1000 times and then a histogram (frequency distribution plot) of these rate of return results versus probability of occurrence is prepared. The number of iterations (RoR results) that are required is the number that will give the same shape of frnal RoR results frequency distribution graph that would be obtained if many more iterations were made. To illustrate. examples in Figure

consider hypothetical cases

I and 2 shown

s

\o

o

o

() 25

:20 o o

o15

15

o

't0

Ero

a6 -oo5l (L1

o 5 o-

0

30

8zs

20

= o 6

ih Figure 6-3.

5

't0 15 20

Rate of Return, 7o 100 Simulations (Note multimodal maxima)

Case

1

25 Flate of Return,

9,o

500 or 1000 Simulations (Constant shape, unimodal) Case 2

Figure 6-3 Frequency Distribution of RoR for Varying simulations

Cnapter 6: Uncertainty and Risk Analysis

293

'rhe

histograrn fbr case t has murti-modar (more than one maxima) peaks indicating that statisticalry we have not mad-e enough simurations to get ,a rate of return frequency distribution with constant shape. If the input data frequency clisuibution is unimodal (having one peak as'iitusirated in Figure 5-l; the ourtrrut rare of return freirue,cy ciistribuiion plot str,;urd be uni_ mcdal. case 2 iiemonstrates for this hyporheticar situation thar if we to to 5il0 or 1000 simulations we g"t a unimtdar graph *.ith the same shape indi_ ;;iting that 500 simulations are sufiicient fbr anaryzing this hypotheticar iuresrment using probabilistic sensitivity analysis. An iniportant thing to.note about probabilistic sensitivity anarysis resurts is that y'ou i-ro not gei a single resrrt,iut instead you get a iarg" over which the results vary as a function or prouaurtity of occunJr""aJ*so you get a m'st expected result. In many iuvestmenisituations tt.,tup" ot this curve is more important rt, varue. For exampri a project with a most expecred RCR ofln:-ryl,rr.*p..i.o 25vc with ara,ge of po-rsibre ,.Ji; from negative RoR to positi'e 4c7o might be consideri ress cssirabt. tt un a r_,rcrject wirh a i,lr)it expecied ROR oi lgvo and a range u.f pos.;ible resurts from rQvo to 25vc because the certainiy associateJ ,rirtr, tn. tsz, mosi-expected RoR inr"estment is greater.tho,t th"..rtointy r.socrieted with the other investment. Prohabilistic sensitivity anarysis .*.ot.i-tr," decision get a firmer fecirng concerning rhoeff-ecis or.irirra "r"t.r^," uncertainty on economic anarysis resuirs than an-v otlrer analysis approxsh gi1.sE.

The weak pr:int of trre prooauriistic ariarysis method ries in the subjectire assi,uning of probabiritie. of occurrence to the rer,.els of pararneters that go int. the arrarysis' it is gene'aily considered to be best to specificallv staie the probabililies 'o::.u:r, of o.-.r.."n.. based on the best judgement of peopic invoh'ed rvith a project and then to ba.se the anaiysis on these esti_ maies even though they are subjective in nature. In the finar analysis any evaluatio, technique is only as gooo as the estimates of the input parameters and rnust be used in conjunction with good engineering logic and managerial judgement' Assigning probabilities to"pararneter estimates is just one more step in quantifying the assumptions thai are made. These rechniques provicle managcment with addirionai toors to aiir in the decision-.uung'p.o."rr. Folloiving is a simprified exampre that ilrustrares the principles of apprying probabilistic analysis to project ROR sensitivity analysis.

EXAMPLE 6-9 A Simple probabilistic Sensitivity Analysis A new product to be produced by one of two different processes. rt is felt that there is a 60% prooaoitity that the process serected wiil

294

Economic Evaluation and lnvestment Decision Methods

have initial cost of $50,000, a life of five years and zero salvage value. There is a 40"/" probability that an improved process will be selected with iriitial cost of $4O,OOO, a life of five years and zero salvage value. With either process there is a 50ol" probability that annual profit will be $20,000 for the five year project life and a 25"/o probability that the annual profits will be $15,000 or $25,000 per year. Plot project ROR versus probability of occurrence assuming the parameter values are independent of each other.

Solution: The following table presents the possible combinations of different investment costs, annual profits, probabilities of occurrence and ROR.

lnvestment

50,000 50,000 50,000 40,000 40,000 40,000

Annual

Profit

15,000 20,000 25,000 15,000 20,000 25,000

Probability of Occurrence (.6X.25) (.6X.50) (.6X.25) (.4X.2s) (.4X.50) (.4X.25)

=.15 =.so =.15

=.to =.zo =.10

P/Ai.s

3.334 2.500 2.000

2.667 2.000 1.600

RoR (%) s.2 28.7 41.1 25.4 41.1

56.0

1.00

The most probable project ROR is 41.1"/" with a 35% probability of occurrence. The cumulative probability diagram shows a cumulative probability o175"/" that the ROR will be 28.7% or above in Figure 6-5. Instead of mathematically determining the probability of occurrence of the various ROR results for this problem we could have used the general Monte Carlo simulation technique to get the same results. The general idea of this method as described earlier is to first develop curves for cumulative probability of occurrence versus the economic ltarameter similar to Figure 6-4. Then random numbers between zero and one are related to cumulative probability of occurrence so that selection of a random number fixes the initial investment for a calculation. Selection of another random number selects the cash flow for that calculation. ROR is then calculated using these values. This procedure is then repeated several hundred or maybe a thousand times until the shape of the ROR versus probability of occurrence curve does not change with additional calculations. For a large number of Monte Carlo simulations the results using this technique for Example 6-3 will be identical to those

Chapter 6: Uncertainty and Risk Analvsis

295

given in Figure 6-5. The Monte carlo simulation data are evaluated by forming a histogram from the RoR results. For instance, if one thousand runs are made tlren approximately tluee hundreci of the RoR rcsults ,rrorr.i bc 2g.i7o, since we know the mathematical probability of occurrence of this resylt is .30. In general, the variations ir.r input crata such as seiling price, oirL-raiing cost. production rale, borrowed money interesr rete and so forth that are evaluated will be continuous functions of cumulative probability of occurrence rather than the step functions illusrrated in Figure 6-4. Coniinuous input data give a continuous RoR versus probabiliiy of occurrence histograrn graph for lrlonte Carlo simulation in general.

Cumulative Probability

of Occurrence

1.00

1.00

.80

.80

.60

.60

.44

.40

.20

.24

0

0

15,000

Initial lnvestment

Profit

(a)

(b)

25,000

Figure 6-4 Cumulative Probability Diagram

Probability of Occurrence

.30 .20 .10 0

1.00 .80 Cumulative Probability of

Occurrence

.60 .40 .20

0L 0

10 20 30 40 50

60

ROR, %

Figure 6-5 Cumulative probability of Occunence

296

6.5

Economic Evaluation and lnvestment Decision Methods

Expected Value Analysis (Economic Risk Analysis)

Expected value is defined as the dffirence between expected profits and expected costs. Expected profit is the probability of receiving a certain profit times the profit and expected cost is the probabitity that a certain cost will be

irtcurred times the cosr. If you define cost as negative profit and keep the signs straight, you can do as some text authors do and define expected value as the algebraic sum of the expected valuq of each possible outcome that could occur if the alternative is accepted. Either definition leads to the same expected value result, which sometimes is called a "risk adjusted" result. Several examples of expected value analysis when time value of money considerations are not relevant or significant will be presented first. Then time value of money related examples will be illustra.ted.

EXAMPLE 6-4 Expected Value Analysis of a Gambling Game

A wheel of fortune in a gambling casino has s4 different slots in which the wheel pointer can stop. Four of the s4 slots contain the number 9. For $1 bet on hitting a g, the gambler wins $10 plus return of the $1 bet if he or she succeeds. what is the expected value of this gambling game? what is the meaning of the expected value result?

Solution: Probability of Success = 4/54 Probability of Failure = SOIS4 ExPected

Var

ue

:,?ffi,'*,T

:lffi ;;: * -"-::l

The meaning of the -$0.195 expected value result is that it is the rverage monetary loss per bet of this type that would be realized if he gambler made this bet over and over again for many repeated trirls. lt is important to recognize that the gambler is not going to lose 80.185 on any given bet. over a large number of bets, however, the oss per bet would average $.18s. This result should make it evident hen that a positive expected value is a necessary condition for a satsfactory investment, but not a sufficient condition as will be dis:ussed later.

Chapter 6: Uncertainty ar':C Flisk Analysis

297

EXAMPLE 6-5 Expected Value Analysis of a Simplistic

. ,:,DrillingVenture

I

lf you spend $500,000 drilling a wildcat oil well, geologists estimate the probability of a dry hole is 0.6 with a probabiiity of 0.3 that

I i

the well will be a producer that can be sold immediately for

l

$2,000,000 and a probabiiity of 0.1 that the weil will produce at a rate that will generate a $1,000,000 immediate sale value. What is the oroject expected value?

!

I { {

, f

Solution, All Values in Thousands of Dollars: Expec'ied Va ue

I

il:ffi

I I

:

I

= +$200

:;ffi ; :lT:::::H,

_ o 6(500)

or rearrangtng:

I

Expected value = 0.3(2,000) + 0.1(1 ,000)

- 1.0(500) = +$200

I I I i

1

t

i I I

tf

It

lI I *

t

Over the long run, investments of this type will prove rewarding, but remember that the +$200,000 expected value is a statistical longterm average profit that will be realized over many repeated investments of this type. The expected value of an investment alternative is the average profit or loss that would be realized if many investments of this type were repeated. ln terms of Example 6-5 this means if we dritied 100 wells of the type descrrbed, we expect statistics to begin to work out and assuming our probabilities of occurrence are correct, we would expect about 60 dry holes out of 100 wells with about 30 wells producing a $2,000,000 income and about 10 wells producing a $1,000,000 income. This makes total income of $70,000,000 from '100 wells drilled costing a total of $50,000,000 leaving totai profit of $20,000,000 after the costs, or profit per well of +$200,000, which is the expected value result for Example 6-5. Certainly if you have enough investments of this type in which to invest and enough capital to invest, statistics are very favorable to you, and you would expect to come out ahead over the long run if you made many investments of this type. However, if the loss of the $500,000 drilling investment on a dry hole would break you, you would be foolish to invest in this type

298

Economic Evaluation and lnvestment Decision Methods

of project because there is only a 4avo chance of success on any given try. only if you can stick with this type of investment for many times can you expeci statistics to work in your fuvor. This is one important reason why most large companies and individuals carry insurance oi various types even though in nearly all cases the expected profit from self-insuring ii positive and therefore favorable to the company or individual. If a disaster from fire can break a company cr individual financially, that company cannot afford to self-insure. This is why insurance companies spread large policies over many insurance companies. If disaster does strike a large poti.y holder, the loss will be distributed over several companies, lessening the iikelihood of financial disaster for any one company. It is also the r"u.on most individuals carry fire insurance, homeowners or tenant insurance, and car insurance. The direct financial loss or lawsuit loss potential is so great that most of us cannot afford to carry that risk alone even though exp-cted value is favorable to us if we self insure. The conclusion is thit a pisitive expected value is a necessary br.tt not a sfficient condition for a satisfactory iivestment. It should now be evident that although expected value has deterministic meaning only if many trials are performed, if we consistently follow a decision-making strategy based on selecting projects with positive expected values, over the long run statistics will work for us and income should be more than sufficient to cover costs. on the other hand, if you consistently take the garnbler's ruin approach and invest or bet on investments or gambling games with negative expected values, you can rest assured that over the long run, income will not cover your costs and if you stick with negative expected value investments long enough, you will of course, lose all your capital. This is exactly the situation that exists with all of the gambling garnes in places such as Las vegas, Reno and Atlantic city. The odds are alrvays favorable to rhe house, meaning the gambling housl has a positive

expected value and therefore the gambler has negative expected value. The gambler has absolutely no realistic hope for success over the long run under

these negative expected value conditions. He will lose all the money set aside to gamble with if he sticks with the games long enough.. The reader should notice that in Example 6-5, two different, but equivalent equations were usec to calculate expected value as follows:

Let P = probability of success, I Expected Value = (P)(Income

or

-

-p

= probability of failure

Cost)

-

(1 _ pXCost)

=(P)(Income)-(i.O)(Cost)

6-2 6-2a

C;,apter 6: Uncertainty and Risk Analysis

6.6 Expected

NPV, Expected pVR, and Expected ROR Analysis

when time value of money considerations are significant, expected Npv, PVR and RoR anarysis are merhods of incrudrrg ir" p."ir"uiii,;"s of suc_ cess and failure in analyses when costs and revenues occur ar different ptrints in time. If we use appropriate time ralue of monel. present rvorth fac_ ttlrS ro convert costs and profits at different points in time to lurnp sunr r.al_ ucs at time zero or some other chosen tinre, the expected value anarysis approach can be applied to determine if rhis type crt.- investment woulcl be snitable over the long run for many repeated investments of the same type. \{'ith e-rpected Npv and pvR *r u.., of course, looking for alternatives with a positive expected with expected RoR anarlsis we calcurate the expected RoR value,'arue. "i", that will rnake the expected Npv equation cquai to zero. An acceptabre expected RoR must be greater than the minimum ROR.

EXAMPLE 6-6 Expected Vatue Apptied to ROR, NpV and pVR

Analysis

A research and deveropment project is being considered. The project is expected to have an initial ihvestment cost of $90,000 and a

probability of 0.4 that annual profits of $50,000 will be reatizeO during the 5 year life of the project with a probabitity of 0.6 of faiting. Sal_ vage value is expected to be zero for success or failure. Assume the minimum discount rate is lOoh on a risk_free basis.

should the project be done? compare expected varue, nel present value, expected rate of return and expectedexpected present

value ratio analysis with corresponding non-risk adjusted evaluation results.

Solution, Values in Dollars: C = $90,000

P=0.4

|

=$50,000 . . . . I =$50,000

1............s

P=0.6

L=0

i

300

Economic Evaluation and lnvestment Decision Methods

A) Expected vatue Anarysis rncruding Time varue of Money at i' = lgolo 3.7908 EV = 6.4150,000(P/A1 Oo/o,S)

-

9O,O0O)

- .6(90,000)

= _$14,1g4

The negative expected varue indicates rejeci investing in the project.

The expected varue approach is most usefur when statisticaily more complex models are utilized. ln many of these cases, the various outcomes that are possible in a model are defined, associated chance factor is derived for each branch. rn this "no ", t*o outcomes exist which can be rabered ,,success', "r."rpr" and ,fairure." By carculating the NPV for each separatery, the chance factors (in .outcome this modeljust the probabirity of success and fairure) can to.the appropriate outcomes to determine the identicalbe appiied expected value (EV) as shown: Expected value per outcome (Npv of outcome)(chance = Factor) summing ail of the project's expected varues per outcome gives the overall project expected value. 3.7908 EV Success = {50,000(p/Aj _ 39,g16 Oy",S) 90,000X0.4) EV Failure = (_go,ooo)(0. = -54,000 Project Expected Value = -14,184 The same calculation was introduced in the expected value solution to this problem.

=

B) Expected Net present Value This analysis is identicar to the (A) anarysis, except we generaily use Equation 6-2a to determine Expected Npv. Thi; just is a rear_ ranged form of the Expected Value equation from part,,A,,. 3.7908 ENPV = 0.4(50,00O)(ptA1O%,5)

-

1.0(90,000) = _$1 4,184

Since the ENpv is negative, we shourd not invest in the project from an economic viewpoint. Note the expected varue anarysis in oart (A) accounting for the time varue of money ro7" p"iyear gave e result identical with the EV result from Case "t A.

Chapter 6: Unce(alnty and Risk Analysis

For these statistically simplistic models, another approach for calculating the ENPV is to first, risk adjust the cash trows, and then, carculate ENPV using the same present worth equation format previously developed. This approach is helpful in making expected value calcuiations on a hand calculator but again, it shor.rli be emphasized that the resuiting cash flow siream does not represent the expected ca-sh flows for any single investment. lnstead, ihe calculated values reflect the average cash fiows that mignt be expected after many repeated investments of this type with success occurring 40% of the time and failure occurring 60% oi the time.

Cash Flow.

-$90,0i,09.0)__!9900!04).. .. s0,000(0.4)

0 Risk Adjusted Cash Ftows -$90,000

ENpv = -e0,000 + 20,000(priliijr, *14,184 = This approach can be more difficurt to appry to more comprex statistical models than summing the expected vaiues for all outcornes. lf you look at non-risk adjusted NpV (risk free NpV) which implicitly assumes 1007o probability of success, the project economics look very acceptable Risk Free NpV = (50,000)(pr"^133^,r,- (e0,000) +$ee,540 > 0 = obviously adjusting for risk of failure or not adjusting for risk of fail_ ure has a very significant impact on economic results aid conclusions.

C) Expected Rate of Return Expected RoR is the "i" value that makes Expected NpV equal 0. Expected Present worth lncome @ "i" present worth cost ,,i,,= @

-

50,000(P/Ai,S)(.4)

-

0

90,000 = 0

by trial and error, "i" = Expected RoR g..ay" < i* 10% so reject = = Non-risk adjusted or risk free rate of return analysis gives a different conclusion:

302

50,000(P/A1,5)

Economic Evaluation and lnvestment Decision Methods

-

90,000 = 0

by trial and error, f i" = ROR

=

47.60/o> i*

= 10% so accept

This result is much greater than the 10% minimum RoR indicating very acceptable economics. As a variation of expected RoR analysis, some people account for risk by increasing the minimum ROR by what they consider to be an appropriate amount. The difficulty with this approach is that there is no consistent, rational way to adjust the minimum RoR appropriately to account for risk in different projects. For this example, the risk free RoR is about 42.6% (based on probability of success of 1.0 instead of 0.4) compared to the expected RoR of 3.6%. Expected RoR of 3.6% compared to risk free minimum RoR of 1oh indicates the project is economically unsatisfactory. To get the same conclusions based on comparison of risk free RoR and risk adjusted minimum RoR results requires increasing the minimum ROR to about 132% (where l1yo/3.6/" = Xl4Z.6/q therefore X = 13:2%). A majority of people who attempt to compensate for risk by adjusting the minimum RoR end up significantly under-compensating for risk. For this example many peopre wilr propose increasing the minimum RoR inversely proportional to probability of success 6to.q) from 10"/o to 25% when as previously discussed the increase should be from 10% to about 1go%. However, there is no way to know this without making an expected RoR type of analysis. Expected value" analysis using RoR, NPV or. PVR is the preferred approach to incorporate risk into economic analysis calculations.

D) Expected Present Value Flatio Analysis EPVR = ENPV / Expected PW Cost = -14,184/90,000 = -0.16

The negative expected PVR indicates the project economics are ;nsatisfactory for the project parameters built into this analysis. Risk Free PVR = +99,540/90,000 = +1..l1

consistent with the other criteria, the risk free pVR indicales very rcceptable economics which is the opposite conclusion reached with lxpected PVR.

Chapter 6: Uncertainty and Risk Analysis

Expected value anarysis in general involves constructing a diagram showing investmenr cosrs and all subsequ"r, riilues that are anticipated. Standard si;mbolism"t*."^;;;;;, and dolrar uses circles to designiite chance nodes tiom which different delrees of success and fairure may be -rh,"rn ttr r-rccLlr. l''c sum of the proh.b'ilities of occurrence on the dittbrent branches ernanariirg from a .hu,.,"" node must adil up a r.o. Trtese e-rpec'ted r'.;lua L!trigrtuns" are someriutes called ,,rlecisiori rree d.iagrants,, . be-cause decisior: options concerning whether to proceed in one or more di ferent wa)'s or to terminate the project aiways .^irt prio, to each chance node where different degrees oi ,r.."r, or failure may occur. These diagrams often ha'e murtiple branches and rook u.ry -u.h like a drawing of a tree' which has led to the name "decision ree analysis,, being used in industry pracrice to refer to this type of analysis. In typicai decision tree anaiyses, at dift-erent stages of projects, probabilities of success and failure cha3ge, As you progress from the i"r.ur.t or exproration stage of a project to.c.eveiopmenr and production, risk oi' failure ,rgniii.unrry. This is illustrated in the follorving two examples. "hung",

,:

EXAMPLE 6-7 Expected varue Anarysis of a petroreum proiect Use Expected NpV anarysis for a minimum RoR of 2o"hto evaruate the economic potentiar of buying and driiling an oir lease with the following estimated costs, ,."rlnr". and suc-cess probabirities. The lease would cost g.100,000 at time 0 and it is considered 100% certain that a wefi wourd be driiled to the point of .ornpr"tion on" year later for a cost of $500,000. There is a boz pronaoitity that welr lggs will took good enough.to comprere the 1 for $400,000 compretion .o.i. tf tre wirr rogs are ,n.rtirtr.tory a an abandonment cost of $40,000 wi, be incurred at year 1. rf the we, is completed it is estimated there will be a 50"/" prooroitity of generat_ ing production thar will give $450,000 per year net income for years 2 through 10 and a 3S^y" probability of generating $000,000 per year net income for years 2 through io, witn a 1so/o piobanitityof the weil comple-tion being unsuccessiur, due to water or unforeseen compretion. difficulties, giving a year 2 salvage value of $2SO,OO0 for pro_ ducing equipment.

*!riril"ar

304

Economic Evaluation and lnvestment Decision Methods

Solution, in Thousands of Doltars: l=450

l=450

(c)

(D) C=40

Times 1 and 1+ are effectively the same point in time, the end of year 1. Normally drilling and completion time are separated by weeks or months which puts them at the same point in time wittr annual periods. Times 1 and 1+ are separated on the diagram to make room for the probabilities of occurrence associated with different events. Expected Value

. *Determine the possibte different outcomes and the subsequent NPV for each. Apply the probability of each outcome to the calculated NPV's giving ENpv per outcome. summing each gives the project's overall ENPV. There are four (4) possible outcomes:

A) Successful Development leading to incomes of $450 per year. B) Successful Development leading to incomes of $300 per year. C) Failure with a salvage of $250 at the end of year two. D) Failure with an abandonment cost of $40 at year one. For Case A, the chance factor is; (0.6X0.5)r For Case B, the chance factor is; (O 6X0.35)\ For Case C, the chance factor is; (O.OiiO.f S)

\

I-100 ?l t-100 9) t-100 D) t-100 -

1)

eoo(p /F 20,1) + a50(p/A 20,eXp/F zo e00(p tF 20"1) + 300(p/A

2['!11er

rltlsol

;;:j,]

e00(ptF 20"1)-1-250(p/F i6"ill(0.00i"" 540(P/F16"1)l (o 4) Project Expected Net present Value lftrln4

l---

= +198.48 io.zr i = +33.13 '

=

-60.87

= -219.99

=

-49.26

Chapter 6: Uncertainty and Risk

Analysis

g0

Expected Net present Value (ENPV) at

4.031

2}o/o

4.031

.8333 {[450(PiA20,eX.5) + 300(piA20,ex.ss) + zs0(n{1X. j5) _ 400](.6 .8333

-

40(.4)

- 500xP/Fz},i _ 100 = _49.26

This

resurt is onry- srighfly ress than zero compared tc the totar pro. ject costs of $1 miilion, therefore, srighily unsatisfact"iy o,, break. even

economics are indicated.

Alternate Form of (ENpV) Equation

4.031

.8333

4s0(P t Azo, (. 5) (P/F20, e)

.6944 +zso (p'/ F 20,z) (. 1sX. 6) .8333 -500(P/F20,1X1 .0)

-

1

_

X.

4.0g1 .8933

4oopi

100 =

.ffi33

6) + 000(p/A2s e) (. 35) (p/Fio, r X o)

; ;;.

1 X. 6)

_ +o

.8339

pir"ll1; i: +1

-49.26

Risk Adjusting the Cash Flows

-500(1.0) 450(0.6X0.5) -jlBIS

cF(prob Year

) _i00(1 0)

RiskAdj

cF -1oo -zs6

O

1

?i IBBIB\Y'Y/\v' Bi[B ?Ei tet

450(0.6X0.s) 3oo(0 6iio 3b) g_10

ffi

ENPV = -100 -756(p/F20,1)+ 220.S(p/F29,2) +'t 98(p/A2 0,A) (p ff ,0,r1 ENPV = -49.26 EXAMPLE

6-8

Expected value Economics of a New process _ use Expected NpV and pVR anarysis for a minimum rate of return of 2a.0"/" to evaluate the economic potentiar of buying ano Jevetoping the rights to a new process with the foilowing estimated costs, revenues and success probabilities. The process rights would cost g100,000 at

J

306

Economic Evaluation and lnvestment Decision Methods

time zero, and, it is considered 100% certain.that experimental devel_ pilot plant work wiil be done one year raier for 9ql"ll a cost of $500,000. There is a 60.0% probabirity that the experimentar development results will look good enough to iake the project to production flr a $400,000 capital cost at year 6ne. (This capital cost is estimated to be incurred in the first six months of year one which is closer to year one than year z.) lf the experimental development results are unsatisfactory, a pilot prant abandonment cost of $+o,ooo wiil bL-incurred at year one- If the project is taken to production, it is estimateci there will be a 50.0% probabirity of generating production that wirr tive g4s0,000 per year net positive cash flow for years two through ten, i 35.0% prob_ ability of generating $300,000 per year net positive cash frow for years two through ten with a 15.0% probabirity of the project deveropment being unsuccessfur due to unforeseen iechnicai oiiticutties giving a year two salvage value of $250,000 for production equipment.

Solution, in Thousands of Dollars:

l=450

!=1OO lru

P=1.0 C-

P=0.6

l=450

(A)

P=0.35 l=300 l=300

01

P=0.4

(D) C=40

P=0.1 5

(c) Salv=250

Expected Value

..letermine the possibre different outcomes and the subsequent

App]y the probabirity of each outcome to the carcul\lv. Igl "uch. lated NPV's giving ENpv per outcome. Summing gives the project's overall ENpV. "r.n There are four (4) possible outcomes:

A) successfur Deveropment reading to incomes of $450 per year. B) Successful Development leadin! to incomes of per year. c) Faiture with a sarvage of $2s0 ai tne end of y"ri$gOO t*o. D) Failure with an abandonment cost of $40 at'year

one.

Chapter 6: Unce.tainty and Risk Ahalysis

For Case A, the chance factor is; (0.6)(0.S)r

\

\ - e00(PlF zo,t) + 450(P/A 20 eXp/F 20 il fo.eoy= +1e8.48 e00(P/F zo',t) + 300(p/A 2['eylerr zo. jlj tt'.z1)= +33.13 !) i-t00 - e00(Pilzo',1) .250(piF i6',ill (c.obi" 9) f-100 = -60.87 D) [-'100 - 540(P tF zo',t)] (0 4) = -219.99 =l'roject Expected Net Present Value (ENPV) = _49.26 1)

t-100

Risk Adjusting the Cash Flows

-500(1.0) 450(0.6x0.5) 450(0.6X0.s) -400(0.6) 300(0.6x0.35) 300(0.6)(0.35) CF(Prob.) -100(1.0) -40(0.4) 250(0.6X0.1s)

Year0lzg_10 Risk Adj CF -100

zzo.s

-7s6

198

ENPV = -100 -756(PlF20,1)+ 220.5(plF29,2) + 1 98(p/A2 g,g) (p /F 2g,2) ENPV = 49.26 Expected Net Present Value (ENPV) at20o/o

4.031

4.03.1

{1450(P I A2O, 9X. 5) + 300( P/A20, g) (. 35)

.8333

+

ZSo (p I F

20,

(. 1 1)

5)

- 4001 (. 6)

.8333

-

40(.4)

- s00)(p/F2},i

-

100 = _4s.26

This result is only slighfly less than zero compared to the total pro-

. costs of million, ject therefore, slightly unsatisfactory or break_ $1 even economics are indicated.

Expected Present Value Ratio (EPVR) EPVR = 49.26 / 100+[500 + a00(.6) + 0(.a)](p /F20,1) = -0.07 The small negative EPVR result indicates the same slighily unsatisfactory or break-even economics shown earlier with ENpV analysis.

308

Economic Evaluation and lnvestment Decision Methods

EXAMPLE 6-9 Expected NPV Anatysis Calculate the,,Expected NPV of a project which will cost $270,000 at time zero. This investment has a 60.0% probability of generating downstream development and equipment costs-at tne=end-of yeai one estimated to total $500,000. lf the secOnd expenditure at the end of year one is successful, there is a g0.0% probability it would lead to the generation of net cash flows totaling $400,000 per year at the end of each of years two through ten. Failure from the time zero investment would result in no additional cost or benefit to the investor. However, should the project fail after the year one cost, a net cost of $250,000 would be realized at the end of year two from dismantlement costs and salvage of equipment. Should this project be accepted? Use a minimum rate of return of 1Z.Ooh.

Solution: All Values in Thousands.

.-$270

P=(0.60)

-$500

P=(0.4)

(c)

P=(o.eo)

$400.

..$4oo

,......-*

(n)

P=(0.10)

$o

(B)

-$2s0

Expected Value There are three (3) possible outcomes in this solution: A) Successful Development, Chance Factor,

P=(0.6)(0.e) =(0.54) p = (0.6X0.1) = (0.06) c) Failure at Time Zero, Chance Factor, p = (0.40) B) Failure at Year 2, Chance Factor,

EVA) [-270-500(P/F1 2,1) + 400(P/\2.9XP/F p,i)(0.s4) = +640.71 EVs) [-270 - 500(P/F1 2,i - 250(PlF p,2)] (0.00) = -54.94 EV6) [-270] (0.40) = -108.00 Project Expected Net Present Value (ENPV) = +477.77

Chaoter 6: Uncertainty and Risk Analysis

Risk Adjusted Cash Flows

Year

0. -

CF(Prob.) Risk Adj

-270fi.q

CF -270

ENPV = -270

-

309

.,,

1

3-10

2

400(0.6x0.e) -500(0.6) -2s0(0.6x0.1) 400(0.6x0.e) 201 216 -300

300(P/F1 2,1) +

201(PlFp,2)

+ 216(PlA12,g(PlFe,Z)

= +477.77 > 0, accept Expected Net Present Value

ENpv @

12.0o/o

= +0o17;ffiX0.e)3/8Fe122:?,,0 0.79719

-

250(P/F1 2,2)(0.1X0.6)

-

u,

0.89286 500(P/F12,1X0.6)

- 270 = +477.77 > 0, ok Example 6-94 Utilizing the data from Example 6-9, what additional cost could be incurred at time zero tor either research or geological/geophysical data and give the investor the same risk adjusted NPV of $477.77? Assume the additional time zero cost will increase the probability of success in year '1 from 0.6 to 0.8. Therefore, the probability of failure in the same period will be reduced from 0.4 to 0.2.

Solution: Let X equal the additional cost to be incurred at time zero.

-x ^-270

P=(0.8)

400

-500

400 (A)

0 P=(0.1)

P=(0.2) 0 (c)

,!

-250

(B)

310

Economic Evaluation and lnvestment Decision Methods

ENPV Approach:

Ecohomicary equivarent, mutuary_excrusive

arternatives wi, always have equar net preseirt r"ir".. Therefore, this sorution rooks at equating the current project Npr;ith the Npv br tnlr"uired prob_ abilities based on the new invest*.ni, x at time zero as forows: 477 .77 = [400(p/A eX,g)(0.9) _ 500J(p/ F ex,[email protected]) - 250(p/F12/",2)(0.1)(0.S) _ z7O _ X 477.77 = [400(s.s2825X0.9) _ so0](0.89286)(o.B) _ 2s0(0.7e71exo.1x0.8) _270

_X

477.77 = 1012.98_ 15.94

X

_270_X

= 249.27

Risk Adjusted Cash Flow Approach, ENpV:

-x -270 P=(0.8) _5W P=(0.9) 4OO P=(0.2

400.

.400

;; . -,

(n)

P=(0.1)

0 (c)

-250

(B)

Risk Adjusted Cash Flow Catcutations: -270(1.0)

-500(o.s)

01

Risk Adjusted Cash Ftows: _4oo

-.270

400(0.72) -250(0.08)

4oo((0.72)

0.......... 268

288

10

. . .288

3..........10 ENpv = -

27

o-

400(p?F81Yji"?, + z6s@

4.9676 + 2Eg(p / A1

ENPV = 727.02

o.7g71g

2"7",g) (p / F 1 2y",2)

/{1\ir,

Chapter 6: Uncertainty and Risk Analysis

,11

The difference between the New ENpv of 227.oz and the originar ENPV ot 472.27 is 249.25 which represents the additional cost that could be incurred at time zero and ailow the invest,oi to obtain the desired ENPV of 477.27.

It was emphasized earlier in this section that expected value represents the average gain or loss per investment that an investor would realize over many repeated investments of the type being analyzed.

whether we work with expected vaiue, expected Npv, expected pvR or expected RoR, the average meaning of results is similar. A common misconception that some people have about expected value analysis is that it oft;n is not valid because investors serdom repeat the same type investments over and over. These people have missed the basic .*p".t.d value analysis premise that even though each specific investment ff remaining book values at the end of project year 5. Determine lroject DCFROR if the initial $100,000 investmenl goes into service n year 1 and is handled in four different ways for lfter-tax analysis )urposes. Consider the 9100,000 investment is:

Cnapter 8: lncome Tax, Working Capital, and Discounted Cash Flow Analysis

A) Depreciable straight line for a 5 year life assuming the half-year

1

convention.

B; Depreciable by MACRS for a 5 year life assuming the half-year

1

conver,ticn.

C) Expensed as a research cost in year 0 with negative taxable income carried forward to be used against project income (stand alone econornics). D; Expensed as research cost in year 0 assuming other taxable income exists against which to use the deduction.

Solution: All Values in Thousands of Dollars lJcte that the cumulative amount of tax deductions is $100,000 by ali four methods of analysis. Only the timing of the tax deductions differs between methods. Since a!r methods of analysis involve the same cumulative revenues and tax deductions, they also involve the same cumulative tax and cash flow. Hou;ever, as you go frcm A) straight line depreciation, to, B) MACRS depreciation, to, C) expensing and carrying forward, to, D) expensing against other income, the timing of tax deductions, and therefore tax savings, is affected significantly causing notable differences to occur in the DCFROR results. ln reviewing the four solutions, note that in each case, the cumulative net income will equal the cumulative cash flow generated by the project. ln all cases, the cumulative value is $102 but to obtain this value for the Case C) net income, combine the cumulative income with the loss forward deductions.

This equality between cumulative net income and cumulative cash flow is not by chance. ln calculating the after-tax cash floy,r, capital costs are charged to the project while depreciation is deducted to determine taxable income and then added back to net income. Therefore, the depreciation deduction is cancelled out, except for the tax effects. ln focusing on net income, depreciation and write-offs represent an allocation of the capital costs, rather than a tax deduction. The timing difference in the two series is what's critical to the economic evaluation process.

402

Economic Evaluation and lnvestment Decision Methods

A) Straight Line Depreciation The half-year 1 deduction causes book value amounting to a harf year depreciation deduction.to exist at the end of year.s.,This book value is deducted (written-off) at year 5. Note that cumulative depreciatlon over the 5 year project rife prus the write-ot"qruis the $100 capital cost. Note that the cumurative income tax paid over the five-year rife is $68 and the cumulative cash flow is $loz. you wili observe that these cumulative numbers are the same for cases B, c and D. This is not a coincidence! only the timing of the deductions varies which affects the timing of the income tax alnd cash flow from cases A to D. Year

5

Revenue -Oper. Costs

-Depreciation -Write-off Taxable lncome -Tax @ 4O/o

lncome +Depreciation Net

+Write-off -Capital Costs -100.0

80.0 84.0

88.0 _34.0

92.0

Cumulative

96.0

44A.O

-30.0 -32.0 -36.0 -38.0 -10.0 -20.0 -20.0 -20.0 -20.0

40.0 32.0 34.0 -16.0 -12.8 -13.6 24.0 10.0

36.0 _14.4

19.2 20.4 20.0 20.0

21.6 20.0

-10.0

-170.0 -90.0 -10.0

28.0

170.0

-11.2

-68.0

+ 41.6(P/F;,4) + 46.8(p/F;,5)

DCFROR = 27.45o/o

r? I .l

16.8 20.0 10.0

-100.0 34.0 39.2 40.4 41.6 46.8 PWEq:0 = -r99 + se.2(p/Fi,2) + 40.4(p/Fi,s) i.:o_o(P/F;,1) Cash Flow

i:

102.0 90.0 10.0 _100.0 102.0

I

I

Chapter 8: lncome Tax, Workrng Capital, and Discounted Cash Flow Analysis

B) Modified ACRS Depreciarion

I I q

i i

Note that cumulative depreciation over the 5 year project life plus the write-off equals the $100 capital cost as with straighi line depre_ ciaiion. However, the timing is different and the taster deductions (bigger deductions in early years) with MACRS depreciation retative to straight line give faster tax benefits and better economics as shown by the 29.0% DCFROR with MACFIs depreciation compared lo 27 .45"/" with straight line depreciation.

Year012g4 80.0 84.0

Revenue -Oper Costs

88.0

5 Cumulative 92.0 96.0 440.0

-30.0 -32.0 -34.0 -36.0 -38.0 -170.0 -20.0 -32.0 -19.2 -11.5 -11.5 -94.2

-Depreciation *Write-off

-5.8

Thxable lncome -Tax @ 40"/"

Net lncome +Depreciation +'vVrite-off

30.0 20.0 34.8' 44.5 40.7 170.00 -12.0 -8.0 -13.9 -17.8 _16.3 _68.0 18.0 12.0 20.9 26.7 24.4 102.0 20.0 32.0 19.2 1 1.5 1 1.5 94.2 5.8

-Capital Costs *100.0

PWEq:0

i-

=

-100 + 38.0(P/F;,1 ) + aa.OftFi,2) * + 38.2(P/Fi,4) + 41.7(P/Fi,5) DCFROR = 29.02/"

5.8

-100.0

-100.0 38.0 44.0 40.1 38.2

Cash Flow

-5.8

41.7

40.1 (p/Fi,3)

102.0

Economic Evaluation and lnvestment Decision Methods

404

C) Expense Research and Carry Loss Forward (Stand Alone) Remember, a "stand alone" financial scenario assumes the project

being evaluated is the only source of income available for the investor. Therefore, any negative taxable income (a loss in that year) must be carried forward and used against positive taxable income in later years. Note again, the cumulative deduction realized equals the $100 cost but the deduction and tax benefits from the deduction are real-

ized more quickly than for either depreciation case. Therefore, expensing the $100 cost gives a better economic result, as the 32.65% DCFROR compared to the smaller depreciation case results illustrates.

4

Year

Revenue -Oper Costs

-Research -Loss

-100.0

Fonruard

lnc.

Taxable -Tax @ 40"h

-100.0

-50.0 -0.8

Flow -100.0 50.0 0 = -100

-1s0.0

2.0 54.0

-100.0 -50.0

-50.0 .2 Forward 100.0 50.0

PW Eq:

Cumulative

80.0 84.0 88.0 92.0 96.0 440.0 -30.0 -32.0 -34.0 -36.0 -38.0 _ll3:3

Net lncome -100.0 +Loss -Capital Costs Cash

5

1

51

-21

58.0 -23.2

-68.0

33.6 34.8

-48.0

56.0

.6 -22.4

32.4

.2 32.4 33.6 34.8

i i

20.0

150.0 102.0

+ 50(P/F1,1)+ 51.2(P/Fi,2) + 32.4(P/F;,3)

+ 33.6(P/F;,4) + 34.8(P/F1,5)

i = DCFROR=32.65%

n

Chapter 8: lncome Tax, Working Capital, 6nd Drscounted Cash Fiow Analysis

D) Expense Research Against.Other lncome Again, the cumulative deduction equals the $100 cost, but having other income on the investor tax return in year 0 against which to use the negative taxabie income (-$tOO; gives the investor the tax benefit of inflow of money immediately in year 0. This gives a better economic result than any of the other cases. ln the U.S., wh:re quar-ter-ly estimated tax payments must be made by all business investors, tax savings from tax deductions generally are realized within three months of incurring tax deductible costs.

4

Year

80.0

Revenue -Oper Costs

84.0

-30.0 -32.0

-Research

-100.0

5

Cumulative

88.0 92.0 96.0 44A.A -34.0 -36.0 -38.0 -170.0 -100

-68.0

Flow -60.0 30.0 91.2 32.4 33.6 g4.B

1.02.0

'170.0

*Capital Costs Cash 'i

0

' Taxable lnc. -100.0 50.0 52.0 84.0 5e .0 58.0 -Tax @ 40% 40.00 -20.A -20.8 -21.6 -22.4 -23_2 Net lncome *60.0 90.0 g1.Z gZ.4 93.6 34.8

PW Eq:

0 = -60.0 + 30.0(P/F;,1)

102.0

+ 31 .2(plFi,2) + Sz.ap/F,,g)

+ 33.6(P/F;,4) + 34.8(p/Fi,5)

i

= DCFROR=44.16%

The reader should observe from these anaiysis results that the faster an investor realizes tax deductions and the tax benefits from the tax deductions, the better the economics of projects become. Expensing the $100,000 cost against other income gives a 60"/o increase in the DCFROR that is obtained by straight line depreciation of the cost. lf you have to carry negative taxable income forward to make the project economics "stand alone', as in part ,,C,,'the project economics do not look as good as when other income is assumed to exist against which to use deductions in the year incurred, as in part "D."

Economic Evaluation and lnvestment Decision Methods

part "D" as Finally, as an alternative to treating the research cost in of 1'0 in rate a wlth I tax ex[ense_ item, consider it to be depreciablepraciice, so in induStry rcat A. fnis iS an approach'sometimes'used :he reader should be'aware of the equivalence of either apprgach aS "D" illustrate' :he following year 0 cash flow calculations for part An Alternative to

"D"

year

o

an

Research as ExPensed Cost Revenue -Oper Costs

-Besearch -Research as DePreciation

-100.0

Taxable lncome -Tax @40"h

-100.0

year 0 Research as a DePreciable Cost

-100.0 -100.0

40.0

40.0

Net lncome +Depreciation -Capital Costs

-60.0

-60.0

Cash Flow

-60.0

100.0

-100.0 -60.0

Example 8-6 involved a single investment cost that was either depreciated invenor expenied for tax deduction purposes. Most businesses also require ,ory .ortr, commonly called working capital' which are not depreciable as discussed in the following section.

8.10 lVorking CaPital worliing capital is the money necessary to operate a business on-a day+o-day inventory basis. It normally is comprised of mouey requireJ for raw material and receivable' in-process ,r,ut"iiul, inventory, product inventory, accounts considered to ready cash. For evaluation purposes, working capital generally is and to be Ue put into a project at the itart of a business or production operation are liquidated' inventories full-v recovered at the end of the project life when Working capital is not allowable as a tax deduction in the year it is incurred capital so it often has a very negative effect on project economics. working inventory until depleted or amortized cost may not be expensed, depreciated, working capital assets are actually used or put into service. One way to explain

E

Chapter 8: lncome Tax, Working Capital, and Discounted Cash Ftow Analysis

407

and w'hy it is not deductible for tax pulposes in the yezr it is incurred, is to con_ sider the determination of the "cost of Goods sold" as it is handled on corpor.rte or individual business tax returns. Table 8-3 illilstrards the sreps necessarv to calculate the annual cost ofgoocls solii for a business operated either by iii; iilCii idual, partiership or corporation. in this cost o1'go64siold calculation, i.riue oi inventories rrt the;,ear end is working capital and is not rax deductible.

Begir:ning of Year Inventory + R.tu lvlaterial Costs from purchases During the Year + Liii:t;r Costs to Convert Rarv Material or parts Into products + lUirterials, Parts & Supply Costs Incured During the year + Other Costs Related to production of products = Cosl of Materials, Supplies ,nd G,,odl*uilubl" f* *- Inventory value at year End Based on Lesser of cost or value = Cost of Goods Sold (Deductible as Annual Operating Cost) Table 8'3 calculation of cost of Goods Sold Related to working capital \\brking capital represents the capital cost required to generate raw material inventories, in-process inventories. product inventories and parts and supplics inventories. As inventorics are used and prociuct sold, working capilal .:c;st items beconre allou'able tax deductions as operating costs through the cost of grlods sold calcr-rlation. However, as inventory items are used they tl pically are replaced so inventories are maintained at a similar level over the project life. If significant increases or decreases in working capital are projected to occur from year to year, positive or negative working capital costs can be accounted for from year to year in pro;eit analyses. Now it should occur to you that raw material and parts in inventory often are acquired at different costs durin_q a year. How do you determine the value of iterns left in inventory at the end of a tax year when items u,ere acquired fbr difi'erent costs during the year with some used and some left in inventory? FIFO, LIFO and average inventory accounting are the three basic inventory accounting systems that detennine the cosr.s of items used during a tax year to be deducted as operating expenses and the costs of items left in inventory and treated as working capital. FIFo is the acronym that stands for,,First-In-Firstout." using FIFo inventory accounting, the first items to go into inventory are considered to be the first items to come out and be used and deducted as operating expenses. Therefore, under FIFo inventory accounting, the last

408

Economic Evaluation and lnvestment Decision Methods

items purchased during a tax year are the cost basis for inventory assets tied up in working capital.

LIFO is the acronyrn for "Last-In-First-Out." Using LIFO inventory accounting, the last items to go into inventory are,considered to be the fust items to come out and be used and deducted as operating expenses. Therefore, under LIFO inventory accounting, the lirst items purchased during a tax year or in inventory from earlier years are the cost basis for inventory assets tied up in working capital. In an inflationary climate the cost of items purchased during a year generally increases and LIFO gives tax deduction for the bigger cost items purchased later in the tax year than are realized with FIFO. In a deflationary climate the opposite is true. A majority of U.S. companies use LIFO inventory accounting and LIFO is the implicit inventory accounting assumption built into the handling of working capital in this text. Under LIFO, assuming uniform quantities of rnaterial in inventory each year, money tied up in working capital is constant each year with changes in item costs accounted for as operating cost changcs. Average inventory accounting is based on using annual weighted average prices or values of assets in inventory for the cost of goods sold and working capital calculations. In most western world countries other than the U.S., LIFO inventory accounting is not permitted. Therefore, FIFO and average inventory accounting are emphasized in countries other than the U.S. In accounting terminology working capital is defined as the difference between current assets and current liabilities. This definition is consistent with our "Cost of Goods Sold" calculation explanation of working capital. When a new business or production facility is started-up, it often generates and produces product for three or four months before product is sold and income is received for product sold. Assuming the business pays cash lor raw materials, parts and supplies during the start-up period, the cost of these items increases the "current assets" of the business. lf all items have been paid for with cash (no time payments), no current liabilities are accrued, so current assets minus current liabilities equals the working capital which is the value of items in inventory including product inventory.

EXAMPLE 8-7 Project Analysis with Annual Changes in Working Capital: FIFO, LIFO, and Average lnventory Accountin g A project is being analyzed that has product selling price, production costs, annual production and annual sales summarized as follows:

L

Chapter 8: lncome Tax, Work;ng Capital, ail._l Discounted Cash Flow Analysis

409

Product Price and Production Cost lnformation Year

Selling Price, $/Unit Production Cost, $/Unit Prod uction/l

$21

$zt

$21

Ci 2

$zt

$10

$15

$tz

1,000,000 1,000,000

1,200,000

nventory lnformation

Year

Units Produced Units Sold

Change in lnventory Cumulative lnventory

500,000

1,000,000

0

800,000

5O0,0OO

500,000

200,000

700,000

s00,000

0

-700,000

700,000

0

Cost of Units Produced $5,000,000 913,000,000 $15,000,000 $8,500,000

To generate this prociuction, ayear 0 capital cost of $10,000,000 is projected to be incurrecJ with I year life MACRS depreciation applicable starting in year 1. The project will terminate at the end of year 3, with zero salvage value and a write-off on remaining depreciable book value. The effective income tax rate is 40"n. calculaie prcject DCFROR assurning the cost of goods soid (coGS) operating cost and working capitai valuations ai.e based on:

A) First-ln-First-Out (FIFO) inventory accounting B) Last-ln-First-Out (LtFO) inventory accounting C) Average inventory accounting

Solution: In comparing the FlFo, LlFo, and average inventory accounting economic results for the analysis, note that LlFo givel the largest cost of goods sold operating cost deductions and the smallest working capital costs in early project years relative to FlFo and average inventory accounting results. Therefore, the best economic results occur with LlFo. with escalating production costs from year to year, LlFo always gives faster tax deductions relative to FlFo and aveiage inventory accounting, which is why virtually all large U.s. companies use LlFo inventory accounting for all major raw miterial and product inventory items. For this analysis, and in general for all analysis situations, average inventory accounting givel project results that are in between FIFO and LIFO results.

410

A)

Economic Evaluation and lnvestment Decision Methods

FIFO lnventory Accounting

Cash plowslijsing Cost Of Goods Sotd and Working Capital . :. Based on FIFO

23 Revenue - Cost of Goods Sold" - Depreciation - Deprec. Write-off

0 0 0

Taxable lncome

0 0

-fax

@ 4Oo/o

16,800,000 21 ,000,000 25,200,000 -8,900,000 -1 3,600,000 -1 9,000,000 -1,429,000 -2,449,000 -1,749,000 -4,373,000

6,471,000 -2,599,400

4,951,000

-1,990,400

79,000

-31,200

Net lncome 0 3,892,600 2,970,600 46,900 + Depreciation 0 1,429,000 2,449,000 6,122,000 - Capital Equipment -10,000,000 - Working Capital*. -5,000,000 -4,1oO,OOO -1,4oO,OOO 1o,50o,OOO. Cash Flow

DCFROR = 15.150/"

-15,000,000

1

,21

1

,600 4,019,600

16,668,900

NPV @ 12o/o= $1,150,709

*Cost of Goods Sold = COGS COGS = Value of Units From tnventory + production Yr 1 COGS: (500,000 * $10) + (300,000 * $13) = g8,900,000 Yr 2 COGS: (700,000 x $13) + (300,000 * $1S) = g18,600,000 Yr 3 COGS: (700,000 x $15) + (500,000 x $17) = g19,000,000 Note: The year 3 COGS represents the gg,500,000 cost of product produced in year 3, along with the $10,500,000 write-off value of inventories drawn down to meet product sales in that year. **Working Capital = Cost of Units produced - COGS Yr 0 Work Cap: 500,000 * $10 - 0 = $5,000,000 Yr 1 Work Cap: 1 ,000,000 * $13 - $8,900,000 = $4,100,000 Yr 2 Work Cap: 1,000,000 + 915 - 913,600,000 = $1,400,000 Yr 3 Work Cap: 500,000 * $17 - $19,000,000 = (g10,500,000). 'Yr 3 Working Capital is a credit for reducing inventory.

-tl

i

j ,! 1

t

n il :i

Cha,:te!'B: Income Tax, Working Capitai. and Dlscounted Cash Flow Analysis

41'l

B) LIFO lnventory Accounting cash Flows using cost of Goods Sold and working capital Based on LIFO Y,aar

0

Revenue - Cost of Goods Sold. - Depreciation - Deprec. Write-off

6,800,000 21,000,000 25,200,000 0 -1 0,400,000 -15,000,000 -16,100,000 0 -1,429,000 -2,449,000 -1,749,000 -4,373,000

Taxable lncome

0 0

-Tax @ 40"/"

'r

4,97't,000 3,551,000

Net lncome 0 2,992,600 + Depreciation 0 1,429,000 - Capital Equipment -10,000,000 - V/orking Capital." -S,000,000 -2,600,000 Cash Flow

DCFROR

2,130,600 1 ,786,800 2,449,000 6,'122,000

0

-15,000,000 1,811,600 4,579,600

-

15.7A%

2,978,000

-1,989,400 -1,420,400 -1,191,200

7,600,000. 15,508,800

NPV @ 12Y"= $1,307,187

*Cost of Goods Sold = COGS coGS = Value of Last units produced + Necessary lnventory Yr 1 COGS: (800,000 * $13) = 910,400,000 Yr 2 COGS: (1,000,000 * $15) = $1S,OO0,0OO Yr 3 COGS: (500,000 * $17) + (200,000 * $13) + (500,000 yr 0 production) x g1O = $16,100,000 Note: The year 3 COGS represents the gg,500,000 cost of product produced in year 3, along with the 97,600,000 write-off value of inventories drawn down to meet product sales in that year. ** Working Capital = Cost of lnventory produced - COGS Yr 0 Work Cap: 500,000 * $10 - $O = $5,000,000 Yr 1 Work Cap: 1,000,000 * giS - 910,400,000 = 92,600,000 Yr 2 Work Cap: 1,000,000 * 915 - $15,000,000 $0 = Yr 3 Work Cap: 500,000 * $17 - $t 6,1 o0,0oo = (g7,600,000). "Yr 3 Working Capital is a credit for reducing inventory.

412

Economic Evaluation and lnvestment Decision Methods

C) Average lnventory Accounting

Cash Flows Uslng Cost Of Gooits Sold hnd Working Capitat BaseC on Average lnventory Year

Revenue - Cost of Goods Sold* - Depreciation - Deprec. Write-off

0 0 0

16,900,000 2'1,000,000 25,200,000 -9,600,000 -13,764,706 -18,135,294 -1,429,000 -2,449,000 -1,749,000 -4,373,000

Taxable lncome

0 0

5,77'.1,O00 4,796,294 -2,309,400 -1,914,519

-Tax

@ 4O%

0 0

Net lncome + Depreciation - Capital Equipment -10,000,000 - Working Capital** -5,000,000

942,706 .-377,O92

3,462,600 2,871,776 565,624 1,429,000 2,44q,OOO 6,122,000 -3,400,000 -1,235,294 9,635,294"

Flow -15,000,000 1,4g1,600 4,OgS,4g2 16,g22,91g DCFROR = 15.35% NPV @ 12o/o = g1,207,03g

Cash

*Cost of Goods Sold - COGS coGS - Average Varue of Units produced and sotd Each yr Yr 0 COGS: (500,000 produced, none sold) g0 = Yr 1 COGS: (($tO * 500,000 + $13 * 1,000,000)/1,500,000) * 800,000 = $9,600,000 Yr 2 COGS: (($tZ * 700,000 + 915 * .1,000,000)/1,700,000) * 1,000,000 = $1 9,764,706 Yr 3 COGS: ($13.70 x 700,000 + $17 * 500,000) g1B,.t gS,Zg4 = Note: The year 3 COGS represents the $g,500,000 cost of product produced in year 3, along with the $9,635,294 write_off value of inventories drawn down to meet product sales in that year. ** Working Capital = Cost of Goods produced - COGS Yr 0 Work Cap: $10 x 500,000 - $O = $5,000,000 Yr 1 Work Cap: g'13 ,r 1,000,000 - 99,600,000 $3,400,000 = Yr 2 Work Cap: g1S x 1,000,000 g19,764,206 = $1,23i,2g4 Yr 3 Work Cap: 917 * 500,000 $t g,1g1,Zg4 $9,635,294" = 'Yr 3 Working Capital is a credit for reducing inventory.

ll

?

i

chapter 8: lncome Tax, working capitar, and Discounted cash Frow Anarysis

413

EXAMPLE 8-8 Rerative sensitivity of DcFBoR and Npv to Project Life and Start of production A new project is being considere,J that would require the investment of S200,000 for processing equipment and $60,000 fcr workir..:g capiiai at y'ear 0. The equipment would be depreciated using year 5 lrfe sti-aight line depreciation starting with the half-year conveni;cn in year 1 when the equipment is expected to go into service. Annual r,uu"nr", are projected to be $300,000 and annuar operating costs are projected to be $200,000 with a wash-out of escaiation of o-per"ating costs ind revenue eacf salvage value and working capital return are expected to -year. total $100,000 at the end of the prolect. The effective income tax rate is 4ao/" and rninimum DcFRoR is 12%. calculate DCFROR and NpV for: Case A) A 10 year project evaluation life Case B) A20 year prcject evaluation life. case c) Assume technical difficulties or envii-onmental permitting delays cause the case A cash flows in years 1 through 10 to be realized in years 2 thi'ough 11 with zeio cash frow in year 1. Solution: All Values in Thousands of Dollars Case A) 10 Year Evatuation Llfe

'

Year

0

Revenue

300

-Operating Costs -Depreciation -Write-off Taxable lncome -Tax @ 4A"h Net lncome r-Depreciation +Write-off -Capital Costs Cash Flow

1 -200

-oo

: 80

60

-32

-24

48

_;

Z_s 300 -2AO

v

7-9

10

300

300

400

-2A0

-200

-200

100

-60 140

-40

-56

-:o

80 -JZ 48

.:

60

+68 +76 +68 +60 . Revenue includes-260 $100 salvage and working

84 +60

+144

capital return. working capital invesiment tax deduction write-off. NPV Eq: 0 = -260 + 68(piF;,1) + 76(p/A; ,4)(ptFi,1) + 68(p/F;,6) + 60(P/A;,3)(p/F;,6) + 1 44(p /Fij g) DCFROR = 25.24o/o, NPV @ 12/o +$160.6 =

.. original

/L

**

414

Economic Evaluation and lnvestment Decision Methods

Case B) 20 Year Evaluation Life

Year

O

Revenue

300

-Operating Costs -Depreciation -Write-off

-200

-!

Net lncome +Depreciation +Write-off -Capital Costs Cash

Flow

7-19

2-5

300 -200

i'

300

-200

-!

80 60 -32 -24

Taxable lncome -Tax @ 40"/"

*

1

48

v

36

:,

80

-32 48

.:

20

300 400. -200 -200 -60 "*

100 -40

140

-56

60

84

;

-260 -260

+68 +76 +68 +60

+144

Revenue includes $100 salvage and working capital return. *" Original working capital investment tax deduction write-off.

NPV Eq: 0

+ 68(P/F;,1) + 76(P/A; ,4)(PlFi,1) + 68(P/F;,6) + 60(P/A;, 1 3XP/F;,0) + 1 44(P /F i,2g)

= -260

DCFROR =26.77"/", NPV @ 12oh=+$251.5

Although beforetax profit literally doubles for the 20 year life project as compared to the 10 year life project, DCFROR only increases 1.5% (trom 25.2/" lo 26.7"h, a 6% change). The change in NPV due to doubling the project li{e, however, is much more significant. The 20 year life NPV of +$251.5 is $90.4 greater than the 10 year life prolect NPV of $160,6 (a 56% increase). Discount rate magnitude is the reason NPV results, in this case and in general, are more sensitive than DCFROR results to changes in cash flow beyond 10 years in the future. 'l-he NPV discount rate of 12/"is smaller than the DCFROR results of 25.2/" and 26.7"/". As a result of the mathematical definition of the single payment present worth factor, (1/(1+i)n), larger values of "i" cause the present worth factors to be much smaller than for smaller discount rates when the evaluation period, n, is 10 or greater. ln this analysis, since the 12% NPV discount rate is much smaller than the DCFROR rates, this causes the years 11 through 20 cash flows to have a much greater impact on the NPV result than on DCFROR result.

Chapter 8: lncome Tax, Worring Capital. and D:scounted Cash Flow Analysis

415

Case C) Rework Case A for 1 year Startup Delay Year

Cash

Flow -260 O

3-6 7 8-10 11 +69 +76 +6g +60 +144

i\PV Eq: 0 = -200 + 68(p/F;,2) + 76(piAi ,4\plFi,Z) + 68(p/F;,7) + 60(PiAi,3)@Fi.) + 144{p/Fi,1l DCFROR = 19.78o/o, NPV @ 12.0% +$1 15.6 =

This is a 21.6% reduction in DCFROR to 1g.7g% from the base case A result o'f 2s.24/o and a zg.a% reduction in Npv to +g115.6 from the base Case A result of +g160.6. These discounted cash flow c:'iteria changes are sign.ificant enough to emphasize the importance of the timing as weil as the magnitud! of cosis ano revenues that go inic anaiyses. 8.11 International project Evaluation Considerations Companies, individuals and sovemments invest and sell products outside their own countries for many difrerent reasons. Reduction of operating costs, penetration of irrternational markets. hedging against curency exchange rate variations and improvement of technical servic.: to intemational customers ;ire so;ne of the reasons- Whether y()u iue evaluating intemational inyestments fiorn the viewpoint of a domestic U.S. cornpany considering investing or seiling product in anorher counriJ. or from the viewpoint of a foieign company investirrg or selling product in another country, tw'o intemational evaluation consideratictrrs tlnt ure not present in clomestic ev,aluations must be given serious atten-

tiort. First, pt'ojecting c,urrenc)- exchange rates for each"year of ttrc rtfe of o- major uncertaintl. in intemational investment or sales agreement evaluatiorzs. whether you are investing or selling in a foreign market' you must project curcncy .*.hurg" rates over ihe life of projects so tirat )'ou can express all project costs and i"u"nu", in terms of the same currency to make a valid economic analysis of these in'estmenrs. projecting projects to be evaluated is

exchange rates invoives significant uncertainty and probably is at least as diffrcult as projecting product selring prices. second, joreign investment projects rnust be evahnted ayer-tax using the tax law of the couiry in which the investnrcnt is located. wcstern world country tax treaties permit companies with a base of operation in one country to use taxes paid on projects in another foreign country as tax credits against domestic income tax. If foreign tax is higher than domestic tax, as is often the case for U.S. companies, then the for-

416

Economic Evaluation and lnvestment Decision Methocls

eign tax cash flow usually is the worst case analysis that the investor should use to evaluate the ecolomic potential of the foreign project. However, differ_ ences in tax deduction methods (for example, depletion usually is not applica_ ble in foreign countries) and asset tax lives, as well as tax iate diffeiences, affect foreign project evaluations. Investors must be careful to analyzeproject economics from both a foreign tax and domestic tax viewpoint to determine the worst case project cash flow stream that is relevant ftr evaluation pur_ poses. In doing the u.S. tax analysis of a foreign U.S. project, ailowable tax deductions generally are different (usually smaller; ttu, ro, a oomestic u.s. project. For example, u.S. mine development or intangible drilling costs can be 70vo expensed, 30vo amortized over five years by specified u.s. domestic producers, but these costs must be deducted straightlin" or"r 10 years for u.s. tax on foreign projects. Allowed depreciation on foreign projects seems analogous to allowed domestic U.s. depreciation for alternative minimum tax. contact your international tax department for specific project tax details.

These tax deductions differences can significantly

tte of a "hung" foreign project in comparison to an equivarent domesiic "conomics U.S. project. The following example illustrates how exchange rate projections are used in an economic analysis involving two currencies, and the sensitivity of DCFRoR and NPV results to exchange rate projection variations. EXAMPLE 8-Ba Exchange Rate variation for DcFRoR and Npv

,.

Sensitivity To illustrate how exchange rate projections rerate to an international. project anarysis, consider the Exampre g-g, case A project to be a u.s- project so arr revenues, sarvage varue, capitar costs, operating costs, tax deductions and cash flows are in u.s. oottars. How_ ever, assume the revenues have been generated by seiling 1,ooo grodugJ units per year in Austraria at a fr-xed contraci price of 9400 Australian per unit for a base case exchange rate of per U.S. $b.ZS $1.00 Australian. This gives $400,000 Australian revenue per year

which converts to $300,600 U.S. per year for the $0.75 U.S. per Aus_ tralian dollar base exchange rate- This yierds the Exampre B-g, case case analysis results of DCFROR 25.24h and NpV @ l^b^q." = 12.0% = $160,600. Anaryze the sensitivity of these base case economic results to changing the $0.75 base case exchange rate to:

1)

$0:65 U.S. per $1.00 Australian due to a strengthened

dollar.

Chapter B: lncome Tax. Working Capital, and Discounted Cash Flow Analysis

2)

417

$0.85 U.s. per $1.00 Australian due to a weakeneci u.s. dollar. (Note that requiring $0.9S U.S. to buy $t.00 Austratian versus $0'75 means the domestic currencv lu.s. doilarf has weakened relative to the Australian dollar.

Solution: All Values in Thousands o{ U.S. Dollars Case 1) Exchange Rate $0.65 U.S. / $1.00 A = Annual Revenue = $400 A ($0.0S U,S./$1.00 A) = $260 U.S. Year 2-5 7-9

260 260 260 -2A0 -200 -200 -20 40 _20

Revenue - Operating Costs - Depreciation * Write-off Taxable lncome

* Tax @ 40"/o

l.let lncome + Depreciation + Write-off - Capital Costs

260 _200 0

10

*360 -2AO 0

*"-50

0

40

2A

40

60

1'30

0

-16

-8

-16

-24

-+U

02412243660 02A402000 0000060 -260

Cash Flow -260 44 52 44 120 * Revenue includes $100 U.S. salvage and working capital return. *" original working capitar investmenl tax deduction wiite-ott.

36

N

PV Eq: 0 = -260 + 44(p lF i,1) + S2(p / Ai, )(p /F i,1) + 36(P/A;,3)(p/F;,6) + 1 20(p/F;, g)

+

44(p lF i,6)

1

DCFROR = 14.19%, NpV @ 1Z.Oyo +$2S.0 = Projecting exchange rates is difficult and involves great uncertainty. lt is necessary, however, in multiple currency analysls due to the sensitive impact that exchange rates have on analyiis results. strengthening of the U.S. dollar to $0.65 U.S. per .OO A from $f $0.7S U.S. per $1.00 A has weakened the economics of this hypothetical project significantly as measured by either DCFROR or6pping to 14.19"h trom 25.24% or, NpV dropping to $2S,OOO from g1Ob,OO6. Anywhere in the world, strengthening oi a domestic currency makes the eco-

Economic Evaluation and lnvestment Decision Methods

418

nomics of export projects less desirable. On the other hand, as Case of a domestic currency makes export project

2 shows,

better.

l

case 2) Exchange Rate = $0.85 U.S. / $1.00 A Annual Revenue = $400 A ($0.es u.s. / $r.00 A) = $340 U.s. (Note the U.S. dollar has weakened relatively to the $0.75 U.S. per $1.00 A exchange rate since more U.S. dollars are required to purchase an Australian dollar) 7-9

10

340

340

-200 -20

-200

"440 -200

2-5

Year

340 340 -200 -200 -20 40

Revenue - Operating Costs - Depreciation - Write-off Taxable lncome - Tax @ 40% Net lncome + Depreciation + Write-off - Capital Costs

Flow

0 0

120

-48

100

40

0 72 60 020402000 0000060

0

140 -56 72 84

0

**-60

120

180

-48

-72 108

-260

-260 92 100

92

84

Cash 168 * Revenue includes $100 U.S, salvage and working capital return. .. Original working capital investment tax deduction write-off. NPV Eq: 0

= -260 + 92(P/F;,1)+ 100(P/Ai,4)(P/Fi,t) + 92(P/F;,6) + B4(P/A;,3XP/Fi,6) + 1 68(P/F;,1 g)

DCFROR =35.48/", NPV @ 12.0% = +$296.2 This weakened U.S. domestic currency analysis shows that export project economics are improved by weakening the value of a domestic exchange rate. The price paid for this benefit is higher prices for imports. lmport project economics are hurt by a weaker domestic exchange rate and import project economics are enhanced by strengthening domestic exchange rates. Governments try to establish and execute exchange rate policies that keep exchange rates in a range that is acceptable to both import and export businesses.

Chapter 8: lncome Tax, Working Capital, and Discounteo Cash Flow Analysis

419

obviously, that is a difficult objective to achieve consistently in this age of interactive international finance. .l

8.12 Nlining and Petroleum Project At'ter-Thx Analysis i\lining and perroieirn': project discounted cash florv analyses are sirnilar to non-*rineral anahses in terms of general procedure. In any discounted cash florv type analvsis you iirst convert all project relenues and costs to positive and ncgatile cash flows. lbu do this by accounting for the tax deductibiliry of costs and the tax to be paid, or tax savings to be redized, on resulting positive or nr:gative taxable income each year.

The unique feuture about discounted cash flow analysis of mining or petroJeum projects. compared to non-mineral projects, is the handling of certain tax cleiluctions. Chapter 7 addressed the tix handling of mining exploration and deve;upment costs und petroleum inrangihle drilling costs and pointed out that lfi)%' of these costs rnal' be expensed bl, "indit,iduar" minerel project opet.Lt-

or "independtnf" pefiolenmptoducers. "corporcte mining operators," or "hiegrated petrolewn producers," nmr- only expense 70vo of these cosrs. The other 307o of the intangible drilling or mining development costs are anwrtii*

=12."/o,

new compressor is satisfactory

Npv

@

4.111 0.4523 i lzx = -408 + 168(piAi2,6) + 156(prF12,7) 2.402

0.4523

+ 1 44(Pl A12,9(Plr

12,7) = + $51 0 > 0,

satisfactory

The DCFBOFI of 39.2"/o, which is more than three times the minimum DCFROR of 127", indicates very satisfactory economics for the nev'/ compressor, consistent with positive NPV of $510,000 that is greater than tne cosi of $420,000 that generated the NPV. Whenever NPV is pasitive and similar in magnitude to the cost that generated it, project economics are very good and typically relate to a proiect with a DCFROR three or four times the minimum DCFROR. 9.'1 Sunk Costs and Opportunity Costs in Evaluations Srtttk costs are cost., that have already been incurred in the past and that n()llting v'e do now or in the.t'uture cen affect. Economic analysis studies for invesrrnenr decision making purposes deal with project costs and revenues artd iax ettrcts yet to be incurred now or in the future. Sunk costs are not r.'levont ro the anal ,-sis of either income or sertice producing investment alternativ,es except for remaining sale value and tax effects, yvhich are opporturtitl' cost considerations discussed in the next paragraph. Past commitments to expend money as well as past expenditures are sunk revenues and costs. Revenues realized in the past from a projerct are sunk revenues the same as past costs are sunk costs. Classic examples of sunk costs include the costs of equiprnent acquircd several years ago and now being considered for replacement, the costs for research or exploration work incurred in earlier years, an i* = 157o, so satisfactory

Case C) Year -1 Cost ls Sunk and an Opportunity Cost Exists The year -1 cost and tax effects are still sunk. However, the year 0 sale value of $200 minus tax of 0.40($200) or $80 would yield sale cash flow of $120. An investor who passes up the opportunity to realize positive cash flow from selling in order to retain or develop, incurs an opportunity cost equal to the positive sale cash flow. This opportunity cost occurs naturally from proper incremental analysis of the mutually exclusive develop versus sell alternatives as follows:

-101-45

Year

Develop Cash Sell Cash Develop -

Flow -90(Sunk) -252 112 -90(Sunk) +120 0

Florr Sell

0

-372 112

104 0 104

PWEq@Yr0: 0=

-372 + 112(Pl Ai,a) + t 04(P/F;,5)

i = DCFROR

= 14.94/o < i" = 157o, so slightly unsatisfactory

450

Economic Evaluation and lnvestment Decision Methods

From an economic viewpoint, development is slighfly less desirable than- selling. NAte_ tha! the Develop minus_Sell incremental alalysis converts the sale positive cash flow of $120 to a negative incremental $120 cash flow. This is effectively a $120 opportunity cost that the investor incurs In addition to the year 0 development cost if development is accepted. Even though development alone looks satisfactory as shown in the "8" analysis, proper accounting for the opportunity cost from keeping the property instead of selling makes selling a slightly better or break-even alternative compared to developing.

Case D) Year -1 Cost is Sunk but Tax Effects are not Sunk. The time zero sale cash flow is the $200 sale value minus the tax on the sale taxable income of $200 - $150 land book value which yields tax of $SO(0.4) = $20. This gives after-tax sale cash flow of $200 - $20 tax = $180. Although the land cost of $150 is sunk, the remaining sale.value and tax effects are not sunk and give sale value cash flow of $180 instead of the 9120 cash flow in the,,C', analysis when the year -1 cost and all tax effects were sunk. lf the project is developed instead of being sold, the land book value of $150 will be written off at the end of year five against other income, saving $150(0.4 tax rate) = $60 in tax at year five. This makes the year 5 develop cash flow 9104 plus $60, or $t O+. Year

1-4

-1

Develop Cash Flow -150 (sunk) Sell Cash Flow -'150 (sunk) Develop - Sell 0

-ZS2 +112 +164

+180 O 0 492 +112 +164

PW Eq @ Time Zero: O

= -432 + 112(P / Ai,4) + t64(P/F;,5)

i=

DCFROR = 12.1"/o i*, ROCE is satisfactory

'Asset book value" refers to the book value of all assets at the beginning of a period (for either tax or financial shareholder reporting purposes) for a corporation, but again; this definition can vary slightly for each consultant. Rearranging the above inequality by multiplying each side times the "asset book value" gives: Net Income > i*(Asset Book Value), is satisfactory

This tells management and investors alike that successful corporations need to generate net income in excess of the interest that could have been earned had the company liquidated the assets and invested the cash in other perceived opportunities (a measure of an opportunity foregone). Note that this assumes the asset book value is representative of the cash value (market value) of assets from liquidation of the assets, which may be a significant assumption!

Rearranging the inequality once again by subtracting the product of i*(Asset Book Value) from both sides results in the following: Value is Added

When; Net Income - i*(Asset Book Value) > 0

trapter

9: After-Tax lnvestment Decision Methor,{s and Applications

485

This is the basic detrnition of value added provided earlier in this section. Note the direct reiationship of this approach to the RocE calculation introriuced eariier. Further, you can see that successtul investors must generate net income in quantities -srearer than the product of the asset book value rirnes rire opportunity cosr oi'capital il value is to be aticed to rhe portibliu. while many compiinies may base these calculations on tinancial treatnlent o1'L-xpenditures - in his book, "The Quesr for \hlue," G. Bennett slew'ait recomurend:i several modiiications to the tlnancial reporting procetlures iir order to make value added results more meaningfui in relationship to casir liu,w. Some of the adjustments rvould include the ad.option of LIFo inventory procedures, adjusting for deferred taxes. capitalizing of all R&D and utiiizing full cost accounting so all R&D, development and exploration e ,rirr-qes arc reflected in the capital base - not just successful expenditures. Such ari.lustmenrs are intended to allow operating costs to reflect actual L'\pendirures for goods soid during the year. As was illustrated in chapter g, ir: inflirtionary rimes, the LtFo methodology vzill lower taxable income and tax, rvhich increa.ses cash flow and value when compared to the FIFO approach. stewart argues that by making his recommended adjustments, the asset book value lvill more clearly represent actual value of expenrlitures incurred and hence. the true investnrent required to generate the revenues realizc'd for the year. Such adjustments rvould be u'elcome, but may still not prot'ide a halance sheet or net income statemeni that rellects the true market raiue. wlirch is u'hat true opportunitl co,t is based on. If \A or RocE are to be used for economic decision-making, three considcrations should be addressed in attempting to capture the true measure of value being added. (1) tax deductions, rather than shareholder report hnancial deductions, must be the basis of the analysis so that net income is based on actual tax paid, not an accrual based on straight line, project life depreciation. This can also be accomplished by adjusting the financial net income for deferred tax considerations. (2) rhe opportunity cost of capital, rather than the financial cost of capital must be utilized. opportunity cost of capital repre.sents the rate of rerurn potentiai for those other opportunities that exist for investment of funds. Investors don't want to accept investments that simply achieve the financial cost of capital, so why should the value added opportunity cost calculation be any different? As discussed in chapter 3, section 3.J, use of financial cost of capital as a minimum rate of return will show investors the projects that will make money for them, but it is necessary to use opportunity cost of capital to determine the investments that generate maximum value possible from available investment capital

486

Economic Evaluation and lnvestment Decision Methods

and assets. If a company has a financial cost of capital of 12.07o and rationed or lirnited available capital, and.other investment opportunities to invest all available capital at 20.0o/o or higher, accepting a l5.0Vo rate of return would be making su-b:optimal use of'funds.and not'add.maximum value. (3) For VA or ROCE use in economic analysis of existing projects or business units, the actual "marked to the market" opportunity cost value of business assets being analyzed (best represented by the after-tax cash flow realized if all assets were liquidated) should be the basis rather than either tax or shareholder book value. To illustrate, assume a company owns an office building that is almost fully depreciated for tax and or shareholder reporting purposes. The company wants to analyze whether it is better to sell the building and invest the after-tax cash flow at their opportunity cost of capital or to keep and operate the building. The remaining tax book value is only relevant in determining the gain or loss from the sale while the financial book value really has no economic impact. The market determines the building value at any time based on the future cash flow that assets might be expected to generate and the investor must project the actual market vaiue to make a valid analysis. Four situations where value added calculations may usefully augment discounted cash flow economic analysis of projects are discussed:

i

I

I I T

1)

VA forces managers to think about the balance sheet and the assets that are under their control and to what extent those assets are being utilized. However, thii is the basic axiom of opportunity cost as advocated by these authors for years. So while certainly not new in concept, VA may provide a different approach to understanding this important evaluation consideration. There is a cost to holding idle plant facilities, working capital or other non-performing assets.

2)

VA or ROCE analysis gives investors a post analysis procedure for checking whether a given project or business unit is meeting its economic objectives at any current point in time. Looking at a one-year picture of performance using VA or ROCE is much easier than looking at discounted cash flow analysis for the life of a project. However, VA and ROCE can only be usetl as short-term indicators.

3) VA and ROCE provide a short term indicator of the economic performance of business units involving many combined projects that would

involve much effort to analyze for the life of a project with discounted cash flow. However, if VA or ROCE results indicate change is needed,

$ I

Ct:"nIer9:After-TaxlnvestmentDecisionMethodsandApplications

aa7

to discounted cash flow analysis should be done for the business unit to due generation flow evaluate_ the economic impact on future cash with selling p.oposed crrrrent changes and how those results compare or ihutting down. This analysis should be based on market value 0oportunitv costs and an opportunity cost of capital discount rate, not linarrcial reporting book values and financial cost of capital.

4)

Companies sometimes like to use

\A

or ROCE analysis techniques

as

abasistoevaluatemanagerialperformance.Discountedcashflow a analysis isn,t very useful for this purpose since it typically Co\'ers improvements rewarding tonger period. Generally, the basis for given should not be associated with the absolute value added in any period, but on whether value added can be consistently increased over

aperiodoftime.Thiscanhelpavoitlshortrunmanagementdecisions to sell now or defer capital expenditures for the big bonus this year, tiren rvorry about the future later. often it's not easy to compare mantwo agers fairly using the vA for a given period. To illustrate, suppose a 3g-year-old operates one company, ,iunug"r, *ork for the same fully depreciated plant while the other manages a recently upgraded faciiity.Theopportunitycostschar.gedagairistnetincomervillmost tikely be highei for the newer plant given the recent capital expenditures.However,thatdoestl'tnecessitrilymeanthenewpiantmanager is urtder-performing compared to the old plant manager' By comparingtherelativechangeinvalueaddedo.;ertime,eachmanagerwill be evaluated on a Inore level playing field'

A simplistic illustration of value added is presented in Example 9-12 and 9-12a.

Example 9-12 Value Added (VA) To illustrate the concept of VA calculations, determine the after-tax value added each year from Exampie 9-11 and compute the correpresent sponding present value for the annual figures. compare.the value of vA to the project after-tax NPV. ln making the value Added calculation, adjust'the financial net income for deferred taxes and book base the oppoitunity cost on the beginning ol period financial value (from straignf tine depreciation) each year' The financial net income data from Example 9-11 Part B is summarized below. The corporate after-tax opportunity cost of capital remains al12o/o.

,-----

488

Economic Evaluation and lnvestment Decision Methods

Year

Revenue - Oper. Costs - Depreciation Taxable lncome - lncome Tax 40,/" Net lncome

9:40

8.40

-3.50 -3.50'

'

7.40

-3.50

6.40.'

-3.50

5.40

-3.50

-'1.00 -2.00 -2.00 -2.00 -3.00 4.90 2.90 1 .90 0.90 -1 .10

.96 -1 .16 -0.76 -0.36 0.44 2.94 1.74 1.14 0.54 -0.66

-1

The book value necessary for calculating the annual cost of capital, or annual opportunity cost, is based on the book value of the assets at the "beginning" of each year which is summarized below per the use of straight-line depreciation: Year Beg Book Value

10.00

9.00

7.00

5.00

3.00

(Book Value)(i-=12%)

Deferred tax is based on the difference between the actual tax paid in each of years 1-5 and the tax reported to the shareholders in the financial report for each of those years. so, using the tax paid in Example 9-10 parts A and the financial tax reported to shareholders in Part B, the deferred tax is calculated as follows: Year Actual Tax Pd (A) -Financial Tax (B) Deferred Tax

-1.56 -0.68 -0.79 -0.70 -0.07 -1.96 -1.16 -0.76 -0.36 0.44 0.40 0.48 -0.03 -0.34 -0.51

Adjusting the Financial Net lncome (based on sL depreciation) for the deferred taxes and the cost of capital, gives the project "value Added" each year: Year

Net lncome +Deferred Tax -Cost of Capital Value Added

2.94 0.40 -1.20 2.14

1.74 0.48

-1.08 1.14

1.14 0.54 -0.66

-0.03 -0.34 -0.51 -0.84 -0.60 -0.36 o.27 -0.40 -1.53

Chapter 9: After-Tax lnvestment Decision Methods and Applications

PV @ 1 2%

- 2.1 4(P lF

1

Z"/",1) +

1 .1

4(P lF

1

489

Z/.,2\ + 0.27 (P lF 1 2% S)

0.40(P/F 12"/.,4) - 1.53(P/F 12"/o,S) = 1.889 equivalent ta the After-tax NPV using the f'n AC R S tax ded ucti on s.

-

For all the extra effcrt, the resuiting present value of the value added each year is the same measure of perfcrrnance that is utillzed by most corporations and individual investors alike, l",lPV! But a downside of this concept is the focus on a net income based criteria which may force the early closure of this project at the end of year 3 or 4 depending on whether the focus is value added oriented or cash flow oriented. This project continues to generate positive cash flow, which is adding value and generating the NPV of 1.889, yet VA or FIOCE would demand suspension of the project before its full value may be obtained! EXAMPLE 9-12a Vatue Added Using Tax (MACRS Depreciation) Rather Than Financial Shareholder Deductions

Re-calculate tire VA from Example 9-12 based on the MACRS depreciation used for regular tax, which eliminates ihe deferred tax adjustment. All other assumptions rematn the same. The previous calculations for MACRS depreciation that were presented in Example 9-11a down to net income are summarized as follows: Year

Revenue - Oper. Costs - Depreciation Taxable lncome - lnc Tax @ 40%

Net lncome Beg Bk Value Cost of Cap @ 12"/" Net Income - Cost of Capital Value Added

9.40

8.40 7.40 6.40

5.40

-3.50 -3.50 -3.50 -3.50 -3.20 -1 .92 -1 .15 -1.73 3.90 1.70 1.98 1.75 0.17 -1.56 -0.68 -0.79 -0.70 -0.47 -3.50 -2.00

2.34 1.02 1.19 1.05 0.10 10.00 8.00 4.80 2.88 1.73

-1.20 -0.96 -0.58 -0.35

-0.21

2.34 1.02 1.19 1.05 0.10

-1.20 -0.96 -0.58 -0.35 4.21 1 .14 0.06 0.61 0.70 -0.11

490

Economic Evaluation and lnveslment Decision Methods

Due to limited space, VA is rounded above, but more detail is provided below in the present worth equation: PW EQ: 1 .14(PlF 12/"J,) + 0.06(P/F 12"/",2) + 0.61 2(PlF1Z%,g) + 0.7 O44(P lF p/o,4) - 0. 1 OSO(P /F pt,S)

= 1.889 whlch is identical to the after-tax NpV!

9.ll

"Regulated" Company Investment Analysis

The maximum return on investment allowed for regulated company investments is limited by federal and state law in accordance with rules governed by federal and state regulatory commissions. Typical regulated investments include the telephone communications industry electric utility power generation, transmission and distribution companies, interstate pipeline natural gas transmission companies and intrastate natural gas pipeline distribution companies. The various federal and state regulatory commissions are required by law to establish investment return rates that are 'Just and rea-

sonable" for regulated investments from the viewpoints of both the public purchasing a product and the investor producing or transporting the product. The regulatory commissions must walk a narrow line to determine regulated investment rates that are adequate to permit a company to stay in business and provide the needed service, but not permit rates that would give exces-

sive return on investment from the public viewpoint. In other words, the regulatory commission strives to set regulated rates that do not cause "undue discrimination" nor give "unjust preference" to the consumer, to the investor, and to the general public interest.

The terms "revenue requirement" and "cost of service" often are used interchangeably in referring to the revenue that is required to cover all costs for providing a service and to give the investor an adequate return on investment. In equation form: Revenue Requirement Per Year =

Allowed Regulated Return on Equity Rate Base + Operating and Maintenance Expenses + Income Taxes + Regulated Depreciation + Interest on Debt if Applicable

Eq.9-2

Chaprer g: After-Tax lnvestment Decision Methods and Applications

491

In the simplest of analysis situations the annual revenue requiremenr is divided by the total unirs of service to be provided per year to obtain the revenue requirement per unit of service. However, in most real world situa_ tions, annual revenue requirements differ from year to year as do units of service to be proiluced. This requires dctermination of ,,equivalent annual revenue requiremenis" to be divided by "equivalent annual production,, to obtai, a time value ol inoney weighted average revenue requirement per iri.iir oi'sr-rvice pro