AN EXPERIMENT EN APPLICA'HON OF
THE MONTE CARLO METHOD FOR
SEMUEATENG CAPITAL WDGEFWG
DECESEONS UNLEER UNCERTAINW

Thesis {or the Day?“ o§ D. B. A.
MICBEGAN STA'i‘E UHWERSETY
Leon Warren Woodfield

1966

 

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Michigan State
University

 

This is to certify that the

thesis 'entitled
AN EI‘CPERILERT IN 'IJPLIQEI (2% CF.

TEE MONTE CARLO I-.'IETELOD FOR SILIULrTIi‘fl CAPITAL

BUDGETII‘IG DECISICNS UNDER UHCBRTAIET
presented by

Le on Warren Wood fie 16.

has been accepted towards fulfillment
of the requirements for

D.B.A. degree in Accounting

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Major professor

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0—169

 

ABSTRACT
AN EXPERIMENT IN APPLICATION OF
THE MONTE CARLO METHOD FOR SIMULATING CAPITAL
BUDGETING DECISIONS UNCER UNCERTAINTY

by Leon warren WOOdfield

A decision to invest in an asset involves
assumptions about the future, for by its nature an asset,
to have value, must yield benefits in future periods of
time. The decision is therefore subject to elements of
uncertainty since future technological and economic events
cannot be projected with any great degree of preciseness.

A theory that purports to explain the decision
process should inclmkaas one of its bases the recognition
of uncertainty. .Any method that is designed to aid in the
decision process should.also take uncertainty into
consideration.

The hypothesis made is that a model (for capital
budgeting decisions), in which uncertainty is considered
explicitly, can be applied to actual situations in business
organizations with the conclusions furnishing useful
information in the capital budgeting decision process.

A model using the Monte Carlo method was applied
to a limited number of actual asset acquisition proposals

in a variety of companies, each representing a different

Leon Warren Woodfield

Through continual improvement of
estimates and refinement of the model it
useful tool to aid management in meeting

the factor of uncertainty as it concerns

the subjective
can become a
and evaluating

capital budgeting.

AN EXPERIMENT IN APPLICATION OF
THE MONTE CARLO METHOD FOR SIMULATING CAPITAL

BUDGETING DECISIONS UNDER UNCERTAINTY

By

Leon warren Woodfield

A THESIS

Submitted to
Michigan State university
in partial fulfillment of the requirements
for the degree of

DOCTOR OF BUSINESS ADMINISTRATION
Department of Accounting and Financial Administration

1965

ACKNOWLEDGEMENTS

The author wishes to express his thanks to his
doctoral committee; Dr. Gardner M. Jones, chairman, and
Dr. Richard F. Gonzalez and Dr. James Don Edwards,
committee members, each having assisted greatly in the
preparation of this dissertation and also having offered
freely their encouragement and time throughout the course
of study.

Special thanks is expressed to Dr. James Don
Edwards and the faculty of the Department of Accounting
and Financial Administration for providing financial aid
and an atmosphere conducive to the completion of the degree.
The Brigham Young University, Price Waterhouse & Co. and
others have also provided financial assistance which has
been extremely helpful. The study would not have been
possible without the cooperation of the firms interviewed;
to them this indebtedness is acknowledged and appreciation
is expressed.

Gratitude is also expressed to my parents, to my

wife's parents and to my children; Janalee, Heidi and

ii

Melia, who have each offered continual cooperation and
support.

I am deeply grateful and indebted to my wife, Janet,
for constant encouragement, advice and support. Her
devotion and assistance have been the basis for the success—

ful completion of this stage of our life together.

iii

TABLE OF CONTENTS

ACKNOWLEDGEMENTS . . . . . . . . . . . . . . .

LIST OF FIGURES . . . . . . . . . . . . . . .

LIST OF TABLES AND EXHIBITS . . . . . . . . .

LIST OF APPENDICES . . . . . . . . . . . . . .

Chapter
I.

II.

III.

INTRODUCTION . . . . .‘. . . . . . . .

Purpose . . . . . . . . . . . . . .
Risk versus uncertainty . . . . . .
Capital Expenditure Decision . . . .

METHODOLOGY AND USES OF INFORMATION .

Methodology . . . . . . . . . . . .
The Simulation Model . . . . . . . .
Use of the Data . . . . . . . . . .
Sources of Data . . . . . . . . . .

ANALYSIS OF THE PROPOSALS FOR ASSET

ACQUISITION . . . . . . . . . . .

Background Information . . . . . . .
Summary of Data . . . . . . . . . .
Application of the Data to the Model
Analysis of Cases . . . . . . . . .

Summary . . . . . . . . . . . . . .

iv

Page

ii

vi

vii

viii

NH

l4
19
27

29

29
38
43
47

87

Chapter Page
IV. EVALUATION OF THE PROPOSED MODEL . . . . 89

Comparison with Methods Currently

Being Used . . . . . . . . . . . . . 89
Cost versus Results . . . . . . . . . . 90
Problem of Size . . . . . . . . . . . . 92
Availability of Data . . . . . . . . . 93

Aid in the Evaluation and Preduction
of Future Results . . . . . . . . . . 96

Prerequisites for Effective

Application and Use . . . . . . . . . 97
V. SUMMARY AND CONCLUSIONS . . . . . . . . . lOO
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . 109
APPENDIX . . . . . . . . . . . . . . . . . . . . 116

Figure

10.
ll.
12.

13.

Case

Case

Case

Case

Case

Case

Case

Case

Case

Case

Case

Problem of

11

12

LIST

Size

OF FIGURES

Appendix A — Example . . . .

vi

Page
49
53
57
61
66
68
7O
76
80
82
85
94

121

LIST OF TABLES AND EXHIBITS

Page
Table l . . . . . . . . . . . . . . . . 39
Exhibit 1 . . . . . . . . . . . . . . . 45

vii

LIST OF APPENDICES

Appendix Page
A. Example Case . . . . . . . . . . . . . 116
B. Program Procedures . . . . . . . . . . 123
C. Computer Program . . . . . . . . . . . 133
D. Miscellaneous Information . . . . . . . 140
E. Proposed Letter . . . . . . . . . . . . 143

viii

CHAPTER I

INTRODUCTION: Statement of Purpose and
Discussion of Problem

Purpose

My hypothesis is that a model (for capital
budgeting decisions), in which uncertainty is considered
explicitly, can be applied to actual situations in business
organizations with the conclusions furnishing useful
information in the capital budgeting decision process. It
is proposed to study the capital budgeting decision making
process of a limited number of firms; apply the model to some
of the alternative proposals for the use of capital funds;
analyze the results; suggest uses of the data obtained and
attempt to indicate the advantages and disadvantages of the
proposed model when compared with methods currently being

used to aid management in this decision making area.

Risk versus Uncertainty

Any decision yet to be made is concerned with a
future choice between the available alternatives and is
always subject to unknown elements concerning the future.
The lack of complete data in the decision environment
should not limit the attempt to forecast and to use the
forecast as a guide for action. The reliability of the
estimates will, in part, depend upon whether the individual
is faced with a £i§k_or an uncertainty situation. Dr.
Shewhart wrote the following:

What can we say about the future behavior of a
phenomenon acting under the influence of unknown
or chance causes? I doubt that, in general, we
can say anything. For example, let me ask: “What
will be the price of your favorite stock thirty
years from today?" Are you willing to gamble much
on your powers of prediction in such a case?
Probably not. However, if I ask: “Suppose you
were to toss a penny one hundred times, thirty years
from today, what proportion of heads would you
expect to find?“ Your willingness to gamble on
your powers of prediction would be of an entirely
different order than in the previous case.

The above statement indicates that certain decision

areas may be treated by the mathematics of probability. In

 

1W..A. Shewhart, Economic Control of_Quality of
Manufactured Product (Princeton, New Jersey: D. Van Nostrand
Co., Inc., 1931), p. 8.

these areas the chance or probability of occurrence of a
certain event can be measured objectively. The knowledge
of the future event is imperfect; however, because of
objective verifiable data the probabilities of the alternatives
can be determined. This kind of circumstance should be
referred to as risk. Some examples of risk taking are playing
black jack for money and buying insurance (preferring a
certain small expense to a small chance of a large loss).

When the knowledge of the outcome of future events
is imperfect and the probability of the event cannot be
objectively determined the area of ignorance should be
referred to as uncertainty.1 The forecast of economic
events will always include elements of uncertainty since
there are always variables whose value cannot be objectively
measured. It is not realistic to assume that uncertainty is
ignored in the decision process. Each assumption implicitly
or explicitly made includes its own degree of uncertainty.
The assumptions may be thought to have a minor effect on the
accuracy of the final result when in fact the total effect

may be material in amount.

 

1For a discussion on alternative approaches to the
theory of choice, refer to Kenneth J. Arrow, ”Alternative
Approaches to the Theory of Choice in Risk Taking Situations,”
Econometrica, Vol. 19, No. 4 (October, 1951), pp. 404-37.

 

A theory that purports to explain the decision
process should surely include as one of its variables the
area of uncertainty. Any method that is designed to aid in
the decision process should also take uncertainty into
consideration. Joel Dean has made the following statement
concerning uncertainty in the decision area:

Adjustments to allow for uncertainty may be challenged
as nothing more than guesses. Perhaps they are. But
even so, they are guesses that must be made, and will
be made, either explicitly or implicitly. Failure to
apply the probability adjustment does not enable
management to avoid the problem; it merely transfers

the guess element in a disguised form to some other
stage of the decision-making process.1

Capital Expenditure Decision

The decision to invest in an asset involves the
future since by its nature the asset to have value must
benefit future periods of time. The importance of skilled
decision making in the area of capital budgeting is
adequately demonstrated by referring to the successes and
failures of business firms as reported periodically in

financial reports, magazines and newspapers.

 

lJoel Dean, Managerial Economics (Englewood Cliffs,
New Jersey: Prentice-Hall, Inc., 1951), Tenth printing 1960,
p. 568.

There are numerous methods that can be used in
estimating the worthiness of capital expenditures. These
will include among others, the payback method which will
indicate the length of time required to recover the initial
investment; the accounting average rate of return which
indicates an estimate of a rate of return based on the cost
of the asset; and discounted cash flow methods. Of all the
methods currently in use the discounted cash flow methods
appear to have the best theoretical justification. Assuming
that the data is accurate, these methods can indicate the
excess of the present value of a stream of future benefits
over the cost, or can give the rate of return that is to be
expected from the investment. The information required is
by its nature subject to uncertainty; however, a condition
of certainty is assumed or at least implied in the very fact
of using these methods.

Even though current methods used assume that estimates
of the future are correct, the existence of uncertainty is
recognized implicitly and is adjusted for by modification of
desired rate of return, differential handicaps, informal
judgements, selection of arbitrary payback periods, and
sensitivity analysis. These methods of adjustment are

deficient in that they do not provide an estimate of the

likelihood of obtaining a particular value. Harry V. Roberts
has noted:
The most serious deficiency in the present state of
knowledge about capital budgeting is the absence of
a satisfactory framework for incorporating uncertainty
into the analysis. Much of the ultimate success or
failure of analytical methods of capital budgeting
will hinge on future developments in the treatment of
uncertainty.1
Whenever a person is involved in uncertainty he is
dealing with a subjective phenomenon, the reason being that
there is not sufficient historical data upon which a
mathematical probability can be based. Subjective
probabilities can be determined; however, the expectations
cannot be established with objective certainty.2
“Subjective probability technique“ is a means by
which an individual quantifies his attitudes toward the
investment opportunity. John H. Norton has noted that

subjective probabilities could be determined by questioning

the person directly to express his judgements as to the chance

 

1Harry V. Roberts, ”Current Problems in the Economics
of Capital Budgeting," Elements of Financial Administration,
ed. John O'Donnell and Milton S. Goldberg (Columbus, Ohio:
Charles E. Merrill Books, Inc.), pp. 278-84.

2Milton H. Spencer and Louis Siegelman, Managerial
Economics - Decision Making and Forward Planning (Homewood,
Illinois: Richard D. Irwin, Inc.), p. 8.

of an event occurring.1 A second method has been suggested
by Robert Schlaifer; an individual is offered the choice
between an uncertain event and a reference event (standard
lottery) having an equal reward. The point at which the
individual is indifferent between the uncertain event and
a given percentage of the total lottery tickets is his
probability estimate for the uncertain event.2
Methods used to obtain the subjective probability
may be successful in quantifying the person's estimate in
the problem; however, they do not add to the validity of
the judgements that are required. The possibility of poor
estimates on the part of the individual points up the need
to obtain the judgement of mature persons having experience
in related situations. Even though subjective probabilities
are judgements that cannot be objectively verified it has

been demonstrated, experimentally, that subjective

probabilities can be amazingly accurate (the estimates

 

1John H. Norton, “The Role of Subjective Probability
in Evaluating New Products Ventures,“ Symposium Series 42
2§tatistics and Numerical Methods in Chemical Engineering”,
Vol. 59 (American Institute of Chemical Engineers, 1963),
pp. 49-54.

2Robert Schlaifer, Probability and Statistics for
Business Decisions, (New York: McGraw-Hill Book Co., Inc.,
1959), pp. 12—13.

made reflect the actual conditions known to exist in the
experiment) when opinions of mature persons are sought.1
The problem of uncertainty should be recognized in
capital budgeting projects undertaken for study. The
subjective estimates should be made since uncertainty is a
factor that must be adjusted for. Therefore, it is better
that the estimates required to be made be in an explicit
form.
A mathematic analysis (where appropriate) furnishes
a formula that will provide an appropriate answer to all
problems having similar characteristics. Through exper-
imentation, an approximation of the mathematical analysis
can be obtained. Solving these problems through exper-
imentation, when the mathematical analysis is not applied,
is known as the Monte Carlo method.2 A number of experiments

will be conducted using subjective probabilities and random
numbers in an attempt to apply to actual business situations
a method that considers uncertainty in an explicit form. A
discussion of the proposed model and its use is included

in Chapter II.

 

lNorton, loc. cit.

2Schlaifer, Robert, Probability and Statistics for
Business Decisions (New York: McGraw-Hill Book Company,
Inc., 1959), p. 320.

CHAPTER II

METHODOLOGY AND USES OF INFORMATION

Methodology

There are numerous methods that may be used in
estimating the worthiness of capital expenditures. Of
these methods the discounted caSh flow approach appears
to have the best theoretical justification and will
therefore, be used in this model

The internal rate of return method of discounting
the net cash flow is a procedure whereby we solve for
"r" (internal rate of return), so that the expected profit
rate of a project can be compared with other proposed
projects and also with the firm's cost of capital. The yearly
net cash benefit when discounted at the appropriate rate of
return would equal the present value of the cost of the
investment required to undertake the proposed project. This
rate is the maximum average rate that could be disbursed over

the life of the asset without incurring a loss on the project.

9

10

A formula to determine the internal rate of return

is:
Bl 32 Bn-t-S
c= (1+r) + (l+r)2+...+ (l+r)n

Where C is the cost of the investment, B is the net periodic
cash benefit, S the salvage value in period n and r the
unknown rate of return that is to be solved for.

The present value method of discounting the net
cash flow determines the present value of future benefits
when discounted at an assumed rate of return. The
discounted value is then compared to the required investment
to establish a ratio of profitability by which various
alternatives can be ranked. A formula that can be used to

arrive at the present value is:

.5; B2 Bn + S
PV= (1+r) + (la-r)"2 +. ..+(1+r)n

Where PV is the unknown discounted present value of the
future cash benefits and r is the assumed rate of return
(cost of capital).

These two methods will lead to the same decision in
an accept or reject decision unless there is a problem of

dual rates of return.1 When using the present value method,

 

lEzra Solomon, "The Arithmetic of Capital Budgeting
Decisions,“ The Management of Corporate Capital, ed. Ezra
Solomon (Chicago: The Free Press of Glencoe, Graduate School
of Business, The university of Chicago, 1963), p. 77.

11

under conditions of certainty, any project will be accepted
if the discounted present value is greater than the
investment required for the project. The decision will be
favorable when using the internal rate of return approach
if the calculated rate of return on the proposal is greater
than the rate of cost of capital.

When the decision involves mutually exclusive projects
(non—independent) and a choice has to be made between one
or the other, the two discounted cash flow methods may not
lead to the same solution (i.e. decision) to the problem.

A contradiction as to the ranking of mutually exclusive
projects may appear whenever there is a time disparity
(different timing of receipts over the life of the project),
a size disparity (different total investment requirements)
and/or a difference in the estimated useful life of the
mutually exclusive events.

The source of the problem is an implicit assumption
made under each of the methods. The internal rate of
return approach assumes that the net cash benefits will be
reinvested at the rate of return noted in the computation.
The present value approach assumes that the funds will be

reinvested at the company‘s rate of cost of capital.1

 

lIbid., p. 76.

12

If the proposals do not have equal lives when
dealing with mutually exclusive investments it is then
necessary to determine a rate of return on each proposal.
The period on which the rate of return computation is based
is the life of the asset having the greatest longevity.

This adjustment requires an explicit assumption as to the
rate to be applied to the reinvested funds. The reinvestment
rate used may be any rate that is consistent with the firm's
policies with the minimum normally being at least equal to
the firm's cost of capital. If the mutually exclusive
proposals have equal lives but the timing of the net cash
benefits and/or the size of the required investments differ,
the return on the incremental benefits must be determined
before the internal rate of return approach will furnish a
guide that is consistent with that of the discounted
present value method.

If the rate of discount varies from year to year
the two methods will not give identical results.1 The
variation in the rate of discount may result from the
limitation of available capital funds with management

changing the required discount rate from year to year in

 

lHarold Bierman and Seymour Smidt, The Capital
Budgeting Decision (New York: The Macmillan Company, 1960),
p. 34.

13

an attempt to limit the number of proposals that qualify
for capital funds in a particular year.

Except as noted, the two discounted present value
methods will furnish consistent results if they are used
correctly.

When an individual is trying to reach an optimal
position between investments (which some authors have
suggested is a process whereby individuals distribute
consumption over time) and the consumption function, it
has been claimed that the discounted present value methods
will maximize the investment area (opportunity for production);
however, the individual may be able to improve his position
by borrowing funds and thus enabling him to reach a higher
indifference curve. This optimal position may not be
obtained if the individual invests without considering the
means of financing the asset acquisition.1

The discounted present value approach appears to be
the easier of the two methods to use since adjustments to

the normal means of computation are not required to arrive

at the "correct” solution. The internal rate of return is

 

1For a discussion on reaching the optimal position,
refer to J. Hirshleifer, “On the Theory of Optimal Investment
Decisions,“ The Management of Corporate Capital, ed. Ezra
Solomon (Chicago: The Free Press of Glencoe, Graduate School
of Business, The University of Chicago, 1963), pp. 205-28.

14

preferred by some in that the solution is given in a form
of a rate of return on the investment. Others may prefer
to analyze and compare different ratios of the discounted
present value to cost.

The method to be preferred is a matter of personal
opinion and both methods could be used in the model under
consideration. Thus, keeping in mind the possible problem
areas, the internal rate of return method will be used for
this discussion since it is felt that the results will be
more easily interpreted and understood when expressed in

terms of an estimated rate of return.

The Simulation Model

The decision to invest in an asset involves
variables that are stochastic in nature (subject to a
range of possibilities). By introducing these variables
and an estimate of the subjective probability into the
analysis, an approximation of the proposed project"s rates
of return and the relative frequency of each is possible.
A probability will be assigned to each rate of return that

is equal to the relative frequency determined in the analysis.

15

As was noted in Chapter I, the problem under
consideration is in the realm of uncertainty and as such
the probability of occurrence cannot be objectively verified
and therefore,subjective data must be used. It has been
suggested by Elwood S. Buffa, Robert Schlaifer, Sidney W.
Hess and Harry A. Quigley that a mathematical analysis to
arrive at a probability distribution may prove to be very
difficult, costly and in some cases impossible. 1’ 2' 3
Therefore, a next best substitute, a simulation model, will
be used to arrive at the likelihood of each particular rate
of return of any given project.

In Chapter I, a distinction was made between risk
and uncertainty. It was noted that in a condition of

uncertainty subjective data must be used to arrive at an

estimate of the probability of an event occurring. After

 

lElwood S. Buffa, Models for Production and Operations
Management (New York: John Wiley & Sons, Inc., 1963), p. 506.

 

2Robert Schlaifer, Probability and Statistics for
Business Decisions (New York: McGraw-Hill Book Company, Inc.,
1959), p. 320.

3Sidney W. Hess and Harry A. Quigley, “Analysis of
Risk in Investments using Monte Carlo Techniques,“ Symposium
Series 42 “Statistics and Numerical Methods in Chemical
Engineering“, Vol. 59 (American Institute of Chemical
Engineers, 1963), p. 57.

 

16

the estimate of probability has been established the
analysis will then proceed as if it were an analysis of a
risk situation; that is, although the knowledge of the
future event is imperfect, we use the best information we
have (probability estimates) to project the “values" of
the several possible outcomes. If subjective data is not
available so that a probability estimate concerning the
future is impossible the uncertainty problem would then
have to be approached by use of game theory if it
(uncertainty) were to be explicitly considered.1

The problem under consideration is only a portion
of the larger area of capital budgeting which in turn is
part of the overall management and administration of the
firm. Uncertainty is involved in the determination of the
internal rate of return and/or discounted present value
and the likelihood of each. Other factors such as the
firm's cost of capital, availability of funds, control,
areas of responsibility and overall goals of the organization

are not to be considered at this time.

 

1For a discussion of game theory and capital budgeting,
refer to Edward G. Bennion, Capital Budgeting and Game Theory
(Harvard Business Review, Nov.-Dec. 1956, Vol. 34, No. 6),
pp. 115-23 and to W. G. Nelson, “Could Game Theory Aid Capital
Budgeting,“ NAA Bulletin 43, Section 1 (June, 1962), pp. 49—58.

17

The minimum factors whose values will have to be
determined are the estimated cost of the proposed investment
(the relevant cost being the incremental cash expenditures
of the proposed project), the incremental operating expenses
being classified as fixed and variable and the estimated
useful life of the project. The proceeds to be received in
case of a new revenue producing project, or the annual cost
savings for projects reducing the costs of operation, and
the estimated terminal salvage value of the asset are also
necessary factors that will have to be determined.

Where applicable, the market share, production
capacity level and other factors that would materially
affect the decision under study will also be considered.

For each of the above, subjective probability estimates
will be obtained.

At this point in the analysis, each relevant factor,
with its range of values and the probability of each, will
have been obtained for each capital budgeting proposal to
be studied.

If the model were to be applied with the use of
hand calculators the distribution of each variable would
be assigned numbers ranging from 0 to 99 (refer to Appendix
A). The size of the group of numbers assigned will be

dependent upon the subjective probability of the factor

18

under consideration. For example: If there is estimated
to be a 15%.chance that the sales will be X dollars,
numbers 00-14 will be assigned to that particular level
of sales. This same procedure will be duplicated for each
factor having a range of values. Then, by use of random
number tables, factors such as the level of sales, cost,
estimated useful life will be obtained. Based on this
information a range of rates of return, with their
likelihoods of occurrence, can be determined; however, in
order to obtain an estimate of a possible range of rates
of return and their likelihood of occurrence, a number of
experiments (determination of individual rates of return)
will have to be made. The number of trials will depend
upon the time, cost, and availability of equipment with
the greater number of trials giving the more reliable
results. The illustrated problem (Appendix A) consists
of fifty experiments requiring approximately eight hours
of work when using a hand calculator. The results based
on the fifty experiments are very similar to the solution
arrived at when using the expected value for each factor.

Harry A. Quigley and Sidney W. Hess have suggested

that one hundred experiments will give results that are

19

very close to the theoretically correct solution.1 The
problem of sample size has not been completely solved in
current literature; however, this should not affect the
basic methodology under consideration. With this in mind
a minimum of one hundred experiments will be established

for this model.

Use of the Data

The data obtained should furnish information to
management that will aid them to predict the outcome of
the project and be useful to them within reasonable limits
of cost.

When there are no limits on the available capital,
and adjustments for time and size disparity (problems noted
in prior section) have been made, a decision rule may be
established that, for any project, if the rate of return is
greater than the cost of capital the project should be
accepted. This rule is made under an assumed condition of
certainty. When uncertainty is introduced into the analysis,

if the individual is indifferent between two projects having

 

1Hess and Quigley, loc. cit., p. 55-63.

20

the same expected rate of return even though the range of
possible gains or losses is different the comparison should
be made between the rate of cost of capital and the expected
rate of return. The use of this model will furnish the
information required to determine the expected rate of
return.

The condition of being indifferent between two
projects having the same expected rate of return has been
referred to as being linear with respect to money, it is,
however, unreasonable to expect each individual (management
group) to be linear with respect to money inasmuch as they
may have an aversion to or a liking for projects subject to
risk and uncertainty. Management's attitude toward
uncertainty will have to be determined before the accept—
ability of a project can be known. under these conditions
the information obtained would have to be presented to
management and, depending upon its attitude toward uncertainty,
the accepted project could very well have an expected value
greater than, equal to or less than the expected value of
an alternative project. Robert Schlaifer has suggested
that an “expected utility” can be determined when comparing
the proposed project with a reference contract. By

determining the indifference point between the two contracts,

21

the individual's (or organization's) attitude toward risk,
profit and loss in a particular type of situation can be
determined, and based on the finding of this type of analysis,
the utilities of various cash consequences could be
determined.1 Therefore, management's attitude and its
acceptance or rejection of a particular project could be
predicted by referring to the “expected utility” function
for this organization. This type of analysis is beyond
the scope of this study; however, the information obtained
from the present model could be used as a basis for
extension into the “expected utility” if it was so desired.
A limitation by management may be placed on the size
of the capital budget in any one period of time. This
limitation may take the form of either a limit on expend-
itures or an arbitrary rate of return that is greater than
the firm“s cost of capital. Under these conditions there
is no longer an accept or reject decision in the sense that
a comparison is made between the estimated return and the
cost of capital but it is now necessary to obtain the best

,combination of projects all having rates of return that are

 

lRobert Schlaifer, Probability and Statistics for
Business Decisions, (New York: McGraw—Hill Book Co., Inc.,
1959), chpt. 2.

22

greater than the cost of capital. In this respect each
project is competing with the other projects for limited
capital funds. One suggestion for a solution to this
problem is that when dealing with limited funds competing
projects (proposals competing for funds) may be treated as
conflicting projects (mutually exclusive). The best combi-
nation being the one yielding the greatest effective rate of
return balanced against the objectives of management.1
Under conditions of uncertainty it may no longer be
sufficient that the rate of return is greater than the
rate set by management in its attempt to limit the use of
funds for capital expenditures. It may be necessary to
consider the aggregate of projects in such a way that the
total return is maximized subject to the limits of a certain
expenditure amount and the limits of variance in the rates
of return and/or in the estimated costs of projects.

Neil R. Paine and Joel Cord have suggested possible

solutions to this problem area; however, each assumes that

 

1For a more complete discussion of the limited

capital problem under conditions of certainty, refer to
James H. Lorie and Leonard J. Savage, “Three Problems in
Rationing Capital," The Management of Corporate Capital,
ed. Ezra Solomon (Chicago: University of Chicago, 1963),
p. 56-66.

 

23

l, 2
subjective probability estimates can be obtained. No

completely satisfactory solution to the problem of how to
allocate limited capital funds has been found. It is
evident that any adequate solution must contain some
explicit considerations of uncertainty, and in order to do
that, it must be possible to obtain and apply subjective
probability estimates.

The information obtained from the model indicates
the likelihood of a return being received based on the
subjective estimates furnished by those individuals having
good judgement, experience and a knowledge of the capital
budgeting process as demonstrated by past performance; still,
it should be remembered that two persons furnishing estimates
on the same project may assign probabilities that vary from
one another; however, individuals having the same experience
should be expected to assign probabilities to the event that
are quite similar.

The quantifying of uncertainty does not add to the

validity of the estimates required. The analysis of the

 

lNeil R. Paine, “Uncertainty and Capital Budgeting,”
Accounting Review, Vol. XXXIX, No. 2 (April, 1964), pp. 330-
32.

 

2Joel Cord, ”A Method for Allocating Funds to
Investment Projects When Returns are Subject to Uncertainty,"
Management Science, Vol. 10, No. 2 (January, 1964), pp. 335-
41.

 

24

rate of return and its likelihood will not in and of itself
answer the question as to what happens if the actual results
differ from that forecasted. That is, what will be the
effect on the rate of return if the range of values and
the subjective probabilities are in error. By making a
sensitivity analysis of the factors used in computing the
rate of return it is possible to explain the way in which
each factor interacts within the system which would aid in
evaluating this problem area. Assume, for example, that
the data was fed into a computer and one hundred or a
thousand individual computations were made of the rate of
return. By having the computer print out the factors (cost,
estimated useful life, etc.) that were used in the determina—
tion of each rate of return and through an analysis of this
data it will be possible to determine the effect, for
example, of changes in the useful life on the estimated
rate of return. This type of analysis should furnish
additional information that will aid in arriving at the
final decision as to whether the proposal should be accepted
or rejected.

The model generates the frequencies of each of the
factors used in the computation of the rate of return; from

these frequencies statistical tools such as the mean and

25

standard deviation could be used. The use of the standard
deviation generally assumes a normal distribution of the
factors under consideration; however, as was noted by
Frederick S. Hillier that if the distribution was non-
normal the only result is that a precise probability
statement cannot be made.1 The analysis of the factors
using the standard deviation would furnish an indication

as to the probability that the factor being analyzed would
fall within a given range of values. However, since the
subjective estimates are based on the judgement and
experience of the individual furnishing the data and
assuming that the original estimates are rational, the
basis for revision of the subjective probabilities would be
from added experience and as such the analysis of factors
using the mean and standard deviation would not be a reason
for rejecting the prior probabilities and for a posterior
probability (revision of prior probabilities as a result

of additional information and experience). It is for this

reason that these tools will not be used in this analysis.

 

lFrederick S. Hillier, ”The Derivation of Probability
Information For the Evaluation of Risky Investments,”
Management Science, Vol. 9, No. 3 (April, 1963), pp. 443—451.

26

Successful application of the proposed model will
depend on whether there is available data, and if not
immediately available, whether it is obtainable. To be
useful the information furnished from the application of the
model should describe within reasonable limits the actual
experience and should aid in the prediction of the operating
results that pertain to the capital budgeting project in
question.

The added information resulting from this model
will be of value to the organization, if the costs of
obtaining the data are less than or equal to the benefits
received. The benefits received, in most cases, will not
be of the type that are entirely measurable in dollar and
cents; nevertheless, the net results (hopefully) should be
an improvement in the application of principles that under-
lie the practice of capital budgeting and should be an aid
in the profitable employment of capital invested.

The model and information obtained from its
application will not replace sound judgement, for the
program as outlined is no better than the judgement of the
individuals who have furnished the information. It should
furnish, at a minimum, additional data that will enable an

individual to maintain and improve his competitive position

27

through more sound decisions made possible by useful

data upon which to base a decision.

Sources of Data

By way of preparing for a better understanding of
corporate capital budgeting problems so that a better
application of the model can be made, individuals responsible
for the capital budgeting decision will be interviewed. In
addition, a number of completed projects will be analyzed
and traced through the organization of the firm from the
inception to completion of the project. This review will
furnish information on the procedures currently in use and
also furnish an indication as to where in the decision
process and in what form uncertainty is introduced into the
process.

It is proposed that a postdictive study be made.
Either projects that have currently been approved or Will
be completed in the immediate future will be used for the
review. Based on this data, the necessary factors to apply
the model will be determined. Each variable to be applied
will be discussed with the individual having the responsi—

bility for the area. An example is a forecast of sales

28

being reviewed with the salesmanager and other interested
persons. The subjective probability will be a quantification
of the manager‘s opinions as to the likelihood of each
occurring.

The source of the information will be firms currently
involved in capital budgeting decisions. The number of firms
involved in the study will depend upon the size of the firms.
It is necessary to have a considerable number of capital
budgeting “projects” to apply the technique to. One or two
larger firms would be adequate for the purpose; however, if
smaller firms are available a larger number would be required
in order to obtain a sufficient sample of individual project

cases.

CHAPTER III

ANALYSIS OF THE PROPOSALS FOR ASSET ACQUISITION

Business organizations, the industry in which each
Operates, the economic climate, and the political setting
have peculiar characteristics that make a reference to an
average of little value in this type of analysis; if indeed
one could be determined. The following introductive
material applies to five firms in different industries with
no attempt being made to compare them with an average. The
purpose of interviewing and obtaining information was to
determine if the model can be applied to actual capital

budgeting proposals.

Background Information

The business concerns contacted were interested in
the project. As expected, some of the organizations, even

though expressing an interest, did not make themselves

29

30

available because of the time required to determine the
necessary data, and/or their particular business did not
lend itself to this type of analysis. All of the firms
that cooperated in the study were very helpful in their
willingness to furnish data, discuss the problem area and
also to make available individuals who were responsible for
this area of the business activity. There was some
difficulty in finding companies that were willing to
cooperate; however, this problem fell within the realm

of expectation.

The asset acquisition proposals studied can be
grouped as cost savings, competing proposals to meet the
need for increments to an established line of business,
establishment of new branch offices and retail outlets
for existing services and products, and asset replacement.
Various types of projects were deliberately reviewed to
aid in the evaluation of the applicability of the proposed
model. The acquisition proposals studied were those that
were currently being approved, or those for which approval
had just been granted. One exception was a project that
had been in operation for a few years, that still had
elements of uncertainty surrounding the future course of

action to be taken in regard to the asset.

31

The availability of proposals to be reviewed within
the organization was limited when individuals having made
the original proposals were unavailable; when the acquisition
was so large as to not be practical for the purpose of the
study; and also when a quantitative analysis had not been
made to help justify the acquisition of the asset. When
individuals within a company were unavailable so that
proposals of a certain area or type could not be studied,

a second source or company was located. An example of

where there was a size limitation and also a limitation
because quantitative methods of analysis had not been made
is a firm that proposed a complete change in the data
processing system. A study taking the major portion of a
year had been made to determine if there was a need and also
if the proposed system would meet the need. In their
analysis no attempt was made to determine the information
necessary to calculate return on the investment.

Sources of data are an insurance company, a
financial institution, a refining and marketing company of
oil products, a manufacturer of industrial products and a
manufacturer of component parts for the auto industry.
Although these organizations are in different industries

there seemed to be at least two common characteristics for

32

the group. The first being that each felt that the
competitive situation and the conditions of supply and
demand were peculiar for their firm and industry and that
the risk and uncertainty facing them were as great, if not
greater, than in other types of business activity. The
second similarity was a desire to obtain a reasonable
return on the investment.

Before the model could be effectively applied to
specific proposals it was necessary to obtain an under-
standing of the procedures used by each firm. The
procedures being used will be summarized in order to provide
the reader with an understanding of the methods used.

Of the firms interviewed, two were using a
discounted present value method; the internal rate of
return and the profitability index. Two firms used the
payback method, supplemented with the accounting rate of
return analysis. One organization did not have or did not
use an analysis that attempted to indicate a promised rate
of return or a capital recovery period, but attempted to
determine if a need existed and if the proposal would meet
that need. All of the firms stated that the quantitative

methods used, if any, in the last analysis were only a tool

33

and that good judgement on the part of the individual or
group making the decision was required for effective
operations.

When the proposal has been analyzed, a decision
must be made as to whether it will be accepted or rejected.
Many authors of financial literature have suggested that
this decision could best be met by establishing a standard
upon which to judge each proposal. The two firms using the
payback method establish a minimum period of one to five
years, with the organization requiring the one year
recovery having recently changed from a three year period.
The firm using the profitability index method established
a minimum payback period of five years. This then was
converted to a minimum rate of return after adjusting for
tax effects and the method of depreciation accounting. The
reasons given for the level of each established standard
were the competitive conditions in which the firms found
themselves and also the availability of funds for long term
asset acquisition. No mention was made of an attempt to
earn a return which at least equaled a cost of capital.

The organization using the internal rate of return

stated that a standard could not be established; that each

34

project had to be analyzed individually with the promised
rate of return being only one factor to be considered.

Other standards used were the effect on the cost
per transaction, and a comparison of the out-of—pocket cost
of the old and new projects to see if there was a reduction
in the dollar amount of the yearly net expenditure.

The control over the authorized expenditures was
through the normal organization of the internal control
established by the firm. The supporting documents varied
with the size of the organization and the method of analysis
used. In all firms an authorization had to be received
before the project could be undertaken. The control over
costs during the construction and/or acquisition stage was
normally a function of the purchasing and accounting
department, with excess funds requiring additional
authorization before they would be supplied.

There was a tendency to establish control by using
total dollar amounts which could and did allow for variations
within the various parts of the project. As a result,
surplus funds were diverted to other projects or to additions
to the approved project without authorization from the
individual or group responsible for the original author-

ization.

35

Post audits were not generally made, although one
firm indicated that in one of its operating areas a sample
was taken and the selected asset's performance was compared
with the estimate made in the original proposal. The other
firms indicated that the estimates were indirectly reviewed
by an analysis of the overall operating performance. For
an example: Standards were adjusted for changes in the
methods and the variations from standards were in turn
analyzed. The major limitation of the post audit in cases
where it was felt to have merit was that the classification
of revenue and expense was such that the evaluation of an
individual asset's performance was very difficult, if not
impossible. The importance of the post audit was recognized
and where it was currently not a normal procedure it was
anticipated that improvements would be forthcoming.

The retirement of assets was controlled by the
accounting department after approval was obtained from one
having the authority with a yearly inventory of fixed
assets being made by some establishments.

The procedures, as outlined by the firms (if
followed), were adequate to provide a physical control over
the assets. The major weakness noted was that of what seemed

to be a lack of control over appropriations that were

36

approved in total but not related to specific projects
and subgrouping within the project, and the limited
analysis of estimates versus actual performance.

Operating budgets were common for both long and
short run estimates; however, the long term estimates for
asset acquisition both as to the individual project and
the dollar requirement, were felt to be either unsatisfactory
and in need of improvement or were non-existent. The annual
budgets for asset acquisitions were reasonably reliable when
compared with the uses to which they were put; still, this
does not mean that improvements would not be necessary in
the budgeting procedures if additional information and
analysis were desired.

The individuals responsible for preparation and
interpretation of the analysis used to quantify the estimates
of the project's performance, with few exceptions, seemed
to understand the major assumptions made under each method
and its limits. However, a majority of the firms were in
need of improved communications concerning their purposes
and objectives in this area since individuals not directly
responsible did not know the procedures that were being
followed or if they did; did not appear to have an adequate

understanding of them.

37

Most of the ideas for use of funds were the result
of a need to meet a customer's specific requirements, to
reduce costs of the current operating methods or to fulfill
general guide lines as established by management. A general
weakness involving an insufficient number of alternatives
investigated was apparent. An example of this is that one.
organization had established a need for new information
and methods to obtain data; the analysis of ways to meet
the need was limited to one source and type of asset when
other sources with competitive methods were available.

The problems of risk and uncertainty were met
through judgements made by officers responsible for the
decision area and were based upon past experience and a
feeling as to the future business conditions. An attempt
to quantify uncertainty took the form of either making
several estimates based upon two or three assumed levels
of activity or the establishment of standards that, for
all practical purposes, approved only those projects having
very little uncertainty as to the recovery of the required
investment. The requirement that each project should have

a payback period of one or less years is an example of this.

38

To summarize: For each company interviewed there
was an attempt being made to improve the means of analysis.
This included such things as changing the financial reporting
so that better control over specific asset areas could be
obtained; selling the necessity of good budgeting procedures
to supervisors and employees; a growing awareness that
something better must be looked for; a willingness to
investigate new ideas and procedures; and the establishment
of a group of individuals within the organization whose
purpose it is to study the systems and procedures and also
be a source of new ideas and alternative ways of accomplishing

the goals of the organization.

Summary of Data

Table 1 represents the estimates of a proposal for
the acquisition of an asset that was reviewed and for which
the model has been applied. The classification of information
obtained on each of the twelve proposals studied has been
the same. Of these proposals, one has been selected as an
example to illustrate the data collected with the final
output and analysis being made for each acquisition proposal

in a later section of this chapter. Limiting factors were

TABLE 1

RANGE OF VALUES AND SUBJECTIVE PROBABILITIES

I Estimated Useful Life

II Estimated Investment Required

III Gross Benefits
Years one - three

Fourth Year (Illustration
of distribution for years
four - twenty)

IV Operating Expenses

V Asset Replacement

VI Value of Asset at the end of
its Useful Life
End of tenth year

End of the fifteenth or
twentieth year

39

DOLLAR
OR
YEAR

 

10 Years
15
20

$64,640
61,560
58,480

$29,370
26,700
24,030

$31,670
31,420
31,090
28,800
28,570
28,290
25,930
25,760
25,490

$ 7,400
6,000
5,000

None

$38,780
36,930
35,080
27,180
25,850
24,560

None

CUMULATIVE
SUBJECTIVE
PROBABILITY

 

25%
65
100

50%
75
100

34%
67
100

11%
23
34
45
56
67
78
89
100

10%
30
100

40%
60
80
90
95
100

40

considered in arriving at the estimates of the variables
used in the model, for example: The level of plant capacity
and limitations of demand were considered in determining

the level of sales and expenses, and obsolescence was
considered in the estimated useful life of each asset.

The company, in analyzing the proposal noted in
Table 1, used the payback period to justify the acquisition
with a three year period being established as a standard.
The original proposal did not include an estimate of the
useful life since it was not required in the payback
analysis used.

It is interesting to note that the investment
figure used in the original analysis was $61,560, even
though it was not the most likely one. The estimated
gross benefits were determined by estimating the possible
rates of growth and the variation from each over the asset's
life and then assigning the subjective probability to each
attainable level of activity. For the first three years
it was felt that the gross benefits would not change, with
the years thereafter changing at a rate of from 6%.through
8%. The fourth year's gross benefit had a range from

$25,490 to $31,670. In the twentieth year the range was

41

from $64,500 to $101,650 with the subjective probability
being an equal chance for each.

The operating expenses (made up of maintenance
expense) would vary over the life of the asset; however,
it was the opinion of the engineer that the pattern of
variability could not be estimated with a reasonable amount
of accuracy; therefore, an average annual amount was
estimated for the life of the project.

The asset was felt to have a value for resale or
for use within the organization if used within a ten year
period. The higher range of $35,080 to $38,780 is the
estimated value of the asset if used within the organ-
ization. The value of $24,560 to $27,180 is the estimated
sales value of the asset if sold within a ten year period.
The asset for tax purposes was to be depreciated over a
twenty five year period, even though the maximum useful
life was felt to be twenty years.

Persons questioning their ability to make subject-
ive probability estimates normally gave one of the following
reasons for their inability to do so: First, that the
estimates made in the original proposal were realistic and
correct. When the assumption being made, as to the condition

of certainty, was pointed out, each person was willing to

42

acknowledge that there were other estimates that had merit
and they were then willing to express a probability for
each. A second reason, usually implied by various state-
ments concerning their method of analysis, was that only
a figure that was certain to be obtained would be used in
the estimate since the individual would be held accountable
for an estimate made that was not attained. The third
reason was actually not a reason but a statement that
only those estimates that would assure the acceptance of
the project would be furnished in the analysis. For
example: One organization noted that a minimum sales figure
would always be used to assure that the project would be
accepted. The last two reasons are an indication that the
organization has not communicated to the individuals the
goals of effective capital budgeting which would enable
management to better meet their responsibility as effective
custodians of the corporation's resources. Not being able
to make an estimate was given as the last reason; however,
those who did not seem to have an understanding of the
capital budgeting process and were normally not directly
involved in the area of asset acquisition gave this reason.
The comment was made by some of the firms that in

certain types of business operations, in order to stay in

43

a competitive position, investments were required to be
made in areas that were subject to a great amount of
uncertainty and because current investments were required
that would not promise a return for twenty to thirty

years that when using the discounted cash flow method the
present value of the uncertain future benefit would be

zero or next to it; therefore making this form of analysis
almost worthless. It is recognized that the above condition
may exist in a few areas of asset acquisition; however,

if these conditions are very prevalent, the author suggests
that it may be necessary to analyze not the single asset
acquisition but the overall area of business and if

these conditions are normal, then other types of investment
may be a better source of investment of equity funds that

do not fall in the classification of funds for speculation.

Application of the Data to the Model

A detailed description of the steps required to
apply the model is included in Appendix B. The first part
of Appendix B is the description of the input and output
requirements for each factor used in analyzing each proposal.

Parts II through V are the steps required to convert the

44

data into an estimate of the rate of return and furnish the
desired output. Reference is also made to Exhibit 1 for

a flow chart of the computer program used in the analysis.
A detailed computer program is included in Appendix C.

For the purpose of applying the data to the model
the level of activity in any one year is assumed to be
independent within that year; that is, any value within
the range indicated for a particular year is assumed to be
possible for the proposal under study. An example is that
the lowest value in one year would not restrict the attain—
ment of the highest level in Subsequent years. It is
recognized that for certain types of investment alternatives
this assumption would have to be modified; however, for the
projects under study it is felt to be a reasonable assumption.

Losses and gains from disposal of assets in the
year of retirement are assumed to be offset against other
capital gains or losses in the year each is incurred.
Operating profit and losses are also assumed to be offset
against other operating areas.

The tax law has special provisions that affect the
capital asset acquisition decision. Such items as the
investment credit that applies to tangible personal property_

and other tangible property used in certain types of business

EXHIBIT 1

LNITIALIZE M= Number of trials
to be performed
N= Years of Estimated

useful life

  

 

|=I,2

     

 

GENERATE ESTIMATED
Ll F E

GENE RATE ESTIMATED
C0 ST

 

 

 

 

 

 

 

 

.Oj

I GE NE RATE ANNUAL REVENUE]

GENERATE ANNUAL
OPERATING EXPENSE v
w _

LGENERATE ANNUAI; REPLACEMENTS]
QALCULATE ANNUAL DEPRECIATION]
_ {I
L___.I:ALCULATE BENEFIT FROM
DISPOSAL OF ASSET
I
IN E

I

 

 

 

 

 

 

 

 

 

 

* CALCULATE ANNUAL NET
CASH BENEFIT

mALCULATE RA? OF RETURNF—y
{PRINT ITESULTS]

 

 

 

 

 

 

 

46

operations allow a 7%.credit to be applied against the tax
liability subject to limitations as specified in the
Internal Revenue Code. There is also a first year allowance
on an aggregate cost of $10,000 at the rate of 20%.that is
allowed to be deducted to arrive at taxable income. The
accelerated depreciation methods, along with the above

noted examples (if used for tax purposes) could affect

the annual net benefits that are used in an analysis of this
type. For this study the straight line method of depreciation
is used. The residual value is deducted to arrive at the
depreciable base only when it is material in amount. The
investment credit and first year 20% depreciation allowance
are not included in the model.

It is assumed that the cash is received and disbursed
in the year the revenue is earned and expense incurred and/or
the balance of the receivables and accrual and accounts
payable do not vary from year to year so that in effect the
analysis is on a cash basis. Asset replacements that are
minor in amount are handled as an expense item in the year
of replacement. For replacements that are material in
amount the annual depreciation is adjusted to reflect the

change in the depreciable base of the investment.

47

The basic assumption underlying the application of
the model is that the dollar range for each factor and the
subjective probabilities furnished are reasonable in amount
and are rational. In interviewing companies care was taken
to obtain the estimates from persons having responsibility
and experience in the operations of the particular invest-
ment area and the principles involved in the application of

capital budgeting techniques.

Analysis of Cases

The following is a summary of the twelve acquisition
proposals that were used in applying the model to actual
capital budgeting projects. For each case the data has been
summarized into three areas. They are a summary of the rates
of return obtained in the simulation of the asset acquisition,
an analysis of the factors affecting the rates of return and
a comparison of the results of the simulation model and the
capital budgeting methods currently used to evaluate the
proposals for investment of long term capital funds.

With the exception of Case 8, a Figure is furnished
indicating the relevant rates of return and the probability

that each will be obtained. The source of the data appearing

48

in each Figure is a summary of the individual calculations
of the rates of return. For this analysis one hundred
computations were made. The rates of return are summarized
and the probabilities assigned are equal to the frequency
of each rate of return obtained in the simulation.

The simulation of the results of the asset proposals
for eleven cases was through the use of the computer using
the Fortran language. (Refer to Appendix C for an example
of the program). One simulation of an asset proposal was
performed by the use of a hand calculator. The reason for
this is that the time involved to obtain the simulation
results by hand methods was less for this particular
proposal than what would have been required to write a
computer program. This condition was an exception and would

not normally be expected to apply.

Case 1 (Figure 1)

Rate of Return

There is a 68%.probability that the present value
of the net cash benefits will be equal to or greater than
the present value of the required investment, in other words,
a positive rate of return is promised 68% of the time, with

the maximum rate being 14%.

LOO

Probability of Reaching Indicated Return or Larger

.95
.90
.85
.80
.75
.70
.65
.60
.55
.50
.45
.40
.35
.30
.25
.20
. I 5
.I O

.05
.00

-

-

 

 

 

 

49

FIGURE I -CASE I

IOO Computations of Rate of Return

- - --Excluding trials with dual rates of return

1 1 L I i l L L k _]

0% 2 4 6 8 IO I2 l4 l6 I8 20

Anticipated Return

50

Analysis of Factors Affecting the Rate of Return

Factors having the major effect on the rate of
return are the estimated useful life and the level of
annual revenue and expense. The resale value of the asset,
acquisition cost and asset replacements have limited ranges
in which they can vary; therefore, the variation of these
factors does not have a material effect on the calculated
rate.

The useful life is estimated to be two, three and
twelve years with a probability of .25, .05 and .70
respectively. The net benefits for years one through three
are not sufficiently large to provide for a positive return
on the investment requirement. Management felt that if the
proposal could survive past the third year the useful life
would then be twelve years. The effect of the variation
in the estimated useful life can be illustrated by referring
to Figure 1. For all computations of the rate of return
based on a two or three year useful life the resultant
return is zero or less. The rates of return obtained when
a twelve year useful life is assumed has a range from 6%
to 14%. (Refer to the solid line on Figure l). The inter-
action of the factors other than the variation in the useful

life causes the rate of return to have a 6% to 14% range

51

with the annual revenue and expense being the major factor
accounting for the variation.

In Chapter II it was noted that the internal rate
of return would not provide a ranking of projects that was
consistent with the discounted present value method if
there were a condition where dual rates of return were
possible. This problem arises whenever there is what has
sometimes been called a nonconventional flow of annual net
benefits. It is normally assumed that the initial investments
and any negative net amounts will occur during the initial
part of the asset's useful life. Positive net benefits are
then assumed to follow the initial investment and the
negative net benefits. In some cases there will be a positive
annual net benefit that is followed by an annual figure in
which the benefits are negative in amount. When this occurs
a dual rate of return is possible. This problem may be
adjusted for by carrying forward, at an assumed reinvestment
rate, the positive net benefits that fall between the
negative values to a future year where there are consistently
positive values; the rate of return can then be computed
on the revised values.

There were a number of computations within the

simulation of this case that could give rise to the problem

52

being discussed. If these situations were eliminated from
the sample the effect on the range of rates of return and
the probabilities of each can be observed in Figure l by
reference to the dotted line which represents the smaller
sample. The major effect of the elimination of these
computations from the sample is an increase in the frequency
in which a positive rate of return is estimated to be
received. This is demonstrated in Figure l by the increase
in the assigned probability from 68% to 72% for a rate of
return being equal to a positive rate of return.

The individual computations of rates of return, when
there was a possibility for a dual rates of return problem
were adjusted and recomputed. The effect of this adjust-
ment did not change the original distribution of the rates
of return and the frequency of each; therefore, the
probabilities being indicated by the solid line in Figure

l are the appropriate weights to be used for this analysis.
Case 2 (Figure 2)

Rate of Return
The relevant rates of return for Case 2 are 22%
through 31.5%. This represents a limited range in that a

return equal to or greater than 30%.will be received over

I.00I-\_
.95

.90
.85

Probability of Reaching Indicated Return or Larger

.80
.75
.70
.65
.60
.55
.50
.45
.40
.35
.30
.25
.20
.I5
.I 0

.05

.0 0
22% 23

-

-

 

l

53

FIGURE 2- CASE 2

 

 

l l l l l _1 l l

I J

 

4 25 26 27 28 29 30 3|
Anticipated Return

32 33

54

80%.of the time, with the probability of a greater rate of
return decreasing very rapidly. The reason for the limited
range is that the case was handled, in the model, as if the
investment were incurred in the current year and the net
benefits for years one through five were certain to be
received.

The internal rate of return method determines the
rate that causes a condition of equilibrium between the
present value of the required investment and the annual
future net benefits. In the case under study, inasmuch
as the investment was made prior to the current date and
also as there have been benefits derived from the investment,
it would normally be necessary to carry forward at an
assumed reinvestment rate the costs incurred and net benefits
received. The resultant figure would then be the present
value of the past transactions. This value would then be
compared with the future benefits in arriving at the internal
rate of return as of the current date. This type of analysis
was not made since it was desired to analyze the effect of
factors on the rate of return that are certain to occur

during the early part of the asset's useful life.

55

Analysis of Factors Affecting the Rate of Return

As noted above the investment required for the
acquisition of the asset and the gross benefits and expenses
for the first five years are assumed to be certain; there—
after, a range and subjective probability is introduced for
each of the remaining years of the asset's useful life.
The relative certainty of the major factors accounts for
the majority of the promised rates of return falling into
a narrow range. One factor, however, causes a variation
in the return that is material in amount even under conditions
that are relatively certain. ‘This is illustrated by noting
that whenever the asset's estimated useful life is ten years,
the calculated return is between 22.5%.to 24%.or only a
variation of 1.5%” The effect of the useful life is
demonstrated in that when the useful life is greater than
ten years the return is increased by approximately one-
fourth. It was felt by management that if the asset was
not disposed of within the first ten years it would then
have a very good chance of being in operation for an
additional ten to twenty years, therefore contributing to

the profitability of the investment.

56
Case 3 (Figure 3)

Rate of Return

Figure 3 illustrates that the return should be
between 12% and 21%.based on an investment of $161,000.
The investment required to undertake this business
opportunity is known; all other factors are subject to

uncertainty.

Analysis of Factors Affecting the Rate of Return

The useful life of the asset is estimated to be
between ten and thirty years and is the single most important
factor limiting profitability for this asset acquisition.
When the minimum life is used the lowest level of returns
are due to a combination of a low level of revenue, salvage
value and average or higher operating expenses. This means
that, if the useful life of ten years is held constant, and
other factors are all improved, the maximum return that can
be received is 15.8%

The useful life is also the most significant
factor in obtaining the highest return on the investment
with other factors causing a variation in the rate within
a fairly narrow range. An example of the variation due to

factors other than the useful life is that 18% is the lowest

57

 

 

4
1+
3 1
E
M In
C
_ n
3
E i
R
U
G 1
I
F
J
.1 r. FT. _ F. p _ u L _ _ _ p F. p
050505050505050505050
O.99£37.7.6.£55A4.33.22JJ0.0.
I (out: .8 East b.2933: 2:5qu xo 5.53330‘

I9 20 2| 22

l4 l5 l6 l7 l8
Anticipated Return

I3

ll°/o l2

58

"return calculated when the useful life is assumed to be
thirty years, with a maximum.being 20.9%.

It is observed in Figure 3 that a return of 19%.
or greater has a probability of 35%q whereas, a return
greater than or equal to 20%.has a 9%.probability. The
reason for this significant change in the probability with
a change of 1% in the return is due again to the estimated
life and the subjective probabilities being assigned to
each. The useful life of each is ten, fifteen and thirty
years, having a probability of 50%, 12% and 38%” The
maximum return received when the useful life is fifteen
years or less is 18%; however, the 18%.return is the upper
limit as can be observed in Figure 3 in that the frequency
of occurrence is decreasing for this value. It should be
recalled that for an analysis of this type the probabilities
assigned in each figure are equal to the frequency of
occurrence of each rate of return.

The 18%.is also the lower limit when the useful
life is thirty years with the combination of other factors
contributing to the 18% return occurring infrequently.

To summarize: Since the.estimated useful life is.
the major factor:h1determining the return in this analysis

the frequency of occurrence of a ten year life will be the

59

greatest since it is assigned a subjective probability of
50%” The life of fifteen years and the rates of return it
contributes will be the most infrequent inasmuch as it was
felt to occur only 15%.of the time. The frequency of
occurrence for this range of rate of return will be greater
than 15%.inasmuch as the extreme upper and lower returns
obtained when the useful life is ten and thirty years
respectively, also fall within this range. The rates of
return acquired when a thirty year life is used is the

second most frequent as can be observed in Figure 3.

Comparison with Methods Currently Being Used

Cases 1 through 3 are similar types of investment
opportunities that are available to a single business
organization. Case 1 is felt to be the most uncertain.
The factors in the second case are assumed to be constant
for the first five years. Case 3 is subject to uncertainty
in all areas with the exception of the required initial
investment.

The analysis made by the firm was a proforma
statement of income, with individual classifications of
expense and revenue being fnirly well detailed and supported.

The projection was made to determine the period of time

60

required to break-even, with the analysis then being
discontinued; that is, the projections were not made
beyond the required time to break-even, unless it occurred
prior to the third year. In this event it was a normal
procedure to estimate the operating results for a three
year period.

The model and the information obtained from its
application provides an estimate of the rates of return and
likelihood of occurrence; a means by which the major factor
affecting the return may be analyzed; data that may be used
to determine the break-even point; payback period; etc. and
the analysis is carried beyond the break-even point and
also provides information that can be used as a basis for
future decisions providing the subjective estimates need
not be revised (the revision, if any, being based on added
experience gained with the passage of time). The analysis
used by the firm does not provide this information in an

explicit form.
Case 4 jgigure 4)

Rate of Return
The rate of return varies from 1.9% to 11.6%u The

wide range for this particular type of asset is contributed

61

|.OO-—\ FIGURE 4 - ans: 4

 

.95 -

.90 -

_ L
5 0
8 8

:53

b
5
7.

so

 

bbpp
0505
766.5

95.8%. b.2938 S

L.

5.50

_ _ b L _ b _ _ b
5 0 5 0 5 0 5 0 5
A 4. 3 3 2 2 I l 0.

82393: go. armxxcmeokl

 

O
O

9 l0 ll l2

8

Anticipated Return

l%

62

to by all factors considered in the computation of the

rate of return.

Analysis of Factors Affecting the Rate of Return

The most important factors affecting the lower rates
of return are the resale value and the useful life of the
asset. The estimated resale value is $50,000 to $150,000,
with an equal probability being assigned to each value
within the range. A combination of a short life, low resale
value, and average or lower revenue results in a low return.
If all factors remain the same except for increments in
the resale value, the effect on the return will be an
improvement of 3% to 4%.

The higher extrenuas of rates of return will be
received if the useful life is fifteen to twenty years as
compared with ten years in the prior analysis and also if
the promised revenue is average or better. The resale
value still has an effect on the return; however, this
will be offset with a lengthening of the useful life. The
cost of the asset can range from $160,000 to $180,000;
however, this factor has very little effect on the final
result. The reason for this being that even though there
is a range of $20,000 the probability of the cost being an

extreme value is quite small.

63

Comparison with Methods Currently Being Used

The organization used the internal rate of return
to analyze this asset proposal. Four rates were determined
ranging from 11%.to 7.9%” The variation in the return was
due to the elimination of cost and expense factors. The
higher returns were the result of excluding from the
computation the cost of the land and incremental overhead.
The lower limit was the result of including the land cost
and also an incremental overhead allowance. All factors
used in the analysis were handled as if they were certain
to occur.

The 7.9%.is comparable with the model under
consideration except that the salvage value was ignored in
the organization's computation and as was noted this
factor was one of the major ones affecting the return.
Since the majority of the resale value is due to the land
involved in the transaction and the organization is not in
the land speculation business it may be suggested that the
return should exclude the gains due to factors other than
the normal operations of the business. The effect of this
on the results of the application of the model would be to
reduce the probability of obtaining a given return. Each
return, excepting the higher extremes, would still be

probable.

64

The analysis used by this company indicates the
effects of variations in two factors: the overhead and land
investment. It does not provide information as to the
effect of other factors used in the computation and does
not furnish any information as to the possible range and
frequency that each may be received. The figures used as
a basis in the original proposal were based on past
experience of a similar type of operation. When attempting
to assign a range of values and the subjective probabilities
of each it was noted that past experience had a limited
application as the new operation was servicing a different
market; therefore, the uncertainty surrounding the gross
revenue estimates and useful-life was greater than if the
asset was to service the normal market area. The simulation
model furnishes data that is useful in evaluating this
uncertainty.

Cases 5 through 7 are analyses of one operating
area. The first two represent the promised return on two
mutually exclusive investments with a substantial rate of
return. The reason for the extremely high return is that
the proposal is an addition to an existing and established

operating area having excess capacity. A relatively small

65

investment results in an incremental revenue that is very
large without a proportional increase in the operating
expenses. Case 7 is an incremental analysis of Cases 5

and 6.

Case 5 (Figure 5)

Rate of Return

The return has a range of 43%.with an upper and
‘1ower limit of 221.8%.and 178.7%.respectively. The return
is based on an estimated investment of between $59,000

and $65,000.

Analysis of Factors Affecting the Rate of Return

A major factor causing an increase or decrease in
the profitability is the level of revenue and expense in
the first few years. The return being received is high
enough so that the present value of benefits to be received
(when discounted at the current rate) after only a few
years has a negligible present value and therefore has a
minor effect on the final results. The lower limit (if
178%.is low) is the result of a combination of (relatively
speaking) a low annual revenue and a high level of annual
expenses. The greatest rates of return are due to the

opposite condition; that of a high level of revenue and

|.00

Probability of Reaching Indicated Return or Larger

.95
.90
.85
.80
.75
.70
.65
.60
.55
.50
.45
.40
.35
.30
.25
.20
. l 5
.l 0

.05

.00
I75% I80 l85

 

l

l

l

66

FIGURE 5 - CASE 5

l J l l l l

 

I90

I95 200 205 2|0 2|5 220 225

Anticipated Return

67

low operating expenses in the first few years of operation.
The minimum life for the asset is ten years with a maximum
of twenty years. The variation in life does not affect the
return since the present value of a dollar to be received
in the tenth year is nil when discounted at the rates of
return promised from the investment. An example of this

is that both upper and lower extremes of rates of return
include proposals whose assumed useful life is ten years.
The lowest return obtained in the simulation model is from
an assumed useful life of twenty years; however, the net
benefit for the first and second years are below average.
The amount of the required investment affects the return.
This is evident in that the highest rates of return had the
lowest cost figure of the alternatives available. The
lower promised rates of return each were calculated on the

highest required investment for this project.
Case 6 (Figure 6)

Rate of Return

The range for this proposal is 19%.with the limits
being 105%.to 124%.based on an investment of $117,000 to
$130,000, with the upper limit of cost being the most likely

to occur .

l.00

Probability of Reaching Indicated Return or Larger

.95
.90
.85
.80
.75
.70
.65
.60
.55
.50
.45
.40
.35
.30
.25
.20
. I 5
.l 0

.05
.00

 

l

68

FIGURE 6 - CASE 6

l l l l l l l

 

I04°/o|06 |08 HO "2 “4 IIS "8 l20 l22 l24 l26

Anticipated Return

69

Analysis of Factors Affecting the Rate of Return

Cases 5 and 6 each have identical revenue
possibilities. The area of difference is in the required
investment and operating expenses. The factors accounting
for the majority of the rate variation are the level of
revenue, expense, and the required investment. The
discussion of factors affecting the return for Case 5

therefore apply to this case study.

Case 7 (Figure 7)
In this incremental analysis the excess investment
of Case 6 over 5 is compared against the savings in operating

-expenses that Case 6 will provide.

Rate of Return

The incremental investment having a range of $58,000
to $65,000 will provide to the investors a return with a
range of 9%.having a lower and upper limit of 18%.through
27%m The major factors contributing to a lower limit are
a useful life of ten years and the investment of $65,000;
which is the upper limit for this factor. The highest
rates of return are due to an increase in the useful life

accompanied with a minimum investment requirement.

7O

22 23 24 25 26 27 2e 29

Anticipated Return

 

 

7 l
E

M n
C

_ ..
7

E ..
R

U

6 l
I

F

_ P _ _ p i? P r L L _ _ P _ L 7 _ L L

050505050505050505050
0.998.377.5555AA5322JI00
I .3364 so 936% 6366.35 93:366.: we 5.53331

l8% :9 20 2|

71

The factors causing a variation in the return
based on an incremental value differ from Case 5 and 6
in that the estimated life beyond ten years becomes a
contributing factor; also, the net benefits for the first
and second years are not as influential in determining the

overall promised return.

Comparison with Mefiuods Currently Being Used

When using the internal rate of return approach
(as was noted in Chapter II) if there is a disparity in
the size of the required investment between two mutually
exclusive projects, in order to arrive at the ”correct"
solution a return must be computed on the incremental values.
If the rate is greater than the established standard (assumed
to be the cost of capital) the more costly proposal should
be accepted. If it could be assumed that the return to be
received as determined in the incremental analysis is
greater than the cost of capital the 6th proposal (Case)
should then be undertaken even though it does not promise a
rate of return that is as great as that being received under
Case 5, inasmuch as it provides for a profitable investment

opportunity for available resources.

72

If the organization is not investing in capital
assets until the return on the last proposal is equal to
the cost of capital, the comparison should be between the
alternative (competing) projects and the return on the
incremental investment. This then becomes a problem of
limited capital funds which has been commented on in the
second chapter.

An incremental analysis should be undertaken even
if a condition of certainty is assumed in order to maximize
the firm's position when using the internal rate of return
method. The business, in analyzing this investment
opportunity, recognizing the potential of the asset, made
an incremental analysis to help determine between the two
mutually exclusive proposals. The payback method was used
with a minimum of three years being established as the
standard. Under certain conditions the reciprocal of the
payback period will provide an estimate of the return that
is very close to the return as determined under the discounted
present value methods. Assuming the payback reciprocal was
used as the minimum standard the company's analysis would
have rejected the 6th project in favor of the 5th.

The information obtained from the application of

the model provides management with a range of rates of return

73

and the frequency that each should occur. It provides the
means whereby the more important variables affecting the
return may be isolated and evaluated. It also provides
the information necessary to make the choice between the
two mutually exclusive projects providing some realistic
standard has been established. The above information is
not furnished in an explicit form when the payback method

is used.

Case 8

This case is concerned with an area where there are
rapid technological changes taking place. As a result the
estimated useful life of the asset is between two and five
years. The two year useful life was assigned a subjective
probability of 50%.whereas the chance of the asset being
used in the fifth year was felt to be only 5% or 6%.

The benefits to be obtained are in the form of
cost savings, with each being assigned a range of values.
The cost of the asset is assumed to be certain since it
would be acquired through a supplier who manufactures
similar products at a fixed selling price with the install-

ation costs etc. being minor in amount.

74

Rate of Return

The computation of the return indicates that there
is only a 6%.probability that the investment will earn a
return greater than zero. In other words, there is a 94%
probability that the net benefits received will be less

than the required investment.

Analysis of Factors Affecting the Rate of Return

The major area of uncertainty is the useful life
of the asset. A positive return will be obtained only if
the asset could profitably be used for five or more years.
Because of the continuing improvement and change in the
equipment being considered the chance of profitably using
the equipment for this length of time is very small. As a
result, the major factor to be considered is that of useful
life of the equipment. Unless management prefers to take
a large amount of risk with only a limited promised return,

the project in that form would be rejected.

Comparison with Current Methods Being Used
There was no attempt made to determine if a
favorable return was possible from the proposed investment.

There are investments for particular assets that are required

75

to support the overall operations of the business which,
because of their characteristics, may not be profitable
from a quantitative analysis approach; this is recognized.
It is suggested, however, that before management can
intelligently perform their functions it is necessary to
at least know What the prospective gain or cost (in the
form of possible losses) of a decision is. When an
analysis is made that does not attempt to quantify the data
this information is not available in an explicit form.

It is not a question of the data not being available,
since it was obtained when the request was made. The
reason is that a quantitative capital budgeting policy has

not yet been established within the organization.
Case 9 (Figure 8)

Rate of Return
There is a variation of 45%.between the two limits
of 88%.through 143%u This return is based on an investment

having a minimum cost of $9,960 with a maximum of $14,370.

Analysis of Factors Affecting the Rate of Return
The factors causing the major variations in the

rate of return are the estimated cost, and the reduction in

|.00

Probability of Reaching Indicated Return or Larger

.95
.90
.85
.80
.75
.70
.65
.60
.55
.50
.45
.40
.35
.30
.25
.20
.I5
.I 0

.05
.00 A

 

 

88% 9 98

76

FIGURE 8 - CASE 9

 

I I l J l l l 1 ~

l03 I08 ”3 "8 l23 l28 I33 I38 I43
Anticipated Return

77

operating expenses to be obtained within the immediate
future. The estimated useful life beyond the minimum of

ten years does not have a material effect on the return to

be received. The reason is the extremely small present value
of a dollar when discounted at the rate of return to be
earned from the investment. The wide range of possible
returns is caused by a combination of nine values that are
obtained from the range of costs and probabilities assigned
to each, along with three combinations of cost savings. An
example illustrating this variation in return is a comparison
of two computations of rates of return. All factors are
identical for the first six years with the exception that
computation A receives in the first year a benefit that is
greater than B by $4,000. A's rate of return is greater

than B's by 12%m

Comparison with Methods Currently Being Used

The method of analysis to justify this proposal
was the payback method supplemented with a rate of return
determined by the accounting method. The payback period
for the asset was less than one year. The rate of return

for the first two years before taxes was 216%.and 232%, and

78

after taxes was 100% and 107%“ The analysis was not
carried beyond the second year.

The advantages of the discounted present value
methods when compared with other evaluation methods will
not be discussed inasmuch as they are readily available in
financial literature. It is sufficient to say that the
advantages would equally apply to the model used in this
analysis. The discussion of the prior cases have also
noted advantages that equally apply in this case, an example
being the determination of the rate of return and its
probability.

An organization that establishes a goal of a
single payback period and can locate proposals to meet
this standard for all practical purposes is facing a
problem of limited capital and is using the established
standard to help determine which of the capital budgeting
proposals should be accepted. It would be easy to conclude
that proposals which promise such an obvious and profitable
return could be accepted without the cost involved in
computing the rate of return by a method having theoretical
justification since an accounting loss will not be incurred

on any of the proposals. If it is a logical assumption

79

that the business, when possible, is trying to maximize
its income position it is then faced with a problem of
trying to decide which proposal should be accepted to meet
the established goal. Reference is again directed to
Chapter II and the discussion of the limited capital
problem. The data obtained from the application of the
model should furnish information that will aid management
in meeting the limited capital problem. The necessary
information is not furnished when using the payback and

accounting rate of return methods.

Case 10 (Figure 9)

Rate of Return

The rate of return obtained in simulating this
investment opportunity was between 88% and 67%, with there
being a 52% chance of obtaining a return equal to or greater
than 76%. The return is calculated upon an investment of

between $7,000 and $8,000.

Analysis of Factors Affecting the Rate of Return
The cost of the asset and variation in annual net
benefits accounts for the major portion of the variation in

the calculated rate. The variations in the estimated useful

80

FIGURE .9 - CASE IO

 

   

 

 

 

65i-

— h — F _ P P — — r _ — — _ _ L
5 0 5 0 0 0 5 5 0 5 0 5 0 5 O 5
9 9 8 8 7 6. 5 4. 4. 3 3 2 2 I... l 0.

.00

|.00

_ _
5 0
. 7. . . 5. . . . .
.3364 so 93on 633.63 66.3669: *6 5:.8663.‘

66% 68 70 72 74 76 78 80 82 84 86 88

‘ Anticipated Return

81

life do not affect the return since the minimum useful life
is sufficiently long so that the present value of a dollar
would be nil if received in a period beyond the minimum life

of the asset.

Comparison with Methods Currently Being Used

The accounting rate of return and payback method
were used to analyze the proposal. The payback period for
this particular asset was one year. The rates of return as
determined by the organization for the first and second years
were 80%.and 103%.before taxes and 37%.and 48% after taxes.
Refer to the discussion of Case 9 for additional comments
in this area since the projects being analyzed and the
methods used are similar and the comments apply equally to

this analysis.

Case 11 (Figure 10)

Rate of Return

An investment of $3,040 promises to return a rate
of between 55%.and 61.5%t The reason the rate of return
has limited range is that investment is subject to very

little uncertainty.

82

 

FIGURE IC- CASE II

 

 

 

____ L_____L—_
0505 50.5050505
7655 44.3322110.

. L
5 O
3 9.

LCD
.00

3.36.4 s 55.3%.636365 Steak .3. 55.36.63“;

62 63

53% 54 55 56 57 58 59 60 6|

Anticipated Return

83

Analysis of Factors Affecting the Rate of Return

The variation in the net annual benefits accounts
for changes in the rate of return for this asset proposal.
The other factors, with the exception of the useful life
are either minor in amount or subject to a limited amount
of uncertainty. The minimum useful life is estimated to be
ten years with the maximum life of twenty five. However,
the benefits received after the tenth year have a present
value that is so small in amount that it would not have a

material effect on the rate computation.

Comparison with Methods Currently Being Used

The original analysis indicated a payback period of
less than one year with a rate of return computed by use of
the accounting method in the first and second year and before
taxes of 213%.and 224% and after taxes at a rate of 98% and
102%.

A more careful examination of the company's
original proposal indicated that there was a duplication
of benefits between this and another investment; therefore
reducing the annual benefits by almost one half. Reference
is again made to the discussion of Case 9 which applies

equally to this case analysis.

84
-Case 12 (Figure 11)

Rate of Return

An investment of $16,300, plus or minus $300, will
return a rate having a range of 4%. The narrow range of
the rate of return is the result of a limited capacity of
the equipment. Within the first five years of the asset‘s
life it is estimated that this particular item of equipment
will be operating at its maximum level. The result of this
being a limitation of the range of values of one of the
major factors causing a variation in the profitability of

the investment.

Analysis of Factors Affecting the Rate of Return

The factor causing the narrow range of rates of
return was noted above as being due to the limited capacity
of the equipment. Within this range the variations in the
estimated useful life and level of annual benefits are the
major factors affecting the calculated rate of return. The
major source of benefits obtained from the investment is
assumed to be certain after the maximum level of capacity
is obtained with the other annual benefits and the variation

in the cost of the asset and salvage value being minor in

85

_ nouns ll — ones l2

1

 

 

l.00

.75 r-

. _ _ _ L L _ _
5 0 5 0 O 5 0 5
9. 9 8 8 7 6 6. 5

6.6.23 .6 56.3%. 6363.65

.
0
5.

u

_
5
4

.40 *-

6.£...v66t .3. 55.36.6654

- _ — b — _ b
5 0 5 0 5 0 5 0

40

38 39

Anticipated Return

37

36

35%

85

FIGURE II - CASE I2

 

 

l.00

LLLL
5050
6366

sowxuw .L

°.75#

L L L L L
0 5 0 5 0
7. 6. 6. 6 6
566% 6366.65 6

L P L L L L p
5 0 5 0 5 0 5
4 3 2 2 l l 0.

.40 ‘-

L
5
. 3. . .
c.2366% so 5.566666%

0
O.

37 38 39 40
Anticipated Return

36

35%

86

amount. The effect of these factors when combined with

any one of the assumed useful lives is a variation of
approximately 2%.in the rate of return. A return of 36%
through 38%.is received for assets having a useful life of
ten years. The 37%.through 40%.return is obtained when the
useful life is eighteen through twenty five years. There

is some overlapping of the return between the above areas;
however, the useful life of the asset is the factor causing
the expected rate to fall within the higher or lower extremes

of rate of return.

Comparison with Methods Currently Being Used

The organization used the profitability index for
evaluating the asset proposal. The estimates were made for
the investment of funds and other factors such as the
incremental savings and operating expenses with the amounts
so determined then being assumed to remain constant over
the useful life of the asset with a resultant profitability
of 24.7%.'

The method used in arriving at the level of
profitability assumes the factors for each year will be
identical to the preceding one and that a condition of

certainty exists. These assumptions are, of course, subject

87

to question. The results obtained do not furnish in an
explicit form, information that enables an evaluation of
the effect of each factor on the return and it furnishes
limited information that can be used in evaluating the
uncertainty of the project. The application of the model
contributes information in each of these areas that is not

available from the normal evaluation method used.

Summary

Chapter III summarizes the capital budgeting methods
employed by five business establishments with no inference
being made as to the methods being used for all business
organizations. An example of the data obtained is
furnished in Table 1. It is felt that an adequate descript-
ion of the methods being used is provided in the body of the
report and also in the Appendices. To provide complete
details of each case study would be a violation of confidences
that exist between the interviewer and organization.

A description of the procedures followed in applying
the data to the model is furnished, with the results of each
study being analyzed in the form of a comparison of the model

with methods currently being used, a discussion of the rate

88

of return and an analysis of the major factors affecting
the return., Where applicable, a Figure illustrating the
range of rates of return and the probability of each is

furnished and is the basis for the discussion.

CHAPTER IV

EVALUATION OF THE PROPOSED MODEL

Comparison with Methods Currently Being Used

The model includes a discounted present value
method for determining the rate of return. It is, therefore,
subject to the same strengths and weaknesses of these
methods. It does not assume a condition of certainty for
the factors being used in the computation of the rate of
return, as is normally assumed in the current methods being
employed. However, one of the basic assumptions is that a
person having business experience can provide rational
subjective probability estimates that are in turn used in
applying the model.

This assumption has been accepted as reasonable; if
it is, the model is an improvement over the current methods
being used in that it furnishes additional information in

an explicit form that will aid management in evaluating

89

90

capital budgeting proposals that are subject to conditions
of uncertainty. If this basic assumption is not true, the
model, though workable, will provide information that is of
questionable value. It is suggested that if the assumption
is not true then the discounted present value methods
currently being used are also of questionable value inasmuch
as they are subject to subjective estimates concerning

future economic events.

Cost versus Results

The application of the model is itself subject to
incremental costs, by virtue of the work necessary for its
application although the organization using a quantitative
analysis in the capital budgeting area does have at its
disposal the information required to apply the model.
Therefore, the incremental costs apply to the mechanical
application of the model. The major cost (assuming the use
of a computer) is the initial cost of obtaining a workable
computer program. -For a skilled programmer this should
involve, at the most, a single working day. For someone
with limited experience additional time should be allowed.

For example: The programs used in this study, with the aid

91

of an experienced programmer to guide the author's progress,
were composed in three days, on the average, for the eleven
programs. This, it is felt, should be the maximum time
required. When the program has once been obtained future
applications can use the same program with minor modifications
being necessary. The maximum computer time was one and a
half minutes to compute and print out the results. There
are, of course, other costs such as the material (cards)
and time required to key punch the data; however, based on
the experience of this study it is suggested that if the
information obtainable from the use of the proposed model
is felt to have value to the prospective user, the cost of
obtaining the data should not be the limiting factor.

The organization currently using non—quantitative
methods in analyzing proposals will find the model more
costly to apply inasmuch as the required data would not
have been generated in the normal operating procedures.

At such time as there is a policy change so that an analysis
in a quantitative form is desired the application of the

model would not add materially to the incremental costs.

92
Problem of Size (Number of Computations of
Rates of Return)

The number of computations of rates of return used
in each application of the model was one hundred. In order
to determine if the results obtained would be reasonable,

a number of tests were applied to the model. The first
attempt to justify the sample size was the use of fifty
computations in Appendix A. It was noted that the results
of this analysis, based on fifty computations, was similar
to the return obtained when the expected value of each
factor was used. In preparing the computer program an
intermediate step was taken to have the computer determine
the average value for the major factors generated within the
program. This was then compared against the expected value
of the appropriate factor. The results of this test
furnished values whose variation from the expected value
was not material in amount. Reference is also directed to
Figure 12. Using Case 3 as a basis, one and two hundred
computations of the rates of return were obtained. It can
be observed that the two lines have similar slopes with the
major turning points being almost identical. The one area
of the greatest deviation results in a variation of nine-

tenths of a percentage in the rate of return. Reference is

93

also made to Chapter II wherein this problem was
discussed.

The review of literature and the limited tests
made in applying the model resulted in the selection of
one hundred experiments to be made in each case. It is
not suggested that the problem of sample size has been
resolved; however, for the purposes of the study the

results obtained were reasonable.

Availability of Data

The factors obtained in applying the simulation
model are basic to the application of the discounted
present value methods under the assumed condition of
certainty. To obtain the dollar range for each variable
and the subjective probability estimates it was advantageous
to use the proposal forms as prepared by the firm. The
individual originating the data had considered the factors
without attempting to express the range of each in an
explicit form. It was therefore necessary to have the
person express his estimates, using the data already
obtained as a basis for his estimates. The procedure of

some of the firms was to indicate the revenue and the

|.00

Probability of Reaching Indicated Return or Larger

.95
.90
.85
.80
.75
.70
.65
.60
.55
.50
.45
.40
.3'5
.30
.25
.20
.I5
.I o

.05
.00

 

94

man: 12 - PROBLEM OF SIZE

 

.__I00 Computations of rate of

- return
_ — —200 Computations of rate of

return
L \\
- \

\

- \

\
h \
I-

I I . I I I I I L I

"96 I2

I3 I4,I5 I6 I7 I8 I9 20 2|
Anticipated Return <

95

operating expenses for a few years and then assume that
the subsequent years“ results would be identical to those
of prior years. For example, one organization, in determining
the cost savings to be obtained for the proposed acquisition,
estimated the savings for the first year and then used the
same estimate for the remaining fifteen years of the asset's
life. This type of analysis not only assumes that the
figure used is certain to occur in the first year but also
that each year thereafter will be identical to the first.
The analysis would be improved, even assuming a condition
of certainty, if each year were to be considered individually
and changes between periods of time were recognized. The
process of asking the individual to assign a range of values
and estimate the probability encouraged a more comprehensive
evaluation of the items to be included in the determination
of the rate of return.

Organizations using the payback and accounting
rate of return methods generally had not considered
explicitly all of the variables required in the application
of the discounted present value methods. An example of
factors not being considered was the total useful life and

an estimate of the salvage value. The period required to

96

recover the investment was determined in the payback
analysis. If the payback period met the established
standard the proposal was generally accepted with the
remaining life of the asset not being considered in an
explicit form. The rate of return determined by the
accounting method was calculated for the first few years,
with the balance of the asset's useful life being ignored.
Even though some of the variables were not included in the
proposal when the above noted methods were used the
original investigation of the acquisition proposal furnished
data that enabled an estimate of these variables to be
made.

Most of the factors needed to apply the model
under study were determined when the quantitative analysis
was made. Thus the information was available as needed.
When quantitative methods were not used to justify an
acquisition the data was not readily available; however,

it was obtainable.

Aid in the Evaluation and Prediction
of Future Results

Since this analysis does not extend over a period

of time that allowed for the comparison of the estimates and

97

actual results, the following advantages in the evaluation
and prediction of future results are suggested for this form
of analysis over the procedures assuming a condition of
certainty.

Living with uncertainty is a way of life; to the
extent that information is obtained that aids in predicting
future results of a decision yet to be made, the likelihood
that the organization will reach its goals will be improved.
This model furnishes data that more clearly presents the
alternative outcomes of a decision to commit funds whose
benefits, if any, will be received in the future. The
information furnished makes it possible to have a more
complete analysis of factors affecting the rate of return.
This information is obtained from analyzing the individual
calculation of the rates of return and observing the factors

that cause an improvement or reduction in them.

Prerequisite for Effective Application
and Use

The factors contributing to a well managed capital
budgeting program include, among others, a means to measure

the worth of the project and a standard to judge the results

98

by.1

A well managed organization must be present for the
most effective application of the model.

There should be adequate communication and
cooperation between departments so the desired information
may be obtained and prescribed procedures will be adhered
to. When the individuals involved with the program feel
they have made a contribution in the prescribed methods
being used, the communication and cooperation will be improved.

In order to obtain adequate input data experienced
personnel must be used as a basis for estimating the factors
required to apply the model. These individuals should also
have an understanding of the procedures being used. The.
application of the data can be by hand methods or designed
so a computer may generate the output data. When the model
is to be applied to a number of projects, the most practical
application would be to use the computer. The application
after the data has once been obtained is not too difficult;

however, to apply it by the use of a hand calculator is a

time consuming project. If a computer is not available the

 

lJoel Dean, ”Measuring The Productivity of Capital,”
The Management of Corporate Capital, ed. Ezra Solomon
(Chicago: The Free Press of Glencoe, Graduate School of
Business, The University of Chicago, 1963), p. 21-34.

 

99

mechanical generation of variables from the data would not
require highly trained personnel; although the final
preparation and interpretation of the results should be
reserved for those individuals understanding the complete
capital budgeting system.

The information obtained from the model is based
on subjective estimates; therefore, the forecasts should
be reviewed and revised as new data and added experience
is gained for it is only by having rational estimates and
improving the ability to furnish them that will enable the
model to become a useful tool to aid in the effective

management of the company.

CHAPTER V

SUMMARY AND CONCLUSIONS

An investment involves suppositions about the
future, since by its nature an asset, to have value,
must yield benefits in future periods of time. The
decision is therefore subject to elements of uncertainty
inasmuch as future technological and economic events
cannot be forecasted with any great degree of preciseness.
Even though the investment decision is subject to future
events that cannot be objectively verified, a condition
of certainty is assumed when using the techniques currently
in use to evaluate capital investment opportunities. In
order to overcome this weakness an experimental method
(Monte Carlo) using subjective probability estimates and
random numbers was used in this study in an attempt to

consider uncertainty in an explicit form.

100

101

The hypothesis made is that a model (for capital
budgeting decisions), in which uncertainty is considered
explicitly, can be applied to actual situations in business
organizations with the conclusions furnishing useful
information in the capital budgeting decision process.

The model was applied to a limited number of actual
asset acquisition proposals in a variety of companies,
each representing a different industry. A range of values
and subjective probabilities therefor were obtained for
each of the five factors used in determining the internal
rate of return. These sets of values and probabilities
served as inputs to the computerized Monte Carlo model.

The data were obtained from individuals having experience
and a knowledge of the capital budgeting procedures being
used by each firm; the proposals analyzed were those being
considered currently by the business organizations
interviewed.

When the above data had been obtained, random numbers
were used to determine the value of each factor to be used
in the computation of the internal rate of return. Having
obtained each factor's value the internal rate of return
was then determined by use of a formula such as the

following:

102

Bl B2 Bn'I-S
C=(1«I-r)+(1-I-r)2 +...+ (1~I-r)n

Where C is the cost of the investment, B is the net
periodic cash benefit; S the salvage value in period n
and r the unknown rate of return that is to be solved for.
A hundred trials (computation of individual rates of
return) were made to obtain a range of rates of return
and the frequency of each. A probability equal to the
frequency of occurrence was then assigned to each rate of
return.

The model made use of the “internal rate of return
method” to evaluate the investment alternatives; however,
unlike the normal procedures used when computing the
internal rate of return, a condition of uncertainty is
assumed to exist.

The data required to apply the model were generally
available; however, where not readily available it was
obtainable with a relatively small effort on the part of
the organization. There was also a demonstrated willing-
ness to provide an estimate of a range of values and the

required subjective probabilities.

103

Generation of New Information

The results obtained yielded, in each case,
information which had not been explicitly considered in
the firms' evaluation of the expenditure proposals. For
example, where a single year payback had been the acceptance
criterion or standard, the analysis via the model demonstrated
that the firm could not only expect a payback period of less
than one year, but could also expect a 111%.rate of return
or greater having a probability equal to 50%. In another
case, where a uniform standard of acceptance had not been
established, an asset promised to return the required
investment in five years. However there was only a 6% prob—
ability that a positive rate of return would be received.
The reason for the limited probability was the uncertainty
surrounding the useful life of the asset.

This type of information aids in the evaluation of
the outcomes of predicted economic events. This is
possible as it furnishes information whereby an analysis
of the effect of factors on the rate of return and the
alternative outcomes of a commitment to invest funds can
be determined. The importance of duration of life, initial

cost, etc., as factors bearing on the rate of return and

104

the determination of the alternative outcomes of investment
of funds was demonstrated in Chapter IV. The availability
of this data enlarges the scope of the analysis so that it
is possible to compare the relative value of the possibility
of a substantial gain or loss against an alternative

investment opportunity that is relatively certain.

Effective Application

The model can best be applied where there is a
well managed capital budgeting program. The most critical
requirement for effective application is that of having
individuals with experience and knowledge of the
procedures used being required to furnish the range
of values and subjective probability estimated for each

factor required in computing the internal rate of return.

Existing Awareness of Uncertainty

In the particular firms visited there was an
awareness of the existence of uncertainty. The uncertainty
problem was met through subjective judgements and limited
quantification of data. The judgements were based on
past experience and a feeling as to future business

conditions. Quantification of data was in the form of

105

either making several estimates based on different assumed
levels of activity without attempting to indicate the
likelihood of occurrence or through a felt need to
anticipate a higher rate of return.
Incremental Cost of Applying the Model and Test
to Determine the Reliability of the Results

The incremental costs of applying the model, when
compared with applying the discounted present value methods,
was found to be an immaterial factor when considering the
relative merits of the results of the model. Limited
tests were applied to determine the number of trials
(individual computations of rates of return) necessary to
obtain reasonable results; one hundred trials were
concluded to be sufficiently large to produce dependable
results for the problem under study.
Improvement of Procedures Being Used
for Capital Budgeting

Furnishing information in the form of a range of
values for each factor and the subjective probability of
each will help to limit such practices as using an average
performance for each factor, submitting only values that

“guarantee“ acceptance of the project, and estimating

106

values that will be attainable 100% of the time. In other
words, the application of the model should encourage the
use of sound capital budgeting procedures. The method used
here requires specific managerial consideration of, and
specific statement of, feelings and expectations about
whether relevant events are or are not likely to occur,

and expression in finite form of judgements about factors
bearing on the capital budgeting decision. Such formulation
increases the likelihood of communication between
individuals as to what decision criteria are considered
important by managers responsible for the commitment of

corporate resources.

Aid to Unsolved Problems

Though the solution to each of the following is
not provided since it is beyond the scope of this study,
the information furnished in applying the model is useful
when attempting to solve the problems of limited capital,
and evaluating the quantifying attitudes toward uncertainty.
There have been suggestions in current literature as to
how these problems should be solved; however, it is
normally assumed that subjective probabilities are given.

The data used in applying the model will provide the sub—

107

jective probabilities for each factor used in the deter-
mination of the internal rate of return and the application
of the model will provide the probability that each rate
will occur; each of these probability estimates have

been suggested as being necessary to arrive at solutions

for the above noted areas.

Sound Judgement is Always Required

The application of the model will not replace sound
judgement, for the results cannot be better than the
judgement of the individuals furnishing the data. Only
through continual improvement of the subjective estimates
and refinement of the model will it become a useful tool
to aid management in meeting and evaluating the uncertainty
area as it concerns capital budgeting.

There was an awareness within each company interviewed
that an attempt to continually improve must be a policy of
management. The improvement not only should include the
application of new tools and techniques to furnish data
but also include all areaSincluded in the management of
capital budgeting with one of the most critical areas being
that of generating ideas for alternative uses of capital

funds.

108

Suggestion for Further Study

The assumption that rational subjective probability
estimates were obtained for the application of the model,
though accepted for this study, needs further analysis
and investigation. This may take the form of obtaining
posterior probabilities and also the comparison of actual
and forecasted results by the use of a post audit. These
two areas are the subject of anticipated studies to be

undertaken in the future.

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APPENDIX A

EXAMPLE CASE

The following information is used to demonstrate
the proposed use of the internal rate of return and a
simulation method. It is assumed that the model is
applied with the use of a hand calculator. The assumed

information of the case is as follows:

lst Year 2nd Year 3rd Year

Estimated cost $ 14,000

Estimated life - 3 years

Estimated net cash flows 8,050 $ 8,925 $ 9,020
Salvage value 0

Based on the above information the prospective rate of
return is 19%.

The decision whether to invest will be determined
when the rate of return is compared with the firm's cost
of capital, other alternative uses of funds, and judgement
factors such as an evaluation of risk inherent in project,
needs and goals of the organization.

The above analysis does not determine the likelihood
of obtaining the indicated 19% on the investment; it also

is limited in that the main factors causing the experienced

116

117

rate of return to vary from the forecasted rate have not
been isolated.

To overcome the above weaknesses, subjective
probabilities were obtained from individuals having the
responsibilities and experience in the area under study.
The following is the information required to determine
the rate of return and the likelihood of a given rate of
return being earned for this particular example.

Estimated Life of

 

 

 

 

 

 

 

Cost of Equipment Asset
Estimated Probability
Probability Cost Estimated Life
.10 $17,000 .20 2
.20 15,000 .70 3
.40 14,000 .10 4
.20 13,000
.05 12,000 1.00
.05 10,000
Estimated sales and cost figures:
Sales price per unit: $1.00
Costs (except for depreciation):
Units sold Variable Variable Variable
at $1.00 Costs Fixed Costs Fixed Costs Fixed
75,000 65¢ $20,250 65¢ $20,000 -64¢ $25,400
80,000 65 20,250 65 20,000 64 25,400
90,000 64 25,400 64 25,400 64 25,400
100,000 64 25,400 62 25,400 63 30,000
107,500 62 32,350 62 25,400 63 30,000
110,000 62 32,800 62 32,800 62 32,800
115,000 62 32,800 62 32,800 62 32,800
120,000 64 33,200 64 33,200 62 33,200
125,000 64 33,200 64 33,200 64 33,200

118

The fourth year is assumed to have the same sales and

cost estimates as the second year.

The following are the estimates of quantities

that will be sold over the life of the asset:

 

 

 

First Year Second Year Third Year Fourth Year
Prob- Items Prob- Items Prob- Items Prob— Items
ability, sold ability sold ability sold ability sold
.10 75,000 .10 80,000 .10 90,000 same as
.25 90,000 .25 90,000 .30 100,000 second year
.40 107,500 .35 110,000 .35 110,000
.20 110,000 .25 115,000 .20 120,000
.05 120,000 .05 120,000 .05 125,000
1.00 1.00 1.00

numbers from 0 to 99.
the subjective probability of each factor.
In the first and second year there
probability that 75,000 and 90,000

Numbers 0 - 9 for the first year's

The distribution of each variable is assigned

The numbers

assigned depend upon
For example:
is a 10% and a 25%
units will be sold.

probability and 10 -

34 for the second year are therefore assigned to each level

of units sold in their respective year.

The same procedure

was repeated for the remaining levels of sales in the first

and remaining years.

The same procedure was followed for

the estimated life and cost of the asset since these factors

also have a distribution of possible values.

In this

problem it is assumed that there were no inventories and

119

and thus the costs of production were the same as cost
of sales. As a result the expenditures were based on the
quantity of goods sold.

The next step is to refer to a table of random
numbers. Reading the numbers from the table will indicate
the level of sales, costs and estimated life, since the
corresponding number has been assigned to each factor.
Having obtained the required information, a rate of return
is determined. The following example will demonstrate the
pricing out procedure.

The period of three years, level of sales of
$90,000, $110,000 and $110,000; cost of $17,000 were
obtained from the numbers noted in the random table and
the number assigned to each factor. As was indicated

before, the expenditures are based on the quantities sold.

 

Period

__1_____2____3___
Revenue $90,000 $110,000 $110,000
Expenditures 83,000 101,000 101,000
Excess 7,000 9,000 9,000
Depreciation 5,666 5,666 5,666
Net income before taxes 1,334 3,334 3,334
Tax (assume 50%) ' 667 1,667 1,667
Net income 667 1,667 1,667
Plus non-cash expenses 5,666 5,666 5,666

Net cash flow $ 6,333 $ 7,333 $ 7,333

120

Discounted rate of return: 11%
Total net cash flow: $21,000
Total cost: $17,000

Life of Asset: Three years
Depreciation: $5,666

Fifty such trials were made. This then gave fifty
estimates of the rate of return which were then grouped
into a frequency distribution. The frequency distribution
was converted into an estimate of probability for each rate
of return as noted in Figure 13.

In the original presentation of the investment
proposal the asset acquisition promised a rate of return
of 19%.with an implied condition of certainty. The proposed
model indicates the likelihoods attaching to a range of
rates of return (Figure 13). For example: It is noted
that there is a 50%.chance of obtaining a 19% or better
return on the asset.

In addition, it was determined through a sensitivity
analysis that the main reason for a low rate of return
(there is a 10% Chance of obtaining less than an 8% return)
is due to an asset life of two years or less. For all of
the experiments that reported a return of 6% or less the

expected life was two years. The highest return obtained

with a life of two years was 16%.and this was a result of

121

FIGURE I3 - APPENDIX A

l.00

 

  
   

 

I5 20 25 30 35 4o 45 so

Anticipated Return

 

 

5
9

L L L
O 5 O
9 8 8

L
5
7.
o

L
0
7

L
5
6.

t

L L L L L L P L P L L L
0 5 O 5 O 5 O 5 O 5 O 5
6 5 4. 4 3 3 2 2 I I O.

5
66664 L $33 626263 663.62% .3 5.566666%

.00

I0

0% 5

122

a low required investment and fairly high total net cash
receipts. Of the rates of return of 26% and above the
main contributing factor was a low cost of the asset (mean
of under $12,000) and a life of three years and above.

The two main factors affecting the rate of return
are the estimated life of the asset and the cost of the
asset. The variation in revenue was not too important in
this problem since the majority of the costs were variable

in nature.

APPENDIX B

PROGRAM.PROCEDURES

The following is a detailed description of the
steps required to be taken to apply the model to asset
acquisition proposals when using a computer to process

the data.

Part I
Required steps - determination of:

I Estimated useful life
II Estimated cost of the asset
III Gross benefits
IV Operating expenses
V Asset replacement
VI Salvage value
VII Depreciation expense
VIII Net benefit from sale of assets

Part II

Determination of the yearly net cash flow (Source
of the information--Part I)

Gross Benefits:

Revenue from operations (1) xxxxx
Cost savings (1) xxxxx
Total Benefits: xxxxx (A)

123

124

Total Benefits: (continued) xxxxx (A)
Less Operating expenses xxxxx (B)

Net Cash Benefit before non-cash expenses and
taxes $ xxxxx

52% of a negative net Cash Benefit if B is

greater than A (xxxxx)
3
52% of Net Cash Benefits if A is greater than B xxxxx
Plus:

48% of the yearly depreciation (increase in

cash benefits from tax savings because of

the tax deductibility of depreciation

expense) xxxxx

Net Cash Benefits from Operations xxxxx
Plus:

Funds received because of a gain or loss on

the sale of an asset (2) xxxxx

Less:
Replacement of assets (3) (xxxxx)
Net Cash Benefits for a given Year xxxxx

The above would have to be repeated for each year
of the asset's useful life as determined in Step 1 of Part I.

(1) The particular project would be either type of
project but not both.

(2) Only a periodic item (arising when an asset is
replaced during the life of the project or at
the end of the asset's useful life.

(3) A periodic disbursement over the project's useful
life.

125

Part III

Determination of the internal rate of return—~an
example of the formula that may be used.

El 82 Bn + S
C = (1 + r) + (1 + r)2 + . . . + (l + r)n
C = Cost of the asset
B = Net cash flow
n = Estimated useful life
r = The rate of return to be determined
S = Salvage value
Part IV

Repeat the prior three parts for as many trials
as is wanted or required.

Part V
The final product:

1. Summary of the frequency of each rate of return.
2. Print out of the factors used in Part III and
the rate of return for use in sensitivity

analysis.

Detail of Part I

Step I-—Estimated useful life of the asset:

 

A. Input
Subjective Cumulative
Years Probability Probability
Example xxx .xx 9L .xx 96
xxx .xx .xx
xxx .xx x.xx

B. Machine

Compare:
1. Random numbers obtained from the program
determining random numbers.
2. The above cumulative probability.

C. Output

The appropriate estimated useful life obtained from
the comparison made by the machine. The life of the project,
so determined, will determine the number of yearly revenue
expense, etc. that has to be used in each case to arrive at
a rate of return.

Step II—-Asset cost (two possible forms):

Form l--Estimated cost (asset cost broken down into
parts with a cost range and likelihood given for each)-

 

 

 

A. Input
Cost Subjective Cumulative
Item Range Probability Probability
Press $ xxxx .xx %. .xx %
xxxx .xx .xx
xxxx .xx x.xx

126

Item

 

Chutes
Conveyor sections

Installation costs

Rearrangement costs

Contingency

B. Machine

127

Em:

$ xxx
xxx

$ xxx
xxx
xxx

$ xxx
xxx
xxx

$ xxxx
xxxx
xxx

Subjective Cumulative

Probability Probability

 

 

X.XX‘% x.xx
x.xx x.xx
.xx % .xx
.xx .xx
.xx x.xx
.XX‘% .xx
.xx .xx
.xx x.xx
.xx % .xx
I XX 0 XX
.xx x.xx

‘%

%

%

%

1. Compare the random numbers obtained from the

program with each assigned number noted above.

2. Sum the cost of each item determined from the
above comparison to obtain the total cost.

C. Output

The total cost of assets to be acquired.

Form 2--Total costs are given with no detail

breakdown.

A. Input

Cost

32.11.92

$ xxx
xxx
xxx

Subjective Cumulative

Probability Probability

 

.xx % .xx %

.XX .XX

.XX XOXX

128

B. Machine

Same as item 1 under machine above.

C. Output

Cost of the asset to be used.

Step III-—Gross Benefits (two forms: revenue producing
and cost savings)

Form 1-—Revenue producing

A.

C.

 

 

12222
Subjective Cumulative
Amount Probability Probability
Revenue $ XXXX‘ .xx %. .xx %
xxxx .xx .xx
xxxx .xx x.xx

(Note: There may be more than one source with
various likelihoods.)

Machine

Compare and select one of each of the above
for each year of the asset's life. There will,
in some cases, be more than one source of
revenue; therefore, the machine will have to
select one revenue amount from each source

and then sum these items. The total will then
be used in arriving at the yearly net cash
benefits.

Output

Total gross benefits to be received for each
year of the asset's useful life.

129

Form 2--Cost savings (The data will be in the same
form as the revenue producing case).

Step IV--Operating Cost

 

 

A. Input
Subjective Cumulative
Range Probability Probability
Operating
costs $ xxx .xx % .xx %
xxx .xx .xx
xxx .xx x.xx

B. Machine

Compare and select one of each of the above for
each year of the asset's useful life. There will
be, in some cases, more than one source of expense;
therefore, the machine will have to select one
expense amount from each source and then sum

these items.

C. Output

The total operating expenses to be incurred for
each year of the asset's useful life.

Step V--Asset Replacement

 

 

A. Input
Subjective Cumulative
Range Probability Probability
$xxxx .xx % .xx %
xxxx .xx .xx

XXXX . XX X . XX

C.

Step VI--Sa1vage

A.

B.

Machine

130

Comparison of the assigned numbers and the random
numbers and selection of the amount to be used.
(There may be more than one source; therefore, a
total figure will have to be arrived at.)

Output

The total dollar amount and the year the expenditure
applies to.

(Note:

Input

(Note:

Output

These will not be yearly figures in most
cases. They may take the form of an
expenditure every fifth year, etc.)

 

 

 

Value
Estimated Subjective Cumulative
Amount Probability Probability
$xxxx .xx %. .xx %
xxxx .xx .xx
xxxx .xx x.xx

There may be more than one asset disposed
of; therefore, a total salvage value will
have to be determined from the estimated
amounts and likelihood of each asset. Also
the salvage value may be different depending
upon the year of retirement.)

The total salvage value selected and the year it
applies to.

131

Step VII--Depreciation

A.

Input

1. Bases of depreciation - cost of the asset as
determined by the machine in Step II of Part I.

2. Estimated life for depreciation purposes will
be the tax life — this figure will be given.

Machine

1. Method to be used - the straight line method
(cost + tax life) equals yearly depreciation.

2. The time period that the depreciation is to be
taken over life of project:

a) The tax life

or
b) The useful life of the project, whichever
is less.

3. A depreciation amount will have to be determined
for each asset acquired since they will have
different tax lives, cost ranges and likelihoods.

4. The accumulated depreciation taken on each asset
class will have to be maintained for the use in
the determination of the gain or loss on sales
of the asset.

Output

The output is the total depreciation expense for
each year. This amount will be the total taken
for each year adjusted for replacements and items
retired, since the retirement of the asset would
reduce the years depreciation amount and a
replacement will increase the annual charge.

132

Step VIII-~Net Benefit from the sale of the asset (net
after taxes)

How determined:

Net book value of asset-cost

 

 

 

(determined in Step 1) $ xxx
Less
Accumulated depreciation (determined
in Step 8) (xxx)
xxx (1)
Value of asset at date of sale (Step 6) xxx (2)
Gain on sale of asset (if 2 >'l) xxx
Loss on sale of asset (if 1 > 2) (xxx)

 

Tax effect:

If gain on sale Gain x 25% tax due

If loss on sale Loss x 25%

tax benefit

Total benefit:

 

If ain M
Salvage value (Step VI) xxxx xxx
if gain deduct tax (xxx)
if loss add tax benefit xx
Total net cash benefit from sale
of asset xxx xxx

 

 

 

JOB,4
SCOPE
FTN,L

700
5000

APPENDIX C

COMPUTER PROGRAM

60lI7,MOCSER,S.WOODFIELD,LEON w.

5.l008

ex:*

PROGRAM MOCSER

DIMENSION ESTLIFE(IOO),~ESTCOST(I00),R(I00),SALV
IAGE(I00), DEPRACC(I00), PROFITA(I00), SALEGAIN(I00),
2XNETBV(I00), ESTCOSTL(20), ESTCOSTB(20), esrcoer(26
3), ESTCOSTY(20) GRYRREV(20), 0THERINC(20), 0PEREXYR(
uz6L 0THEREXP(20), CASHBBTX(20), CASHBATX(20), BENOPE
5R(26), NETCSHBN(26), FNC(2I), REPLACE(20), DEPREXPB(2
60L DEPREXPY(20), DEPREXPEI20),DERREXP(20)

DO 700 M=I ,IOO

ESTLIFE(M)=0. o

ESTCOST(M)=0.0

R(M)=o.o ‘

SALVAGE(M)=0.0

DEPRACC(M)=0.0

PROFITA(M)=0.0

SALEGAIN(M)=0.0

XNETBV(M)=0.0

PRINT 5000

FORMAT(HH)

DO |000N=I, I00

DO70I J=I, 2o

ESTCOSTL(J)
ESTCOSTB(J)
esrcoer(J)
ESTCOSTY(J)
GRYRREV(J)=
0THERINC(J)
OPEREXYR(J)
OTHEREXP(J;

)
)

0.0
O.

OO

C 00000 o(DCDCD

CASHBBTX(J
CASHBATX(J
BENOPER(J)
NETCSHBN(J
FNC(J)=O. o
REPLACE(J)=0.0
DEPREXPB(J)=0.0
DEPREXPY(J)=0.0

.0

IIOIIIIIIIIIIOIIII

0 0000000

133

C

70I

CW (13% 0\ U1? VON

134

-I
o)
N)

IF(RN—.SS),
ESTLIFE(N)

GO TO 5
ESTLIFE(N)

RN=RANF(-I
IF(RN .05)
ESTCOSTB(J

60 TO I0

IF(RN .95)

ESTCOSTB(J

GO TO I0

ESTCOSTB(J

ESTCOSTL(J

RN: RANF(-I
IF(RN- .34)

ESTCOSTE(J

)
J

60 TO I5
ESTCOSTE(J =3I
RN=RANF(-l)

IF(RN-.02)I6,l7,l7
esrcosrv(J)=2zooo

GO TO I20

IF(RN-.07)I8,I9,I9
ESTCOSTY(J)=I7I60

60 TO I20

IF(RN-.97)20,2l,2l
ESTCOSTY(J)=I56OO

GO TO I20

ESTcosrv(J)=Iuouo
ESTCOST(N)=ESTCOSTB(J)+ESTCOSTL(J)

vy—

I+ESTCOSTE(J)+ESTCOSTY(J)

C OMPUTE GROSS BENEFITS

22

23
24

25

J=I
RN=RANF(-I)
IF(RN-.l0)22,23,23
OTHERINCIJI=h3680
60 T0 30
IF(RN-.2o)2h,2s,25
OTHERINc(J)=3u9hu
GO T0 30
IF(RN-.uo)26,27,27

26

27
28

29
30
3|

32
33

3h
35

36
37

38
39
40

AI
42

#3
Ah

#5
A6

#7
A8
50

SI
52

53

54
55

56

OTHERINC(J)=26208
GO TO 30
IF(RN-.90)28,29,29
0THER|NC(J)=2I840
GO'T0'30
0THERINC(J)=IS720
J=J+I

RN=RANF(-I)
IF(RN-.I0)3I,32,32
OTHERINc(J)=52h20
GO TO 39

IF(RN-.2o)33.3h,3u
OTHERINC(J)=h3680
GO TO 39
IF(RN-.uo)35 36,36
0THERINC(J)=2 62I o
60 TO 39
IF(RN-.80)37. 38, 38
OTHERINC(J)=2 I84 no
GO TO 39
OTHERINc(J)=|7u72

J=J+I
RN: RANF(- I)
IF(RN- l0)40,4 I
OTHERINC(J)=6I II
60 T0 52
IF(RN- 20)uz,
OTHERINc(J)=5
60 T0 52
IF(RN- .3o)u,
OTHERINciJIR
GO TO 52
|F(RN- so)u6,
OTHERINC(JI=3
GO TO 52
IF(RN- 6o)h,
OTHERINc(J)3
GO TO 52
IF(RN-. 90)50, 5|
OTHERINc(J)= 262Io
60 T0 52
OTHERINC(J)=IS720
J=J+I

DO93J=h,20 I

RN: RANF(- II

IF(RN- .03)535 (Sh
OTHERINCIJI=6I 50
60 TO 93

IF(RN .05)55, 56, 56

OTHERINC(J)=5 Zhl 6
60 TO 93
IF(RN-.08)57 58,58

135

‘ OTHER I NC( J )=143680

GO TO 93
lF(RN-.|3)59,60,60
OTHERINC(J)=393|0
GO TO 93

IF(RN- l5)6l, 62, 62
OTHERINc(J) =30576
GO TO 93
IF(RN-.23)63,6u,6h
OTHERINC(J)=262I0
GO TO 93
IF(RN-.25)65,66,66
OTHERINC(J)=IS720
GO TO 93

IF(RN- .28)67, 68, 68
OTHERINc(J)=5 7852
GO TO 93

IF(RN- .30)69, 70,70
OTHERINC(J)=5 06I6
GO TO 93
lF(RN-.33)
OTHERINC(

IF(RN- 38
OTHERINC(

'fl
A
:0
Z
I
J?
O
V Lv Lv LV (—

GO TO 93
|F(RN- 56)8I, 82, 82
OTHERINc(J)= 56952
GO TO 93
lF(RN-.60)83,8h,8h
OTHERINC(J) =h88I6
GO TO 93

IF(RN- .66)85, 868
OTHERINc(J)- =u0680
GO TO 93
lF(RN-.76)87,88,88
OTHERINC(J)=366I2
GO TO 93

IF(RN- 80)89, 90, 9o
OTHERINc(J) =28h76
GO TO 93

136

90
9|

92
93

95
96

97
98

99

IOO

137

IF(RN-.96)9I,92,92
OTHERINC(J)=2th8

GO TO 93
OTHERINc(J)=IuéuO
CONTINUE

OO9AJ=I,2O,I
GRYRREV(J)=OTHERINC(J)
CONTINUE

OMPUTE OPERATING EXPENSE
J=l

OTHEREXP(J)=I52I6
DO97J=2,20 I
OTHEREXP(J5=A308
CONTINUE

DO99J=|,20 I
OPEREXYR(J5=OTHEREXP(J)
CONTINUE

OMPUTE ASSET REPLACEMENT
DOIO0J=|,|O,I
REPLACE(J)=0.0

CONTINUE

J=ll

REPLACE(J)=32lO
DOIOIJ=|2 20,I
REPLACE(J$=O.O

CONTINUE

C 0MPUTE SALVAGE VALUE

l02

l03
IOh

IOS
l06

|O7

l08

l09

IIO

RN=RANF(-I)
IF(PN-.3A)I02,IO3,IO3
SALVAGE(N)=I50750

GO TO |06
IP(RN-.67)IOA,I05,I05
SALVAGE(N)=IOOSOO

GO TO I06
SALVAGE(N)=50250
OMPUTE DEPRECIATION EXPENSE
J=|
ADAMB=ESTCOSTB(J)/IS
DOIO7J=I,I5,I
DEPREXPB(J)=ADAMB
CONTINUE

J=|
ADAMY=ESTCOSTY(J)/l5
DOIO9J=|,|5,|
OEPREXPY(J)=AOAMY
CONTINUE

J=l
ADAME=ESTCOSTE(J)/6
DOIIIJ=I,6,|

138

DEPREXPE(J)=ADAME

CONTINUE

00II3J=7,20,I

0EPREXPE(J)=0.0

CONTINUE

00II5J=I6,20,I

DEPREXPB(J)=0.0

CONTINUE

DOII7J=I6,20,I

DEPREXPY(J)=0.0

CONTINUE

00II9J=I,20,I

DEPREXP(J)=0EPREXPB(J)+0EPREXPY(J)+

I0EPREXPE(J)
II9 CONTINUE
C OMPUTE NET CASH BENEFIT FROM SALE OF ASSET
J: I
lF(ESTLlFE(N)-l0)l2l, I2I, I22

I2I DEPRACC(N)= 0EPREXPB(J)*I6+0EPREXPY(J)*

IIO+DEPREXPE(J)*6

00 TO I23

I22 J=I
DEPRACC(N)=ESTCOSTB(J)+ESTCOSTY(J)+

IESTCOSTE(J)

I23 XNETBv(N)- -ESTCOST(N)- 0EPRACC(N)
PROF|TA(N)= SALVACE(N)- XNETBv(N)
IF(SALVAGE(N)- XNETBV(N»Izu, I2h, I25

IZh SALEGAIN(N)= SALVAGE(N)+(PROFITA(N)*. 25)
GO TO I26

I25 SALEGAIN(N)= SALVAGE(N)-(PROFITA(N)*.25)

I26 00802J= I, 20, I
CASHBBTX(J) =GRYRREV(J) -0PEREXYR(J)
CASHBATX(J)=0. 52*CASHBBTX(J)
BENOPER(J)=CASHBATx(J)+0.h8*0EPREXP(J)
lF(J-ESTLIFE(N))800,8OI,80l

800 NETCSHBN(J)=BENOPER(J)-REPLACE(J)

00 TO 802

80l NETCSHBN(J)=BENOPER(J)-REPLACE(J)+SALEGAIN(N)

802 CONTINUE
R(N)=0.0
SPNC=0,0
N2=ESTLIFE(N)+|
N3: ESTLIFE(N)

FNC(|)=-I .0*ESTCOST(N)
00 803 L: 2, N2
803 FNC(L)= NETCSHBN(L-l)
00 2003 J=l, N2
2003 SFNC= SENC+FNC(J)
IF(SFNC)2009, 2I02,2OOA
2009 00 2052 J=I,7

cow O\U'| «PW N '—

139

2050 R(N)=R(N)+O.l**J
SFNC=0,O
00 205I J=I,N2
M=N3+l-J
205I SFNC=SFNC+FNC(J)*(l.0+R(N))**M
IF(SFNC)2052,2050,2050
2052 R(N)=R(N)-O.I**J
R(N)=R(N)*I00.0+0.0005
GO TO 2I02
2009 00 20I2 J=I,7
20I0 R(N)=R(N)-O.l**J
SFNC=0.0
00 20II J=I,N2
M=N3+l-J
20II SFNC=SFNC+ENc(J)*(I.0+R(N))**M
lF(SFNC)20I0,20lO,20I2
20I2 R(N)=R(N)+O.l**J
R(N)=R(N)*IO0.0-0.000S
2I0I FORMAT(*3RATE = *F8.3* , ESTLIFE = *F2.0*, ESTCOST =
I*F6.0*, SALVAGE = *F6.0* , OEPRACC = *F6.0* , SALEGA
2IN = *F7.0)
2I02 PRINT 2I0I,R(N),ESTLIEE(N),ESTCOST(N),SALVACE(N),OEP
IRACC(N),SALECAIN(N)
LIFE=ESTLIFE(N)
PRINT 2I03
2IO3 FORMAT(IHO,6X,*YEAR*|6X*GRYRREV*ISX*OPEREXYR*I6X*DEP
IREXP*I6X*REPLACE*I6X*NETCSHBN*)
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APPENDIX D

MISCELLANEOUS INFORMATION

Steps Taken While at Individual Company

The following steps were taken in gathering the

necessary information:

A.

A tour of the business was taken in order to
obtain a knowledge of the type of organization
and some of its problems.

Individuals responsible for decisions were
interviewed in the capital budgeting area. The
purpose of this was to determine the policies

and organizational structure. (Refer to the list
of general and specific areas determined.)

Some of the current asset acquisitions were
reviewed and investigated with the documents

and working papers being traced from the inception
to completion of the project. The purpose of this
was to gain additional information concerning the
policies and organizational structure.

The projects studied were obtained from either
projects just currently being completed and/or
projects for which approval was just given the
go-ahead.

The data gathered was applied to the model.

The data was then summarized and interpreted.

The organizations were revisited and the results
of the tests were reviewed.

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The following general areas were investigated in

order to gain an understanding of the firm and its

organization and procedures:

A.

K.

What are the sources of the ideas for the
proposed projects.

Is there a long range capital budgeting plan
which is related to the overall goals of the
firm.

Is a yearly (short term) budget prepared
listing the proposed projects to be undertaken
by the firm.

What measurement is used to determine the worth
of each project (payback, average rate of return,
etc.).

What standards are required to be met before
approval is given (cost of capital, payback

period, etc.).

What is the system of control over authorized
outlays.

Is there a review and comparison of actual and
forecasted results.

What are the policies for retirement of the asset.

Obtain a knowledge of forms and procedures used by
the organization.

Does there seem to be an understanding of the
economics of capital budgeting.

How is uncertainty currently being accounted for.

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In order to apply the model the following specific
factors were determined for each project that was reviewed:
A. Estimated cost of the project.
B. Estimated life of the asset.

C. Estimated cash proceeds or cost savings and year
of receipt.

D. Estimated operating costs (fixed and variable) and
year of expenditure.

E. Estimated salvage value.
For each of the above, the range of values and
subjective probability was determined.
Depending upon the nature of the project, other
factors such as production capacity, share of the market,

were added to the above list.

APPENDIX E

PROPOSED LETTER

The following letter was sent to each firm
indicating the purpose of the study. Introductions were
made previously through a faculty member and through
appointments at the several companies. This letter was
presented to each firm requesting a written description

of the analysis to be made.

Dear Sir:

The following will present, in general terms, a
description of what is involved and the estimated time
required for the study.

Whenever an individual is considering the purchase
of an asset, an assumption is made that there is a
possibility of a future net benefit to be received. It is
common to estimate the required operating expenditures and
future benefits. Estimates are also made as to the cost
and life of the project. After determining this information,
through some means such as a feeling, determination of a
rate of return, a minimum recovery period of the investment,
past experience, or a combination of these a decision is
made to accept or reject the proposal.

It has been said that the only thing that is certain
is death and taxes. The decision to purchase assets is
subject to uncertainty concerning future events; however, in
trying to determine when to acquire an asset the problem is

143

144

treated by many as if we were in a state of certainty. For
example: A manager will ask the engineering department to
estimate the cost of the project; the sales manager will

be asked to estimate the sales and the accountant the
operating costs. These will then be combined and through
the experience of management a judgement will be made.

The single sales and cost figures may not be enough to
make the decision and so each department may be asked to
furnish the most likely, highest possible and lowest

range in order to shed some light on the problem. But

even now the data, in most cases, will be handled as if

the results were certain. In some cases the results may
be adjusted because of experience when the forecasts seem to
be a little high or low but by how much?

I hope to determine that a method (for capital
budgeting) in which uncertainty is considered explicitly
can be applied to actual situations with the conclusions
furnishing useful information. I propose to become
acquainted with the capital budgeting decision making
process of your firm, apply a model to some investment
proposals you are now completing or have currently approved,
analyze the results, make suggestions as to possible uses
of the data obtained and attempt to indicate the advantages
and disadvantages of the proposed method when compared with
methods currently being used.

While at your organization I would like to approach
the problem in the following manner:

1. Take a tour of your organization in order to
obtain a knowledge of the organization and a
feeling for some of the problems.

2. Interview individuals responsible for decisions
and making estimates in the capital budgeting
area.

3. Review and investigate some of the current asset
acquisitions tracing the documents and working
papers from the inception to completion of the
project.

145

4. Select some projects to be studied from the
currently approved projects or those currently
being completed. (These projects would then be
used in an attempt to apply the model I will be
using.) .

5. After having studied the projects and applied the
model the results would be summarized and discussed
with you.

In general terms; I will be attempting to determine
the factors that affect the decision such as cost of the
project, estimated operating cost, estimated revenue or
cost savings, life of the asset, etc. These required items
will normally already be available. Using this information
I would then attempt, by interviewing each individual who
has had experience in each area and helped to furnish an
estimate of each factor, to determine a range of possible
values and the likelihood of each. After having obtained
this data it will be worked with, the result being, at a
minimum, an estimate of the internal rate of return and
the likelihood of each.

It is realized that this will be subjective in
nature and the data will be no better than the judgements
made; however, it is felt that these can be made. A quote
by Joel Dean, a noted author and teacher, may best indicate,
in general, what I hope to accomplish: “Adjustments to
allow for uncertainty may be challenged as nothing more
than guesses. Perhaps they are. But even so, they are
guesses that must be made, and will be made, either
explicitly or implicitly. Failure to apply the probability
adjustment does not enable management to avoid the problem;
it merely transfers the guess element in a disguised form
to some other stage of the decision making processi" It is
my hope that this adjustment can be brought out in an
explicit form and the results, at a minimum, being useful
to management in attempting to arrive at solutions to
their capital budgeting problems.

It is difficult to suggest the time that will be
required while at your organization; however, it is
estimated that the minimum would be one week with the
maximum of two. The cost to you would involve the time

146

required in interviewing your personnel and also any
inconvenience created by my presence within your
organization. In return, it is felt that some benefit

will be received by your organization; a minimum being

an exchange of ideas which may help in the capital budgeting
area. I am sure that from this experience I will gain a

better understanding of business operation and the problems
involved.

Very truly yours,

IIHIIIIIIIHI

980

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