Title: Financial Analysis, Planning and Forecasting Theory and Application
1Financial Analysis, Planning and
Forecasting Theory and Application
Chapter 12
Capital Budgeting Under Certainty
 By
 Alice C. Lee
 San Francisco State University
 John C. Lee
 J.P. Morgan Chase
 Cheng F. Lee
 Rutgers University
2Outline
 12.1 Introduction
 12.2 Cashflow evaluation of alternative
investment projects  12.3 Alternative capitalbudgeting methods
 12.4 Comparison of the NPV and IRR method
 12.5 Different lives
 12.6 Equivalent Annual NPV and Equivalent Annual
Cost  12.7 Capital rationing decision
 12.8 Summary
 Appendix 12A. NPV and breakeven analysis
 Appendix 12B. Managers views on Alternative
capitalbudgeting methods  Appendix 12C. Crossover rate
312.2 Cashflow evaluation of alternative
investment projects
 (11.18)
 Rt NtPt Ntdt WSMSt It,
(12.1)  where
 Rt Revenue in period t,
 NtPt New equity in period t,
 Ntdt Total dividend payment in period
t,  WSMSt Wages, salaries, materials, and
service payment in period t,
 It Investment in period t.
412.2 Cashflow evaluation of alternative
investment projects
 Annual AfterTax Cash Flow
 ICFBT  (ICFBT  ?dep)t
 ICFBT (1  t) (dep)t,
(12.2)  where
 ICFBT Annual incremental operating cash
flows,  t Corporate tax rate,
 ?dep Incremental annual depreciation
charge, or the annual depreciation
charges on the new machine less the
annual depreciation on the old.
512.2 Cashflow evaluation of alternative
investment projects
 ICFBT ?Rt  ?WSMSt.
(12.3)  (12.4)
612.3 Alternative capitalbudgeting methods
 Accounting rateofreturn
 Internal rateofreturn
 Payback method
 Net present value method
 Profitability index
712.3 Alternative capitalbudgeting methods
TABLE 12.1 TABLE 12.1 TABLE 12.1 TABLE 12.1 TABLE 12.1
Year A B C D
0 100 100 100 100
1 20 0 30 25
2 80 20 50 40
3 10 60 60 50
4 20 160 80 115
812.3 Alternative capitalbudgeting methods
 (12.5)
 where
 APt Aftertax profit in period t,
 I Initial investment
 N Life of the project.
912.3 Alternative capitalbudgeting methods
 (12.6)
 where
 CFt Cash flow (positive or negative) in
period t,  I Initial investment,
 N Life of the project.
1012.3 Alternative capitalbudgeting methods
1112.3 Alternative capitalbudgeting methods
1212.3 Alternative capitalbudgeting methods
Project Initial Outlay Present Value of Cash Inflows NPV PI
A 100 200 100 2
B 1000 1300 300 1.3
1312.4 Comparison of the NPV and IRR method
 Theoretical criteria
 Multiple RatesofReturn
 Reinvestment Rate Problem
 Practical perspective
1412.4 Comparison of the NPV and IRR method
 Fig. 12.1 NPVs of Projects A and B at different
discount rates.
1512.4 Comparison of the NPV and IRR method
Year
0 1 2
Cash Flow 50 750 800
1612.4 Comparison of the NPV and IRR method
IRR 0.1557 or 12.84.
1712.4 Comparison of the NPV and IRR method
Year
0 1 2
Cash Flow 100 250 160
1812.4 Comparison of the NPV and IRR method
Year Year Year Year Year
Project 0 1 2 3 NPV
A 100 50 100 500 380.2537
B 200 600 100 50 451.02269
C 300 100 700 100 418.49945
AB 300 650 200 550 831.27505
BC 500 700 800 150 869.52214
AC 400 150 800 600 798.75182
TABLE 12.2a
gtIRR
A 1.10438
B 2.18184
C 0.76360
A 1.67275
BC 1.19227
AC 0.87172
1912.5 Equivalent Annual NPV and Equivalent Annual
Cost
 Mutually Exclusive Investment Projects with
Different lives
Year Project A Project B
0 100 100
1 70 50
2 70 50
3 50
2012.5.1 Mutually Exclusive Investment Projects
with Different lives
 NPV(N,t) NPV(N)(1 H H2 ... Ht).

(12.10) 
 HNPV(N,t) NPV(N)(H H2 ... Ht Ht1).

(12.11) 
 NPV(N,t)  (H)NPV(N,t) NPV(N)(1  Ht1),
2112.5.1 Mutually Exclusive Investment Projects
with Different lives
2212.5.1 Mutually Exclusive Investment Projects
with Different lives
 For Project A
 For Project B
2312.5.1 Mutually Exclusive Investment Projects
with Different lives
 (12.13)
 where the annuity factor is
 1  (1 K)N/K.
24Equivalent Annual Cost
 NPV(N) K NPV(N,8) Annuity Factor

(12.14)  NPV(N) C Annuity Factor
 (12.15)
 C K NPV(N,8)
(12.16) 
 (12.17)
25Equivalent Annual Cost
 C565.47
 NPV (N, 8) 1749.47(10.1)4 / (10.1)41
5654.71 
 C K NPV (N, 8) 0.1 5654.71 565.47
2612.6 Capital rationing decision
 Basic concepts of linear programming
 Capital rationing
2712.6.1 Basic Concepts of Linear Programming

 Maximize (or minimize) Z c1X1 c2X2 ...
cnXn,  Subject to
 a11X1 a12X2 ... a1nXn ?(?) b1,
 a21X1 a22X2 ... a2nXn ?(?) b2,
 . .
 . .
 . .
 am1X1 am2X2 ... amnXn ?(?) bm,
 Xj ? 0, (j 1, 2, ..., n).
2812.6.2 Capital Rationing
Year Year Year Year Year Year Year
Project Project 0 1 2 3 4 5
X X 100 30 30 60 60 60
Y Y 200 70 70 70 70 70
Z Z 100 240 200 400 300 300
Investment NPV
X 65.585
Y 52.334
Z 171.871
Year 0 Year 1 Year 2
300 70 50
2912.6.2 Capital Rationing
 Maximize V 65.585X 52.334Y 171.871Z
0C 0D 0E 
 100X 200Y 100Z C 0D 0E 300.

 30X  70Y 240Z  C D 0E 70,

 30X  70Y 200Z 0C  D E 50.
3012.6.2 Capital Rationing
 X ? 1, Y ? 1, Z ? 1.

 X 1.0, Y 0.6586, Z 0.6305.
Funds Constraint Shadow Price
1st period 0.4517
2nd period 0.4517
3rd period 0.0914
3112.7 Summary
 Important concepts and methods related to
capitalbudgeting decisions under certainty were
explored in this chapter. Cashflow estimation
methods were discussed before alternative
capitalbudgeting methods were explored. A
comparison of the NPV and IRR methods was
investigated in accordance with both theoretical
and practical viewpoints. Issues relating
different project lives were explored in some
detail. Finally, capitalrationing decisions in
terms of linear programming were discussed. In
the next chapter, issues relating to capital
budgeting under uncertainty will be explored. In
Chapter 14, the leasevs.buy decision will be
investigated.
32Appendix 12A. NPV and breakeven analysis
 (12.A.1)
 where
 NPV(k) Net present value of the project
discounted at costofcapital rate k  R(t) Stream of cash revenues at time
t  C(t) Stream of cash outlays at time t
 T Investment time horizon
 ? Continuously compounded discount
rate  which is equal to loge(1 k)
33Appendix 12A. NPV and breakeven analysis
 (12.A.2)
 where
 R RDTE costs,
 I Total initial outlay on production
facilities,  A Time up to the onset of production.
34Appendix 12A. NPV and breakeven analysis

 YQ Y1Qb
(12.A.3)  where
 Q Number of aircraft produced
 YQ Cumulative average production cost
for  Q aircraft produced
 b log (?)/log(2)
 ? Learning coefficient, which
remains  constant over all Q
 Y1 First unit cost of production.
35Appendix 12A. NPV and breakeven analysis

 TC(t) Y1Q(t)(1b)
(12.A.4) 
 (12.A.5)

 Q(t) (t  A)N.
(12.A.6)
36Appendix 12A. NPV and breakeven analysis

 C(t) (1  b)Y1(t  A)bN(1b)
(12.A.7)  for
 A 42,
 B 0.369188,
 Y1 100 million,
 t gt A.
37Appendix 12A. NPV and breakeven analysis
 (12.A.8)
 where
 kj Effective annual aftertax cost per
dollar of the jth source of funds  Wj Proportion of the jth source of funds
in the longrun capital structure.
38Appendix 12A. NPV and breakeven analysis

 k 0.3kd 0.7ke
(12.A.9)  where
 kd aftertax cost of debt, and
 ke aftertax cost of equity.
39Appendix 12A. NPV and breakeven analysis
 (12.A.10)
 where
 D dividend per share,
 P Net proceeds per share after flotation
costs,  g Average annual compound growth rate
40Appendix 12A. NPV and breakeven analysis
 R(t) PN for t gt A,
(12.A.11)  (12.A.12)
 where
 tx Effective tax rate on corporate profits
 for Lockheed, and
 ? Discount rate.
41Appendix 12A. NPV and breakeven analysis
 Fig. 12.A.1 (From Reinhardt, H. E., Breakeven
analysis for Lockheeds Tri Star An
Application, Journal of Finance 28 (September
1973) 830. Reprinted by permission.)
42Appendix 12B. Managers views on Alternative
capitalbudgeting methods
 In an attempt to determine exactly what
tools were needed by practitioners and what
methods they were currently using in capital
budgeting, Mao (1970), Hastie (1974), Fremgen
(1973), Brigham and Pettway (1973), Shall,
Sundem, Geijsbeek (1978), and Oblak and Helm
(1980) conducted surveys and field studies of
companies. The papers that emerged from these
studies provide great insight into the gulf that
exists between theory and practice, and attempt
to explain the reasons for this gulf.  Mao (1970) in Survey of Capital Budgeting
Theory and Practice, specifically examines three
areas of capital budgeting and the disparity
between theory and practice in each area. He
first considers the objective of financial
management, which, according to theory, is to
maximize the market values of the firms common
shares. Price per share is, according to theory,
a function of its expected earnings, the pure
rate of interest, the price of risk, and the
amount of risk as measured by covariance between
its return and other returns. Of course, current
theory does not provide any allencompassing
criteria by which to choose between alternative
time patterns of share prices within the planning
horizon, so the businessman has no way to
accurately implement plans to increase share
price.
43Appendix 12B. Managers views on Alternative
capitalbudgeting methods
 Nevertheless, most executives interviewed
implied that maximization of the value of the
firm was their goal, although they phrased the
idea in more operationally meaningful terms.
However, in a break from theory, most executives
didnt consider diversification by investors as
having much impact on the value of the firm.
According to theory, in a portfolio context only
the nondiversifiable risk is relevant. While the
major institutional investors, with large staffs
of investment analysts, may fit into this
portfolio context, many other investors will not.
The executives saw consistent growth as a more
important factor determining share value.  Mao next considered the theory and practice
of risk analysis. The theoreticians measure risk
by the variance of returns. Mao suggests, and I
agree, that semi variance is a better measure of
risk because it measures only downside risk.
Management will not see the possibility of excess
returns as a risk, but will focus on the risk of
failing to earn an adequate return. The
executives interviewed also emphasized downside
risk and one called the chance of excess returns
a negative risk (a sweetener). Those
interviewed also expressed risk as a danger of
insolvency when a large amount of capital was to
be invested.
44Appendix 12B. Managers views on Alternative
capitalbudgeting methods
 Theory recommends either of two methods for
incorporating risk into investment analysis the
certaintyequivalent approach and the
riskadjusted discountrate approach. These two
approaches will be explored in Chapter 13. When
more than one investment may be made, the theory
advocates the use of the portfolio approach.  The practitioners depended in general on a
riskadjusted discount rate approach to
incorporate risk, although their actual methods
may be more rudimentary than the purely
theoretical approach dictates. Consideration is
given to the human factors of enthusiasm and
dedication to the project, qualities that are
nonquantifiable. Interviews also disclosed a
definitional difference between theorists and
practitioners about the word diversification. In
theory, every project should be evaluated in
terms of its covariance with other projects in
the portfolio. In practice, diversification is a
much more subjective, longrange process where
only major activities and their impact on
diversification are considered.
45Appendix 12B. Managers views on Alternative
capitalbudgeting methods
 Mao next revives a topic considered earlier
how to measure returns on projects. Theory
immediately discounts payback period and
accounting profit in favor of internal
rateofreturn and net present value. Interview
results show that only two of the eight companies
use Internal RateofReturn alone, whereas six
use payback and accounting profit alone or in
conjunction with internal rateofreturn.
Theorists have advanced two explanations for this
incongruence. First, internal rateofreturn and
net present value do not consider the effect of
an investment on reported earnings. Stability of
estimated EPS is important to management and
investors alike, and these two criteria do not
give management an indication of expected
stability of earnings. Many companies neglect
the netpresentvalue method because of the
extreme difficulty of determining the appropriate
discount rate. Individual company
characteristics also determine, to a large
extent, which measurement criteria are most
appropriate. Lastly, Mao recommends types of
research that can make theory more useful and
meaningful to practitioners.  K. Larry Hastie (1974), himself a
practitioner, also tries to give the academic
world some advice on how to better aid the
businessman. According to Hastie, in One
Businessmans View of Capital Budgeting, what is
needed is not refinement or multiplication of
measurement techniques but a reevaluation of the
assumptions inherent in the capitalbudgeting
process.
46Appendix 12B. Managers views on Alternative
capitalbudgeting methods
 Hastie outlines the major problems
practitioners face in capital budgeting. First,
most companies are limited by capital rationing,
so the problem becomes not one of finding
adequate projects, but of choosing from among the
acceptable projects. Theory offers no means of
ranking projects with different risks, strategic
purposes, and quality of analytical support.
Ranking per se is not an adequate selection
method unless the more qualitative criteria can
somehow be incorporated into the process.  Judgments enter into any process in which
uncertain profits must be estimated. Hastie
highlights two types of errors in judgment that
can lead to failure to achieve expected returns
on projects. The first is caused by excessive
pessimism or optimism, with only the second
posing a serious problem. Overpessimism is akin
to upside risk in that the company will not
fail to meet its goal. Overoptimism is caused by
poor judgment concerning future uncertainties,
which in many cases could be cured only by hiring
accurate fortune tellers.
47Appendix 12B. Managers views on Alternative
capitalbudgeting methods
 Hastie also recognizes that, in many cases,
it is not the measurement method but the
financial analyst who fails. The financial
analyst must have a good grasp of the
quantitative and qualitative impacts of each
project and must be able to communicate this
information to the decision makers. Those
preparing expenditure requests should be
objective and realistic.  Hastie recommends several methods to improve
capitalbudgeting techniques. First, corporate
strategy must be clarified and communicated so
that projects incompatible with this strategy
will not be needlessly analyzed. Second,
analytical techniques must be evaluated. They
should be understood by all who work with them
and should generate the type of information used
by the company in decision making. Hastie
recommends the use of sensitivity analysis to
isolate critical variables and give an expanded,
more realistic range of estimated profits. What
is essential is that those involved in the
capitalbudgeting process understand corporate
strategy and policy and generate realistic data,
which can effectively communicate to toplevel
management.
48Appendix 12B. Managers views on Alternative
capitalbudgeting methods
 James Fremgen (1973) in Capital Budgeting
Practices A Survey, continues the analysis of
practitioner use of capitalbudgeting techniques,
and offers some support for Hasties position
that measurement techniques are not the only
important factor in capital budgeting. His
survey again finds that payback period and
accounting profit are widely used as selection
criteria, contrary to theoretical approval of
these methods, but also finds strong support for
the use of internal rateofreturn. His results,
however, do highlight a problem encountered when
using the internal rateofreturn method  the
multiple internal rateofreturn. His results
also give some support to Doenges recommendation
that firms try to predict reinvestment rates for
the funds to be received form projects being
currently evaluated. Although of the 29 percent
which projected reinvestment rates, the majority
used current ratesofreturn or costs of capital,
some tried to estimate future reinvestment rates
based on predicted future rateofreturns or cost
of capital.  A majority of those questioned used some
technique to measure risk and uncertainty when
analyzing investment projects. Again, however, a
problem arises when deciding how to quantify this
risk into the analysis. Most firms appear to
require an unspecified amount of additional
profit for additional risk. Of course, much of
the analysis of projects is based on nonfinancial
or nonquantitative judgments, and companies may
feel that risk is best handled in this manner.
49Appendix 12B. Managers views on Alternative
capitalbudgeting methods
 Fremgen confirmed the previously mentioned
conclusion that capital rationing is a major
influence on the capitalbudgeting process. This
rationing, commonly caused by a limitation on
borrowing, was dealt with by most of the surveyed
companies through ranking of projects. Although
Hastie says this is not an adequate method of
project selection, Fremgen makes little mention
of nonfinancial, subjective methods of
selection. Since project selection must be based
on both financial and nonfinancial data, the
results received must be due to wording of the
question, which disallowed nonfinancial answers.  Providing impressive support for Hasties
position, Fremgen next described three stages of
capital budgeting, only one of which dealt with
financial analysis of the project. The results
clearly reveal that financial analysis is
considered neither the most critical nor the most
difficult stage of the capitalbudgeting process.
More academic attention should be focused on the
stage of project definition and estimation of
cash flows, and the implementation and review
stage of the process. Although these two stages
are more difficult to adapt to quantitative
methods, they would be more useful for the
practitioner.
50Appendix 12B. Managers views on Alternative
capitalbudgeting methods
 One final analysis of capitalbudgeting
theory and practice deals with a specific, fairly
unique industry. Eugene Brigham and Richard
Pettway (1973), in Capital Budgeting by
Utilities, studied the practices in this heavily
regulated industry. Regulation has a profound
effect on capitalbudgeting practice, and the
theory behind this regulation has become
antiquated with the advent of doubledigit
inflation.  The regulators specify a target
rateofreturn for utility companies, which then
determine the rates they can charge consumers.
However, inflation has caused the actual
rateofreturn to fall below the reasonable
rateofreturn, and, due to the lags in the
regulatory process, new targeted
ratesofreturns, when implemented, already have
fallen behind inflation.
51Appendix 12B. Managers views on Alternative
capitalbudgeting methods
 Another unique feature of the utility
industry is that, due to legal requirements, they
must make mandatory investments when needed to
provide service upon demand. These mandatory
investments, the major component of the capital
budget, frequently offer ratesofreturn below
the utilitys cost of capital. Although
discretionary investments may provide higher
returns, rarely can these excess returns
counterbalance the effects of inflated operating
costs, rising cost of capital, mandatory
investments, and regulatory lags. Thus, the cost
of capital exceeds the actual rateofreturn in
the capitalinvestment budget.  Because of this unique situation, utilities
must be very cautious when deciding which
discretionary projects to accept. Projects with
high rates of return are needed to help
compensate for other losses. For mandatory
investments, revenues are disregarded and
alternatives evaluated solely on the basis of
costs on a discounted cashflow basis. Due to
the urgency of keeping costs as low as possible
for mandatory investments, and profits as high as
possible for discretionary investments, 94
percent of the companies use the discounted
cashflow method to project future financial
results more accurately. Risk is also formally
analyzed by over 50 percent of the utilities
questioned.
52Appendix 12B. Managers views on Alternative
capitalbudgeting methods
 Surprisingly, only 49 percent of these
companies indicated that they have experienced
capital rationing in the past five years, and
most of these indicated that their response would
be to apply for a rate increase to alleviate the
problem. The most serious problem they face is
securing permission to build new generating
plants, a problem not shared with other
industries. Since it is so crucial for rate
determination, most utilities have ready
costofcapital figures to use in
capitalbudgeting analysis.  Obviously, many of the problems facing the
utility industry are unique to the industry, and
the managers have developed different
perspectives and policies on capital budgeting to
cope with these problems. There is a message in
this for all those involved with financial
management. Regardless of the academicians
recommendations, the competitions practices, and
the markets signals, capitalbudgeting policy
and practice must be adapted to suit the
individual firms characteristics and needs.
Theory and practice are helpful only to the
extent that they can be successfully integrated
into the individual companys financial
structure. Theorists must try to recognize the
needs of financial practitioners, but the
practitioners must also realize that no mere
formula will guarantee success, and realistic
theories will help their financial analysis and
planning decisions.
53Appendix 12B. Managers views on Alternative
capitalbudgeting methods
 The reader should be aware that, in
practice, most firms use a combination of capital
budgeting techniques to arrive at investment
decisions. For instance, in a survey of large
firms, Schall, Sundem, and Geijsbeek (1978) found
that 17 percent of those firms responding used
four of the capitalbudgeting techniques outlined
above, and 34 percent used three of the four in
making decisions. More surprisingly, although 86
percent of the firms used at least one of the
discounting methods, the most popular technique
was found to be the payback method, despite its
disregard of several important factors. Perhaps
the continued use of simpler methods combined
with the more accurate NPV or IRR, points to the
importance of ease of calculation for
practitioners. In addition, despite the
frequently noted ambiguities accompanying use of
the IRR, the method enjoys a substantial and
continuing popularity in practice. In their
paper Survey and Analysis of CapitalBudgeting
Methods used by Multinationals, Oblak and Helm
(1980) found that the IRR method and the payback
method are two most popular capitalbudgeting
methods used by multinational firms. The
continued use of IRR may be due to the fact that
the rateofreturn of a project has a more
intuitive appeal and is therefore easier to
explain and justify within the firm than the more
esoteric NPV criterion.
54Appendix 12C. Derivation of Crossover Rate
Period 0 1 2 3
Project A 10,000 10,000 1,000 1,000
Project B 10,000 1,000 1,000 12,000
Cash flows of BA 0 9,000 0 11,000
55Appendix 12C. Derivation of Crossover Rate
 Figure 12.C.1 Net Present Value and IRR for
Mutually Exclusive Projects
56Appendix 12C. Derivation of Crossover Rate
 NPV(A) 10,000 10,000 / (1Rc) 1,000 /
(1Rc)2 1,000 / (1Rc)3  (12.C.1)
 NPV(B) 10,000 1,000 / (1Rc) 1,000 /
(1Rc)2 12,000 / (1Rc)3  (12.C.2)
 NPV(A)NPV(B)
57Appendix 12C. Crossover rate
58Appendix 12C. Crossover rate
 where
 CF0(BA) The different of net cash inflow
between project A and project B at
time 0.  CF1(BA) The different of net cash inflow
between project A and project B at
time 1.  CF2(BA) The different of net cash inflow
between project A and project B at
time 2.  CF3(BA) The different of net cash inflow
between project A and project B at
time 3.  In other word, Rc is the IRR of the project (B
A).