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Title: Financial Analysis, Planning and Forecasting Theory and Application


1
Financial 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

2
Outline
  • 12.1 Introduction
  • 12.2 Cash-flow evaluation of alternative
    investment projects
  • 12.3 Alternative capital-budgeting 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 break-even analysis
  • Appendix 12B. Managers views on Alternative
    capital-budgeting methods
  • Appendix 12C. Crossover rate

3
12.2 Cash-flow 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.

4
12.2 Cash-flow evaluation of alternative
investment projects
  • Annual After-Tax 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.

5
12.2 Cash-flow evaluation of alternative
investment projects
  • ICFBT ?Rt - ?WSMSt.
    (12.3)
  • (12.4)

6
12.3 Alternative capital-budgeting methods
  • Accounting rate-of-return
  • Internal rate-of-return
  • Payback method
  • Net present value method
  • Profitability index

7
12.3 Alternative capital-budgeting 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
8
12.3 Alternative capital-budgeting methods
  • (12.5)
  • where
  • APt After-tax profit in period t,
  • I Initial investment
  • N Life of the project.

9
12.3 Alternative capital-budgeting methods
  • (12.6)
  • where
  • CFt Cash flow (positive or negative) in
    period t,
  • I Initial investment,
  • N Life of the project.

10
12.3 Alternative capital-budgeting methods
  • (12.7)
  • (12.6)
  • (12.8)

11
12.3 Alternative capital-budgeting methods
  • (12.8')
  • (12.9)

12
12.3 Alternative capital-budgeting methods
Project Initial Outlay Present Value of Cash Inflows NPV PI
A 100 200 100 2
B 1000 1300 300 1.3
13
12.4 Comparison of the NPV and IRR method
  • Theoretical criteria
  • Multiple Rates-of-Return
  • Reinvestment Rate Problem
  • Practical perspective

14
12.4 Comparison of the NPV and IRR method
  • Fig. 12.1 NPVs of Projects A and B at different
    discount rates.

15
12.4 Comparison of the NPV and IRR method
Year
0 1 2
Cash Flow -50 750 -800

16
12.4 Comparison of the NPV and IRR method
IRR 0.1557 or 12.84.
17
12.4 Comparison of the NPV and IRR method
Year
0 1 2
Cash Flow -100 250 -160
18
12.4 Comparison of the NPV and IRR method
  • TABLE 12.2

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
19
12.5 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
20
12.5.1 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),

21
12.5.1 Mutually Exclusive Investment Projects
with Different lives
  • (12.12)

22
12.5.1 Mutually Exclusive Investment Projects
with Different lives
  • For Project A
  • For Project B


23
12.5.1 Mutually Exclusive Investment Projects
with Different lives
  • (12.13)
  • where the annuity factor is
  • 1 - (1 K)-N/K.

24
Equivalent 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)

25
Equivalent Annual Cost
  • C565.47
  • NPV (N, 8) 1749.47(10.1)4 / (10.1)4-1
    5654.71
  • C K NPV (N, 8) 0.1 5654.71 565.47

26
12.6 Capital rationing decision
  • Basic concepts of linear programming
  • Capital rationing

27
12.6.1 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).

28
12.6.2 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
29
12.6.2 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.

30
12.6.2 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
31
12.7 Summary
  • Important concepts and methods related to
    capital-budgeting decisions under certainty were
    explored in this chapter. Cash-flow estimation
    methods were discussed before alternative
    capital-budgeting 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, capital-rationing 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 lease-vs.-buy decision will be
    investigated.

32
Appendix 12A. NPV and break-even analysis
  • (12.A.1)
  • where
  • NPV(k) Net present value of the project
    discounted at cost-of-capital 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)

33
Appendix 12A. NPV and break-even analysis
  • (12.A.2)
  • where
  • R RDTE costs,
  • I Total initial outlay on production
    facilities,
  • A Time up to the onset of production.

34
Appendix 12A. NPV and break-even analysis
  • YQ Y1Q-b
    (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.

35
Appendix 12A. NPV and break-even analysis
  • TC(t) Y1Q(t)(1-b)
    (12.A.4)
  • (12.A.5)

  • Q(t) (t - A)N.
    (12.A.6)

36
Appendix 12A. NPV and break-even analysis
  • C(t) (1 - b)Y1(t - A)-bN(1-b)
    (12.A.7)
  • for
  • A 42,
  • B 0.369188,
  • Y1 100 million,
  • t gt A.

37
Appendix 12A. NPV and break-even analysis
  • (12.A.8)
  • where
  • kj Effective annual after-tax cost per
    dollar of the jth source of funds
  • Wj Proportion of the jth source of funds
    in the long-run capital structure.

38
Appendix 12A. NPV and break-even analysis
  • k 0.3kd 0.7ke
    (12.A.9)
  • where
  • kd after-tax cost of debt, and
  • ke after-tax cost of equity.

39
Appendix 12A. NPV and break-even analysis
  • (12.A.10)
  • where
  • D dividend per share,
  • P Net proceeds per share after flotation
    costs,
  • g Average annual compound growth rate

40
Appendix 12A. NPV and break-even 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.

41
Appendix 12A. NPV and break-even analysis
  • Fig. 12.A.1 (From Reinhardt, H. E., Break-even
    analysis for Lockheeds Tri Star An
    Application, Journal of Finance 28 (September
    1973) 830. Reprinted by permission.)

42
Appendix 12B. Managers views on Alternative
capital-budgeting 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 all-encompassing
    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.

43
Appendix 12B. Managers views on Alternative
capital-budgeting 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.

44
Appendix 12B. Managers views on Alternative
capital-budgeting methods
  • Theory recommends either of two methods for
    incorporating risk into investment analysis the
    certainty-equivalent approach and the
    risk-adjusted discount-rate 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
    risk-adjusted 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, long-range process where
    only major activities and their impact on
    diversification are considered.

45
Appendix 12B. Managers views on Alternative
capital-budgeting 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
    rate-of-return and net present value. Interview
    results show that only two of the eight companies
    use Internal Rate-of-Return alone, whereas six
    use payback and accounting profit alone or in
    conjunction with internal rate-of-return.
    Theorists have advanced two explanations for this
    incongruence. First, internal rate-of-return 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 net-present-value 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 re-evaluation of the
    assumptions inherent in the capital-budgeting
    process.

46
Appendix 12B. Managers views on Alternative
capital-budgeting 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.

47
Appendix 12B. Managers views on Alternative
capital-budgeting 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
    capital-budgeting 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
    capital-budgeting process understand corporate
    strategy and policy and generate realistic data,
    which can effectively communicate to top-level
    management.

48
Appendix 12B. Managers views on Alternative
capital-budgeting methods
  • James Fremgen (1973) in Capital Budgeting
    Practices A Survey, continues the analysis of
    practitioner use of capital-budgeting 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 rate-of-return. His results,
    however, do highlight a problem encountered when
    using the internal rate-of-return method -- the
    multiple internal rate-of-return. 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 rates-of-return or costs of capital,
    some tried to estimate future reinvestment rates
    based on predicted future rate-of-returns 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.

49
Appendix 12B. Managers views on Alternative
capital-budgeting methods
  • Fremgen confirmed the previously mentioned
    conclusion that capital rationing is a major
    influence on the capital-budgeting 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 non-financial, 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 capital-budgeting 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.

50
Appendix 12B. Managers views on Alternative
capital-budgeting methods
  • One final analysis of capital-budgeting
    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 capital-budgeting practice, and the
    theory behind this regulation has become
    antiquated with the advent of double-digit
    inflation.
  • The regulators specify a target
    rate-of-return for utility companies, which then
    determine the rates they can charge consumers.
    However, inflation has caused the actual
    rate-of-return to fall below the reasonable
    rate-of-return, and, due to the lags in the
    regulatory process, new targeted
    rates-of-returns, when implemented, already have
    fallen behind inflation.

51
Appendix 12B. Managers views on Alternative
capital-budgeting 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 rates-of-return 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 rate-of-return in
    the capital-investment 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 cash-flow 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
    cash-flow method to project future financial
    results more accurately. Risk is also formally
    analyzed by over 50 percent of the utilities
    questioned.

52
Appendix 12B. Managers views on Alternative
capital-budgeting 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
    cost-of-capital figures to use in
    capital-budgeting 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, capital-budgeting 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.

53
Appendix 12B. Managers views on Alternative
capital-budgeting 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 capital-budgeting 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 Capital-Budgeting
    Methods used by Multinationals, Oblak and Helm
    (1980) found that the IRR method and the payback
    method are two most popular capital-budgeting
    methods used by multinational firms. The
    continued use of IRR may be due to the fact that
    the rate-of-return 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.

54
Appendix 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 B-A 0 -9,000 0 11,000
55
Appendix 12C. Derivation of Crossover Rate
  • Figure 12.C.1 Net Present Value and IRR for
    Mutually Exclusive Projects

56
Appendix 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)

57
Appendix 12C. Crossover rate
  • (12.C.3)

58
Appendix 12C. Crossover rate
  • where
  • CF0(B-A) The different of net cash inflow
    between project A and project B at
    time 0.
  • CF1(B-A) The different of net cash inflow
    between project A and project B at
    time 1.
  • CF2(B-A) The different of net cash inflow
    between project A and project B at
    time 2.
  • CF3(B-A) 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).
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