1. Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng F. Lee Rutgers University Chapter 12 Capital Budgeting Under Certainty

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 Equivalent Annual NPV and Equivalent Annual Cost  12.6 Capital rationing decision  12.7 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) R t + N t P t = N t d t + WSMS t + I t, (12.1) where R t = Revenue in period t, N t P t = New equity in period t, N t d t = Total dividend payment in period t, WSMS t = Wages, salaries, materials, and service payment in period t, I t = Investment in period t. Annual After-Tax Cash Flow = ICFBT - (ICFBT - Δdep)τ = ICFBT (1 - τ) + (dep)τ, (12.2) Where ICFBT = Annual incremental operating cash flows, τ = Corporate tax rate, Δdep = Incremental annual depreciation charge, or the annual depreciation charges on the new machine less the annual depreciation on the old.

4. 12.2 Cash-flow evaluation of alternative investment projects ICFBT( the annual incremental operating cash flows ) = ΔR t - ΔWSMS t. (12.3) (12.4) 12.3Alternative capital-budgeting methods TABLE 12.1 YearABCD 0-100 12003025 280205040 31060 50 4-2016080115

5. 12.3Alternative capital-budgeting methods (12.5) Where AP t = After-tax profit in period t, I= Initial investment, and N = Life of the project, the depreciation is $25. 12.3.1 Accounting Rate of Return

6. 12.3Alternative capital-budgeting methods (12.6) where CF t = Cash flow (positive or negative) in period t, I = Initial investment, N = Life of the project. 12.3.2 Internal Rate of Return

7. 12.3Alternative capital-budgeting methods (12.6’) By the geometric series, Equation (12.6’) can be written as (12.7) Assume R=Cf1=Cf2=…=Cfn, Equation 12.6 can be written as the equation (12.6’) Equation (12.7) define the special relationship of payback method and IRR 12.3.3 Payback Method

8. 12.3Alternative capital-budgeting methods  The payback method calculates the time period required for a firm to recover the cost of its investment. It is that point in time at which the cumulative new cash flow from the project equals the initial investment. 12.3.4 Net Present Value (NPV) Method

9. 12.3Alternative capital-budgeting methods (12.8) (12.8′) 12.3.4 Net Present Value (NPV) Method NPV method NPV and break-even quantity

10. 12.3Alternative capital-budgeting methods ProjectInitial Outlay Present Value of Cash Inflows NPVPI A1002001002 B100013003001.3 12.3.5 Profitability Index (12.9)

11. 12.4Comparison of the NPV and IRR method Fig. 12.1 NPVs of Projects A and B at different discount rates. 12.4.1 Theoretical criteria

12. 12.4Comparison of the NPV and IRR method Year 012 Cash Flow － 50 750 － 800 12.4.2 Multiple Rates-of-Return IRR = 0.1557 or 12.84.

13. 12.4Comparison of the NPV and IRR method Year 012 Cash Flow － 100 250 － 160 12.4.2 Multiple Rates-of-Return

14. 12.4Comparison of the NPV and IRR method TABLE 12.2 Year Project 0 1 2 3NPV A -10050100500380.2537 B -20060010050451.02269 C -300100700100418.49945 A+B -300650200550831.27505 B+C -500700800150869.52214 A+C -400150800600798.75182 >IRR A1.10438 B2.18184 C0.76360 A1.67275 B+C1.19227 A+C0.87172 TABLE 12.2a 12.4.3 Reinvestment Rate Problem

15. YearProject AProject B 0 － 100 1 7050 2 7050 3 12.5 Equivalent Annual NPV and Equivalent Annual Cost  12.5.1 Mutually Exclusive Investment Projects with Different lives

16. 12.5.1 Mutually Exclusive Investment Projects with Different lives NPV(N,t) = NPV(N)(1 + H + H 2 +... H t ). (12.10) H[NPV(N,t)] = NPV(N)(H + H 2 +... + H t + H t+1 ).(12.11) NPV(N,t) - (H)NPV(N,t) = NPV(N)(1 - H t+1 ), (12.12)

17. 12.5.1 Mutually Exclusive Investment Projects with Different lives For Project A: For Project B: (12.13) where the annuity factor is [1 - (1 + K) -N ]/K.

18. Equivalent Annual Cost NPV(N)= K × NPV(N,∞) × Annuity Factor (12.14) NPV(N) = C × Annuity Factor (12.15) C = K × NPV(N,∞) (12.16) (12.17) C=565.47 NPV (N, ∞) = 1749.47×(1+0.1) 4 / [(1+0.1) 4 -1] = 5654.71 C = K* NPV (N, ∞) = 0.1× 5654.71 = 565.47

19. 12.6.1 Basic Concepts of Linear Programming Maximize (or minimize) Z = c 1 X 1 + c 2 X 2 +... + c n X n, Subject to: a 11 X 1 + a 12 X 2 +... + a 1n X n  (  ) b 1, a 21 X 1 + a 22 X 2 +... + a 2n X n  (  ) b 2,.. a m1 X 1 + a m2 X 2 +... + a mn X n  (  ) b m, X j  0, (j = 1, 2,..., n). 12.6Capital rationing decision

20. 12.6.2 Capital Rationing Year Project012345 X － 100 30 60 Y － 200 70 Z － 100 － 240 － 200 400300 InvestmentNPV X65.585 Y52.334 Z171.871 Year 0Year 1Year 2 $300$70$50 12.6Capital rationing decision

21. 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. X  1,Y  1, Z  1. If V=$208.24, then X = 1.0, Y = 0.6586, Z = 0.6305. Funds ConstraintShadow Price 1st period0.4517 2nd period0.4517 3rd period0.0914

22. 12.7Summary 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.

23. 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; ρ = Continuously compounded discount rate which is equal to log e (1 + k)

24. 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. Y Q = Y 1 Q -b (12.A.3) where Q = Number of aircraft produced; Y Q = Cumulative average production cost for Q aircraft produced; b = – log (γ)/log(2); γ = “Learning coefficient,” which remains constant over all Q;Y 1 = First unit cost of production.

25. Appendix 12A. NPV and break-even analysis (12.A.5) Q(t) = (t - A)N. (12.A.6) C(t) = (1 - b)Y 1 (t - A) -b N (1-b) (12.A.7) for A = 42, B = 0.369188, Y 1 = $100 million, t > A. (12.A.8) where k j = Effective annual after-tax cost per dollar of the jth source of funds; W j = Proportion of the jth source of funds in the long-run capital structure. The cumulative total production cost TC(t) = Y1[Q(t)] (1-b) (12.A.4) The rate of production cost

26. Appendix 12A. NPV and break-even analysis k = 0.3k d + 0.7k e (12.A.9) where k d = after-tax cost of debt, and k e = after-tax cost of equity. (12.A.10) Where D = dividend per share, P = Net proceeds per share after flotation costs, g = Average annual compound growth rate

27. Appendix 12A. NPV and break-even analysis R (t) = PN for t > A, (12.A.11) (12.A.12) where tx = Effective tax rate on corporate profits for Lockheed, and ρ = Discount rate.

28. Appendix 12A. NPV and break-even analysis Fig. 12.A.1 (From Reinhardt, H. E., “Break- even analysis for Lockheed’s Tri Star: An Application,” Journal of Finance 28 (September 1973): 830. Reprinted by permission.)

29. 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 firm’s 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.

30. 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 didn’t 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.

31. 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.

32. 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 Businessman’s 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.

33. 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.

34. 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.

35. 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 Hastie’s 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.

36. 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 Hastie’s 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.

37. 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.

38. 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 utility’s 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.

39. 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 academician’s recommendations, the competition’s practices, and the market’s signals, capital-budgeting policy and practice must be adapted to suit the individual firm’s characteristics and needs. Theory and practice are helpful only to the extent that they can be successfully integrated into the individual company’s 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.

40. 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.

41. Appendix 12C. Derivation of Crossover Rate Period0123 Project A-10,00010,0001,000 Project B-10,0001,000 12,000 Cash flows of B-A0-9,000011,000

42. Appendix 12C. Derivation of Crossover Rate Figure 12.C.1 Net Present Value and IRR for Mutually Exclusive Projects

43. Appendix 12C. Derivation of Crossover Rate  NPV(A) = -10,000 + 10,000 / (1+R c ) + 1,000 / (1+R c ) 2 + 1,000 / (1+R c ) 3 (12.C.1)  NPV(B) = -10,000 + 1,000 / (1+R c ) + 1,000 / (1+R c ) 2 + 12,000 / (1+R c ) 3 (12.C.2)  NPV(A)=NPV(B)

44. Appendix 12C. Crossover rate (12.C.3)

45. Appendix 12C. Crossover rate where CF 0 (B-A) =The different of net cash inflow between project A and project B at time 0. CF 1 (B-A) =The different of net cash inflow between project A and project B at time 1. CF 2 (B-A) =The different of net cash inflow between project A and project B at time 2. CF 3 (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).