The essence of capital budgeting and resource allocation is a search for good investments in which to place the firm's capital. The process can be simple when viewed in purely mechanical terms, but a number of subtle issues can obscure the best investment choices. The capital-budgeting analyst, therefore, is necessarily a detective who must winnow bad evidence from good. Much of the challenge is in knowing what quantitative analysis to generate in the first place. Suppose you are a new capital-budgeting analyst for a company considering investments in the eight projects listed in Exhibit 1. The CFO of your company has asked you to rank the projects and recommend the "four best" that the company should accept. In this assignment, only the quantitative considerations are relevant. No other project characteristics are deciding factors in the selection, except that management has determined that projects 7 and 8 are mutually exclusive. All the projects require the same initial investment, $2 million. Moreover, all are believed to be of the same risk class. The firm's weighted average cost of capital has never been estimated. In the past, analysts have simply assumed that 10% was an appropriate discount rate (although certain officers of the company have recently asserted that the discount rate should be much higher). To stimulate your analysis, consider the following questions: 1. Can you rank the projects simply by inspecting the cash flows? 2. What criteria might you use to rank the projects? Which quantitative ranking methods are better? Why? 3. What is the ranking you found by using quantitative methods? Does this ranking differ from the ranking obtained by simple inspection of the cash flows? 4. What kinds of real investment projects have cash flows similar to those in Exhibit 1? initial investment Excess of cash flow over 15 Sum of cash flow benefits $ 3,310 $ 2,165 $10,000 $ 3,561 $4,200 $2,200 $ 2,560 $4,150 $ 1,310 S 165 $ 8,000 $ 1,561 $2,200 $ 200 $ 560 $2,150 Year 1 1234567890221 $ 330 330 $ 1,666 334* 165 330 330 330 330 $10,000* 330* $1,000 Initial investment $(2,000) Project number: 1 2 3 4 $(2,000) $(2,000) $(2,000) $(2,000) $(2,000) $(2,000) Exhibit 1 The Investment Detective Projects' Free Cash Flows (dollars in thousands) opy of P $ 280 $(2,000) $2,200* $ 1,200 $ (350) 900* (60) 300 60 90 350 70 700 1,200 $2,250* Po 8 Project Number 1 2 3 4 5 7 8 Initial Investment ($2,000) ($2,000) ($2,000) ($2,000) ($2,000) ($2,000) ($2,000) ($2,000) Year 1 $330 $1,666 $0 $160 280 $2,200 2 330 334 0 200 280 $1,200 900 ($350) (60) 3 330 165 0 350 280 300 60 4 330 0 395 280 90 350 5 330 0 432 280 70 700 6 330 440 280 1,200 7 330 442 280 2,250 0.9090909 0.9090909 0.8264463 1.7355372 0.7513148 2.486852 0.6830135 3.1698654 0.6209213 3.7907868 0.5644739 4.3552607 0.5131581 4.8684188 8 1,000 0 444 280 0.4665074 5.3349262 9 0 446 280 0.4240976 5.7590238 10 0 448 280 11 0 450 280 0.3855433 6.1445671 0.3504939 6.495061 12 0 451 280 0.3186308 6.8136918 13 0 451 280 0.2896644 7.1033562 14 15 0 452 280 0.2633313 7.3666875 10,000 (2,000) 280 0.239392 7.6060795 Sum of Cash Flow Benefits $3,310 $2,165 $10,000 $3,561 $4,200 $2,200 $2,560 $4,150 Excess of Cash Flow Over Initial Investment $1,310 $165 $8,000 $1,561 $2,200 $200 $560 $2,150 Asterisk indicates year in which payback is accomplished. Analysis Total Life of Investment 8 3 15 15 15 1 5 Payback (Years) 7 2 15 6 8 1 2 7 Average ROI (See Note 1) 20.7% 36.1% 33.3% 11.9% 14.0% 110.0% 25.6% 29.6% Net present Value at: 10% $73 ($85) $394 $228 $130 $0 $165 $183 11% (11) (107) 90 127 13 (18) 132 51 12% (90) (129) (173) 30 (93) (36) 99 (72) 13% (164) (150) (401) (60) (191) (53) 68 (188) 14% (234) (170) (599) (146) (280) (70) 37 (296) 15% (300) (190) (771) (227) (363) (87) 8 (397) 16% (362) (210) (921) (304) (439) (103) (21) (493) Internal Rate of Return 10.9% 6.3% 11.3% 12.3% 11.1% 10.0% 15.3% 11.4% PV Index (See Note 2) Equivalent Annuity (Note 3) Equiv. Annuity (to infinity) Notes: 1.037 0.957 1.197 0.706 1.065 1.000 1.083 1.563 $13.7 $137.0 ($34.4) $51.8 ($343.6) $517.9 $30.0 $17.1 $0.0 $43.5 $37.6 $300.1 $170.5 $0.0 $435.4 $375.9 1. Average return on investment is calculated as the average of the cash flows over the life of the project divided by the $2,000 investment up front. 2. The present value index is calculated as the present value of all inflows (at a 10 percent discount rate) divided by the present value of all outflows. Ordinarily this will rank projects identically to the standard NPV except where there are outflows in later years, as in projects 4 and 8--in these cases, it changes the ranking significantly.