BM_3ed_SM07 - Solutions to Chapter 7 NPV and Other...

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7-1 Solutions to Chapter 7 NPV and Other Investment Criteria 1. NPV A = –100 + 40 × annuity factor(11%, 4 periods) = $24.10 NPV B = –100 + 50 × annuity factor(11%, 3 periods) = $22.19 Both projects are worth pursuing. 2. Choose the project with the higher NPV, project A 3. If r = 16%, then NPV A = $11.93 and NPV B = $12.29. Therefore, you should now choose project B. 4. IRR A = Discount rate at which 40 × annuity factor(r, 4 periods) = 100 IRR A = 21.86% IRR B = 23.38% 5. No. Even though project B has the higher IRR, its NPV is lower than that of project A when the discount rate is lower (as in Problem 1) and higher when the discount rate is higher (as in Problem 3). This example shows that the project with the higher IRR is not necessarily better. The IRR of each project is fixed, but as the discount rate increases, project B becomes relatively more attractive compared to project A. This is because B’s cash flows come earlier, so their present values fall less rapidly when the discount rate increases. 6. The profitability indexes are as follows: Project A 24.10/100 = .2410 Project B 22.19/100 = .2219 In this case, with equal initial investments , both the profitability index and NPV will give projects the same ranking. This is an unusual case, however, since it is rare for initial investments to be equal. 7. Project A has a payback period of 100/40 = 2.5 years. Project B has a payback period of 2 years. 8. Project A Year Cash Flow ($) Discounted Cash Flow ($) @ 11 percent Cumulative Discounted Cash Flow ($) 0 -100 -100 -100 1 40 36.04 -63.96 2 40 32.48 -31.48 3 40 29.24 -2.24 4 40 26.36 +24.12 NPV= 24.12
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7-2 Assuming uniform cash flows across time, the fractional year can now be determined. Since the discounted cash flows are negative until year 3 and become positive by Year 4, the project pays back sometime in the fourth year. Note that out of the total discounted cash flow of $26.36 in Year 4, the first $2.24 comes in by 2.24/26.36 = 0.084 year. Therefore, the discounted payback period for Project A is 3.084 years. Project B Year Cash Flow ($) Discounted Cash Flow ($) @ 11 percent Cumulative Discounted Cash Flow ($) 0 -100 -100 -100 1 50 45.05 -54.95 2 50 40.60 -14.35 3 50 36.55 +22.20 NPV= 22.20 The discounted payback for Project B is 2 years + 14.35/36.55 = 2.39 years. 9. No. Despite its higher payback, Project A still may be the preferred project, for example, when the discount rate is 11% (as in Problems 1 and 2). Just as in problem 5, you should note that the payback period for each project is fixed, but that NPV changes as the discount rate changes. The project with the shorter payback period need not have the higher NPV. 10. Project A Profits Book Assets Book Year CF Deprec = CF – Dep. Start of year Return 1 40 25 15 100 .15 2 40 25 15 75 .20 3 40 25 15 50 .30 4 40 25 15 25 .60
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7-3 Project B Profits Book Assets Book Year CF Deprec = CF – Dep. Start of year Return 1 50 33.33 16.67 100 .167 2 50 33.33 16.67 66.67 .25 3 50 33.33 16.67 33.33 .50 Notice that book return increases as the book value of the asset falls over time (due to depreciation). The IRR of project A is 21.86% and the IRR of project B is 23.38% (see problem 4). The IRR does not equal book return in any particular year, nor does it equal average book return over the life of the project.
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