Corporate_Finance_9th_edition_Solutions_Manual_FINAL0

306 piii 8500pvifa103 15000 1409 the profitability

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Unformatted text preview: + IRR)3 0 = –$1,350,000 + $890,000 / (1 + IRR) + $330,000 / (1 + IRR)2 + $520,000 / (1 + IRR)3 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: Incremental IRR = 15.78% For investing-type projects, accept the larger project when the incremental IRR is greater than the discount rate. Since the incremental IRR, 15.78%, is greater than the required rate of return of 14 percent, choose the submarine ride project. Note that this is not the choice when evaluating only the IRR of each project. The IRR decision rule is flawed because there is a scale problem. That is, the submarine ride has a greater initial investment than does the deepwater fishing project. This problem is corrected by calculating the IRR of the incremental cash flows, or by evaluating the NPV of each project. c. The NPV is the sum of the present value of the cash flows from the project, so the NPV of each project will be: Deepwater fishing: NPV = –$750,000 + $310,000 / 1.14 + $430,000 / 1.142 + $330,000 / 1.143 NPV = $75,541.46 Submarine ride: NPV = –$2,100,000 + $1,200,000 / 1.14 + $760,000 / 1.142 + $850,000 / 1.143 NPV = $111,152.69 Since the NPV of the submarine ride project is greater than the NPV of the deepwater fishing project, choose the submarine ride project. The incremental IRR rule is always consistent with the NPV rule. 119 12. a. The profitability index is the PV of the future cash flows divided by the initial investment. The cash flows for both projects are an annuity, so: PII = $21,000(PVIFA10%,3 ) / $40,000 = 1.306 PIII = $8,500(PVIFA10%,3) / $15,000 = 1.409 The profitability index decision rule implies that we accept project II, since PIII is greater than the PII. b. The NPV of each project is: NPVI = – $40,000 + $21,000(PVIFA10%,3) = $12,223.89 NPVII = – $15,000 + $8,500(PVIFA10%,3) = $6,138.24 The NPV decision rule implies accepting Project I, since the NPVI is greater than the NPVII. c. Using the profitability index to compare mutually exclusive projects can be ambiguous when the magnitudes of the cash flows for the two projects are of different scales. In this problem, project I is roughly 3 times as large as project II and produces a larger NPV, yet the profitability index criterion implies that project II is more acceptable. The equation for the NPV of the project is: NPV = – $32,000,000 + $57,000,000/1.1 – $9,000,000/1.12 = $12,380,165.29 The NPV is greater than 0, so we would accept the project. 13. a. b. The equation for the IRR of the project is: 0 = –$32,000,000 + $57,000,000/(1+IRR) – $9,000,000/(1+IRR)2 From Descartes rule of signs, we know there are two IRRs since the cash flows change signs twice. From trial and error, the two IRRs are: IRR = 60.61%, –82.49% When there are multiple IRRs, the IRR decision rule is ambiguous. Both IRRs are correct; that is, both interest rates make the NPV of the project equal to zero. If we are evaluating whether or not to accept this project, we would not want to use the IRR to make our decision. 14. a. The payback period is the time that it takes for the cumulative undiscounted cash inflows to equal the initial investment. Board game: Cumulative cash flows Year 1 = $700 Payback period = $600 / $700 = .86 years = $700 120 CD-ROM: Cumulative cash flows Year 1 = $1,400 = $1,400 Cumulative cash flows Year 2 = $1,400 + 900 = $2,300 Payback period = 1 + ($1,900 – 1,400) / $900 Payback period = 1.56 years Since the board game has a shorter payback period than the CD-ROM project, the company should choose the board game. b. The NPV is the sum of the present value of the cash flows from the project, so the NPV of each project will be: Board game: NPV = –$600 + $700 / 1.10 + $150 / 1.102 + $100 / 1.103 NPV = $235.46 CD-ROM: NPV = –$1,900 + $1,400 / 1.10 + $900 / 1.102 + $400 / 1.103 NPV = $417.05 Since the NPV of the CD-ROM is greater than the NPV of the board game, choose the CDROM. c. The IRR is the interest rate that makes the NPV of a project equal to zero. So, the IRR of each project is: Board game: 0 = –$600 + $700 / (1 + IRR) + $150 / (1 + IRR)2 + $100 / (1 + IRR)3 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 42.43% CD-ROM: 0 = –$1,900 + $1,400 / (1 + IRR) + $900 / (1 + IRR)2 + $400 / (1 + IRR)3 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 25.03% 121 Since the IRR of the board game is greater than the IRR of the CD-ROM, IRR implies we choose the board game. Note that this is the choice when evaluating only the IRR of each project. The IRR decision rule is flawed because there is a scale problem. That is, the CD-ROM has a greater initial investment than does the board game. This problem is corrected by calculating the IRR of the incremental cash flows, or by evaluating the NPV of each project. d. To calculate the incremental IRR, we subtract the smaller project’s cash...
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