Corporate_Finance_9th_edition_Solutions_Manual_FINAL0

155 15 450000 pinp 30 1192 pinx 20 80000

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Unformatted text preview: the root of the equation, we find that: IRRNP-30 = 22.85% And the IRR of the NX-20 is: 0 = –$200,000 + $80,000 / (1 + IRR) + $92,000 / (1 + IRR)2 + $105,800 / (1 + IRR)3 + $121,670 / (1 + IRR)4 + $139,921 / (1 + IRR)5 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRRNX-20 = 40.09% The IRR criteria implies accepting the NX-20. 127 c. Incremental IRR analysis is not necessary. The NX-20 has a higher IRR, and is relatively smaller in terms of investment, with a larger NPV. Nonetheless, we will calculate the incremental IRR. In calculating the incremental cash flows, we subtract the cash flows from the project with the smaller initial investment from the cash flows of the project with the large initial investment, so the incremental cash flows are: Year 0 1 2 3 4 5 Incremental cash flow –$250,000 80,000 68,000 54,200 38,330 20,079 Setting the present value of these incremental cash flows equal to zero, we find the incremental IRR is: 0 = –$250,000 + $80,000 / (1 + IRR) + $68,000 / (1 + IRR)2 + $54,200 / (1 + IRR)3 + $38,330 / (1 + IRR)4 + $20,0790 / (1 + IRR)5 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: Incremental IRR = 1.74% For investing-type projects, accept the larger project when the incremental IRR is greater than the discount rate. Since the incremental IRR, 1.74%, is less than the required rate of return of 15 percent, choose the NX-20. d. The profitability index is the present value of all subsequent cash flows, divided by the initial investment, so the profitability index of each project is: PINP-30 = ($160,000{[1 – (1/1.15)5 ] / .15 }) / $450,000 PINP-30 = 1.192 PINX-20 = [$80,000 / 1.15 + $92,000 / 1.152 + $105,800 / 1.153 + $121,670 / 1.154 + $139,921 / 1.155] / $200,000 PINX-20 = 1.739 The PI criteria implies accepting the NX-20. 20. a. The payback period is the time that it takes for the cumulative undiscounted cash inflows to equal the initial investment. Project A: Cumulative cash flows Year 1 = $190,000 = $190,000 Cumulative cash flows Year 2 = $190,000 + 170,000 = $360,000 Payback period = 1 + ($90,000/$170,000) = 1.53 years 128 Project B: Cumulative cash flows Year 1 = $270,000 = $270,000 Cumulative cash flows Year 2 = $270,000 + 240,000 = $510,000 Payback period = 1 + ($120,000/$240,000) = 1.50 years Project C: Cumulative cash flows Year 1 = $160,000 = $160,000 Cumulative cash flows Year 2 = $160,000 + 190,000 = $350,000 Payback period = 1 + ($70,000/$190,000) = 1.37 years Project C has the shortest payback period, so payback implies accepting Project C. However, the payback period does not necessarily rank projects correctly. b. The IRR is the interest rate that makes the NPV of the project equal to zero, so the IRR of each project is: Project A: 0 = –$280,000 + $190,000 / (1 + IRR) + $170,000 / (1 + IRR)2 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRRA = 18.91% And the IRR of the Project B is: 0 = –$390,000 + $270,000 / (1 + IRR) + $240,000 / (1 + IRR)2 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRRB = 20.36% And the IRR of the Project C is: 0 = –$230,000 + $160,000 / (1 + IRR) + $190,000 / (1 + IRR)2 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRRC = 32.10% The IRR criteria implies accepting Project C. 129 c. The profitability index is the present value of all subsequent cash flows, divided by the initial investment. We need to discount the cash flows of each project by the required return of each project. The profitability index of each project is: PIA = [$190,000 / 1.10 + $170,000 / 1.102] / $280,000 PIA = 1.12 PIB = [$270,000 / 1.20 + $240,000 / 1.202] / $390,000 PIB = 1.00 PIC = [$160,000 / 1.15 + $190,000 / 1.152] / $230,000 PIC = 1.23 The PI criteria implies accepting Project C. d. We need to discount the cash flows of each project by the required return of each project. The NPV of each project is: NPVA = –$280,000 + $190,000 / 1.10 + $170,000 / 1.102 NPVA = $33,223.14 NPVB = –$390,000 + $270,000 / 1.20 + $240,000 / 1.202 NPVB = $1,666.67 NPVC = –$230,000 + $160,000 / 1.15 + $190,000 / 1.152 NPVC = $52,797.73 The NPV criteria implies accepting Project C. In the final analysis, since we can accept only one of these projects. We should accept Project C since it has the greatest NPV. Challenge 21. Given the six-year payback, the worst case is that the payback occurs at the end of the sixth year. Thus, the worst case: NPV = –$574,000 + $574,000/1.126 = –$283,193.74 The best case has infinite cash flows beyond the payback point. Thus, the best-case NPV is infinite. 22. The equation for the IRR of the project is: 0 = –$504 + $2,862/(1 + IRR) – $6,070/(1 + IRR)2 + $5,700/(1 + IRR)3 – $2,000/(1 + IRR)4 Using Descartes rule of signs, from looking at...
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