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Unformatted text preview: flows from the larger project’s cash flows. In this case, we subtract the board game cash flows from the CDROM cash flows. The incremental IRR is the IRR of these incremental cash flows. So, the incremental cash flows of the CDROM are: CDROM Board game CDROM – Board game Year 0 –$1,900 –600 –$1,300 Year 1 $1,400 700 $700 Year 2 $900 150 $750 Year 3 $400 100 $300 Setting the present value of these incremental cash flows equal to zero, we find the incremental IRR is: 0 = C0 + C1 / (1 + IRR) + C2 / (1 + IRR)2 + C3 / (1 + IRR)3 0 = –$1,300 + $700 / (1 + IRR) + $750 / (1 + IRR)2 + $300 / (1 + IRR)3 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: Incremental IRR = 18.78% For investingtype projects, accept the larger project when the incremental IRR is greater than the discount rate. Since the incremental IRR, 18.78%, is greater than the required rate of return of 10 percent, choose the CDROM project. 15. a. The profitability index is the PV of the future cash flows divided by the initial investment. The profitability index for each project is: PICDMA = [$13,000,000 / 1.10 + $7,000,000 / 1.102 + $2,000,000 / 1.103] / $5,000,000 = 3.82 PIG4 = [$10,000,000 / 1.10 + $25,000,000 / 1.102 + $20,000,000 / 1.103] / $10,000,000 = 4.48 PIWiFi = [$10,000,000 / 1.10 + $20,000,000 / 1.102 + $50,000,000 / 1.103] / $15,000,000 = 4.21 The profitability index implies we accept the G4 project. Remember this is not necessarily correct because the profitability index does not necessarily rank projects with different initial investments correctly. The NPV of each project is: NPVCDMA = –$5,000,000 + $13,000,000 / 1.10 + $7,000,000 / 1.102 + $2,000,000 / 1.103 NPVCDMA = $14,105,935.39 NPVG4 = –$10,000,000 + $10,000,000 / 1.10 + $25,000,000 / 1.102 + $20,000,000 / 1.103 NPVG4 = $34,778,362.13 b. 122 PIWiFi = –$15,000,000 + $10,000,000 / 1.10 + $20,000,000 / 1.102 + $50,000,000 / 1.103 PIWiFi = $48,185,574.76 NPV implies we accept the WiFi project since it has the highest NPV. This is the correct decision if the projects are mutually exclusive. c. We would like to invest in all three projects since each has a positive NPV. If the budget is limited to $315million, we can only accept the CDMA project and the G4 project, or the WiFi project. NPV is additive across projects and the company. The total NPV of the CDMA project and the G4 project is: NPVCDMA and G4 = $14,105,935.39 + 34,778,362.13 NPVCDMA and G4 = $48,884,297.52 This is greater than the WiFi project, so we should accept the CDMA project and the G4 project. 16. a. The payback period is the time that it takes for the cumulative undiscounted cash inflows to equal the initial investment. AZM MiniSUV: Cumulative cash flows Year 1 = $270,000 = $270,000 Cumulative cash flows Year 2 = $270,000 + 180,000 = $450,000 Payback period = 1+ $30,000 / $180,000 = 1.17 years AZF FullSUV: Cumulative cash flows Year 1 = $250,000 = $250,000 Cumulative cash flows Year 2 = $250,000 + 400,000 = $650,000 Payback period = 1+ $350,000 / $400,000 = 1.88 years Since the AZM has a shorter payback period than the AZF, the company should choose the AZM. Remember the payback period does not necessarily rank projects correctly. b. The NPV of each project is: NPVAZM = –$300,000 + $270,000 / 1.10 + $180,000 / 1.102 + $150,000 / 1.103 NPVAZM = $206,912.10 NPVAZF = –$600,000 + $250,000 / 1.10 + $400,000 / 1.102 + $300,000 / 1.103 NPVAZF = $183,245.68 The NPV criteria implies we accept the AZM because it has the highest NPV. 123 c. The IRR is the interest rate that makes the NPV of the project equal to zero. So, the IRR of the AZM is: 0 = –$300,000 + $270,000 / (1 + IRR) + $180,000 / (1 + IRR)2 + $150,000 / (1 + IRR)3 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRRAZM = 51.43% And the IRR of the AZF is: 0 = –$600,000 + $250,000 / (1 + IRR) + $400,000 / (1 + IRR)2 + $300,000 / (1 + IRR)3 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRRAZF = 26.04% The IRR criteria implies we accept the AZM because it has the highest IRR. Remember the IRR does not necessarily rank projects correctly. d. 17. a. Incremental IRR analysis is not necessary. The AZM has the smallest initial investment, and the largest NPV, so it should be accepted. The profitability index is the PV of the future cash flows divided by the initial investment. The profitability index for each project is: PIA = [$140,000 / 1.12 + $140,000 / 1.122] / $200,000 = 1.18 PIB = [$260,000 / 1.12 + $260,000 / 1.122] / $400,000 = 1.10 PIC = [$150,000 / 1.12 + $120,000 / 1.122] / $200,000 = 1.15 b. The NPV of each project is: NPVA = –$200,000 + $140,000 / 1.12 + $140,000 / 1.122 NPVA = $36,607.14 NPVB = –$400,000 + $260,000 / 1.12 + $260,000 / 1.122 NPVB = $39,413.27 NPVC = –$200,000 + $150,000 / 1.12 + $120,000 / 1.122 NPVC = $29,591.84 c. Accept projects A, B, and C. Since the projects are independent, accept all three projects because the respective profitability index of each is greater than one...
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 Spring '10
 eshmalwi
 Finance, Corporate Finance

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