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Unformatted text preview: C2 / (1 + IRR)2 + C3 / (1 + IRR)3 0 = – $3,500 + $1,800/(1 + IRR) + $2,400/(1 + IRR)2 + $1,900/(1 + IRR)3 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 33.37% And the IRR for Project B is: 0 = C0 + C1 / (1 + IRR) + C2 / (1 + IRR)2 + C3 / (1 + IRR)3 0 = – $2,300 + $900/(1 + IRR) + $1,600/(1 + IRR)2 + $1,400/(1 + IRR)3 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 29.32% 7. The profitability index is defined as the PV of the cash inflows divided by the PV of the cash outflows. The cash flows from this project are an annuity, so the equation for the profitability index is: PI = C(PVIFAR,t) / C0 PI = $65,000(PVIFA15%,7) / $190,000 PI = 1.423 116 8. a. The profitability index is the present value of the future cash flows divided by the initial cost. So, for Project Alpha, the profitability index is: PIAlpha = [$800 / 1.10 + $900 / 1.102 + $700 / 1.103] / $1,500 = 1.331 And for Project Beta the profitability index is: PIBeta = [$500 / 1.10 + $1,900 / 1.102 + $2,100 / 1.103] / $2,500 = 1.441 b. According to the profitability index, you would accept Project Beta. However, remember the profitability index rule can lead to an incorrect decision when ranking mutually exclusive projects. Intermediate 9. a. To have a payback equal to the project’s life, given C is a constant cash flow for N years: C = I/N b. c. To have a positive NPV, I < C (PVIFAR%, N). Thus, C > I / (PVIFAR%, N). Benefits = C (PVIFAR%, N) = 2 × costs = 2I C = 2I / (PVIFAR%, N) 10. a. The IRR is the interest rate that makes the NPV of the project equal to zero. So, the equation that defines the IRR for this project is: 0 = C0 + C1 / (1 + IRR) + C2 / (1 + IRR)2 + C3 / (1 + IRR)3 + C4 / (1 + IRR)4 0 = $8,000 – $4,400 / (1 + IRR) – $2,700 / (1 + IRR)2 – $1,900 / (1 + IRR)3 – $1,500 / (1 +IRR)4 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 14.81% b. This problem differs from previous ones because the initial cash flow is positive and all future cash flows are negative. In other words, this is a financingtype project, while previous projects were investingtype projects. For financing situations, accept the project when the IRR is less than the discount rate. Reject the project when the IRR is greater than the discount rate. IRR = 14.81% Discount Rate = 10% IRR > Discount Rate Reject the offer when the discount rate is less than the IRR. 117 c. Using the same reason as part b., we would accept the project if the discount rate is 20 percent. IRR = 14.81% Discount Rate = 20% IRR < Discount Rate Accept the offer when the discount rate is greater than the IRR. d. The NPV is the sum of the present value of all cash flows, so the NPV of the project if the discount rate is 10 percent will be: NPV = $8,000 – $4,400 / 1.1 – $2,700 / 1.12 – $1,900 / 1.13 – $1,500 / 1.14 NPV = –$683.42 When the discount rate is 10 percent, the NPV of the offer is –$683.42. Reject the offer. And the NPV of the project if the discount rate is 20 percent will be: NPV = $8,000 – $4,400 / 1.2 – $2,700 / 1.22 – $1,900 / 1.23 – $1,500 / 1.24 NPV = $635.42 When the discount rate is 20 percent, the NPV of the offer is $635.42. Accept the offer. e. Yes, the decisions under the NPV rule are consistent with the choices made under the IRR rule since the signs of the cash flows change only once. 11. a. The IRR is the interest rate that makes the NPV of the project equal to zero. So, the IRR for each project is: Deepwater Fishing IRR: 0 = C0 + C1 / (1 + IRR) + C2 / (1 + IRR)2 + C3 / (1 + IRR)3 0 = –$750,000 + $310,000 / (1 + IRR) + $430,000 / (1 + IRR)2 + $330,000 / (1 + IRR)3 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 19.83% Submarine Ride IRR: 0 = C0 + C1 / (1 + IRR) + C2 / (1 + IRR)2 + C3 / (1 + IRR)3 0 = –$2,100,000 + $1,200,000 / (1 + IRR) + $760,000 / (1 + IRR)2 + $850,000 / (1 + IRR)3 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 17.36% 118 Based on the IRR rule, the deepwater fishing project should be chosen because it has the higher IRR. b. To calculate the incremental IRR, we subtract the smaller project’s cash flows from the larger project’s cash flows. In this case, we subtract the deepwater fishing cash flows from the submarine ride cash flows. The incremental IRR is the IRR of these incremental cash flows. So, the incremental cash flows of the submarine ride are: Submarine Ride Deepwater Fishing Submarine – Fishing Year 0 –$2,100,000 –750,000 –$1,350,000 Year 1 $1,200,000 310,000 $890,000 Year 2 $760,000 430,000 $330,000 Year 3 $850,000 330,000 $520,000 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...
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This note was uploaded on 07/10/2010 for the course FIN 6301 taught by Professor Eshmalwi during the Spring '10 term at University of TexasTyler.
 Spring '10
 eshmalwi
 Finance, Corporate Finance

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