Unformatted text preview: the cash flows we know there are four IRRs for this project. Even with most computer spreadsheets, we have to do some trial and error. From trial and error, IRRs of 25%, 33.33%, 42.86%, and 66.67% are found. We would accept the project when the NPV is greater than zero. See for yourself that the NPV is greater than zero for required returns between 25% and 33.33% or between 42.86% and 66.67%. 130 23. a. Here the cash inflows of the project go on forever, which is a perpetuity. Unlike ordinary perpetuity cash flows, the cash flows here grow at a constant rate forever, which is a growing perpetuity. The PV of the future cash flows from the project is: PV of cash inflows = C1/(R – g) PV of cash inflows = $115,000/(.13 – .06) = $1,642,857.14 NPV is the PV of the outflows minus by the PV of the inflows, so the NPV is: NPV of the project = –$1,400,000 + 1,642,857.14 = $242,857.14 The NPV is positive, so we would accept the project. b. Here we want to know the minimum growth rate in cash flows necessary to accept the project. The minimum growth rate is the growth rate at which we would have a zero NPV. The equation for a zero NPV, using the equation for the PV of a growing perpetuity is: 0 = – $1,400,000 + $115,000/(.13 – g) Solving for g, we get: g = 4.79% 24. a. The project involves three cash flows: the initial investment, the annual cash inflows, and the abandonment costs. The mine will generate cash inflows over its 11year economic life. To express the PV of the annual cash inflows, apply the growing annuity formula, discounted at the IRR and growing at eight percent. PV(Cash Inflows) = C {[1/(r – g)] – [1/(r – g)] × [(1 + g)/(1 + r)]t} PV(Cash Inflows) = $175,000{[1/(IRR – .08)] – [1/(IRR – .08)] × [(1 + .08)/(1 + IRR)]11} At the end of 11 years, the Utah Mining Corporate will abandon the mine, incurring a $125,000 charge. Discounting the abandonment costs back 11 years at the IRR to express its present value, we get: PV(Abandonment) = C11 / (1 + IRR)11 PV(Abandonment) = –$125,000 / (1+ IRR)11 So, the IRR equation for this project is: 0 = –$900,000 + $175,000{[1/(IRR – .08)] – [1/(IRR – .08)] × [(1 + .08)/(1 + IRR)]11} –$125,000 / (1+ IRR)11 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 22.26% 131 b. Yes. Since the mine’s IRR exceeds the required return of 10 percent, the mine should be opened. The correct decision rule for an investmenttype project is to accept the project if the discount rate is above the IRR. Although it appears there is a sign change at the end of the project because of the abandonment costs, the last cash flow is actually positive because of the operating cash in the last year. 25. First, we need to find the future value of the cash flows for the one year in which they are blocked by the government. So, reinvesting each cash inflow for one year, we find: Year 2 cash flow = $205,000(1.04) = $213,200 Year 3 cash flow = $265,000(1.04) = $275,600 Year 4 cash flow = $346,000(1.04) = $359,840 Year 5 cash flow = $220,000(1.04) = $228,800 So, the NPV of the project is: NPV = –$750,000 + $213,200/1.112 + $275,600/1.113 + $359,840/1.114 + $228,800/1.115 NPV = –$2,626.33 And the IRR of the project is: 0 = –$750,000 + $213,200/(1 + IRR)2 + $275,600/(1 + IRR)3 + $359,840/(1 + IRR)4 + $228,800/(1 + IRR)5 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 10.89% While this may look like a MIRR calculation, it is not a MIRR, rather it is a standard IRR calculation. Since the cash inflows are blocked by the government, they are not available to the company for a period of one year. Thus, all we are doing is calculating the IRR based on when the cash flows actually occur for the company. 26. a. We can apply the growing perpetuity formula to find the PV of stream A. The perpetuity formula values the stream as of one year before the first payment. Therefore, the growing perpetuity formula values the stream of cash flows as of year 2. Next, discount the PV as of the end of year 2 back two years to find the PV as of today, year 0. Doing so, we find: PV(A) = [C3 / (R – g)] / (1 + R)2 PV(A) = [$8,900 / (0.12 – 0.04)] / (1.12)2 PV(A) = $88,687.82 We can apply the perpetuity formula to find the PV of stream B. The perpetuity formula discounts the stream back to year 1, one period prior to the first cash flow. Discount the PV as of the end of year 1 back one year to find the PV as of today, year 0. Doing so, we find: PV(B) = [C2 / R] / (1 + R) PV(B) = [–$10,000 / 0.12] / (1.12) PV(B) = –$74,404.76 132 b. If we combine the cash flow streams to form Project C, we get: Project A = [C3 / (R – G)] / (1 + R)2 Project B = [C2 / R] / (1 + R) Project C = Project A + Project B Project C = [C3 / (R – g)] / (1 + R)2 + [C2 / R] / (1 +R) 0 = [$8,900 / (IRR – .04)] / (1 + IRR)2 + [–$10,000 / IRR] / (1 + IRR) Using a spreadsheet, financial calculat...
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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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