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ENGR 111 Fall 2011 HOMEWORK 3 ANSWER KEY (1)

# ENGR 111 Fall 2011 HOMEWORK 3 ANSWER KEY (1) - ENGR 111...

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ENGR 111 Fall 2011 HOMEWORK 3 ANSWER KEY 1. We can apply the growing perpetuity formula to find the PV of stream X . 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(X) = [C 3 / (R – g)] / (1 + R) 2 PV(X) = [\$8,900 / (0.12 – 0.04)] / (1.12) 2 PV(X) = \$89,684.31 We can apply the perpetuity formula to find the PV of stream Y . 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(Y) = [C 2 / R] / (1 + R) PV(Y) = [–\$12,000 / 0.12] / (1.12) PV(Y) = –\$89,285.71 If we combine the cash flow streams to form Project C, we get: Project X = [C 3 / (R – G)] / (1 + R) 2 Project Y = [C 2 / R] / (1 + R) Project Z = Project X + Project Y Project Z = [C 3 / (R – g)] / (1 + R) 2 + [C 2 / R] / (1 +R) 0 = [\$9,000 / (IRR – .04)] / (1 + IRR) 2 + [–\$12,000 / IRR] / (1 + IRR) Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 12.09% The correct decision rule for an investing-type project is to accept the project if the discount rate is below the IRR. Since there is one IRR, a decision can be made. At a point in the future, the cash flows from stream X will be greater than those from stream Y . In year 11 the cash flow is going to turn to positive from negative. In addition, in year 20, there will be a one time negative cash flow which makes the changes in signs more than one. When the sign of the cash flows change more than once over the life of the project, there may be multiple internal rates of return. In such cases, there is no correct decision rule for accepting and rejecting projects using the internal rate of return. 2. The IRR is the interest rate that makes the NPV of the project equal to zero. So, the IRR for each project is: 0 = C 0 + C 1 / (1 + IRR) + C 2 / (1 + IRR) 2 + C 3 / (1 + IRR) 3 0 = –\$750 + \$310 / (1 + IRR) + \$430 / (1 + IRR) 2 + \$330 / (1 + IRR) 3 IRR = 19.83%

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0 = C 0 + C 1 / (1 + IRR) + C 2 / (1 + IRR) 2 + C 3 / (1 + IRR) 3 0 = –\$2,100 + \$1,200/ (1 + IRR) + \$760 / (1 + IRR) 2 + \$850 / (1 + IRR) 3 IRR = 17.36% Based on the IRR rule, the first project should be chosen because it has the higher IRR.
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