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Business Finance Answers_Part_41

Business Finance Answers_Part_41 - CHAPTER 9 B-161 12 a The...

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CHAPTER 9 B-161 12. a. The IRR is the interest rate that makes the NPV of the project equal to zero. The equation for the IRR of Project A is: 0 = –$43,000 + $23,000/(1+IRR) + $17,900/(1+IRR) 2 + $12,400/(1+IRR) 3 + $9,400/(1+IRR) 4 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 20.44% The equation for the IRR of Project B is: 0 = –$43,000 + $7,000/(1+IRR) + $13,800/(1+IRR) 2 + $24,000/(1+IRR) 3 + $26,000/(1+IRR) 4 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 18.84% Examining the IRRs of the projects, we see that the IRR A is greater than the IRR B , so IRR decision rule implies accepting project A. This may not be a correct decision; however, because the IRR criterion has a ranking problem for mutually exclusive projects. To see if the IRR decision rule is correct or not, we need to evaluate the project NPVs. b. The NPV of Project A is: NPV A = –$43,000 + $23,000/1.11+ $17,900/1.11 2 + $12,400/1.11 3 + $9,400/1.11 4 NPV A = $7,507.61 And the NPV of Project B is: NPV B = –$43,000 + $7,000/1.11 + $13,800/1.11 2 + $24,000/1.11 3 + $26,000/1.11 4 NPV B = $9,182.29 The NPV B is greater than the NPV A , so we should accept Project B. c. To find the crossover rate, we subtract the cash flows from one project from the cash flows of the other project. Here, we will subtract the cash flows for Project B from the cash flows of Project A. Once we find these differential cash flows, we find the IRR. The equation for the crossover rate is: Crossover rate: 0 = $16,000/(1+R) + $4,100/(1+R) 2 – $11,600/(1+R) 3 – $16,600/(1+R) 4
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