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chap 8 finance notes

# chap 8 finance notes - Solutions to Chapter 8 Net Present...

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Solutions to Chapter 8 Net Present Value and Other Investment Criteria 1. NPV A = –\$200 + [\$80 × annuity factor(11%, 4 periods)] = 20 . 48 \$ (1.11) 0.11 1 0.11 1 \$80 \$200 4 = × - × + NPV B = –\$200 + [\$100 × annuity factor(11%, 3 periods)] = 37 . 44 \$ (1.11) 0.11 1 0.11 1 \$100 \$200 3 = × - × + Both projects are worth pursuing. 2. Choose Project A, the project with the higher NPV. 3. NPV A = –\$200 + [\$80 × annuity factor(16%, 4 periods)] = 85 . 23 \$ (1.16) 0.16 1 0.16 1 \$80 \$200 4 = × - × + NPV B = –\$200 + [\$100 × annuity factor(16%, 3 periods)] = 59 . 24 \$ (1.16) 0.16 1 0.16 1 \$100 \$200 3 = × - × + Therefore, you should now choose project B. 4. IRR A = Discount rate (r) which is the solution to the following equation: 200 \$ r) (1 r 1 r 1 \$80 4 = + × - × r = IRR A = 21.86% IRR B = Discount rate (r) which is the solution to the following equation: 200 \$ r) (1 r 1 r 1 \$100 3 = + × - × r = IRR B = 23.38% 8-1

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5. No. Even though project B has the higher IRR, its NPV is lower than that of project A when the discount rate is lower (as in Problem 1) and higher when the discount rate is higher (as in Problem 3). This example shows that the project with the higher IRR is not necessarily better. The IRR of each project is fixed, but as the discount rate increases, project B becomes relatively more attractive compared to project A. This is because B’s cash flows come earlier, so the present value of these cash flows decreases less rapidly when the discount rate increases. 6. The profitability indexes are as follows: Project A: \$48.20/\$200 = 0.2410 Project B: \$44.37/\$200 = 0.2219 In this case, with equal initial investments , both the profitability index and NPV give projects the same ranking. This is an unusual case, however, since it is rare for the initial investments to be equal. 7. Project A has a payback period of: \$200/\$80 = 2.5 years Project B has a payback period of 2 years. 8. No. Despite its longer payback period, Project A may still be the preferred project, for example, when the discount rate is 11% (as in Problems 1 and 2). As in problem 5, you should note that the payback period for each project is fixed, but the NPV changes as the discount rate changes. The project with the shorter payback period need not have the higher NPV. 9. NPV = - \$3,000 + [\$800 × annuity factor(10%, 6 years)] = 21 . 484 \$ (1.10) 0.10 1 0.10 1 \$800 \$3,000 6 = × - × + At the 10% discount rate, the project is worth pursuing. IRR = Discount rate (r) which is the solution to the following equation: 000 , 3 \$ r) (1 r 1 r 1 \$800 6 = + × - × r = IRR = 15.34% You can solve for IRR using a financial calculator by entering: PV = ( - )3000; n = 6; FV = 0; PMT = 800; and then compute i. Since the IRR is 15.34%, this is the highest discount rate before project NPV turns negative. 8-2
10. Payback period = \$2,500/\$600 = 4.167 years This is less than the cutoff, so the firm would accept the project. r = 2% NPV = - \$2,500 + [\$600 × annuity factor( 2%, 6 years)] = 86 . 860 \$ (1.02) 0.02 1 0.02 1 \$600 \$2,500 6 = × - × + r = 12% NPV = - \$2,500 + [\$600 × annuity factor(12%, 6 years)] = 16 . 33 \$ (1.12) 0.12 1 0.12 1 \$600 \$2,500 6 - = × - × + If r = 2%, the project should be pursued; at r = 12%, it should not be.

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chap 8 finance notes - Solutions to Chapter 8 Net Present...

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