# CH6 - CHAPTER 6 Making Investment Decisions with the Net...

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CHAPTER 6 Making Investment Decisions with the Net Present Value Rule Answers to Practice Questions 1. See the table below. We begin with the cash flows given in the text, Table 6.6, line 8, and utilize the following relationship from Chapter 3: Real cash flow = nominal cash flow/(1 + inflation rate) t Here, the nominal rate is 20 percent, the expected inflation rate is 10 percent, and the real rate is given by the following: (1 + r nominal ) = (1 + r real ) × (1 + inflation rate) 1.20 = (1 + r real ) × (1.10) r real = 0.0909 = 9.09% As can be seen in the table, the NPV is unchanged (to within a rounding error). Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Net Cash Flows/Nominal -12,600 -1,484 2,947 6,323 10,534 9,985 5,757 3,269 Net Cash Flows/Real -12,600 -1,349 2,436 4,751 7,195 6,200 3,250 1,678 NPV of Real Cash Flows (at 9.09%) = \$3,804 2. No, this is not the correct procedure. The opportunity cost of the land is its value in its best use, so Mr. North should consider the \$45,000 value of the land as an outlay in his NPV analysis of the funeral home. 3. Unfortunately, there is no simple adjustment to the discount rate that will resolve the issue of taxes. Mathematically: 1.15 0.35) /(1 C 1.10 C 1 1 - and 2 2 2 2 1.15 0.35) (1 / C 1.10 C - 46

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4. Even when capital budgeting calculations are done in real terms, an inflation forecast is still required because: a. Some real flows depend on the inflation rate, e.g., real taxes and real proceeds from collection of receivables; and, b. Real discount rates are often estimated by starting with nominal rates and “taking out” inflation, using the relationship: (1 + r nominal ) = (1 + r real ) × (1 + inflation rate) 5. Investment in working capital arises as a forecasting issue only because accrual accounting recognizes sales when made, not when cash is received (and costs when incurred, not when cash payment is made). If cash flow forecasts recognize the exact timing of the cash flows, then there is no need to also include investment in working capital. 6. If the \$50,000 is expensed at the end of year 1, the value of the tax shield is: \$16,667 1.05 \$50,000 0.35 = × If the \$50,000 expenditure is capitalized and then depreciated using a five-year MACRS depreciation schedule, the value of the tax shield is: \$15,306 1.05 .0576 1.05 .1152 1.05 .1152 1.05 .192 1.05 .32 1.05 .20 \$50,000] [0.35 6 5 4 3 2 = + + + + + × × If the cost can be expensed, then the tax shield is larger, so that the after-tax cost is smaller. 7. a. \$3,810 1.08 26,000 ,000 100 NPV 5 1 t t A = + - = = NPV B = -Investment + PV(after-tax cash flow) + PV(depreciation tax shield) = + - × + - = 5 1 t t B 1.08 .35) 0 (1 26,000 100,000 NPV [ ] + + + + + × × 6 5 4 3 2 1.08 0.0576 1.08 0.1152 1.08 0.1152 1.08 0.192 1.08 0.32 1.08 0.20 100,000 0.35 NPV B = -\$4,127 47
Another, perhaps more intuitive, way to do the Company B analysis is to first calculate the cash flows at each point in time, and then compute the

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## This note was uploaded on 10/19/2009 for the course FINANCE finance mb taught by Professor Myers during the Spring '09 term at NUCES - Lahore.

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CH6 - CHAPTER 6 Making Investment Decisions with the Net...

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