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**Unformatted text preview: **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. 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. 34 4. 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 0.0576 1.05 0.1152 1.05 0.1152 1.05 0.192 1.05 0.32 1.05 0.20 $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. 5. 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 1.08 .35) (1 $26,000 100,000 NPV B $ [ ] + + + + + × × 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 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 present value of these cash flows: t = 0 t = 1 t = 2 t = 3 t = 4 t = 5 t = 6 Investment 100,000 Cash Inflow 26,000 26,000 26,000 26,000 26,000 Depreciation 20,000 32,000 19,200 11,520 11,520 5,760 Taxable Income 6,000-6,000 6,800 14,480 14,480-5,760 Tax 2,100-2,100 2,380 5,068 5,068-2,016 Cash Flow-100,000 23,900 28,100 23,620 20,932 20,932 2,016 NPV (at 8%) = -$4,127 b. IRR A = 9.43% IRR B = 6.39% Effective tax rate = 32.2% 0.322 0.0943 0.0639 1 = =- 35 6. a....

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