Net present value provides a way for both investors and companies to compare potential investments or projects in today's dollars. Solve for the payment amount, which is the equivalent annual cost. Depreciation150,000150,0004. To compute the annual depreciation expense, determine the total initial cost of the two assets ($162,000 + $54,000 = $216,000) and divide this amount by 15, the economic life of each of the two assets. The NPV is the PV (present value) of all cash inflows minus the PV of all cash outflows. If the stream of payments involves costs as well as benefits then the present value is the sum of the present values of the individual payments treating the costs as negative payments. The difference is the amount subject to capital gains taxes. NPV = -Initial Investment - PV(Maintenance Costs) + PV(Salvage Value) = -$3,000 - $76 + $745 = -$2,331 In order to calculate the equivalent annual cost of the new autoclave, set the NPV equal to an annuity with the same economic life. 7.12 Purchase of New Equipment = -$28,000,000 Since the old equipment is sold at a price that is greater than its book value, the firm will record a capital gain on the sale, and this sale will be subject to the corporate tax rate. net present value method and requires a 6% rate of return. 7.15 Since the problem lists nominal cash flows and a real discount rate, one must determine the nominal discount rate before computing the net present value of the project. Since the cash outlay occurs today, no discounting is necessary. NPV = -Initial Investment PV(Maintenance) + PV(Tax Shield) = -$60,000 - $7,661 + $15,787 = -$51,874 In order to calculate the equivalent annual cost (EAC), set the NPV of the equipment equal to an annuity with the same economic life. Capital Investment- 25,000 - $750,000$345,000$370,000 $40,00010. Its cost ofcapital is 10%. 1+ Real Discount Rate = (1+ Nominal Discount Rate) / (1+ Inflation Rate) Real Discount Rate = [(1.14) / (1.05)] 1 = 0.0857 Find the equivalent annual cost (EAC) of each of the copiers. Keyboards Produced 2. The present value of the five rents is computed as follows: 2.56581 X $20,000 = $51,316.. 17. 230,000 6 4,000 200,000 15,000 230,000 7 4,000 14,000 230,000 8 4,000 13,000 230,000 9 4,000 12,000 10 4,000 11,000 Solution Project A Discount rate Number of years CF 0 CF 1-10 PV of cash inflows NPV of project A The project will be Project B Discount rate CF 0 CF 1 . Chapter 13 Class Exercises Solution 1. Greater than the total cash flow without the net present value applied B. PV(C0) = -$400,000 PV(C1) = $159,200 / (1.15) = $138,435 PV(C2) = $159,200 / (1.15)2 = $120,378 PV(C3) = $158,540 / (1.15)3 = $104,243 PV(C4) = $157,121 / (1.15)4 = $89,834 PV(C5) = $154,834 / (1.15)5 = $76,980 NPV = PV(C0) + PV(C1) + PV(C2) + PV(C3) + PV(C4) + PV(C5) = $129,870 These calculations could also have been performed in a single step: NPV = -$400,000+ $159,200 / (1.15) + $159,200 / (1.15)2 + $158,540 / (1.15)3 + $157,121 / (1.15)4 + $154,834 / (1.15)5 = $129,870 The NPV of the investment is $129,870. The present value break-even point is 20,532 units. The total amount received in salvage value is the resale value minus the taxes paid on the difference between the resale value and the book value: $66,000 = $100,000 - 0.34 ($100,000 - $0). First, find the annual depreciation tax shield, which is the tax rate multiplied by the annual depreciation expense. To find the nominal rate, use the following equation: 1+ Real Discount Rate = (1+Nominal Discount Rate) / (1+Inflation Rate) 1.08 = (1+Nominal Discount Rate) / (1.05) Nominal Discount Rate = 0.134 To find the present value of the depreciation tax shield, apply the four-year annuity formula to the annual tax savings: PV(Tax Shield) = C1 A40.134 = $2,720,000 A40.134 = $8,023,779 PV(C0) = -$32,000,000 = -$32,000,000 PV(C1) = $5,524,200 / (1.08) = $5,115,000 PV(C2) = $31,499,886 / (1.08)2 = $27,006,075 PV(C3) = $31,066,882 / (1.08)3 = $24,661,893 PV(C4) = $17,425,007 / (1.08)4 = $12,807,900 PV(Depreciation Tax Shield) = $8,023,779 NPV = PV(C0) + PV(C1) + PV(C2) + PV(C3) + PV(C4) + PV(Depreciation Tax Shield) = $45,614,647 These calculations also could have been performed in a single step: NPV = -$32,000,000+ $5,524,200 / (1.08) + $31,499,886 / (1.08)2 + $31,066,882 / (1.08)3 + $17,425,007 / (1.08)4 + (0.34) ($8,000,000) A40.134 = $45,614,647 The NPV of the project is $45,614,647. The $225,000 purchase price of the building is a sunk cost and should be ignored. Remember that the cash flow occurs at the end of year 5, and therefore must be discounted back five years. The inflow and outflow of cash other than initial investment occur at the end of each period. Apply the growing perpetuity formula. Total = $109, PV (Revenues) = (1 Tc) (Year 1 Selling Price) (Year 1 Production) GATr,g * PV (Revenues) = (1 - 0.34) ($3.15) (1,000,000) GA50.20, 0.1025 = $7,364,645 * The notation GATr, g represents a growing annuity consisting of T payments growing at a rate of g per payment, discounted at r. The PV of the variable costs is also calculated using the five-year growing annuity formula. 7.27 Use the equivalent annual cost (EAC) method to determine which facility Plexi Glasses should purchase. 2.Revenue Expenses$200,000 50,000$206,000 51,500$212,180 53,045$218,545 54,636$225,102 56,2753.Depreciation 50,00050,00050,00050,00050,0004.Taxable Income [1 2 3]100,000104,500109,135113,909118,8275.Taxes34,00035,53037,10638,72940,4016.Operating Cash Flow [1 2 5]116,000118,970122,029125,180128,4267. b. 7.18 Year 1Year 2Year 3Year 4 Revenues$40,000,000$80,000,000$80,000,000$60,000,000 Labor Costs30,600,00031,212,00031,836,24032,472,965 Energy Costs1,030,0001,060,9001,092,7271,125,509 Revenues-Costs8,370,00047,727,10047,071,03326,401,526 After-tax Revenues-Costs5,524,20031,499,88631,066,88217,425,007 Since revenues and costs are expressed in real terms, after-tax income will be discounted at the real discount rate of 8%. Note that an increase in required net working capital is a negative cash flow whereas a decrease in required net working capital is a positive cash flow.
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