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SOLUTIONS CHAPTER 12 - CHAPTER 12 CAPITAL BUDGETING UNDER...

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CHAPTER 12 CAPITAL BUDGETING UNDER CERTAINTY 12-1 (a) Net Cash Investment Book value of old equipment $ 5,000 Less: market value of old equipment 2,000 Operating loss due to sale $ 3,000 x Tax rate x 0.50 Tax savings $ 1,500 Price of new equipment $20,000 Less: tax savings $1,500 market value of old equipment 2,000 3,500 Net cash investment $16,500 (b) Annual Net Cash Flows Cash savings $ 2,000 Additional sales 4,000 Additional revenues $ 6,000 Less: additional depreciation depreciation of new equipment $4,000 depreciation of old equipment (1,000) 3,000 Taxable income $ 3,000 Less: taxes at 50% 1,500 Earnings after taxes $ 1,500 Add: additional depreciation 3,000 Annual net cash flows $ 4,500 12.2 (a) Year 1 Year 2 Year 3 Revenues $20,000 $20,000 $20,000 Less: operating cost 4,500 4,500 4,500 Depreciation 4,500 3,000 1,500 Taxable income $11,000 $12,500$14,000 Less: taxes at 40% 4,400 5,000 5,600 Earnings after taxes $ 6,600 $ 7,500$ 8,400 Add: depreciation 4,500 3,000 1,500 Annual net cash flows$11,100 $10,500 $ 9,900
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(b) Revenues $20,000$20,000 $20,000 Less: operating cost 4,500 4,500 4,500 depreciation 6,000 2,000 1,000 Taxable income $ 9,500$13,500 $14,500 Less: taxes at 40% 3,800 5,400 5,800 Earnings after taxes $ 5,700$ 8,100 $ 8,700 Add: depreciation 6,000 2,000 1,000 Annual net cash flows 11,700 $10,100 $ 9,700 12-3 (a) Net Cash Investment Book value of old machine $ 5,000 Less: market value of old machine 4,000 Operating loss due to sale $ 1,000 x Tax rate x 0.40 Tax savings $ 400 Purchase price of new machine $ 8,000 Freight and installation cost 2,000 Total cost of new machine $10,000 Less: tax savings $ 400 market value of old machine 4,000 4,400 Net cash investment $ 5,600 (b) Incremental Net Cash Flows OLD MACHINE Years 1-5 Revenues $2,000 Less: operating cost 500 Depreciation 1,000 Taxable income $ 500 Less: taxes at 40% 200 Earnings after taxes $ 300 Add: depreciation 1,000 Annual net cash flows $1,300
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NEW MACHINE Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Revenues $10,000 $9,000 $8,000 $7,000 $6,000 $5,500 Operating cost 3,500 3,500 3,500 3,5003,500 3,500 Depreciation 2,000 2,000 2,000 2,000 2,000 ______ Taxable income $ 4,500 $3,500 $2,500 $1,500 $ 500 $2,000 Taxes at 40% 1,800 2,400 1,000 600 200 800 EAT $ 2,700 $2,100 $1,500 $ 900 $ 300 $1,200 Depreciation 2,000 2,000 2,000 2,000 2,000 Net cash flows $ 4,700 $4,100 $3,500 $2,900 $2,300 $1,200 Incremental Net Cash Flows of the Project Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 New machine $ 4,700 $4,100 $3,500 $2,900$2,300 $1,200 Old machine 1,300 1,300 1,300 1,300 1,300 1,300 Net cash flows$ 3,400 $2,800 $2,200 $1,600 $1,000 - $100 _ 12-4 Net Cash Investment = $35,000 Net cash flows Years 1-7 Savings in operating costs $8,000 Less: depreciation 5,000 Taxable income $3,000 Less: taxes at 46% 1,380 Earnings after taxes $1,620 Add: depreciation 5,000 Annual net cash flows $6,620 (a) Payback period = $35,000 ÷ $ 6,620 = 5.29 years (b) Average rate of return = $1,620 ÷ ($35,000 / 2) = 9.26% (c) Net present value = $6,620 x PVAIF 7,5% - $35,000 = $6,620 x 5.786 - $35,000 = $3,303 or by financial calculator: CF 0 = -35000 C01 = 6620 F01 = 7 NPV; I = 5; CPT NPV = $3305.79 (d) Profitability index = $38,305.79 ÷ $35,000 = 1.09
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(e) To determine the internal rate of return for a project with an even series of net cash flows, use PVAIF n,i = PVA ÷ CF. PVAIF 7,i = $35,000 ÷ $6,620 = 5.287 If we look across the 7 year row of Table D, we find that the discount factor 5.287 is between 7 percent and 8 percent. Thus, we can interpolate between these two rates as follows: Interest Rate 8% IRR------------- y--------------7% . . Discount Factor 5.206 5.287 5.389 IRR = 7% + y = 7% + 0.6% = 7.6% or by financial calculator: IRR AND COMPUTE; IRR = 7.55% 12-5 Project A: $1,000 ÷ $400 = 2.5 years Project B: 2 + ($1,000 - $500 - $400) ÷ 500 = 2.2 years Or years 1 and 2 ($500 + $400) + $100 of year 3 or $100/500 = 2.2 years 12-6 Project C: $500 ÷ ($2,000/2) = 50% Project D: [($600 + $400 + $200)/3] ÷ ($2,000/2 ) = $400 ÷ $1,000 = 40% 12-7 (a) Project E: NPV = $4,100 x PVAIF 4,10% - $10,000 = $4,100 x 3.170 - $10,000 = $2,997 or by financial calculator: CF 0 = -10000 C01 = 4100 F01 = 4 NPV; I = 10; CPT NPV = $2996.45
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Project F: Year
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