【正文】 ion (2): NPV = ( ? CF) – ( ? CF) $1,750 = ? CF CF = $1,750/ = $10,000 in savings each year Substituting CF = $10,000 into equation (1): I = ? $10,000 = $24,020 original investment 3. For IRR: I = df ? CF $60,096 = df ? $12,000 df = $60,096/$12,000 = From Exhibit 20B2, 18% column, the year corresponding to df = is 14. Thus, the lathe must last for 14 years. 459 20–8 Concluded 4. X = Cash flow in Year 4 Investment = 3X Year Cash Flow Discount Factor Present Value .................. 0 (3X) $ (3X) .................. 1 15,000 13,635 .................. 2 20,000 16,520 .................. 3 30,000 22,530 .................. 4 X NPV ....................................................................................................... $ 6,075 –3X + $13,635 + $16,520 + $22,530 + = $6,075 – + $52,685 = $6,075 – = –$46,610 X = $20,117 Cash flow in Year 4 = X = $20,117 Cost of project = 3X = $60,351 20–9 1. Payback period = Investment/Annual cash flow = $9,000,000/$1,500,000 = years The system would not be acquired. 2. NPV = P – I = ( ? $1,500,000) – $9,000,000 = ($525,000) df = $9,000,000/$1,500,000 = IRR is between 10% and 12% (IRR = %). NPV and IRR also signal rejection of the project. 460 20–9 Concluded 3. Payback period = $9,000,000/$1,800,000 = years NPV: Year Cash Flow Discount Factor Present Value 0 ................... $(9,000,000) $ (9,000,000) 1–10................ 1,800,000 10,170,000 10 .................. 1,000,000 322,000 NPV ....................................................................................................... $ 1,492,000 IRR: df = = $9,000,000/$1,800,000 IRR (without salvage value) is now between 14% and 16% (approximately %). Payback, NPV, and IRR all now signal acceptance. The decrease in salvage value does not change the decision for any of the three measures. NPV decreases by $161,000 ( ? $500,000). For this pany, including salvage value is not critical. The increased cash inflow for the expanded market share drives the change in decision. The presence of salvage value, however, increases the attractiveness of the investment and reduces the uncertainty about the oute. 20–10 1. NPV System I: Year Cash Flow Discount Factor Present Value 0 ...................... $(120,000) $(120,000) 1 ...................... — — — 2 ...................... 162,708 134,397 NPV .......................................................................................................... $ 14,397 NPV System II: Year Cash Flow Discount Factor Present Value 0 ...................... $(120,000) $(120,000) 1–2 .................... 76,628 133,026 NPV .......................................................................................................... $ 13,026 System I should be chosen using NPV. 461 20–10 Concluded IRR System I: I = df ? CF $120,000 = $162,708/(1 + i)2 (1 + i)2 = $162,708/$120,000 = 1 + i = IRR = % IRR System II: df = I/CF = $120,000/$76,628 = From Exhibit 20B2, IRR = 18% System II should be chosen using IRR. 2. Modified parison: Year System I System II ..................... 0 $(120,000) $(120,000) ..................... 1 — — ..................... 2 162,708 160,919* *($76,628 ? ) + $76,628 Notice that the future value of System I is greater than that of System II and thus maximizes the value of the firm. NPV signals the correct choice, whereas IRR would have chosen System II. 20–11 Project I: CF = NI + Noncash expenses = $18,000 + $15,000 = $33,000 Project II: CF = –(1 – t) ? (Cash expenses) + (t ? Noncash expenses) = – ? ($30,000) + ( ? $30,000) = –$18,000 + $12,000 = ($6,000) 462 20–12 1. Year Depreciation tNC df Present Value ........... 1 $3,000 $1,200 $ 1,072 ........... 2 6,000 2,400 1,913 ........... 3 6,000 2,400 1,709 ........... 4 3,000 1,200 763 $ 5,457 2. Year Depreciation tNC df Present Value ........... 1 $6,000 $2,400 $ 2,143 ........... 2 8,000 3,200 2,550 ........... 3 2,666 1,066 759 ........... 4 1,334 534 340 $ 5,792 3. MACRS increases the present value of tax shielding by increasing the amount of depreciation in the earlier years. 463 20–13 1. $10,000 – $25,000 = $ (15,000) loss ? tax rate $ 6,000 tax savings Sales price .............. $10,000 Tax savings ............ 6,000 ....Net proceeds $ 16,000 Total cost of new press .......................... $ 50,000 Less: proceeds of old press .......... (16,000) Net investment (cash outflow) $ 34,000 2. Year (1 – t)Ca tNCb CF ............... 1 $(1,200) 2,400 $1,200 ............... 2 (1,200) 3,840 2,640 ............... 3 (1,200) 2,304 1,104 ............... 4 (1,200) 1,382 182 a (1 – ) ? $2,000. b ()($30,000)(). ()($30,000)(). ()($30,000)(). ()($30,000)(). 3. a. Aftertax cash flow (CF): CF = $50,000 = $30,000 (NI) + $20,000 (depreciation) b. Aftertax cash flow from revenues = $72,000 = [(1 – )$120,000] c. Aftertax cash expenses = $30,000 = [(1 – )$50,000] d. Cash inflow tax effect of depreciation = $8,000 = ( ? $20,000) 464 PROBLEMS 20–14 1. Year 0 ................................................................................................. $ (420,000) Year 1: Operating costs ( ? $35,000)..................................... $ (21,000) Savings ( ? $243,000) ................................................. 145,800