【正文】 low Discount Factor Present Value 0 .................. $(750,000) $(750,000) 1 .................. 75,000 66,975 2 .................. 75,000 59,775 3 .................. 525,000 373,800 4 .................. 600,000 381,600 5 .................. 675,000 382,725 NPV ...................................................................................................... $ 514,875 20–6 1. Xray equipment: Payback period = $ 375,000 year 150,000 225,000 ($225,000/$300,000) $ 750,000 years Biopsy equipment: Payback period = $ 75,000 year 75,000 525,000 75,000 ($75,000/$600,000) $ 750,000 years This might be a reasonable strategy because payback is a rough measure of risk. The assumption is that the longer it takes a project to pay for itself, the riskier the project is. Other reasons might be that the firm might have liquidity 456 problems, the cash flows might be risky, or there might be a high risk of obsolescence. 20–6 Concluded 2. Xray equipment: Average cash flow = ($375,000 + $150,000 + $300,000 + $150,000 + $75,000)/5 = $210,000 Average depreciation = $750,000/5 = $150,000 Average ine = $210,000 – $150,000 = $60,000 Average investment = $750,000/2 = $375,000 Accounting rate of return = $60,000/$375,000 = 16% Biopsy equipment: Average cash flow = ($75,000 + $75,000 + $525,000 + $600,000 + $675,000)/5 = $390,000 Average investment = $750,000/2 = $375,000 Accounting rate of return = ($390,000 – $150,000*)/$375,000 = 64% *Average depreciation. 20–7 1. a. Return of the original investment .................................................... $370,000 b. Cost of capital ($370,000 ? 12%) ..................................................... 44,400 c. Profit earned on the investment ($450,000 – $414,400) ............. 35,600 Present value of profit: P = Future profit ? Discount factor = $35,600 ? = $31,791 2. Year Cash Flow Discount Factor Present Value 457 ............... 0 $(370,000) $(370,000) ..... ............... 1 450,000 401,850 NPV ....................................................................................................... $ 31,850 Net present value gives the present value of future profits. (The slight difference is due to rounding in the discount factor.) 458 20–8 1. P = I = df ? CF * ? CF = $120,000 CF = $41,181 *From Exhibit 20B2, 14% for four years. 2. For IRR: (Discount factors from Exhibit 20B2) I = df ? CF I = ? CF (1) For NPV: NPV = df ? CF – I = ? CF – I (2) Substituting equation (1) into equation (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: