【正文】 $5,000,000 ? ? . Note: The asset is disposed of at the end of the fifth year—the end of its class life—so the asset is held for its entire class life, and the full amount of depreciation can be claimed in Year 5. dPurchase cost ($5,000,000) less proceeds from sale of old puter ($500,000)。 thus, there are three years of depreciation to claim, with the last year being only half. Let X = Annual depreciation. Then X + X + X/2 = $2,000,000 and X = $800,000. Buy new MRI equipment: Yr. (1 – t)Ra –(1 – t)Cb tNCc Otherd CF df Pres. Value 0 .... — $600,000 $(4,500,000) $(3,900,000) $ (3,900,000) 1 .... — $(300,000) 400,000 — 100,000 89,300 2 .... — (300,000) 640,000 — 340,000 270,980 3 .... — (300,000) 384,000 — 84,000 59,808 4 .... — (300,000) 230,400 — (69,600) (44,266) 5 .... $427,200 (300,000) 230,400 288,000 645,600 366,055 NPV ........................................................................................................................... $ (3,158,123) a ? ($1,000,000 – Book value), where Book value = $5,000,000 – $4,712,000. b() ? $500,000. cYear 0: Tax savings from loss on sale of asset: ? $1,500,000 (The loss on the sale of the old puter is $2,000,000 – $500,000.) Years 1–5: Tax savings from MACRS depreciation: $5,000,000 ? ? 。 df = Discount factor) CF() = $500,000 CF = $500,000/ = $108,155 454 20–3 1. NPV = P – I = ( ? $1,000,000) – $6,000,000 = ($665,000) The system should not be purchased. 2. df = Investment/Annual cash flow = $1,350,000/$217,350 = IRR = 6% The decision is good. The oute covers the cost of capital. 20–4 1. Payback period = Original investment/Annual cash inflow = $2,340,000/($3,042,000 – $2,340,000) = $2,340,000/$702,000 = years 2. a. Initial investment (Depreciation = $468,000): Accounting rate of return = Average ine/Investment = ($702,000 – $468,000)/$2,340,000 = 10% b. Average investment: Accounting rate of return = ($702,000 – $468,000)/[($2,340,000 + $0)/2] = $234,000/$1,170,000 = 20% 3. Year Cash Flow Discount Factor Present Value 0 ................... $(2,340,000) $(2,340,000) 1–5 ................. 702,000 2,661,282 NPV ....................................................................................................... $ 321,282 4. P = CF(df) = I for the IRR, thus, df = Investment/Annual cash flow = $2,340,000/$702,000 = For five years and a df of , the IRR is between 14% and 16% (approximately %). 455 20–5 Xray equipment: Year Cash Flow Discount Factor Present Value 0 .................. $(750,000) $(750,000) 1 .................. 375,000 334,875 2 .................. 150,000 119,550 3 .................. 300,000 213,600 4 .................. 150,000 95,400 5 .................. 75,000 42,525 NPV ...................................................................................................... $ 55,950 Biopsy equipment: Year Cash Flow 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 equat