Chapter 9 Capital Budgeting Techniques  Solutions to Problems Note to instructor: In most problems involving the internal rate of return calculation, a financial calculator has been used. P9-1. LG 2: Payback Period Basic (a) $42,000 ÷ $7,000 = 6 years (b) The company should accept the project, since 6 < 8. P9-2. LG 2: Payback Comparisons Intermediate (a) Machine 1: $14,000 ÷ $3,000 = 4 years, 8 months Machine 2: $21,000 ÷ $4,000 = 5 years, 3 months (b) Only Machine 1 has a payback faster than 5 years and is acceptable. (c) The firm will accept the first machine because the payback period of 4 years, 8 months is less than the 5-year maximum payback required by Nova Products. (d) Machine 2 has returns which last 20 years while Machine 1 has only seven years of returns. Payback cannot consider this difference; it ignores all cash inflows beyond the payback period.222 Part 3 Long-Term Investment Decisions P9-3. LG 2: Choosing Between Two Projects with Acceptable Payback Periods Intermediate (a) Project A Project B Year Cash Inflows Investment Balance Year Cash Inflows Investment Balance 0 −$100,000 0 −$100,000 1 $10,000 −90,000 1 40,000 −60,000 2 20,000 −70,000 2 30,000 −30,000 3 30,000 −40,000 3 20,000 −10,000 4 40,000 0 4 10,000 0 5 20,000 5 20,000 Both project A and project B have payback periods of exactly 4 years. (b) Based on the minimum payback acceptance criteria of 4 years set by John Shell, both projects should be accepted. However, since they are mutually exclusive projects, John should accept project B. (c) Project B is preferred over A because the larger cash flows are in the early years of the project. The quicker cash inflows occur, the greater their value. P9-4. LG 3: NPV Basic PVn = PMT × (PVIFA14%,20 yrs) NPV = PVn − Initial investment (a) PVn = $2,000 × 6.623 NPV = $13,246 − $10,000 PVn = $13,246 NPV = $3,246 Calculator solution: $3,246.26 Accept (b) PVn = $3,000 × 6.623 NPV = $19,869 − $25,000 PVn = $19,869 NPV = −$5,131 Calculator solution: − $5,130.61 Reject (c) PVn = $5,000 × 6.623 NPV = $33,115 − $30,000 PVn = $33,115 NPV = $3,115 Calculator solution: $3,115.65 AcceptChapter 9 Capital Budgeting Techniques 223 P9-5. LG 3: NPV for Varying Cost of Captial Basic PVn = PMT × (PVIFAk%,8 yrs.) (a) 10 % (b) 12 % PVn = $5,000 × (5.335) PVn = $5,000 × (4.968) PVn = $26,675 PVn = $24,840 NPV = PVn − Initial investment NPV = PVn − Initial investment NPV = $26,675 − $24,000 NPV = $24,840 − $24,000 NPV = $2,675 NPV = $840 Calculator solution: $2,674.63 Calculator solution: $838.19 Accept; positive NPV Accept; positive NPV (c) 14 % PVn = $5,000 × (4.639) PVn = $23,195 NPV = PVn − Initial investment NPV = $23,195 − $24,000 NPV = −$805 Calculator solution: − $805.68 Reject; negative NPV P9-6. LG 3: NPV–Independent Projects Intermediate Project A PVn = PMT × (PVIFA14%,10 yrs.) PVn = $4,000 × (5.216) PVn = $20,864 NPV = $20,864 − $26,000 NPV = −$5,136 Calculator solution: −$5,135.54 Reject224 Part 3 Long-Term Investment Decisions Project B—PV of Cash Inflows Year CF PVIF14%,nPV 1 $100,000 0.877 $87,700 2 120,000 0.769 92,280 3 140,000 0.675 94,500 4 160,000 0.592 94,720 5 180,000 0.519 93,420 6 200,000 0.456 91,200 $553,820 NPV = PV of cash inflows − Initial investment = $553,820 − $500,000 NPV = $53,820 Calculator solution: $53,887.93 Accept Project C—PV of Cash Inflows Year CF PVIF14%,nPV 1 $20,000 0.877 $17,540 2 19,000 0.769 14,611 3 18,000 0.675 12,150 4 17,000 0.592 10,064 5 16,000 0.519 8,304 6 15,000 0.456 6,840 7 14,000 0.400 5,600 8 13,000 0.351 4,563 9 12,000 0.308 3,696 10 11,000 0.270 2,970 $86,338 NPV = PV of cash inflows − Initial investment = $86,338 − $170,000 NPV = −$83,662 Calculator solution: −$83,668.24 Reject Project D PVn = PMT × (PVIFA14%,8 yrs.) PVn = $230,000 × 4.639 PVn = $1,066,970 NPV = PVn − Initial investment NPV = $1,066,970 − $950,000 NPV = $116,970 Calculator solution: $116,938.70 AcceptChapter 9 Capital Budgeting Techniques 225 Project E—PV of Cash Inflows Year CF PVIF14%,n PV 4 $20,000 0.592 $11,8405 30,000 0.519 15,5706 0 07 50,000 0.400 20,0008 60,000 0.351 21,0609 70,000 0.308 21,560 $90,030NPV = PV of cash inflows − Initial investment NPV = $90,030 − $80,000 NPV = $10,030 Calculator solution: $9,963.62 Accept P9-7. LG 3: NPV Challenge (a) PVA = $385,000 × (PVIFA9%,5) PVA = $385,000 × (3.890) PVA = $1,497,650 Calculator solution: $1,497,515.74 The immediate payment of $1,500,000 is not preferred because it has a higher present value than does the annuity. (b) 9%, 5PVA $1,500,000PMT $385,604PVIFA 3.890== = Calculator solution: $385,638.69 (c) PVAdue = $385,000 × (PVIFA9%,4 + 1) PVAdue = $385,000 × (3.24 + 1) PVAdue = $385,000 × (4.24) PVAdue = $1,632,400 Changing the annuity to a beginning-of-the-period annuity due would cause Simes Innovations to prefer the $1,500,000 one-time payment since the PV of the annuity due is greater than the lump sum. (d) No, the cash flows from the project will not influence the decision on how to fund the project. The investment and financing decisions are separate.226 Part 3 Long-Term Investment Decisions P9-8. LG 3: NPV and Maximum Return Challenge PVn = PMT × (PVIFAk%,n) (a) PVn = $4,000 × (PVIFA10%,4) PVn = $4,000 × (3.170) PVn = $12,680 NPV = PVn − Initial investment NPV = $12,680 − $13,000 NPV = –$320 Calculator solution: −$320.54 Reject this project due to its negative NPV. (b) $13,000 = $4,000 × (PVIFAk%,n) $13,000 ÷ $4,000 = (PVIFAk%,4) 3.25 = PVIFA9%,4Calculator solution: 8.86% 9% is the maximum required return that the firm could have for the project to be acceptable. Since the firm’s required return is 10% the cost of capital is greater than the expected return and the project is rejected. P9-9. LG 3: NPV–Mutually Exclusive Projects Intermediate PVn = PMT × (PVIFAk%,n) (a) & (b) Press PV of cash inflows; NPV A PVn = PMT × (PVIFA15%,8 yrs.) PVn = $18,000 × 4.487 PVn = $80,766 NPV = PVn − Initial investment NPV = $80,766 − $85,000 NPV = −$4,234 Calculator solution: −$4,228.21 RejectChapter 9 Capital Budgeting Techniques 227 B Year CF PVIF15%,nPV 1 $12,000 0.870 $10,440 2 14,000 0.756 10,584 3 16,000 0.658 10,528 4 18,000 0.572 10,296 5 20,000 0.497 9,940 6 25,000 0.432 10,800 $62,588 NPV = $62,588 − $60,000 NPV =