CHAPTER 15 CAPITAL BUDGETING 21. a. Payback = $3,000,000 ÷ $600,000 per year = 5 years b. Year 1 2 3 4 5 6 7 8 9 10

Amount $300,000 300,000 300,000 300,000 300,000 400,000 400,000 400,000 400,000 400,000

Cumulative Amount $ 300,000 600,000 900,000 1,200,000 1,500,000 1,900,000 2,300,000 2,700,000 3,100,000 3,500,000

The payback is eight years plus [(3,000,000 – 2,700,000) ÷ 400,000] or 8.75 years. 22. a. Investment = $140,000 + $180,000 = $320,000 Year Amount Cumulative Amount 1 $70,000 $ 70,000 2 78,000 148,000 3 72,000 220,000 4 56,000 276,000 5 50,000 326,000 6 48,000 374,000 7 44,000 418,000 Payback = 4 years + [($320,000 – $276,000) ÷ $50,000] = 4.9 years Based on the payback criterion, Houston Fashions should not invest in the proposed product line. b. Yes. Houston Fashions should also use a discounted cash flow technique so as to consider both the time value of money and the cash flows that occur after the payback period. 23. Point in Time 0 1 2 3 4 5 6 7 8 9

Cash Flows $(1,800,000) 280,000 280,000 340,000 340,000 340,000 288,800 288,800 288,800 260,000

PV Factor 1.0000 0.8929 0.7972 0.7118 0.6355 0.5674 0.5066 0.4524 0.4039 0.3606

Present Value $(1,800,000) 250,012 223,216 242,012 216,070 192,916 146,306 130,653 116,646 93,756

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427

260,000

0.3220

83,720 $ (104,693)

Based on the NPV, this is an unacceptable investment. 24. a. The contribution margin of each part is $1 (or $7.50 – $6.50) Contribution margin per year = $1  100,000 = $100,000 Point in Time 0 1–8 1–8 NPV

Cash Flows $(500,000) (20,000) 100,000

PV Factor 1.0000 5.5348 5.5348

Present Value $(500,000) (110,696) 553,480 $ (57,216)

b. Based on the NPV, this is not an acceptable investment. c. Other considerations would include whether refusing to produce this part for the customer would cause a loss of other business from that customer. The company should also consider going back to the customer and asking for a higher price that would cause the project to have a positive NPV. 25. PI = PV of cash inflows ÷ PV of cash outflows = ($18,000 + $240,000) ÷ $240,000 = 1.08 26. a. PV of inflows: $91,000  6.4177 = $584,011 PV of investment: $600,000 PI = $584,011 ÷ $600,000 = 0.97 b. Cedar City Public Transportation should not add the bus route because the PI is less than 1.00. c. To be acceptable, a project must generate a PI of at least 1; a PI greater than 1 equates to an NPV > 0. 27. a. PV = Discount factor × Annual cash inflow $700,000 = Discount factor  $144,000 Discount factor = $700,000 ÷ $144,000 = 4.8611 The IRR is 13 percent (rounded to the nearest whole percent). b. Yes. The IRR on this proposal is greater than the firm’s hurdle rate of 7 percent. c. $700,000 = 5.9713  Annual cash flow Annual cash flow = $700,000 ÷ 5.9713 Annual cash flow = $117,227 28. a. PV = Discount factor × Annual cash inflow $1,800,000 = Discount factor  $300,000 Discount factor = $1,800,000 ÷ $300,000 = 6.0000 The IRR is 10.5 percent (rounded to the nearest half percent). The project is acceptable because the IRR exceeds the discount rate.

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b. The main qualitative factors would be the effect of the technology on the perceived quality of the food that is processed by the new machinery. An additional consideration would be the effect of the technology on employees, particularly if the investment would cause layoffs. 29. Investment cost = $375,000 × Discount factor for 14%, 7 years = $375,000 × 4.2883 = $1,608,113 NPV = $375,000 × Discount factor (10%, 7 years) – $1,608,113 = ($375,000 × 4.8684) – $1,608,113 = $217,537 30. a. Annual depreciation = $1,000,000 ÷ 8 years = $125,000 per year Tax benefit = $125,000  0.30 = $37,500 PV = $37,500  5.7466 = $215,498 b. Accelerated method $1,000,000  0.30  0.40  0.9259 $600,000  0.30  0.40  0.8573 $360,000  0.30  0.40  0.7938 $216,000  0.30  0.40  0.7350 $129,600*  0.30  0.6806 Total

= = = = =

$111,108 61,726 34,292 19,051 26,462 $252,639

*

In the final year, the remaining undepreciated cost is expensed.

c. The depreciation benefit computed in (b) exceeds that computed in (a) solely because of the time value of money. The depreciation method in (b) allows for faster recapture of the cost; therefore, there is less discounting of the future cash flows. 35. Film studios Cameras & equipment Land improvement Motion picture #1 Motion picture #2 Motion picture #3 Corporate aircraft b. Ranking according to: NPV 1. Film studios 2. MP #3 3. Land improvement 4. Cameras & equip. 5. MP #1 6. MP #2 7. Corp. aircraft

a

NPV $3,578,910 1,067,920 2,250,628 1,040,276 1,026,008 3,197,320 518,916

PI 1.18 1.33 1.45 1.06 1.09 1.40 1.22

PI Land improvement MP #3 Cameras & equip. Corp. aircraft Film studios MP #2 MP #1

c. Suggested purchases: 1. Motion picture #3 @ $8,000,000 2. Land improvement @ $5,000,000

IRR 13.03% 18.62 19.69 12.26 14.09 21.32 18.15 IRR MP #3 Land improvement Cameras & equip. Corp. aircraft MP #2 Film studios MP #1 NPV $3,197,320 2,250,628

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3. Cameras & equipment @ $3,200,000 4. Corporate aircraft @ $2,400,000 Total NPV 35. a. Project Name Film studios Cameras & equipment Land improvement Motion picture #1 Motion picture #2 Motion picture #3 Corporate aircraft d. Ranking according to: NPV 8. Film studios 9. MP #3 10. Land improvement 11. Cameras & equip. 12. MP #1 13. MP #2 14. Corp. aircraft

1,067,920 518,916 $7,034,784

NPV $3,578,910 1,067,920 2,250,628 1,040,276 1,026,008 3,197,320 518,916

PI 1.18 1.33 1.45 1.06 1.09 1.40 1.22

IRR 13.03% 18.62 19.69 12.26 14.09 21.32 18.15

PI Land improvement MP #3 Cameras & equip. Corp. aircraft Film studios MP #2 MP #1

e. Suggested purchases: 5. Motion picture #3 @ $8,000,000 6. Land improvement @ $5,000,000 7. Cameras & equipment @ $3,200,000 8. Corporate aircraft @ $2,400,000 Total NPV

IRR MP #3 Land improvement Cameras & equip. Corp. aircraft MP #2 Film studios MP #1 NPV $3,197,320 2,250,628 1,067,920 518,916 $7,034,784

45. a. ($000s omitted) Investment New CM Oper. costs Cash flow b. Year 1 2 3 4 5 6

t0 –(190) 0 –(190) Cash Flow $40,000 33,000 33,000 33,000 30,000 30,000

t1

t2

t3

t4

t5

t6

t7

t8

60 –20 40

60 –27 33

60 –27 33

60 –27 33

60 –30 30

60 –30 30

60 –30 30

60 –33 27

Cumulative Cash Flow $ 40,000 73,000 106,000 139,000 169,000 199,000

Payback = 5 + [($190,000 – $169,000) ÷ $30,000] = 5.7 years c. Time 0 1

Cash Flow $(190,000) 40,000

PV Factor for 8% 1.0000 0.9259

Present Value $(190,000) 37,036

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2 3 4 5 6 7 8 NPV 46. a. Time: Amount:

b. Year 1 2 3 4 5 6

33,000 33,000 33,000 30,000 30,000 30,000 27,000 t0 ($41,000)

0.8573 0.7938 0.7350 0.6806 0.6302 0.5835 0.5403 t1 $5,900

Cash Flow $5,900 8,100 8,300 8,000 8,000 8,300

t2 $8,100

28,291 26,195 24,255 20,418 18,906 17,505 14,588 $ (2,806) t3 $8,300

t4 $8,000

t5 $8,000

t6 $8,300

Cumulative $ 5,900 14,000 22,300 30,300 38,300 46,600

Payback = 5 years + [($41,000 – $38,300) ÷ $8,300] = 5.3 years c.

44.

Cash Flow Description Purchase the truck Cost savings Cost savings Cost savings Cost savings Cost savings Cost savings Cost savings NPV

47. a. Year 0 1–7 7 NPV

Time t0 t1 t2 t3 t4 t5 t6 t7

Cash Flow $(5,000,000) 838,000 400,000

Amount $(41,000) 5,900 8,100 8,300 8,000 8,000 8,300 9,200

Discount Factor 1.0000 0.9259 0.8573 0.7938 0.7350 0.6806 0.6302 0.5835

PV Factor 1.0000 5.5824 0.6651

Present Value $(41,000) 5,463 6,944 6,589 5,880 5,445 5,231 5,368 $ (80)

PV $(5,000,000) 4,678,051 266,040 $ (55,909)

b. No, the NPV is negative; therefore this is an unacceptable project. c. PI = ($4,678,051 + $266,040) ÷ $5,000,000 = 0.99 d. PV of annual cash flows = $5,000,000 – $266,040 PV of annual cash flows = $4,733,960 PV of annual cash flows = Annual cash flow  5.5824 $4,733,960 = Annual cash flow  5.5824 Annual cash flow = $4,733,960 ÷ 5.5824 = $848,015 Minimum labor savings = $848,015 + Operating costs © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.

t7 $9,200

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= $848,015 + $112,000 = $960,015 e. The company should consider the quality of work performed by the machine compared to the quality of work performed by the individuals; the reliability of the mechanical process compared to the manual process; and perhaps most importantly, the effect on worker morale and the ethical considerations in displacing 14 workers. 48. a. Payback period = $140,000 ÷ ($47,500 – $8,500) = 3.6 years The project does not meet the payback criterion. b. Discount factor = Investment ÷ Annual cash flow = $140,000 ÷ $39,000 = 3.5897 Discount factor of 3.5897 indicates IRR  4 % This is an unacceptable IRR. c. Foster should consider two main factors: (1) the effect of the computer system on tax return accuracy and quality of service delivered to clients and (2) the effect of firing one employee on both the dismissed employee and the remaining employees.

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