442255

CHAPTER 13 CAPITAL INVESTMENT DECISIONS

QUESTIONS FOR WRITING AND DISCUSSION

1. Independent projects are such that the ac-ceptance of one does not preclude the ac-ceptance of another. With mutually exclusive projects, acceptance of one precludes the acceptance of others.

2. The timing and quantity of cash flows de-termine the present value of a project. The present value is critical for assessing wheth-er a project is acceptable or not.

3. By ignoring the time value of money, good projects can be rejected and bad projects accepted.

4. The payback period is the time required to recover the initial investment. Payback = $80,000/$30,000 = 2.67 years

5. (a) A measure of risk. Roughly, projects with shorter paybacks are less risky. (b) Obso-lescence. If the risk of obsolescence is high, firms will want to recover funds quickly. (c) Self-interest. Managers want quick pay-backs so that short-run performance meas-ures are affected positively, enhancing chances for bonuses and promotion. Also, this method is easy to calculate.

6. The accounting rate of return is the average income divided by original or average in-vestment. ARR = $100,000/$300,000 = 33.33%

7. Agree. Essentially, net present value is a measure of the return in excess of the in-vestment and its cost of capital.

8. NPV measures the increase in firm value from a project.

9. The cost of capital is the cost of investment funds and is usually viewed as the weighted average of the costs of funds from all sources. It should serve as the discount rate for calculating net present value or the benchmark for IRR analysis.

10. For NPV, the required rate of return is the discount rate. For IRR, the required rate of return is the benchmark against which the IRR is compared to determine whether an investment is acceptable or not.

11. If NPV > 0, then the investment is accepta-ble. If NPV < 0, then the investment should be rejected.

12. Disagree. Only if the funds received each period from the investment are reinvested to earn the IRR will the IRR be the actual rate of return.

13. Postaudits help managers determine if re-sources are being used wisely. Additional resources or corrective action may be needed. Postaudits also serve to encourage managers to make good capital investment decisions. They also provide feedback that may help improve future decisions.

14. NPV signals which investment maximizes firm value; IRR may provide misleading sig-nals. IRR may be popular because it pro-vides the correct signal most of the time and managers are accustomed to working with rates of return.

15. Often, investments must be made in assets that do not directly produce revenues. In this case, choosing the asset with the least cost (as measured by NPV) makes sense.

16. NPV analysis is only as good as the accura-cy of the cash flows. If projections of cash flows are not accurate, then incorrect in-vestment decisions may be made.

17. The quality and reliability of the cash flow projections are directly related to the as-sumptions and methods used for forecast-ing. If the assumptions and methods are faulty, then the forecasts will be wrong, and incorrect decisions may be made.

18. The principal tax implications that should be considered in Year 0 are gains and losses on the sale of existing assets.

19. The MACRS method provides more shiel-ding effect in earlier years than the straight-line method does. As a consequence, the present value of the shielding benefit is greater for the MACRS method.

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20. The half-year convention assumes that an asset is in service for only a half year in the year of acquisition. Thus, only half of the first year’s depreciation can be claimed, regard-less of the date on which use of the asset actually began. It increases the length of time depreciation is recognized by one year over the indicated class life.

21. Intangible and indirect benefits are of much greater importance in the advanced manu-facturing environment. Greater quality, more reliability, improved delivery, and the ability

to maintain or increase market share are examples of intangible benefits. Reduction in support labor in such areas as scheduling and stores are indirect benefits.

22. Sensitivity analysis changes the assump-tions on which the capital investment analy-sis is based. Even with sound assumptions, there is still the element of uncertainty. No one can predict the future with certainty. By changing the assumptions, managers can gain insight into the effects of uncertain fu-ture events.

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EXERCISES

13–1

1. a 2. e 3. c 4. a 5. d 6. e 7. c 8. b 9. d

10. e 11. b

12. c 13. a 14. e 15. c 16. a 17. e 18. b 19. e 20. c

13–2

1. Payback period = $200,000/$60,000 = 3.33 years 2. Payback period: $125,000 1.0 year 175,000 1.0 year 200,000 0.8 year $500,000 2.8 years 3. Investment = annual cash flow × payback period = $120,000 × 3 = $360,000 4. Annual cash flow = Investment/payback period = $250,000/2.5 = $100,000 per year

442288

13–3

1. Initial investment (Average depreciation = 300,000):

Accounting rate of return = Average accounting income/Investment = ($2,500,000 – $2,000,000 - $300,000)/$1,500,000 = 13.3% 2. Accounting rate of return (ARR):

Project A: ARR = ($12,800 – $4,000)/$20,000 = 44%

Project B: ARR = ($7,600 – $2,000)/$20,000 = 18%

Project A should be chosen. 3. ARR = Average Net Income/Average Investment 0.25 = $100,000/Average Investment Average Investment = $100,000/0.25 = $400,000 Thus, Investment = 2 × $400,000 = $800,000 4. ARR = Average Net Income/Investment 0.50 = Average Net Income/$200,000 Average Net Income = 0.50 × $200,000 = $100,000

13–4 1. NPV = P – I

= (5.650 × $240,000) – $1,360,000 = $(4,000)

The system should not be purchased.

2. NPV = P – I

= (4.623 × $9,000) – $30,000 = $11,607

Yes, he should make the investment.

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3. NPV = P - I I = P – NPV I = 4.355 × $10,000 - $3,550 = $40,000

13–5

1. P = CF(df) = I for the IRR, thus,

df = Investment/Annual cash flow = $1,563,500/$500,000 = 3.127

For five years and a discount factor of 3.127, the IRR is 18%.

2. P = CF(df) = I for the IRR, thus, df = $521,600/$100,000 = 5.216 For ten years, and a discount factor of 5.216, IRR = 14%

Yes, the investment should be made. 3. CF(df) = I for the IRR, thus, CF = I/df = $2,400,000/4.001 =$599,850. 13-6

1. Larson Blood Analysis Equipment:

Year Cash Flow Discount Factor Present Value 0 $(200,000) 1.000 $(200,000) 1 120,000 0.893 107,160 2 100,000 0.797 79,700 3 80,000 0.712 56,960 4 40,000 0.636 25,440 5 20,000 0.567 11,340 NPV $ 80,600

443300

13-6 Concluded

Lawton Blood Analysis Equipment:

Year Cash Flow Discount Factor Present Value 0 $(200,000) 1.000 $(200,000) 1 20,000 0.893 17,860 2 20,000 0.797 15,940 3 120,000 0.712 85,440 4 160,000 0.636 101,760 5 180,000 0.567 102,060 NPV $ 123,060

2. CF(df) – I = NPV CF(3.605) - $200,000 = $123,060 (3.605)CF = $323,060 CF = $323,060/3.605 CF = $89,614 per year Thus, the annual cash flow must exceed $89,614 to be selected.

13–7

1. Payback period = Original investment/Annual cash inflow = $800,000/($1,300,000 – $1,000,000) = $800,000/$300,000 = 2.67 years

2. a. Initial investment (Average depreciation = 160,000):

Accounting rate of return = Average accounting income/Investment = ($300,000 – $160,000)/$800,000 = 17.5%

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13-7 Concluded 3. Year Cash Flow Discount Factor Present Value

0 $(800,000) 1.000 $(800,000) 1 300,000 0.909 272,700 2 300,000 0.826 247,800 3 300,000 0.751 225,300 4 300,000 0.683 204,900 5 300,000 0.621 186,300 NPV $ 337,000

4. P = CF(df) = I for the IRR, thus,

df = Investment/Annual cash flow = $800,000/$300,000 = 2.67

For five years and a discount factor of 2.67, the IRR is between 24 and 26%.

13-8 1. Payback period:

Project A: $ 3,000 1.00 year 4,000 1.00 year 3,000 0.60 year $10,000 2.60 years

Project B: $ 3,000 1.00 year 4,000 1.00 year 3,000 0.50 year $10,000 2.50 years

Both projects have about the same payback so the most profitable should be chosen (Project A).

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13-8 Concluded

2. Accounting rate of return (ARR):

Project A: ARR = ($6,400 – $2,000)/$10,000 = 44%

Project B: ARR = ($3,800 – $2,000)/$10,000 = 18%

Project A should be chosen. 3. P = 9.818 × $24,000 = $235,632

Wilma should take the annuity. 4. NPV = P – I

= (4.623 × $6,000) – $20,000 = $7,738

Yes, he should make the investment. 5. df = $130,400/$25,000 = 5.216

IRR = 14%

Yes, the investment should be made.

13–9

1. a. Return of the original investment $200,000 b. Cost of capital ($200,000 × 10%) 20,000 c. Profit earned on the investment ($231,000 – $220,000) 11,000

Present value of profit:

P = F × Discount factor = $11,000 × 0.909 = $9,999 2. Year Cash Flow Discount Factor Present Value

0 $(200,000) 1.000 $(200,000) 1 231,000 0.909 209,979 Net present value $ 9,979

Net present value gives the present value of future profits (the slight differ-ence is due to rounding error in the discount factor).

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13–10

1. Bond cost = $6,000/$120,000 = 0.05

Cost of capital = 0.05(0.6) + 0.175(0.4) = 0.03 + 0.07 = 0.10 2. Year Cash Flow Discount Factor Present Value

0 $(200,000) 1.000 $(200,000) 1 100,000 0.909 90,900 2 100,000 0.826 82,600 3 100,000 0.751 75,100 Net present value $ 48,600

It is not necessary to subtract the interest payments and the dividend pay-ments because these are associated with the cost of capital and are included in the firm’s cost of capital of 10 percent.

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13–11

1. P = I = df × CF 2.914* × CF = $120,000 CF = $41,181

*From Exhibit 13B-2, 14 percent for four years 2. For IRR (discount factors from Exhibit 13B-2): I = df × CF = 2.402 × CF (1)

For NPV: NPV = df × CF – I = 2.577 × CF – I (2)

Substituting equation (1) into equation (2): NPV = (2.577 × CF) – (2.402 × CF) $1,750 = 0.175 × CF CF = $1,750/0.175 = $10,000 in savings each year

Substituting CF = $10,000 into equation (1): I = 2.402 × $10,000 = $24,020 original investment 3. For IRR: I = df × CF $60,096 = df × $12,000 df = $60,096/$12,000 = 5.008

From Exhibit 13B-2, 18 percent column, the year corresponding to df = 5.008 is 14. Thus, the lathe must last 14 years.

443355

13–11 Concluded

4. X = Cash flow in Year 4

Investment = 2X

Year Cash Flow Discount Factor Present Value 0 $ (2X) 1.000 $ (2X) 1 10,000 0.909 9,090 2 12,000 0.826 9,912 3 15,000 0.751 11,265 4 X 0.683 0.683X NPV $ 3,927

–2X + $9,090 + $9,912 + $11,265 + 0.683X = $3,927 –1.317X + $30,267 = $3,927 –1.317X = ($26,340) X = $20,000

Cash flow in Year 4 = X = $20,000 Cost of project = 2X = $40,000

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13–12

1. NPV:

Project I

Year Cash Flow Discount Factor Present Value 0 $(100,000) 1.000 $(100,000) 1 — — — 2 134,560 0.826 111,147 NPV $ 11,147

Project II

Year Cash Flow Discount Factor Present Value 0 $(100,000) 1.000 $(100,000) 1 63,857 0.909 58,046 2 63,857 0.826 52,746 NPV $ 10,792

Project I should be chosen using NPV. IRR:

Project I

I = df × CF $100,000 = $134,560/(1 + i)2 (1 + i)2 = $134,560/$100,000 = 1.3456 1 + I = 1.16 IRR = 16% Project II

df = I/CF = $100,000/$63,857 = 1.566

From Exhibit 13B-2, IRR = 18 percent. Project II should be chosen using IRR. 2. NPV is an absolute profitability measure and reveals how much the value of

the firm will change for each project; IRR gives a measure of relative profita-bility. Thus, since NPV reveals the total wealth change attributable to each project, it is preferred to the IRR measure.

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13–13

Project A:

CF = NI + Noncash expenses = $54,000 + $45,000 = $99,000 Project B:

CF = –[(1 – t) × Cash expenses] + [t × Noncash expenses] = –(0.6 × $90,000) + (0.4 × $15,000) = –$48,000

13–14

1. Year Depreciation tNC df Present Value 1 $2,000 $ 800 0.893 $ 714 2 4,000 1,600 0.797 1,275 3 4,000 1,600 0.712 1,139 4 2,000 800 0.636 509 NPV $3,637

2. Year Depreciation tNC df Present Value

1 $4,000 $1,600 0.893 $1,429 2 5,334 2,134 0.797 1,701 3 1,777 711 0.712 506 4 889 356 0.636 226 NPV $3,862

3. MACRS increases the present value of tax shielding by increasing the amount

of depreciation in the earlier years.

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13–15

Purchase (assumes MACRS depreciation):

Year (1 – t)C tNC CF df P 0 — — $(30,000) 1.000 $(30,000) 1 $(3,000)a $2,400b (600) 0.909 (545) 2 (3,000) 3,840c 840 0.826 694 3 (3,000) 2,304d (696) 0.751 (523) 4 (3,000) 1,382e (1,618) 0.683 (1,105) 5 (3,000) 1,382e (1,618) 0.621 (1,005) NPV $(32,484) a$5,000 × 0.6 b$30,000 × 0.2 × 0.4 c$30,000 × 0.32 × 0.4 d$30,000 × 0.192 × 0.4 e$30,000 × 0.1152 × 0.4 Lease:

Year (1 – t)C CF df P 0 $(1,000) 1.000 $ (1,000) 1–5 $(7,500)* (7,500) 3.791 (28,433) 5 1,000 0.621 621 NPV $ (28,812)

*$12,500 × 0.6

The car should be leased because leasing has a lower cost.

443399

13–16

1. Standard equipment (Rate = 18%):

Year Cash Flow df Present Value 0 $(500,000) 1.000 $(500,000) 1 300,000 0.847 254,100 2 200,000 0.718 143,600 3–10 100,000 2.928 292,800 NPV $ 190,500

CAM equipment (Rate = 18%):

Year Cash Flow df Present Value 0 $(2,000,000) 1.000 $(2,000,000) 1 100,000 0.847 84,700 2 200,000 0.718 143,600 3 300,000 0.609 182,700 4–6 400,000 1.323 529,200 7 500,000 0.314 157,000 8–10 1,000,000 0.682 682,000 NPV $ (220,800)

2. Standard equipment (Rate = 10%): Year Cash Flow df Present Value

0 $(500,000) 1.000 $(500,000) 1 300,000 0.909 272,700 2 200,000 0.826 165,200 3–10 100,000 4.409 440,900 NPV $ 378,800

CAM equipment (Rate = 10%):

Year Cash Flow df Present Value 0 $(2,000,000) 1.000 $(2,000,000) 1 100,000 0.909 90,900 2 200,000 0.826 165,200 3 300,000 0.751 225,300 4–6 400,000 1.868 747,200 7 500,000 0.513 256,500 8–10 1,000,000 1.277 1,277,000 NPV $ 762,100

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13–16 Concluded

3. Notice how the cash flows using a 10 percent rate in Years 8–10 are weighted compared to the 18 percent rate. The difference in present value is significant. Using an excessive discount rate works against those projects that promise large cash flows later in their lives. The best course of action for a firm is to use its cost of capital as the discount rate. Otherwise, some very attractive and essential investments could be overlooked.

13–17

1. Standard equipment (Rate = 14%):

Year Cash Flow df Present Value 0 $(500,000) 1.000 $(500,000) 1 300,000 0.877 263,100 2 200,000 0.769 153,800 3–10 100,000 3.571 357,100 NPV $ 274,000

CAM equipment (Rate = 14%):

Year Cash Flow df Present Value 0 $(2,000,000) 1.000 $(2,000,000) 1 100,000 0.877 87,700 2 200,000 0.769 153,800 3 300,000 0.675 202,500 4–6 400,000 1.567 626,800 7 500,000 0.400 200,000 8–10 1,000,000 0.929 929,000 NPV $ 199,800

2. Standard equipment (Rate = 14%):

Year Cash Flow df Present Value 0 $(500,000) 1.000 $(500,000) 1 300,000 0.877 263,100 2 200,000 0.769 153,800 3–10 50,000 3.571 178,550 NPV $ 95,450

The decision reverses—the CAM system is now preferable. This reversal is attributable to the intangible benefit of maintaining market share. To remain competitive, managers must make good decisions, and this exercise empha-sizes how intangible benefits can affect decisions.

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PROBLEMS

13–18

1. Accounting rate of return.

• Merits: The ARR method is relatively simple to use and easy to understand. It considers the profitability of the projects under consideration.

• Limitations: It ignores cash flows and the time value of money.

Internal rate of return.

• Merits: It considers the time value of money. It measures the true rate of re-turn of the project and productivity of the capital invested. Furthermore, managers are accustomed to working with rates of return.

• Limitations: It is stated as a percentage rather than a dollar amount. It as-sumes that cash flows are reinvested at the IRR of the project. It may not select the project that maximizes firm value.

Net present value method.

• Merits: It considers the time value of money and the size of the investment. It measures the true economic return of the project, the productivity of the capital, and the change in wealth of the shareholders.

• Limitations: It does not calculate a project’s rate of return, and it assumes that all the cash flows are reinvested at the required rate of return.

Payback method.

• Merits: It provides a measure of the liquidity and risk of a project. • Limitations: It ignores the time value of money. It ignores cash flows

beyond the payback period and, thus, ignores the profitability of a project. 2. Nathan Skousen and Jake Murray are basing their judgment on the results of

the net present value and internal rate of return calculations. These are both considered better measures because they include cash flows, the time value of money, and the project’s profitability. Project B is better than Project A for both of these measures.

444422

13–18 Concluded

3. At least three qualitative considerations that should generally be considered in capital budgeting evaluations include:

• Quicker response to market changes and flexibility in production capacity. • Strategic fit and long-term competitive improvement from the project, or

the negative impact to the company’s competitiveness or image if it does not make the investment.

• Risks inherent in the project, business, or country for the investment.

13–19

1. Schedule of cash flows:

Year Item Cash Flow 0 Equipment $(300,000) Working capital (30,000) 1–7 Cost savings $135,000 Equipment operating costs (60,000) 75,000 5 Overhaul (30,000) 7 Salvage value 24,000 Recovery of working capital 30,000

NPV:

Year Cash Flow df Present Value 0 $(330,000) 1.000 $(330,000) 1–7 75,000 4.868 365,100 5 (30,000) 0.621 (18,630) 7 54,000 0.513 27,702 NPV $ 44,172

Yes, the new process design should be accepted.

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13–20 1. Schedule of cash flows:

Year Item Cash Flow 0 Equipment $(1,100,000) Working capital (50,000) Total $(1,150,000)

1–5 Revenues $ 1,500,000 Operating expenses (1,260,000) Total $ 240,000

6 Revenues $ 1,500,000 Operating expenses (1,260,000) Major maintenance (100,000) Total $ 140,000

7–9 Revenues $ 1,500,000 Operating expenses (1,260,000) Total $ 240,000

10 Revenues $ 1,500,000 Operating expenses (1,260,000) Salvage 40,000 Recovery of working capital 50,000 Total $ 330,000

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13-20 Concluded 2. Year Cash Flow Discount Factor Present Value

0 $(1,150,000) 1.000 $(1,150,000) 1–5 240,000 3.605 865,200 6 140,000 0.507 70,980 7 240,000 0.452 108,480 8 240,000 0.404 96,960 9 240,000 0.361 86,640 10 330,000 0.322 106,260 NPV $ 184,250

The product should be produced.

13-21

1. df = Investment/Annual cash flow = $96,660/$20,000 = 4.833

The IRR is 16 percent. The company should acquire the new system. 2. Since I = P for the IRR:

I = df × CF $96,660 = 6.145* × CF 6.145 × CF = $96,660 CF = $15,730

*Discount factor at 10 percent (cost of capital) for ten years 3. For a life of eight years:

df = I/CF = $96,660/$20,000 = 4.833

The IRR is between 12 percent and 14 percent—greater than the 10 percent cost of capital. The company should still acquire the new sys-tem.

444455

13-21 Concluded

Minimum cash flow at 10 percent for eight years: I = df × CF $96,660 = 5.335 × CF 5.335 × CF = $96,660 CF = $18,118

4. Requirement 2 reveals that the estimates for cash savings can be off by as much $4,270 (over 20 percent) without affecting the viability of the new system. Requirement 3 reveals that the life of the new system can be two years less than expected and the project is still viable. In the lat-ter case, the cash flows can also decrease by almost ten percent as well without changing the outcome. Thus, the sensitivity analysis should strengthen the case for buying the new system.

13–22

1. The IRR using the best estimates:

Per unit Selling price $10 Unit variable cost 4 Unit contribution margin $ 6

Total contribution margin ($6 × 1,000,000 annual sales volume) $ 6,000,000 Less: Fixed costs 2,000,000 Annual cash flow $ 4,000,000

Discount factor = $12,000,000/$4,000,000 = 3.00

Five years and a discount factor of 3.00 implies a rate of approximately 20 percent.

2. a. If the per-unit selling price is reduced 10 percent, the adjusted IRR is 8

percent, as calculated below: Per unit 90% of selling price $9 Unit variable cost 4 Contribution margin $5

Total contribution margin ($5 × 1,000,000 annual sales volume) $5,000,000 Less: Fixed costs 2,000,000 Annual cash flow $3,000,000

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13–22 Concluded

Discount factor = $12,000,000/$3,000,000 = 4.00, which implies an IRR that is approximately 8 percent.

b. If the per-unit sales volume is reduced 10 percent, the adjusted IRR is 13

percent, as calculated below: Per unit Selling price $10 Unit variable cost 4 Contribution margin $ 6

Total contribution margin ($6 × 900,000 annual sales volume) $5,400,000 Less: Fixed costs 2,000,000 Annual cash flow $3,400,000

Discount factor = $12,000,000/$3,400,000 = 3.53, which implies an IRR that is approximately 13 percent (IRR between 12 and 14 percent).

c. If the per-unit variable cost is reduced 10 percent, the adjusted IRR is 24

percent, as calculated below: Per unit Selling price $10.00 Unit variable cost 3.60 Contribution margin $ 6.40

Total contribution margin ($6.40 × 1,000,000 annual sales volume) $6,400,000 Less: Fixed costs 2,000,000 Annual cash flow $4,400,000

Discount factor = $12,000,000/$4,400,000 = 2.73, which implies an IRR that is approximately 24 percent.

3. Sensitivity analysis determines the impact that certain changes in assump-

tions have on IRR or NPV as appropriate. It helps management to identify key variables and to know whether additional information is needed. It also helps determine the volatility of the project. Sensitivity analysis is limited because it provides no information about probability and uncertainty. The range of val-ues possible with their probability of occurrence are important information. It also ignores the fact that assumptions are dynamic and can interact with each other.

444477

13–23

1. First, calculate the expected cash flows: Days of operation each year: 365 – 15 = 350 Revenue per day: $200 × 2 × 150 = $60,000 Annual revenue: $60,000 × 350 = $21,000,000

Annual cash flow = Revenues – Operating costs = $21,000,000 – $2,500,000 = $18,500,000

NPV = P – I = (6.623 × $18,500,000) – $100,000,000 = $122,525,500 – $100,000,000 = $22,525,500

Yes, the aircraft should be purchased. 2. Revised cash flow = (0.80 × $21,000,000) – $2,500,000 = $14,300,000

NPV = P – I = (6.623 × $14,300,000) – $100,000,000 = $(5,291,100)

No, the aircraft should not be purchased. 3. NPV = (6.623)CF – $100,000,000 = 0 CF = $100,000,000/6.623 = $15,098,898

Annual revenue = $15,098,898 + $2,500,000 = $17,598,898

Daily revenue = $17,598,898/350 = $50,283

Seats to be sold = $50,283/$400 = 126 seats (each way)

Seating rate needed = 126/150 = 84%

444488

13–23 Concluded

4. Seats to be sold = $50,283/$440 = 115 (rounded up) Seating rate = 115/150 = 77%

This seating rate is less than the most likely and above the least likely rate of 70 percent. There is some risk, since it is possible that the actual rate could be below 77 percent. However, the interval is 20 percent (70 percent to 90 percent), and the 77 percent rate is only 35 percent of the way into the inter-val, suggesting a high probability of a positive NPV.

13–24

1. 1.00 year $16,800 1.00 year 24,000 1.00 year 29,400 0.13 year* 3,800 3.13 years $74,000

*$3,800/$29,400

Note: Cash flow = Increased revenue less cash expenses of $3,000 2. Accounting rate of return using original investment:

Average cash flow = ($16,800 + $24,000 + $29,400 + $29,400)/4 = $24,900

Average depreciation = ($74,000 – $6,000)/4 = $17,000

Accounting rate of return = ($24,900 – $17,000)/$74,000 = $7,900/$74,000 = 10.7%

Accounting rate of return using average investment:

Accounting rate of return = $7,900/$40,000* = 19.8%

*Average investment = (Investment + Salvage)/2 = ($74,000 + $6,000)/2

444499

13–24 Concluded

3. Year Cash Flow Discount Factor Present Value 0 $(74,000) 1.000 $(74,000) 1 16,800 0.893 15,002 2 24,000 0.797 19,128 3 29,400 0.712 20,933 4 35,400* 0.636 22,514 NPV $ 3,577

*Includes $6,000 salvage value

IRR (by trial and error):

Using 14 percent as the first guess: Year Cash Flow Discount Factor Present Value

0 $(74,000) 1.000 $(74,000) 1 16,800 0.877 14,734 2 24,000 0.769 18,456 3 29,400 0.675 19,845 4 35,400 0.592 20,957 NPV $ (8)

The IRR is about 14 percent.

The equipment should be purchased. (The NPV is positive and the IRR is larger than the cost of capital.) Dr. Avard should not be concerned about the accounting rate of return in making this decision. The payback, however, may be of some interest, particularly if cash flow is of concern to Dr. Avard.

4. Year Cash Flow Discount Factor Present Value

0 $(74,000) 1.000 $(74,000) 1 11,200 0.893 10,002 2 16,000 0.797 12,752 3 19,600 0.712 13,955 4 25,600 0.636 16,282 NPV $(21,009)

For Years 1–4, the cash flows are 2/3 of the original cash flow increases. Year 4 also includes $6,000 salvage value.

Given the new information, Dr. Avard should not buy the equipment.

445500

13–25

Keep old computer:

Year (1 – t)Ra –(1 – t)Cb tNCc CF df Present Value 0 — — — — — — 1 — $(60,000) $32,000 $(28,000) 0.893 $ (25,004) 2 — (60,000) 32,000 (28,000) 0.797 (22,316) 3 — (60,000) 16,000 (44,000) 0.712 (31,328) 4 — (60,000) — (60,000) 0.636 (38,160) 5 $6,000 (60,000) — (54,000) 0.567 (30,618) NPV $(147,426) a(0.60) × $10,000 b(0.60) × $100,000 cYears 1 and 2: 0.40 × $80,000; Year 3: 0.40 × $40,000. The class life has two years remaining; 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 = $200,000 and X = $80,000.

Buy new computer:

Present Yr. (1 – t)Ra –(1 – t)Cb tNCc Otherd CF df Value 0 $60,000 $(450,000) $(390,000) 1.000 $(390,000) 1 (30,000) 40,000 10,000 0.893 8,930 2 (30,000) 64,000 34,000 0.797 27,098 3 (30,000) 38,400 8,400 0.712 5,981 4 (30,000) 23,040 (6,960) 0.636 (4,427) 5 $42,720 (30,000) 23,040 28,800 64,560 0.567 36,606 NPV $(315,812) a(0.60) × ($100,000 – Book value), where book value = $500,000 – $471,200 b(0.60) × $50,000 cYear 0: Tax savings from loss on sale of asset: 0.40 × $150,000 (The loss on the sale of the old computer is $200,000 – $50,000.)

Years 1–5: Tax savings from MACRS depreciation: $500,000 × 0.20 × 0.40; $500,000 × 0.32 × 0.40; $500,000 × 0.192 × 0.40; $500,000 × 0.1152 × 0.40; $500,000 × 0.1152 × 0.40.

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 deprecia-tion can be claimed in Year 5.

dPurchase cost $500,000 less proceeds of $50,000; recovery of capital from sale of machine, end of Year 5, is the book value of $28,800 (original cost less accu-mulated depreciation).

The old computer should be kept since it has a lower cost.

445511

13–26

1. Purchase:

Year (1 – t)Ra –(1 – t)Cb tNCc Cash Flow 0 $(100,000) 1 $33,000 $(12,000) $5,716 26,716 2 33,000 (12,000) 9,796 30,796 3 33,000 (12,000) 6,996 27,996 4 33,000 (12,000) 4,996 25,996 5 33,000 (12,000) 3,572 24,572 6 33,000 (12,000) 3,568 24,568 7 33,000 (12,000) 3,572 24,572 8 33,000 (12,000) 1,784 22,784 9 33,000 (12,000) 21,000 10 45,000d (12,000) 33,000

a0.60 × $55,000 b0.60 × $20,000 c0.40 × 0.1429 × $100,000, 0.40 × 0.2449 × $100,000, etc. dIncludes salvage value as a gain.

Lease—with service contract:

Year (1 – t)R –(1 – t)Ca tNCb Cash Flow 0 $(12,420) $(47,420)c 1 $33,000 (18,420) $1,200 15,780 2 33,000 (18,420) 1,200 15,780 3 33,000 (18,420) 1,200 15,780 4 33,000 (18,420) 1,200 15,780 5 33,000 (18,420) 1,200 15,780 6 33,000 (18,420) 1,200 15,780 7 33,000 (18,420) 1,200 15,780 8 33,000 (18,420) 1,200 15,780 9 33,000 (18,420) 1,200 15,780 10 33,000 (6,000) 1,200 33,200d

aYear 0: 0.60 × $20,700; Years 1–9: 0.60 × $30,700; Year 10: 0.60 × $10,000 b0.40 × $3,000 cIncludes deposit of $5,000 and purchase of contract of $30,000 dIncludes the refund of the $5,000 deposit

445522

13–26 Continued

Lease—without service contract:

Year (1 – t)R –(1 – t)Ca Cash Flow 0 $(12,420) $(17,420)b 1 $33,000 (24,420) 8,580 2 33,000 (24,420) 8,580 3 33,000 (24,420) 8,580 4 33,000 (24,420) 8,580 5 33,000 (24,420) 8,580 6 33,000 (24,420) 8,580 7 33,000 (24,420) 8,580 8 33,000 (24,420) 8,580 9 33,000 (24,420) 8,580 10 33,000 (12,000) 26,000c

aYear 0: 0.60 × $20,700; Years 1–9: 0.60 × $40,700; Year 10: 0.60 × $20,000 bIncludes deposit of $5,000 cIncludes return of $5,000 deposit

2. Purchase:

Year Cash Flow Discount Factor Present Value 0 $(100,000) 1.000 $(100,000) 1 26,716 0.877 23,430 2 30,796 0.769 23,682 3 27,996 0.675 18,897 4 25,996 0.592 15,390 5 24,572 0.519 12,753 6 24,568 0.456 11,203 7 24,572 0.400 9,829 8 22,784 0.351 7,997 9 21,000 0.308 6,468 10 33,000 0.270 8,910 NPV $ 38,559

445533

13–26 Concluded

Lease—without service contract:

Year Cash Flow Discount Factor Present Value 0 $(17,420) 1.000 $ (17,420) 1–9 8,580 4.946 42,437 10 26,000 0.270 7,020 NPV $ 32,037

The equipment should be purchased.

It was not necessary to include all of the costs and revenues for each alterna-tive. The operating revenues and operating costs could have been eliminated because they are exactly the same for both alternatives and, thus, not rele-vant.

3. Lease—with service contract:

Year Cash Flow Discount Factor Present Value 0 $(47,420) 1.000 $ (47,420) 1–9 15,780 4.946 78,048 10 33,200 0.270 8,964 NPV $ 39,592

The equipment should now be leased. Since the revenues of $55,000 per year are the same for both alternatives, they could be excluded from the analysis.

445544

13–27

1. Scrubbers and Treatment Facility (expressed in thousands):

Year (1 – t)Ra –(1 – t)Cb tNCc CF df Present Value 0 $(25,000) 1.000 $(25,000) 1 $3,000 $(7,200) $2,000 (2,200) 0.909 (2,000) 2 3,000 (7,200) 3,200 (1,000) 0.826 (826) 3 3,000 (7,200) 1,920 (2,280) 0.751 (1,712) 4 3,000 (7,200) 1,152 (3,048) 0.683 (2,082) 5 3,000 (7,200) 1,152 (3,048) 0.621 (1,893) 6 3,600d (7,200) 576 (3,024) 0.564 (1,706) NPV $(35,219)

a0.6 × $5,000,000 b0.6 × $12,000,000 cYear 1: 0.4 × 0.2 × $25,000,000; Year 2: 0.4 × 0.32 × $25,000,000; Year 3: 0.4 × 0.192 × $25,000,000; Years 4 and 5: 0.4 × 0.1152 × $25,000,000; Year 6: 0.4 × 0.0576 × $25,000,000

dIncludes salvage value (0.6 × $1,000,000) Process Redesign (expressed in thousands):

Year (1 – t)Ra –(1 – t)Cb tNCc CF df Present Value 0 $(50,000) 1.000 $ (50,000) 1 $9,000 $(3,000) $4,000 10,000 0.909 9,090 2 9,000 (3,000) 6,400 12,400 0.826 10,242 3 9,000 (3,000) 3,840 9,840 0.751 7,390 4 9,000 (3,000) 2,304 8,304 0.683 5,672 5 9,000 (3,000) 2,304 8,304 0.621 5,157 6 9,900d (3,000) 1,152 8,052 0.564 4,541 NPV $ (7,908)

a0.6 × $15,000,000 b0.6 × $5,000,000 cYear 1: 0.4 × 0.2 × $50,000,000; Year 2: 0.4 × 0.32 × $50,000,000; Year 3: 0.4 × 0.192 × $50,000,000; Years 4 and 5: 0.4 × 0.1152 × $50,000,000; Year 6: 0.4 × 0.0576 × $50,000,000

dIncludes salvage value (0.6 × $1,500,000)

The process redesign option is less costly and should be implemented.

445555

13–27 Concluded

2. The modification will add to the cost of the scrubbers and treatment facility (present value is 0.751 × $4,000,000 = $3.004 million). Cleaning up the lake can be viewed as a cost of the first alternative or a benefit of the second. The present value of the cleanup cost gives an additional cost (benefit) between $15.02 and $22.53 million to the first (second) alternative (0.751 × $20,000,000 and 0.751 × $30,000,000). Adding in the benefit of avoiding the cleanup cost makes the process redesign alternative profitable (yielding a positive NPV). Ecoefficiency basically argues that productive efficiency increases as envi-ronmental performance increases and that it is cheaper to prevent environ-mental contamination than it is to clean it up once created. The first alterna-tive is a “cleanup” approach, while the second is a “prevention” approach.

13–28

1. Original savings and investment:

(14 percent rate):

Year CF df Present Value 0 $(45,000,000) 1.000 $(45,000,000) 1–20 $4,000,000 6.623 26,492,000 20 5,000,000 0.073 365,000 NPV $(18,143,000)

445566

13-28 Continued

(20 percent rate):

Year CF df Present Value 0 $(45,000,000) 1.000 $(45,000,000) 1–20 $4,000,000 4.870 19,480,000 20 5,000,000 0.026 130,000 NPV $(25,390,000)

2. Total benefits: ($4,000,000 + $1,000,000 + $2,400,000)

(14 percent rate):

Year CF df Present Value 0 $(45,000,000) 1.000 $(45,000,000) 1–20 7,400,000 6.623 49,010,200 20 5,000,000 0.073 365,000 NPV $ 4,375,200

(20 percent rate):

Year CF df Present Value 0 $(45,000,000) 1.000 $(45,000,000) 1–20 7,400,000 4.870 36,038,000 20 5,000,000 0.026 130,000 NPV $ (8,832,000)

445577

13-28 Concluded 3. Analysis with increased investment:

Year CF df Present Value 0 $(48,000,000) 1.000 $(48,000,000) 1–20 7,400,000 6.623 49,010,200 20 5,000,000 0.073 365,000 NPV $ 1,375,200

(20 percent rate):

Year CF df Present Value 0 $(48,000,000) 1.000 $(48,000,000) 1–20 7,400,000 4.870 36,038,000 20 5,000,000 0.026 130,000 NPV $ (11,832,000)

4. The automated plant is an attractive investment when the additional

benefits are considered—it promises to return at least the cost of capi-tal (even for the high-cost scenario). Using the hurdle rate of 20 per-cent is probably too conservative—especially given the robustness of the outcome using the cost of capital. The company should invest in the new system.

13–29

1. Year Cash Flow* Discount Factor Present Value 0 $(860,000) 1.000 $(860,000) 1 196,400 0.862 169,297 2–5 230,800 2.412 556,690 6 196,400 0.410 80,524 7 162,000 0.354 57,348 8 162,000 0.305 49,410 NPV $ 53,269

*After-tax cash flow = (0.60 × $270,000) + (0.40 × annual depreciation) for Years 1–6. Depreciation = $860,000/5 = $172,000 with ½ taken in Year 1 and ½ taken in Year 6.

445588

13–29 Concluded

2. Year Cash Flow* Discount Factor Present Value 0 $(920,000) 1.000 $(920,000) 1 186,800 0.862 161,022 2–5 223,600 2.412 539,323 6 186,800 0.410 76,588 7 150,000 0.354 53,100 8 150,000 0.305 45,750 NPV $ (44,217)

*After-tax cash flow = (0.60 × $250,000) + (0.40 × annual depreciation) for Years 1–6. Depreciation = $920,000/5 = $184,000 with ½ taken in Year 1 and ½ taken in Year 6.

After the fact, the decision was not a good one. 3. The $100,000 per year is an annuity that produces an after-tax cash flow of

$60,000 ($100,000 × 0.60). The present value of this annuity is $260,640 (4.344 × $60,000). This restores the project to a positive NPV position ($260,640 – $44,217 = $216,423).

4. A postaudit can help ensure that a firm’s resources are being used wisely. It

may reveal that additional resources ought to be invested or that corrective action be taken so that the performance of the investment is improved. A postaudit may even signal the need to abandon a project or replace it with a more viable alternative. Postaudits also provide information to managers so that their future capital decision making can be improved. Finally, postaudits can be used as a means to hold managers accountable for their capital in-vestment decisions.

445599

13–30

1. Old system (dollars in thousands):

Year (1 – t)Ra –(1 – t)Cb tNCc Cash Flow df Present Value* 0 $ 0 1.000 $ 0 1–9 $18,000 $(13,440) $240 4,800 4.303 20,654 10 18,000 (13,440) — 4,560 0.191 871 NPV $ 21,525

a0.6 × $300 × 100,000 b0.6 × $224 × 100,000 c0.4 × $600,000 *Rounded

New system (dollars in thousands):

Year (1 – t)Ra –(1 – t)Cb tNCc Cash Flow df Present Value* 0 $(50,040) 1.000 $ (50,040) 1–10 $18,000 $(7,320) $2,160 12,840 4.494 57,703 NPV $ 7,663

aDirect materials (0.75 × $80) $ 60 Direct labor (1/3 × $90) 30 Volume-related OH ($20 – $5) 15 Direct FOH ($34 – $17) 17 Unit cost $122

Total cash expenses = $122 × 100,000 = $12,200,000 After-tax cash expenses = 0.6 × $12,200,000

bYear 0: Tax savings on loss from sale of old machine = 0.4 × ($6,000,000 – $600,000 – $3,000,000) = $960,000 Years 1–10: Depreciation = 0.4 × $54,000,000/10

cNet outlay = $54,000,000 – $3,000,000 – $960,000 = $50,040,000

The company should keep the old system.

446600

13–30 Continued

2. Old system (dollars in thousands):

Year (1 – t)R –(1 – t)C tNC Cash Flow df Present Value* 0 $ 0 1.000 $ 0 1–9 $18,000 $(13,440) $240 4,800 5.328 25,574 10 18,000 (13,440) — 4,560 0.322 1,468 NPV $ 27,042 New system (dollars in thousands):

Year (1 – t)R –(1 – t)C tNC Cash Flow df Present Value 0 $(50,040) 1.000 $ (50,040) 1–10 $18,000 $(7,320) $2,160 12,840 5.650 72,546 NPV $ 22,506

Notice how much more attractive the automated system becomes when the cost of capital is used as the discount rate.

*Rounded 3. Old system with declining sales (dollars in thousands):

Year (1 – t)R –(1 – t)C tNC Cash Flow df Present Value** 0 $ 0 1.000 $ 0 1 $18,000 $(13,440) $240 4,800 0.893 4,286 2 16,200 (12,300) 240 4,140 0.797 3,300 3 14,400 (11,160) 240 3,480 0.712 2,478 4 12,600 (10,020) 240 2,820 0.636 1,794 5 10,800 (8,880) 240 2,160 0.567 1,225 6 9,000 (7,740) 240 1,500 0.507 761 7 7,200 (6,600) 240 840 0.452 380 8 5,400 (5,460) 240 180 0.404 73 9 3,600 (4,320) 240 (480) 0.361 (173) 10 1,800 (3,180) — (1,380) 0.322 (444) NPV $13,680

*Cash expenses = Fixed + Variable = $3,400,000 (Direct fixed) + $190X where X = Units sold

After-tax cash expense = $2,040,000 + $114X (0.6 × formula above) **Rounded

446611

13–30 Concluded

4. For the new system, salvage value would increase after-tax cash flows in Year 10 by $2,400,000 (0.6 × $4,000,000). Using the discount factor of 0.322, the NPV of the new system will increase from $22,506,000 to $23,278,800 (an in-crease of 0.322 × $2,400,000), making the new investment more attractive. The NPV analysis for the old system remains unchanged.

5. Requirement 2 illustrates the importance of using the correct discount rate.

The rate of 18 percent made the automated alternative look totally unappeal-ing. By using the correct rate, the alternative showed a large net present val-ue, although it was still less than the NPV of the old system. The old system’s projections of future revenues, however, were overly optimistic. The old sys-tem was not able to produce the same level of quality as the new system and took longer to produce—factors that, when taken together, would reduce the competitive position of the firm and cause sales to decline. When this effect was considered (with the correct discount rate), the new system dominated the old. Inclusion of salvage value simply increased this dominance.

13–31

1. Old operating system:

Year Cash Flow* df Present Value 0 $ 0 1.000 $ 0 1–10 (197,000) 5.650 (1,113,050) NPV $(1,113,050)

*[–(0.66 × $350,000) + (0.34 × $100,000)]

446622

13–31 Continued

Flexible system (using MACRS depreciation):

Year (1 – t)Ca tNCb Cash Flow df Present Value* 0 — — $(1,250,000) 1.000 $(1,250,000) 1 $(62,700) $ 60,733 (1,967) 0.893 (1,757) 2 (62,700) 104,083 41,383 0.797 32,982 3 (62,700) 74,333 11,633 0.712 8,283 4 (62,700) 53,083 (9,617) 0.636 (6,116) 5 (62,700) 37,953 (24,747) 0.567 (14,032) 6 (62,700) 37,910 (24,790) 0.507 (12,569) 7 (62,700) 37,953 (24,747) 0.452 (11,186) 8 (62,700) 18,955 (43,745) 0.404 (17,673) 9 (62,700) (62,700) 0.361 (22,635) 10 (62,700) (62,700) 0.322 (20,189) NPV $(1,314,892)

a$95,000 × 0.66 b$1,250,000 × 0.1429 × 0.34, $1,250,000 × 0.2449 × 0.34, etc. (MACRS deprecia-tion for a seven-year asset)

*Rounded 2. Old operating system (with adjustment for inflation):

Year Cash Flow* Discount Factor Present Value** 0 $ 0 1.000 $ 0 1 (206,240) 0.893 (184,172) 2 (215,850) 0.797 (172,032) 3 (225,844) 0.712 (160,801) 4 (236,237) 0.636 (150,247) 5 (247,047) 0.567 (140,076) 6 (258,289) 0.507 (130,953) 7 (269,981) 0.452 (122,031) 8 (282,140) 0.404 (113,985) 9 (294,786) 0.361 (106,418) 10 (307,937) 0.322 (99,156) NPV $(1,379,871)

*{–[(1.04)n × $350,000 × 0.66] + [0.34 × $100,000]}, n = 1 ... 10 **Rounded

446633

13–31 Concluded

Flexible system (with adjustment for inflation):

Year Cash Flow* Discount Factor Present Value 0 $(1,250,000) 1.000 $(1,250,000) 1 (4,475) 0.893 (3,996) 2 36,267 0.797 28,905 3 3,804 0.712 2,708 4 (20,267) 0.636 (12,890) 5 (38,331) 0.567 (21,734) 6 (41,426) 0.507 (21,003) 7 (44,556) 0.452 (20,139) 8 (66,854) 0.404 (27,009) 9 (89,242) 0.361 (32,216) 10 (92,811) 0.322 (29,885) NPV $(1,387,259)

*{–[(1.04)n × $95,000 × 0.66] + [Annual depreciation × 0.34]}, n = 1 ... 10; depre-ciation is MACRS.

3. It is very important to adjust cash flows for inflationary effects. Since the re-

quired rate of return for capital budgeting analysis reflects an inflationary component at the time NPV analysis is performed, a correct analysis also re-quires that the predicted operating cash flows be adjusted to reflect inflatio-nary effects. If the operating cash flows are not adjusted, then an erroneous decision may be the outcome. Notice, for example, that after adjusting for in-flation, there is virtually no difference between the two systems—and given the intangibles associated with the flexible system, it would likely be chosen.

446644

MANAGERIAL DECISION CASES

13–32

The statement that Manny would normally have taken the first bid without hesita-tion implies that the bid met all of the formal requirements outlined by the com-pany. If Manny’s friend had met the bid as requested, then presumably Manny would have offered the business to his friend. The motive for this was friendship and possibly carried with it past experience in dealing with Todd’s company. Per-haps there was some uncertainty in Manny’s mind about the low bidder’s ability to execute the requirements of the bid, especially since the winning bid was from out of state. If there was some legitimate concern about the winning bid and Man-ny was hopeful of eliminating this concern by dealing with a known quantity, then it could be argued that the call to Todd was justifiable. If, on the other hand, the only motive was friendship and Manny was confident that the winning bid could execute (as he appears to have been), then the call was improper. Objectivity and integrity in carrying out the firm’s bidding policies are essential. The fact that Manny was tempted by Todd’s enticements and appeared to be lean-ing toward accepting Todd’s original offer compounds the difficulty of the issue. If Manny actually accepts Todd’s offer and grants the business at the original price and accepts the gifts, then his behavior is unquestionably unethical. Some of the standards of ethical conduct that would be violated are listed below. II. Confidentiality

1. Refrain from disclosing confidential information acquired in the course of their work except when authorized, unless legally obligated to do so.

3. Refrain from using or appearing to use confidential information acquired in the course of their work for unethical or illegal advantage either perso-nally or through a third party.

III. Integrity

3. Refuse any gift, favor, or hospitality that would influence their actions.

446655

13–33

1. Shaftel Ready Mix Income Statement

For the Year Ended 20XX

Sales (35,000 × $45) .................................................. $ 1,575,000 Less: Variable expenses ($35.08 × 35,000) ............. 1,227,800 Contribution margin ................................................. $ 347,200 Less fixed expenses: Salaries ................................................................. $135,000 Insurance .............................................................. 75,000 Telephone ............................................................. 5,000 Depreciation ......................................................... 56,200* Utilities .................................................................. 25,000 296,200 Net income ................................................................. $ 51,000

*Reported depreciation erroneously included $2,000 for the land.

Ratio of net income to sales = $51,000/$1,575,000 = 3.24%

Karl is correct that the return on sales is significantly lower than the company average.

2. Payback period = Original investment/Annual cash flow = $352,000/$107,200* = 3.28 years

*Net income of $51,000 + depreciation of $56,200

Karl is not right. The book value of the equipment and the furniture should not be included in the amount of the original investment because there is no opportunity cost associated with them. Excluding the book value reduces the investment from $582,000 to $352,000. Karl’s payback would be correct if the equipment and furniture could be sold for their book value because there would now be an opportunity cost associated with them and that cost should be included in the original investment.

446666

13–33 Continued

3. NPV:

Year Cash Flow Discount Factor Present Value 0 $(352,000) 1.000 $(352,000) 1–10 107,200 6.145 658,744 NPV $ 306,744 IRR:

df = I/CF = $352,000/$107,200 = 3.284

Thus, the IRR is between 26 percent and 28 percent. If the furniture and equipment can be sold for book value:

NPV:

Year Cash Flow Discount Factor Present Value 0 (582,000) 1.000 $(582,000) 1–10 107,200 6.145 658,744 NPV $ 76,744 IRR:

df = 582,000/$107,200 = 5.4291

Thus, the IRR is between 12 percent and 14.88 percent. Using equipment and furniture for the plant INSTEAD of selling it represents an investment equal to the market value of the assets; the op-portunity cost is the key concept here.

446677

13–33 Continued

4. Break-even:

$45X = $35.08X + $296,200 $9.92X = $296,200 X = 29,859 cubic yards NPV (using break-even amount):

Year Cash Flow Discount Factor Present Value 0 $(352,000) 1.000 $(352,000) 1–10 56,200 6.145 345,349 NPV $ (6,651) IRR:

df = $352,000/$56,200 = 6.263

Thus, the IRR is between 8 percent and 10 percent.

The investment is not acceptable, although it came close. It is possible to have a positive NPV at the break-even point. Break-even is defined for ac-counting income, not for cash flow. Since there are noncash expenses de-ducted from revenues, accounting income understates cash income. Zero in-come does not mean zero cash inflows.

446688

13–33 Concluded

5. Cost of capital = 10 percent for 10 years, so df = 6.145

df = I/CF 6.145 = $352,000/CF 6.145 × CF = $352,000 CF = $57,282 Cash flow $ 57,282 Less: Depreciation 56,200 Net income $ 1,082 Net income = Sales – Variable expenses – Fixed expenses $1,082 = $45X – $35.08X – $296,200 $1,082 = $9.92X – $296,200 $297,282 = $9.92X X = 29,968 cubic yards Sales $ 1,348,560 Less: Variable expenses 1,051,277 Contribution margin $ 297,283 Less: Fixed expenses 296,200 Net income $ 1,083*

*Difference due to rounding

13–34

1. After-tax cash flows

Manual system:

Year (1 – t)Ra –(1 – t)Cb tNCc Cash Flow 1–10 $264,000 $(198,000) $6,800 $72,800

a0.66 × $400,000 b0.66 × $228,000 + [0.66 × ($92,000 – $20,000)] c0.34 × $20,000

446699

13–34 Continued

Robotic system:

Year (1 – t)Ra –(1 – t)Cb tNCc Cash Flow 0 $(425,600)d 1 $264,000 $(136,720) $25,265 152,545 2 297,000 (146,220) 43,298 194,078 3 330,000 (155,720) 30,922 205,202 4 396,000 (174,720) 22,082 243,362 5 396,000 (174,720) 15,788 237,068 6 396,000 (174,720) 15,771 237,051 7 396,000 (174,720) 15,788 237,068 8 396,000 (174,720) 7,885 229,165 9 396,000 (174,720) 221,280 10 409,200 (174,720) 234,480

aYear 1: 0.66 × $400,000; Year 2: 0.66 × $450,000; Year 3: 0.66 × $500,000; Years 4–9: 0.66 × $600,000; Year 10: 0.66 × $620,000 (includes salvage value as a gain)

bAfter-tax cash expenses:

Fixed: Direct labor $20,000 × 0.66 = $13,200 (one operator) Other $72,000 × 0.66 = 47,520 (from income statement) $60,720

Variable: Direct materials (0.16 × Sales) × 0.75 × 0.66 Variable overhead (0.09 × Sales) × 0.6667 × 0.66 Variable selling (0.12 × Sales) × 0.90 × 0.66 Total 0.19 × Sales

Total after-tax cash expenses = $60,720 + (0.19 × Sales)

cYears 1–8: MACRS: 0.1429 × $520,000 × 0.34, 0.2449 × $520,000 × 0.34, etc.

dNet investment: Purchase costs $(520,000) Recovery of capital 40,000 Tax savings on loss 54,400* $(425,600)

*Year 0: 0.34 × ($200,000 – $40,000)

447700

13–34 Continued

2. Manual system: Year Cash Flow Discount Factor Present Value 0 $ 0 1.000 $ 0 1–10 72,800 5.650 411,320 NPV $411,320 Robotics system:

Year Cash Flow Discount Factor Present Value 0 $(425,600) 1.000 $(425,600) 1 152,545 0.893 136,223 2 194,078 0.797 154,680 3 205,202 0.712 146,104 4 243,362 0.636 154,778 5 237,068 0.567 134,418 6 237,051 0.507 120,185 7 237,068 0.452 107,155 8 229,165 0.404 92,583 9 221,280 0.361 79,882 10 234,480 0.322 75,503 NPV $ 775,911

The company should invest in the robotic system.

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3. Managers may use a higher discount rate as a way to deal with the un-certainty in future cash flows. The higher rate “protects” the manager from unpleasant surprises. Since a higher rate favors investments that provide returns quickly, managers may be motivated by personal short-run considera-tions (e.g., bonuses and promotion opportunities).

Using a discount rate of 12 percent:

Year Cash Flow Discount Factor Present Value 0 $(340,000) 1.000 $(340,000) 1–10 80,000 5.650 452,000 NPV $ 112,000 Using a discount rate of 20 percent:

Year Cash Flow Discount Factor Present Value 0 $(340,000) 1.000 $(340,000) 1–10 80,000 4.192 335,360 NPV $ (4,640)

If the 20 percent discount rate is used, the company would not acquire the robotic system.

Using an excessive discount rate could seriously impair the ability of the firm

to stay competitive. An excessive discount rate may lead a firm to reject new technology that would increase quality and productivity. As other firms invest in the new technology, their products will be priced lower and be of higher quality—features that would likely cause severe difficulty for the more con-servative firm.

RESEARCH ASSIGNMENTS

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Answers will vary.

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Answers will vary.

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