Solution Manual, Managerial Accounting Hansen Mowen 8th Editions_ch 13
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CHAPTER 13 CAPITAL INVESTMENT DECISIONS QUESTIONS FOR WRITING AND DISCUSSION 1. Independent projects are such that the acceptance of one does not preclude the acceptance of another. With mutually exclusive projects, acceptance of one precludes the acceptance of others.
11.
If NPV > 0, then the investment is acceptable. 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 resources 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 signals. IRR may be popular because it provides the correct signal most of the time and managers are accustomed to working with rates of return.
15.
6. The accounting rate of return is the average income divided by original or average investment. ARR = $100,000/$300,000 = 33.33%
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.
7. Agree. Essentially, net present value is a measure of the return in excess of the investment and its cost of capital.
NPV analysis is only as good as the accuracy of the cash flows. If projections of cash flows are not accurate, then incorrect investment decisions may be made.
17.
The quality and reliability of the cash flow projections are directly related to the assumptions and methods used for forecasting. 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 shielding effect in earlier years than the straightline method does. As a consequence, the present value of the shielding benefit is greater for the MACRS method.
2. The timing and quantity of cash flows determine the present value of a project. The present value is critical for assessing whether 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) Obsolescence. If the risk of obsolescence is high, firms will want to recover funds quickly. (c) Self-interest. Managers want quick paybacks so that short-run performance measures are affected positively, enhancing chances for bonuses and promotion. Also, this method is easy to calculate.
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.
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20.
21.
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.
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, regardless 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.
22.
Intangible and indirect benefits are of much greater importance in the advanced manufacturing environment. Greater quality, more reliability, improved delivery, and the ability
426
Sensitivity analysis changes the assumptions on which the capital investment analysis 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 future events.
EXERCISES 13–1 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
12. 13. 14. 15. 16. 17. 18. 19. 20.
a e c a d e c b d e b
c a e c a e b e 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
427
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 0 1 2 3 4 5 NPV
Cash Flow $(200,000) 120,000 100,000 80,000 40,000 20,000
Discount Factor 1.000 0.893 0.797 0.712 0.636 0.567
429
Present Value $(200,000) 107,160 79,700 56,960 25,440 11,340 $ 80,600
13-6 Concluded Lawton Blood Analysis Equipment: Year 0 1 2 3 4 5 NPV
Cash Flow $(200,000) 20,000 20,000 120,000 160,000 180,000
Discount Factor 1.000 0.893 0.797 0.712 0.636 0.567
Present Value $(200,000) 17,860 15,940 85,440 101,760 102,060 $ 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 0 1 2 3 4 5 NPV
4.
P = CF(df) = I for the IRR, thus,
Cash Flow $(800,000) 300,000 300,000 300,000 300,000 300,000
Discount Factor 1.000 0.909 0.826 0.751 0.683 0.621
Present Value $(800,000) 272,700 247,800 225,300 204,900 186,300 $ 337,000
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 4,000 3,000 $10,000
1.00 year 1.00 year 0.60 year 2.60 years
Project B: $ 3,000 4,000 3,000 $10,000
1.00 year 1.00 year 0.50 year 2.50 years
Both projects have about the same payback so the most profitable should be chosen (Project A).
431
13-8 2.
Concluded
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 b. Cost of capital ($200,000 × 10%) c. Profit earned on the investment ($231,000 – $220,000)
$200,000 20,000 11,000
Present value of profit: P = F × Discount factor = $11,000 × 0.909 = $9,999 2.
Cash Flow Year 0 $(200,000) 1 231,000 Net present value
Discount Factor 1.000 0.909
Present Value $(200,000) 209,979 $ 9,979
Net present value gives the present value of future profits (the slight difference is due to rounding error in the discount factor).
432
13–10 1.
Bond cost = $6,000/$120,000 = 0.05 Cost of capital
2.
= 0.05(0.6) + 0.175(0.4) = 0.03 + 0.07 = 0.10
Year Cash Flow 0 $(200,000) 1 100,000 2 100,000 3 100,000 Net present value
Discount Factor 1.000 0.909 0.826 0.751
Present Value $(200,000) 90,900 82,600 75,100 $ 48,600
It is not necessary to subtract the interest payments and the dividend payments because these are associated with the cost of capital and are included in the firm’s cost of capital of 10 percent.
433
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.
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13–11 Concluded 4.
X = Cash flow in Year 4 Investment = 2X Year 0 1 2 3 4 NPV
Cash Flow $ (2X) 10,000 12,000 15,000 X
Discount Factor 1.000 0.909 0.826 0.751 0.683
–2X + $9,090 + $9,912 + $11,265 + 0.683X –1.317X + $30,267 –1.317X X Cash flow in Year 4 = X = $20,000 Cost of project = 2X = $40,000
435
= $3,927 = $3,927 = ($26,340) = $20,000
Present Value $ (2X) 9,090 9,912 11,265 0.683X $ 3,927
13–12 1.
NPV: Project I Year 0 1 2 NPV
Cash Flow $(100,000) — 134,560
Discount Factor 1.000 — 0.826
Present Value $(100,000) — 111,147 $ 11,147
Cash Flow $(100,000) 63,857 63,857
Discount Factor 1.000 0.909 0.826
Present Value $(100,000) 58,046 52,746 $ 10,792
Project II Year 0 1 2 NPV
Project I should be chosen using NPV. IRR: Project I I $100,000 (1 + i)2 1+I IRR
= df × CF = $134,560/(1 + i)2 = $134,560/$100,000 = 1.3456 = 1.16 = 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 profitability. Thus, since NPV reveals the total wealth change attributable to each project, it is preferred to the IRR measure.
436
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 1 2 3 4 NPV
Depreciation $2,000 4,000 4,000 2,000
tNC $ 800 1,600 1,600 800
df 0.893 0.797 0.712 0.636
Present Value $ 714 1,275 1,139 509 $3,637
2.
Year 1 2 3 4 NPV
Depreciation $4,000 5,334 1,777 889
tNC $1,600 2,134 711 356
df 0.893 0.797 0.712 0.636
Present Value $1,429 1,701 506 226 $3,862
3.
MACRS increases the present value of tax shielding by increasing the amount of depreciation in the earlier years.
437
13–15 Purchase (assumes MACRS depreciation): Year 0 1 2 3 4 5 NPV
(1 – t)C — $(3,000)a (3,000) (3,000) (3,000) (3,000)
tNC — $2,400b 3,840c 2,304d 1,382e 1,382e
CF $(30,000) (600) 840 (696) (1,618) (1,618)
df 1.000 0.909 0.826 0.751 0.683 0.621
a
$5,000 × 0.6 $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 b
Lease: Year 0 1–5 5 NPV
(1 – t)C $(7,500)*
CF $(1,000) (7,500) 1,000
df 1.000 3.791 0.621
P $ (1,000) (28,433) 621 $ (28,812)
*$12,500 × 0.6 The car should be leased because leasing has a lower cost.
438
P $(30,000) (545) 694 (523) (1,105) (1,005) $(32,484)
13–16 1.
Standard equipment (Rate = 18%): Year 0 1 2 3–10 NPV
Cash Flow $(500,000) 300,000 200,000 100,000
df 1.000 0.847 0.718 2.928
Present Value $(500,000) 254,100 143,600 292,800 $ 190,500
Cash Flow $(2,000,000) 100,000 200,000 300,000 400,000 500,000 1,000,000
df 1.000 0.847 0.718 0.609 1.323 0.314 0.682
Present Value $(2,000,000) 84,700 143,600 182,700 529,200 157,000 682,000 $ (220,800)
Standard equipment (Rate = 10%): Year Cash Flow 0 $(500,000) 1 300,000 2 200,000 3–10 100,000 NPV
df 1.000 0.909 0.826 4.409
Present Value $(500,000) 272,700 165,200 440,900 $ 378,800
df 1.000 0.909 0.826 0.751 1.868 0.513 1.277
Present Value $(2,000,000) 90,900 165,200 225,300 747,200 256,500 1,277,000 $ 762,100
CAM equipment (Rate = 18%): Year 0 1 2 3 4–6 7 8–10 NPV 2.
CAM equipment (Rate = 10%): Year 0 1 2 3 4–6 7 8–10 NPV
Cash Flow $(2,000,000) 100,000 200,000 300,000 400,000 500,000 1,000,000
439
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 0 1 2 3–10 NPV
Cash Flow $(500,000) 300,000 200,000 100,000
df 1.000 0.877 0.769 3.571
Present Value $(500,000) 263,100 153,800 357,100 $ 274,000
df 1.000 0.877 0.769 0.675 1.567 0.400 0.929
Present Value $(2,000,000) 87,700 153,800 202,500 626,800 200,000 929,000 $ 199,800
df 1.000 0.877 0.769 3.571
Present Value $(500,000) 263,100 153,800 178,550 $ 95,450
CAM equipment (Rate = 14%): Year 0 1 2 3 4–6 7 8–10 NPV 2.
Cash Flow $(2,000,000) 100,000 200,000 300,000 400,000 500,000 1,000,000
Standard equipment (Rate = 14%): Year 0 1 2 3–10 NPV
Cash Flow $(500,000) 300,000 200,000 50,000
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 emphasizes how intangible benefits can affect decisions.
440
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 return 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 assumes 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.
441
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 0 1–7
Item
Cash Flow
Equipment Working capital
$(300,000) (30,000)
Cost savings Equipment operating costs
5
Overhaul
7
Salvage value Recovery of working capital
$135,000 (60,000)
(30,000) 24,000 30,000
NPV: Year 0 1–7 5 7 NPV
Cash Flow $(330,000) 75,000 (30,000) 54,000
75,000
df 1.000 4.868 0.621 0.513
Present Value $(330,000) 365,100 (18,630) 27,702 $ 44,172
Yes, the new process design should be accepted.
442
13–20
1.
Schedule of cash flows: Year
Item
Cash Flow
Equipment Working capital Total
$(1,100,000) (50,000) $(1,150,000)
1–5
Revenues Operating expenses Total
$ 1,500,000 (1,260,000) $ 240,000
6
Revenues Operating expenses Major maintenance Total
$ 1,500,000 (1,260,000) (100,000) $ 140,000
7–9
Revenues Operating expenses Total
$ 1,500,000 (1,260,000) $ 240,000
10
Revenues Operating expenses Salvage Recovery of working capital Total
$ 1,500,000 (1,260,000) 40,000 50,000 $ 330,000
0
443
13-20 2.
Concluded
Year 0 1–5 6 7 8 9 10 NPV
Cash Flow $(1,150,000) 240,000 140,000 240,000 240,000 240,000 330,000
Discount Factor 1.000 3.605 0.507 0.452 0.404 0.361 0.322
Present Value $(1,150,000) 865,200 70,980 108,480 96,960 86,640 106,260 $ 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 system.
444
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 latter 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: Selling price Unit variable cost Unit contribution margin
Per unit $10 4 $ 6
Total contribution margin ($6 × 1,000,000 annual sales volume) Less: Fixed costs Annual cash flow
$ 6,000,000 2,000,000 $ 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
445
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) Less: Fixed costs Annual cash flow
$5,400,000 2,000,000 $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) Less: Fixed costs Annual cash flow
$6,400,000 2,000,000 $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 assumptions 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 values possible with their probability of occurrence are important information. It also ignores the fact that assumptions are dynamic and can interact with each other.
446
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%
447
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 interval, suggesting a high probability of a positive NPV.
13–24 1.
1.00 year 1.00 year 1.00 year 0.13 year* 3.13 years
$16,800 24,000 29,400 3,800 $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
448
13–24 Concluded 3.
Year 0 1 2 3 4 NPV
Cash Flow $(74,000) 16,800 24,000 29,400 35,400*
Discount Factor 1.000 0.893 0.797 0.712 0.636
Present Value $(74,000) 15,002 19,128 20,933 22,514 $ 3,577
Discount Factor 1.000 0.877 0.769 0.675 0.592
Present Value $(74,000) 14,734 18,456 19,845 20,957 $ (8)
*Includes $6,000 salvage value IRR (by trial and error): Using 14 percent as the first guess: Cash Flow Year 0 $(74,000) 1 16,800 2 24,000 3 29,400 4 35,400 NPV 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 0 1 2 3 4 NPV
Cash Flow $(74,000) 11,200 16,000 19,600 25,600
Discount Factor 1.000 0.893 0.797 0.712 0.636
Present Value $(74,000) 10,002 12,752 13,955 16,282 $(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.
449
13–25 Keep old computer: Year 0 1 2 3 4 5 NPV
(1 – t)Ra — — — — — $6,000
–(1 – t)Cb — $(60,000) (60,000) (60,000) (60,000) (60,000)
tNCc — $32,000 32,000 16,000 — —
CF — $(28,000) (28,000) (44,000) (60,000) (54,000)
df — 0.893 0.797 0.712 0.636 0.567
Present Value — $ (25,004) (22,316) (31,328) (38,160) (30,618) $(147,426)
a
(0.60) × $10,000 (0.60) × $100,000 c Years 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. b
Buy new computer: a
b
Yr. (1 – t)R –(1 – t)C 0 1 (30,000) 2 (30,000) 3 (30,000) 4 (30,000) 5 $42,720 (30,000) NPV
c
tNC $60,000 40,000 64,000 38,400 23,040 23,040
d
Other $(450,000)
28,800
CF $(390,000) 10,000 34,000 8,400 (6,960) 64,560
a
df 1.000 0.893 0.797 0.712 0.636 0.567
Present Value $(390,000) 8,930 27,098 5,981 (4,427) 36,606 $(315,812)
(0.60) × ($100,000 – Book value), where book value = $500,000 – $471,200 (0.60) × $50,000 c Year 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 depreciation can be claimed in Year 5. d Purchase 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 accumulated depreciation). b
The old computer should be kept since it has a lower cost.
450
13–26 1.
Purchase: Year 0 1 2 3 4 5 6 7 8 9 10
(1 – t)Ra
–(1 – t)Cb
tNCc
$33,000 33,000 33,000 33,000 33,000 33,000 33,000 33,000 33,000 45,000d
$(12,000) (12,000) (12,000) (12,000) (12,000) (12,000) (12,000) (12,000) (12,000) (12,000)
$5,716 9,796 6,996 4,996 3,572 3,568 3,572 1,784
Cash Flow $(100,000) 26,716 30,796 27,996 25,996 24,572 24,568 24,572 22,784 21,000 33,000
a
0.60 × $55,000 0.60 × $20,000 c 0.40 × 0.1429 × $100,000, 0.40 × 0.2449 × $100,000, etc. d Includes salvage value as a gain. b
Lease—with service contract: Year 0 1 2 3 4 5 6 7 8 9 10
(1 – t)R $33,000 33,000 33,000 33,000 33,000 33,000 33,000 33,000 33,000 33,000
–(1 – t)Ca $(12,420) (18,420) (18,420) (18,420) (18,420) (18,420) (18,420) (18,420) (18,420) (18,420) (6,000)
a
tNCb $1,200 1,200 1,200 1,200 1,200 1,200 1,200 1,200 1,200 1,200
Cash Flow $(47,420)c 15,780 15,780 15,780 15,780 15,780 15,780 15,780 15,780 15,780 33,200d
Year 0: 0.60 × $20,700; Years 1–9: 0.60 × $30,700; Year 10: 0.60 × $10,000 0.40 × $3,000 c Includes deposit of $5,000 and purchase of contract of $30,000 d Includes the refund of the $5,000 deposit b
451
13–26 Continued Lease—without service contract: Year 0 1 2 3 4 5 6 7 8 9 10
(1 – t)R $33,000 33,000 33,000 33,000 33,000 33,000 33,000 33,000 33,000 33,000
–(1 – t)Ca $(12,420) (24,420) (24,420) (24,420) (24,420) (24,420) (24,420) (24,420) (24,420) (24,420) (12,000)
Cash Flow $(17,420)b 8,580 8,580 8,580 8,580 8,580 8,580 8,580 8,580 8,580 26,000c
a
Year 0: 0.60 × $20,700; Years 1–9: 0.60 × $40,700; Year 10: 0.60 × $20,000 Includes deposit of $5,000 c Includes return of $5,000 deposit b
2.
Purchase: Year 0 1 2 3 4 5 6 7 8 9 10 NPV
Cash Flow $(100,000) 26,716 30,796 27,996 25,996 24,572 24,568 24,572 22,784 21,000 33,000
Discount Factor 1.000 0.877 0.769 0.675 0.592 0.519 0.456 0.400 0.351 0.308 0.270
452
Present Value $(100,000) 23,430 23,682 18,897 15,390 12,753 11,203 9,829 7,997 6,468 8,910 $ 38,559
13–26 Concluded Lease—without service contract: Year 0 1–9 10 NPV
Cash Flow $(17,420) 8,580 26,000
Discount Factor 1.000 4.946 0.270
Present Value $ (17,420) 42,437 7,020 $ 32,037
The equipment should be purchased. It was not necessary to include all of the costs and revenues for each alternative. The operating revenues and operating costs could have been eliminated because they are exactly the same for both alternatives and, thus, not relevant. 3.
Lease—with service contract: Year 0 1–9 10 NPV
Cash Flow $(47,420) 15,780 33,200
Discount Factor 1.000 4.946 0.270
Present Value $ (47,420) 78,048 8,964 $ 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.
453
13–27 1.
Scrubbers and Treatment Facility (expressed in thousands): Year 0 1 2 3 4 5 6 NPV
(1 – t)Ra
–(1 – t)Cb
$3,000 3,000 3,000 3,000 3,000 3,600d
$(7,200) (7,200) (7,200) (7,200) (7,200) (7,200)
tNCc $2,000 3,200 1,920 1,152 1,152 576
CF $(25,000) (2,200) (1,000) (2,280) (3,048) (3,048) (3,024)
df 1.000 0.909 0.826 0.751 0.683 0.621 0.564
Present Value $(25,000) (2,000) (826) (1,712) (2,082) (1,893) (1,706) $(35,219)
a
0.6 × $5,000,000 0.6 × $12,000,000 c Year 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 d Includes salvage value (0.6 × $1,000,000) b
Process Redesign (expressed in thousands): Year 0 1 2 3 4 5 6 NPV
(1 – t)Ra
–(1 – t)Cb
$9,000 9,000 9,000 9,000 9,000 9,900d
$(3,000) (3,000) (3,000) (3,000) (3,000) (3,000)
tNCc $4,000 6,400 3,840 2,304 2,304 1,152
CF $(50,000) 10,000 12,400 9,840 8,304 8,304 8,052
df 1.000 0.909 0.826 0.751 0.683 0.621 0.564
Present Value $ (50,000) 9,090 10,242 7,390 5,672 5,157 4,541 $ (7,908)
a
0.6 × $15,000,000 0.6 × $5,000,000 c Year 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 d Includes salvage value (0.6 × $1,500,000) b
The process redesign option is less costly and should be implemented.
454
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 environmental performance increases and that it is cheaper to prevent environmental contamination than it is to clean it up once created. The first alternative is a “cleanup” approach, while the second is a “prevention” approach.
13–28 1.
Original savings and investment: (14 percent rate): Year CF 0 $(45,000,000) 1–20 $4,000,000 20 5,000,000 NPV
df 1.000 6.623 0.073
Present Value $(45,000,000) 26,492,000 365,000 $(18,143,000)
455
13-28
Continued
(20 percent rate): Year CF 0 $(45,000,000) 1–20 $4,000,000 20 5,000,000 NPV
2.
df 1.000 4.870 0.026
Present Value $(45,000,000) 19,480,000 130,000 $(25,390,000)
Total benefits: ($4,000,000 + $1,000,000 + $2,400,000) (14 percent rate): Year 0 1–20 20 NPV
CF df $(45,000,000) 1.000 7,400,000 6.623 5,000,000 0.073
Present Value $(45,000,000) 49,010,200 365,000 $ 4,375,200
(20 percent rate): Year 0 1–20 20 NPV
CF df $(45,000,000) 1.000 7,400,000 4.870 5,000,000 0.026
Present Value $(45,000,000) 36,038,000 130,000 $ (8,832,000)
456
13-28 3.
Concluded
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 0 1–20 20 NPV
4.
CF df $(48,000,000) 1.000 7,400,000 4.870 5,000,000 0.026
Present Value $(48,000,000) 36,038,000 130,000 $ (11,832,000)
The automated plant is an attractive investment when the additional benefits are considered—it promises to return at least the cost of capital (even for the high-cost scenario). Using the hurdle rate of 20 percent 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 0 1 2–5 6 7 8 NPV
Cash Flow* $(860,000) 196,400 230,800 196,400 162,000 162,000
Discount Factor 1.000 0.862 2.412 0.410 0.354 0.305
Present Value $(860,000) 169,297 556,690 80,524 57,348 49,410 $ 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.
457
13–29 Concluded 2.
Year 0 1 2–5 6 7 8 NPV
Cash Flow* $(920,000) 186,800 223,600 186,800 150,000 150,000
Discount Factor 1.000 0.862 2.412 0.410 0.354 0.305
Present Value $(920,000) 161,022 539,323 76,588 53,100 45,750 $ (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 investment decisions.
458
13–30 1.
Old system (dollars in thousands): Year 0 1–9 10 NPV
(1 – t)Ra
–(1 – t)Cb
tNCc
$18,000 18,000
$(13,440) (13,440)
$240 —
Cash Flow $ 0 4,800 4,560
df 1.000 4.303 0.191
Present Value* $ 0 20,654 871 $ 21,525
Cash Flow $(50,040) 12,840
df 1.000 4.494
Present Value* $ (50,040) 57,703 $ 7,663
a
0.6 × $300 × 100,000 0.6 × $224 × 100,000 c 0.4 × $600,000 *Rounded b
New system (dollars in thousands): Year 0 1–10 NPV a
(1 – t)Ra
–(1 – t)Cb
$18,000
$(7,320)
Direct materials (0.75 × $80) Direct labor (1/3 × $90) Volume-related OH ($20 – $5) Direct FOH ($34 – $17) Unit cost
tNCc $2,160 $ 60 30 15 17 $122
Total cash expenses = $122 × 100,000 = $12,200,000 After-tax cash expenses = 0.6 × $12,200,000 b
Year 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 c
Net outlay = $54,000,000 – $3,000,000 – $960,000 = $50,040,000
The company should keep the old system.
459
13–30 Continued 2.
Old system (dollars in thousands): Year 0 1–9 10 NPV
(1 – t)R
–(1 – t)C
tNC
$18,000 18,000
$(13,440) (13,440)
$240 —
Cash Flow $ 0 4,800 4,560
df 1.000 5.328 0.322
Present Value* $ 0 25,574 1,468 $ 27,042
Cash Flow $(50,040) 12,840
df 1.000 5.650
Present Value $ (50,040) 72,546 $ 22,506
New system (dollars in thousands): Year 0 1–10 NPV
(1 – t)R
–(1 – t)C
$18,000
$(7,320)
tNC $2,160
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 0 1 2 3 4 5 6 7 8 9 10 NPV
(1 – t)R
–(1 – t)C
tNC
$18,000 16,200 14,400 12,600 10,800 9,000 7,200 5,400 3,600 1,800
$(13,440) (12,300) (11,160) (10,020) (8,880) (7,740) (6,600) (5,460) (4,320) (3,180)
$240 240 240 240 240 240 240 240 240 —
Cash Flow $ 0 4,800 4,140 3,480 2,820 2,160 1,500 840 180 (480) (1,380)
df Present Value** 1.000 $ 0 0.893 4,286 0.797 3,300 0.712 2,478 0.636 1,794 0.567 1,225 0.507 761 0.452 380 0.404 73 0.361 (173) 0.322 (444) $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
460
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 increase 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 unappealing. By using the correct rate, the alternative showed a large net present value, 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 system 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 0 1–10 NPV
Cash Flow* $ 0 (197,000)
df 1.000 5.650
Present Value $ 0 (1,113,050) $(1,113,050)
*[–(0.66 × $350,000) + (0.34 × $100,000)]
461
13–31 Continued Flexible system (using MACRS depreciation): Year 0 1 2 3 4 5 6 7 8 9 10 NPV
(1 – t)Ca — $(62,700) (62,700) (62,700) (62,700) (62,700) (62,700) (62,700) (62,700) (62,700) (62,700)
tNCb — $ 60,733 104,083 74,333 53,083 37,953 37,910 37,953 18,955
Cash Flow $(1,250,000) (1,967) 41,383 11,633 (9,617) (24,747) (24,790) (24,747) (43,745) (62,700) (62,700)
df 1.000 0.893 0.797 0.712 0.636 0.567 0.507 0.452 0.404 0.361 0.322
Present Value* $(1,250,000) (1,757) 32,982 8,283 (6,116) (14,032) (12,569) (11,186) (17,673) (22,635) (20,189) $(1,314,892)
a
$95,000 × 0.66 $1,250,000 × 0.1429 × 0.34, $1,250,000 × 0.2449 × 0.34, etc. (MACRS depreciation for a seven-year asset) *Rounded b
2.
Old operating system (with adjustment for inflation): Year 0 1 2 3 4 5 6 7 8 9 10 NPV
Cash Flow* $ 0 (206,240) (215,850) (225,844) (236,237) (247,047) (258,289) (269,981) (282,140) (294,786) (307,937)
Discount Factor 1.000 0.893 0.797 0.712 0.636 0.567 0.507 0.452 0.404 0.361 0.322
n
Present Value** $ 0 (184,172) (172,032) (160,801) (150,247) (140,076) (130,953) (122,031) (113,985) (106,418) (99,156) $(1,379,871)
*{–[(1.04) × $350,000 × 0.66] + [0.34 × $100,000]}, n = 1 ... 10 **Rounded
462
13–31 Concluded Flexible system (with adjustment for inflation): Year 0 1 2 3 4 5 6 7 8 9 10 NPV
Cash Flow* $(1,250,000) (4,475) 36,267 3,804 (20,267) (38,331) (41,426) (44,556) (66,854) (89,242) (92,811)
Discount Factor 1.000 0.893 0.797 0.712 0.636 0.567 0.507 0.452 0.404 0.361 0.322
Present Value $(1,250,000) (3,996) 28,905 2,708 (12,890) (21,734) (21,003) (20,139) (27,009) (32,216) (29,885) $(1,387,259)
*{–[(1.04)n × $95,000 × 0.66] + [Annual depreciation × 0.34]}, n = 1 ... 10; depreciation is MACRS. 3.
It is very important to adjust cash flows for inflationary effects. Since the required rate of return for capital budgeting analysis reflects an inflationary component at the time NPV analysis is performed, a correct analysis also requires that the predicted operating cash flows be adjusted to reflect inflationary effects. If the operating cash flows are not adjusted, then an erroneous decision may be the outcome. Notice, for example, that after adjusting for inflation, there is virtually no difference between the two systems—and given the intangibles associated with the flexible system, it would likely be chosen.
463
MANAGERIAL DECISION CASES 13–32 The statement that Manny would normally have taken the first bid without hesitation implies that the bid met all of the formal requirements outlined by the company. 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. Perhaps 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 Manny 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 leaning 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 personally or through a third party. III. Integrity 3. Refuse any gift, favor, or hospitality that would influence their actions.
464
13–33 1.
Shaftel Ready Mix Income Statement For the Year Ended 20XX Sales (35,000 × $45) .................................................. Less: Variable expenses ($35.08 × 35,000) ............. Contribution margin ................................................. Less fixed expenses: Salaries ................................................................. Insurance .............................................................. Telephone ............................................................. Depreciation ......................................................... Utilities .................................................................. Net income .................................................................
$ 1,575,000 1,227,800 $ 347,200 $135,000 75,000 5,000 56,200* 25,000 $
296,200 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.
465
13–33 Continued 3.
NPV: Year 0 1–10 NPV
Cash Flow $(352,000) 107,200
Discount Factor 1.000 6.145
Present Value $(352,000) 658,744 $ 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 0 1–10 NPV
Cash Flow (582,000) 107,200
Discount Factor 1.000 6.145
Present Value $(582,000) 658,744 $ 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 opportunity cost is the key concept here.
466
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 0 1–10 NPV
Cash Flow $(352,000) 56,200
Discount Factor 1.000 6.145
Present Value $(352,000) 345,349 $ (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 accounting income, not for cash flow. Since there are noncash expenses deducted from revenues, accounting income understates cash income. Zero income does not mean zero cash inflows.
467
13–33 Concluded 5.
Cost of capital = 10 percent for 10 years, so df = 6.145 df 6.145 6.145 × CF CF
= I/CF = $352,000/CF = $352,000 = $57,282
Cash flow Less: Depreciation Net income Net income $1,082 $1,082 $297,282 X
$ 57,282 56,200 $ 1,082
= Sales – Variable expenses – Fixed expenses = $45X – $35.08X – $296,200 = $9.92X – $296,200 = $9.92X = 29,968 cubic yards
Sales Less: Variable expenses Contribution margin Less: Fixed expenses Net income
$ 1,348,560 1,051,277 $ 297,283 296,200 $ 1,083*
*Difference due to rounding
13–34 1.
After-tax cash flows Manual system: Year 1–10
(1 – t)Ra $264,000
–(1 – t)Cb $(198,000)
a
tNCc $6,800
0.66 × $400,000 0.66 × $228,000 + [0.66 × ($92,000 – $20,000)] c 0.34 × $20,000 b
468
Cash Flow $72,800
13–34 Continued Robotic system: Year 0 1 2 3 4 5 6 7 8 9 10
(1 – t)Ra
–(1 – t)Cb
tNCc
$264,000 297,000 330,000 396,000 396,000 396,000 396,000 396,000 396,000 409,200
$(136,720) (146,220) (155,720) (174,720) (174,720) (174,720) (174,720) (174,720) (174,720) (174,720)
$25,265 43,298 30,922 22,082 15,788 15,771 15,788 7,885
Cash Flow $(425,600)d 152,545 194,078 205,202 243,362 237,068 237,051 237,068 229,165 221,280 234,480
a
Year 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)
b
After-tax cash expenses:
Fixed: Direct labor Other
$20,000 × 0.66 = $13,200 (one operator) $72,000 × 0.66 = 47,520 (from income statement) $60,720
Variable: Direct materials Variable overhead Variable selling Total
(0.16 × Sales) (0.09 × Sales) (0.12 × Sales) 0.19
× × × ×
0.75 × 0.66 0.6667 × 0.66 0.90 × 0.66 Sales
Total after-tax cash expenses = $60,720 + (0.19 × Sales) c
Years 1–8: MACRS: 0.1429 × $520,000 × 0.34, 0.2449 × $520,000 × 0.34, etc.
d
Net investment: Purchase costs Recovery of capital Tax savings on loss
$(520,000) 40,000 54,400* $(425,600)
*Year 0: 0.34 × ($200,000 – $40,000)
469
13–34 Continued 2.
Manual system: Cash Flow Year 0 $ 0 1–10 72,800 NPV
Discount Factor 1.000 5.650
Present Value $ 0 411,320 $411,320
Discount Factor 1.000 0.893 0.797 0.712 0.636 0.567 0.507 0.452 0.404 0.361 0.322
Present Value $(425,600) 136,223 154,680 146,104 154,778 134,418 120,185 107,155 92,583 79,882 75,503 $ 775,911
Robotics system: Year 0 1 2 3 4 5 6 7 8 9 10 NPV
Cash Flow $(425,600) 152,545 194,078 205,202 243,362 237,068 237,051 237,068 229,165 221,280 234,480
The company should invest in the robotic system.
470
13–34 Concluded 3.
Managers may use a higher discount rate as a way to deal with the uncertainty 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 considerations (e.g., bonuses and promotion opportunities). Using a discount rate of 12 percent: Year 0 1–10 NPV
Cash Flow $(340,000) 80,000
Discount Factor 1.000 5.650
Present Value $(340,000) 452,000 $ 112,000
Using a discount rate of 20 percent: Year 0 1–10 NPV
Cash Flow $(340,000) 80,000
Discount Factor 1.000 4.192
Present Value $(340,000) 335,360 $ (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 conservative firm.
RESEARCH ASSIGNMENTS 13–35 Answers will vary.
13–36 Answers will vary.
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472
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