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Questions

1. Capital assets are the long-lived assets that are acquired by a firm. Capital assets provide the essential production and distributional capabilities required by all organizations.

2. Cash flows are the final objective of capital

budgeting investments just as cash flows are the final objective of any investment. Accounting income ultimately becomes cash flow but is reported based on accruals and other accounting assumptions and conventions. These accounting practices and assumptions detract from the purity of cash flows and, therefore, are not used in capital budgeting.

3. Timelines provide clear visual models of

the expected cash inflows and outflows for each point in time for a project. They provide an efficient and effective means to help organize the information needed to perform capital budgeting analyses.

4. The payback method measures the time

expected for the firm to recover its investment. The method ignores the receipts expected to occur after the investment is recovered and ignores the time value of money.

5. Return of capital means the investor is

receiving the principal that was originally invested. Return on capital means the investor is receiving an amount earned on the investment.

6. The NPV of a project is the present value of

all cash inflows less the present values of all outflows associated with a project. If the NPV is zero, it is acceptable because, in that case, the project will exactly earn the required cost of capital rate of return. Also, when NPV equals zero, the project’s internal rate of return equals the cost of capital.

7. It is highly unlikely that the estimated NPV

will exactly equal the actual NPV achieved because of the number of estimates necessary in the original computation. These estimates include the project life, the discount rate chosen and the timing and amounts of cash inflows and outflows. The original investment may also include an estimate of the amount of working capital that is needed at the beginning of the project life.

8. The NPV method subtracts the initial

investment from the discounted net cash inflows to arrive at the net present value. The profitability index is calculated by dividing the discounted cash inflows by the initial investment. Thus, each computation uses the same set of amounts in different ways. The PI model attempts to measure the planned efficiency of the use of the money (i.e., output/input) in that it reflects the expected dollars of discounted cash inflows per dollar of investment in the project. A PI equal or greater than 1.00 is equivalent to a NPV equal to or greater than zero and indicates that the investment will provide a return on capital.

9. The IRR is the rate that would cause the

NPV of a project to equal zero. A project is considered potentially successful (all other factors being acceptable) if the calculated IRR exceeds the company's cost of capital.

10. The amount of depreciation for a year is one

factor that helps determine the amount of cash outflow for income taxes. Therefore, although depreciation is not a cash flow item itself, it does affect the size of another item (income taxes) that is a cash flow.

11. The four questions are:

1. Is the activity worthy of an investment?

2. Which assets can be used for the activity?

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3. Of the assets available for each activity, which is the best investment?

4. Of the best investments for all worthwhile activities, in which ones should the company invest?

12. Risk is defined as the likely variability of the future returns of an asset. Aspects of a project for which risk is involved are:

• Life of the asset • Amount of cash flows • Timing of cash flows • Salvage value of the asset • Tax rates

When risk is considered in capital budgeting analysis, the NPV of a project is lowered.

13. Sensitivity analysis is used to determine

the limits of value for input variables (e.g., discount rate, cash flows, asset life, etc.) beyond which the project's outcome will be significantly affected. This process gives the decision maker an indication of how much room there is for error in estimates for input variables and which input variables need special attention.

14. Post-investment audits are performed to

determine whether the realized return.

matches the expected return on a project Post-investment audits are performed at or near the end of a project’s life.

15. The time value of money refers to the

concept that money has time-based earnings power. Money can be loaned or invested to earn an expected rate of return. Present value is always less than future value because of the time value of money. A future value must be discounted to determine its equivalent (but smaller) present value. The discounting process strips away the imputed rate of return in future values, thus resulting in smaller present values.

16. ARR = Average annual profits ÷ Average

investment

Unlike the rate used to discount cash flows or to compare to the cost of capital rate, the ARR is not a discount rate to apply to cash flows. It is measured from accrual-based accounting information and is not intended to be associated with cash flows.

Exercises 1 7. a. Payback = $375,000 ÷ $75,000 per year = 5.00 years

b. Year Amount Cumulative Amount 1 $ 37,500 $ 37,500 2 37,500 75,000 3 37,500 112,500 4 37,500 150,000 5 37,500 187,500 6 50,000 237,500 7 50,000 287,500 8 50,000 337,500 9 50,000 387,500 Payback = 8 + ($37,500 ÷ $50,000) years = 8.75 years, or 8 years and 9 months

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18. a.

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Year Amount Cumulative Amount 1 $35,000 $ 35,000 2 39,000 74,000 3 36,000 110,000 4 28,000 138,000 5 25,000 163,000 6 24,000 187,000 7 22,000 209,000 Payback = 5 years + ($7,000 ÷ $24,000) = 5.29 years

Based on the payback criterion, Cottonwood should not invest in the proposed product line.

b. Yes. Cottonwood should also use a discounted cash flow technique for

two reasons: (1) to take into account the time value of money and (2) to consider those cash flows that occur after the payback period.

19. Point in Time Cash Flows PV Factor Present Value 0 $(800,000) 1.0000 $(800,000) 1 140,000 0.8929 125,006 2 140,000 0.7972 111,608 3 170,000 0.7118 121,006 4 170,000 0.6355 108,035 5 170,000 0.5674 96,458 6 144,400 0.5066 73,153 7 144,400 0.4524 65,327 8 144,400 0.4039 58,323 9 130,000 0.3606 46,878 10 130,000 0.3220 41,860 NPV $ 47,654 Based on the NPV, this is an acceptable investment. 20. a. The contribution margin of each part is $17 ($30 - $13) Contribution margin per year = $17 x 25,000 = $425,000 Point in Time Cash Flows PV Factor Present Value 0 $ (250,000) 1.0000 $ (250,000) 1 - 8 (20,000) 5.5348 (110,696) 1 - 8 425,000 5.5348 2,352,290 NPV $1,991,594 b. Based on the NPV, this is a very acceptable investment.

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c. Other considerations would include whether the company has the

necessary capacity to produce the additional output, the possibility that the customer would decide to purchase elsewhere or would no longer have need for the parts after the company has made its investment, and whether the company has considered all of the costs that would be affected by the decision to produce the new part—especially labor and overhead.

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21. PI = PV of cash inflows ÷ PV of cash outflows = ($6,000 + $60,000) ÷ $60,000 = 1.10 22. a. PV of inflows: $523,388 ($78,000 x 6.7101) PV of investment: $500,000 PI = $523,388 ÷ $500,000 = 1.05 b. The BBC should accept the project because its PI is greater than 1.00. c. To be acceptable, a project must generate a PI of at least 1; a PI greater

than 1 equates to an NPV > 0. 23. a. PV = discount factor x annual cash inflow $340,000 = discount factor x $72,000 Discount factor = $340,000 ÷ $72,000 = 4.7222

The IRR is 13% rounded to the nearest whole percent.

b. Yes. The IRR on this proposal is greater than the firm's hurdle rate of 8%.

c. $340,000 = 5.7466 x Annual cash flow Annual cash flow = $340,000 ÷ 5.7466 Annual cash flow = $59,165 24. a. Straight-line method Annual depreciation = $2,000,000 ÷ 5 years = $400,000 per year Tax benefit = $400,000 x 0.40 = $160,000 PV = $160,000 x 3.7908 = $606,528 b. Accelerated method $2,000,000 x 0.40 x 0.40 x .9091 = $290,912 $1,200,000 x 0.40 x 0.40 x .8265 = 158,688 $ 720,000 x 0.40 x 0.40 x .7513 = 86,550 $ 432,000 x 0.40 x 0.40 x .6830 = 47,209 $ 259,200* x 0.40 x .6209 = 64,375 Total $647,734 *In the final year, the remaining undepreciated cost is expensed. c. The depreciation benefit computed in part (b). exceeds that computed in

part (a). solely because of the time value of money. The depreciation method in part (b). allows for faster recapture of the cost; therefore, there is less discounting of the future cash flows.

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= $30,000,000 ÷ 8 years = $3,750,000 per year

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25. a. SLD Before-tax CF $6,200,000 Less depreciation 3,750,000 Before-tax NI 2,450,000 Less tax (30%) 735,000 NI 1,715,000 Add depreciation 3,750,000 After-tax CF $5,465,000 Point in Time Cash Flows PV Factor Present Value 0 $(30,000,000) 1.0000 $(30,000,000) 1 - 8 5,465,000 6.2098 33,936,557 NPV $ 3,936,557 The project is acceptable. b. Years 1 and 2 Years 3-8 Before-tax CF $ 6,200,000 $6,200,000 Less Depreciation 6,900,000 2,700,000 Before-tax NI (700,000) 3,500,000 Tax (tax benefit) (210,000) 1,050,000 After-tax NI (490,000) 2,450,000 Add Depreciation 6,900,000 2,700,000 After-tax CF $ 6,410,000 $5,150,000 Point in Time Cash Flows PV Factor Present Value 0 $(30,000,000) 1.0000 $(30,000,000) 1 - 2 6,410,000 1.8334 11,752,094 3 - 8 5,150,000 4.3764 22,538,460 NPV $ 4,290,554 The project is acceptable. c. Recomputation of part (a): Before-tax CF $6,200,000 Less depreciation 3,750,000 NIBT 2,450,000 Less tax (40%) 980,000 NI 1,470,000 Add depreciation 3,750,000 After-tax CF $5,220,000 Point in Time Cash Flows PV Factor Present Value 0 $(30,000,000) 1.0000 $(30,000,000) 1 - 8 5,220,000 6.2098 32,415,156 NPV $ 2,415,156 The project is acceptable.

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Recomputation of part (b): Years 1 and 2 Years 3-8 Before-tax CF $ 6,200,000 $6,200,000 Less Depreciation 6,900,000 2,700,000 NIBT $ (700,000) $3,500,000 Less Tax(tax benefit) (280,000) 1,400,000 After-tax NI $ (420,000) $2,100,000 Add Depreciation 6,900,000 2,700,000 After-tax CF $ 6,480,000 $4,800,000 Point in Time Cash Flows PV Factor Present Value 0 $(30,000,000) 1.0000 $(30,000,000) 1 - 2 6,480,000 1.8334 11,880,432 3 - 8 4,800,000 4.3764 21,006,720 NPV $ 2,887,152 The project is acceptable. 26. a. Tax: $95,000 - $18,000 = $77,000 Financial accounting: $95,000 - $35,000 = $60,000 b. CFAT = Market value now minus taxes = $37,000 - (($37,000 - $18,000) x .40) = $29,400 c. CFAT = $9,000 - (($9,000 - $18,000) x .40) = $12,600 27. a. Cash flow x annuity factor = $60,000 Cash flow x 3.7908 = $60,000 Cash flow = $15,828 b. $60,000 ÷ $15,828 = 3.79 years 28. No solution provided. 29. The main point made in the report should be that stock prices are expected

future cash flows of the firm discounted at an appropriate risk-adjusted discount rate. The risk-adjusted discount rate is a function of both the riskiness of the specific security and the prevailing market rates of interest. As the prevailing market interest rates change, the value of securities change also…especially those that have distant future cash flows that comprise a significant portion of the value of the security, e.g., growth stocks.

30. a. A lease is often found appealing by consumers because it results in a

lower monthly payment in many instances than the monthly payment that is required to purchase a car. This allows the consumer either to enjoy a lower monthly payment or, for the same monthly payment required to amortize the cost of one vehicle, pay a similar monthly amount for a more expensive car.

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b. Yes. A consumer should be provided with all necessary information to

make a fair comparison between the lease and purchase alternative. c. As an accountant, you could provide a financial comparison of the lease

and purchase alternatives. Using a discounted cash flow approach, you could compare the present value of purchasing the vehicle to the present value of leasing the vehicle.

31. Present value = future value x discount factor $7,000 = future value x .6209 Future value = $11,274 32. Cost = $6,000 + PV($900 annuity) = $6,000 + ($900 x 44.955*) = $46,460 *discount factor for 60 months, 1% 33. a. PV = future value x discount factor = $40,000 x .7050 = $28,200 should be invested to achieve the goal b. PV = future value x discount factor = $200,000 x .3101 = $62,020 would be equivalent today c. PV = future value x discount factor = $60,000 x .2146 = $12,876 d. Present value = annuity x annuity discount factor = $100,000 x 3.9927 = $399,270 e. Year 1 receipt: $ 50,000 x .9346 = $ 46,730 Year 2 receipt: $ 55,000 x .8734 = 48,037 Year 3 receipt: $ 60,000 x .8163 = 48,978 Year 4 receipt: $100,000 x .7629 = 76,290 Year 5 receipt: $100,000 x .7130 = 71,300 Year 6 receipt: $100,000 x .6663 = 66,630 Year 7 receipt: $100,000 x .6228 = 62,280 Year 8 receipt: $100,000 x .5820 = 58,200 Year 9 receipt: $ 70,000 x .5439 = 38,073 Year 10 receipt: $ 45,000 x .5084 = 22,878 Present value $539,396

f. No. Using any discount rate above 0, the present value of the future annual cash flows is well below $1,000,000. Only if the friend has substantial other assets would she be a millionaire.

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34. a. Change in net income = $400,000 - ($1,200,000 ÷ 5) = $160,000

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ARR = $160,000 ÷ ($1,200,000 ÷ 2) = 26.67%

Payback = $1,200,000 ÷ $400,000 per year = 3 years b. Yes. The equipment investment meets all investment criteria. The payback

is less than 5 years and the accounting rate of return exceeds 18%. 35. a. Annual cash receipts $14,000 Cash expenses (2,000) Net cash flow before taxes 12,000 Depreciation 6,667 Income before tax 5,333 Taxes (1,600) Net income 3,733 Depreciation 6,667 Annual after-tax cash flow $10,400 b. Payback = $40,000 ÷ $10,400 per year = 3.85 years c. ARR = $3,733 ÷ ($40,000 ÷ 2) = 18.66%

Problems 36. a. ($000s omitted) t0 t1 t2 t3 t4 t5 t6 t7 t8 Investment -190 New CM 60 60 60 60 60 60 60 60 Oper. costs 0 -20 -27 -27 -27 -30 -30 -30 -33 Cash flow -190 40 33 33 33 30 30 30 27 b. Year Cash Flow Cumulative Cash Flow 1 $40,000 $ 40,000 2 33,000 73,000 3 33,000 106,000 4 33,000 139,000 5 30,000 169,000 6 30,000 199,000 Payback = 5 + (($190,000 - $169,000) ÷ $30,000) = 5.7 years

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c.

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Time Cash Flow PV Factor for 10% Present Value 0 $(190,000) 1.0000 $(190,000) 1 40,000 .9259 37,036 2 33,000 .8573 28,291 3 33,000 .7938 26,195 4 33,000 .7350 24,255 5 30,000 .6806 20,418 6 30,000 .6302 18,906 7 30,000 .5835 17,505 8 27,000 .5403 14,588 NPV $ (2,806) 37. a. Time: t0 t1 t2 t3 t4 t5 t6 t7 Amount: ($31,000) $6,800 $7,100 $7,300 $7,000 $7,000 $7,100 $7,200 b. Year Cash Flow Cumulative Year 1 $6,800 $ 6,800 Year 2 7,100 13,900 Year 3 7,300 21,200 Year 4 7,000 28,200 Payback = 4 years + (($31,000 - $28,200) ÷ $7,000) = 4.40 years c. Cash Flow Discount Present Description Time Amount Factor Value Purchase the van t0 $(31,000) 1.0000 $(31,000) Cost savings t1 6,800 .9091 6,182 Cost savings t2 7,100 .8265 5,868 Cost savings t3 7,300 .7513 5,484 Cost savings t4 7,000 .6830 4,781 Cost savings t5 7,000 .6209 4,346 Cost savings t6 7,100 .5645 4,008 Cost savings t7 7,200 .5132 3,695 NPV $ 3,364 38. a. Year Cash Flow PV Factor PV 0 $(5,000,000) 1.0000 $(5,000,000) 1- 7 838,000 5.2064 4,362,963 7 400,000 .5835 233,400 NPV $ (403,637) b. No, the NPV is negative; therefore this is an unacceptable project. c. PI = ($4,362,963 + $233,400) ÷ $5,000,000 = 0.92

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d. PV of annual cash flows = $5,000,000 - $233,400

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PV of annual cash flows = $4,766,600 PV of annual Cash flows = Annual cash flow x 5.2064 $4,766,600 = Annual cash flow x 5.2064 Annual cash flow = $4,766,600 ÷ 5.2064 = $915,527 Minimum labor savings = $915,527 + operating costs = $915,527 + $112,000 =$1,027,527 e. The company should consider the quality of the work performed by the

machine versus the quality of the work performed by the individuals; the reliability of the manual process versus the reliability of the mechanical process; and perhaps most importantly, the effect on worker morale and the ethical considerations in displacing 14 workers.

39. a. Payback period = $96,000 ÷ ($37,500 - $7,500) = 3.20 years The project does meet the payback criterion. b. Discount factor = Investment ÷ annual cash flow = $96,000 ÷ $30,000 = 3.2000 Discount factor of 3.2000 indicates IRR ≈ 10 % This is an unacceptable IRR. c. Ms. Alley should consider two main factors. First, the effect of the computer

system on the accuracy of tax returns and the quality of service delivered to clients. Second, Ms. Alley should consider the effect of firing one employee on both the dismissed employee and the remaining employees.

40. a. The incremental cost of the new machine: $290,000 - $6,000 = $284,000 Cash Flow Discount Present Description Time Amount Factor Value Incremental cost t0 $(284,000) 1.0000 $ (284,000) Cost savings t1 - t8 60,000 4.9676 298,056 NPV $ 14,056 PI = $298,056 ÷ $284,000 = 1.05 Yes, the machine should be purchased because the NPV > 0 and the PI > 1. b. Payback = $284,000 ÷ 60,000 per year = 4.73 years c. Net investment ÷ annual annuity = discount factor of IRR $284,000 ÷ 60,000 = 4.7333 Discount factor of 4.7333 is between 13.0 and 13.5%

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Using interpolation, the actual rate is ≈ 13.40% 41. a. Computation of net annual cash flow: Increase in revenues $ 86,000 Increase in cash expenses (37,500) Increase in pretax cash flow 48,500 Less Depreciation (19,500) Income before tax 29,000 Income taxes (30 percent) (8,700) Net income 20,300 Add Depreciation 19,500 After-tax cash flow $ 39,800 Cash Flow Discount Present Description Time Amount Factor Value Initial cost t0 $(390,000) 1.0000 $(390,000) Annual cash flow t1- t20 39,800 8.5136 338,841 NPV $ (51,159) b. No, this is not an acceptable investment. The net present value is not close

to the cutoff value of $0.

c. Minimum annual after tax cash flow x discount factor = $390,000 Minimum annual after tax cash flow x 8.5136 = $390,000 Minimum annual after tax cash flow = $45,809 $45,809 = (minimum cash revenues - $37,500 -19,500)(1 – tax rate) +$19,500 $26,309 = (minimum cash revenues - $37,500 -19,500) 1- .30) $37,584 = minimum cash revenues - $57,000 Minimum cash revenues = $94,584 Proof: Computation of net annual cash flow: Increase in revenues $ 94,584 Increase in cash expenses (37,500) Increase in pretax cash flow 57,084 Less Depreciation (19,500) Income before tax 37,584 Income taxes (30 percent) (11,275) Net income 26,309 Add Depreciation 19,500 After-tax cash flow $ 45,809

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42. a. Cash flow after tax (CFAT): Year Pretax CF Depreciation Tax CFAT 1 $52,000 $32,000 $6,000 $46,000 2 59,000 51,200 2,340 56,660 3 59,000 30,400 8,580 50,420 4 51,000 24,000 8,100 42,900 5 43,000 22,400 6,180 36,820 Timeline: t0 t1 t2 t3 t4 t5 $(160,000) $46,000 $56,660 $50,420 $42,900 $36,820 b. Year Net Cash Flow Cumulative Cash Flow 1 $46,000 $ 46,000 2 56,660 102,660 3 50,420 153,080 Payback = 3 years + (($160,000 - 153,080) ÷ $42,900) = 3.16 years. Net present value: Time Amount Discount Factor Present Value Year 0 $(160,000) 1.0000 $(160,000) Year 1 46,000 .9259 42,591 Year 2 56,660 .8573 48,575 Year 3 50,420 .7938 40,023 Year 4 42,900 .7350 31,532 Year 5 36,820 .6806 25,060 NPV $ 27,781 Profitability index = ($160,000 + $27,781) ÷ $160,000 = 1.17 IRR, is between 14.5% and 15%. Using a computer, the IRR is found to be 14.68%. 43. a. Maple Commercial Plaza: t0 t1 - t10 t10 $(800,000) $210,000 $400,000 High Tower: t0 t1 - t10 t10 $(3,400,000) $830,000 $1,500,000

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b. Maple Commercial Plaza: Calculation of annual cash flow: Pretax cost savings $210,000 Depreciation ($800,000 ÷ 25) (32,000) Pretax income 178,000 Taxes (40 percent) (71,200) Aftertax income 106,800 Depreciation 32,000 Aftertax cash flow $138,800 t0 t1 - t10 t10 $(800,000) $138,800 $432,000* *Includes $32,000 from tax loss on sale (0.40 × ($400,000 - $480,000)) High Tower: Calculation of annual cash flow: Pretax cost savings $ 830,000 Depreciation ($3,400,000 ÷ 25) (136,000) Pretax income 694,000 Taxes (277,600) Aftertax income 416,400 Depreciation 136,000 Aftertax cash flow $ 552,400 t0 t1 - t10 t10 $(3,400,000) $552,400 $1,716,000*

*Includes $216,000 from tax loss on sale (0.40 × ($1,500,000 - $2,040,000)) c. After-tax NPV, Maple Commercial Plaza: Amount Discount Factor Present Value Year 0 $(800,000) 1.0000 $(800,000) Year 1-10 138,800 5.8892 817,421 Year 10 432,000 .3522 152,150 NPV $ 169,571 After-tax NPV, Hightower: Amount Discount Factor Present Value Year 0 $(3,400,000) 1.0000 $(3,400,000) Year 1-10 552,400 5.8892 3,253,194 Year 10 1,716,000 .3522 604,375 NPV $ 457,569 Based on the NPV criterion, Hightower is the preferred investment

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d. After-tax NPV, Hightower: Amount Discount factor Present Value Year 0 $(3,400,000) 1.0000 $(3,400,000) Year 1-10 180,400 5.8892 1,062,412 Year 1-10 372,000* 4.1925 1,559,610 Year 10 1,716,000 .3522 604,375 NPV $ (173,603) *Rental portion of cash flow = $620,000 × (1 - tax rate) = $620,000 × 0.60 = $372,000 In this circumstance, Maple Commercial Plaza is the preferred investment. 44. a. Project Name NPV PI IRR Film studios $3,578,846 1.18 13.03% Cameras & equipment 1,067,920 1.33 18.62 Land improvement 2,250,628 1.45 19.69 Motion picture #1 1,040,276 1.06 12.26 Motion picture #2 1,026,008 1.09 14.22 Motion picture #3 3,197,363 1.40 21.34 Corporate aircraft 518,916 1.22 18.15 b. Ranking according to: NPV PI IRR 1. Film Studios Land investment MP #3 2. MP #3 MP#3 Land Investment 3. Land Invest. Camera & Equip. Camera & Equip. 4. Camera & Equip. Corp. Aircraft Corp. Aircraft 5. MP #1 Film Studio MP #2 6. MP #2 MP #2 Film Studios 7. Corp. Aircraft MP #1 MP #1 c. Suggested purchases: NPV 1. MP #3 @ $8,000,000 $3,197,363 2. Land invest. @ $5,000,000 2,250,628 3. Cam. & Equip. @ $3,200,000 1,067,920 4. Corp. Aircraft @ $2,400,000 518,916 Total NPV $7,034,827

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5. a. Depreciation per year = $1,500,000 ÷ 14 = $107,143

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4 Before tax cash flows = [300 x 0.80 x ($60 - $10) x 50] - $250,000 = $350,000 per year Before-tax CF $350,000 Less Depreciation (107,143) Income before tax 242,857 Less tax (25%) (60,714) Net income 182,143 Add Depreciation 107,143 After-tax cash flow $289,286 PV of 14 yr. annuity of $289,286 @ 11% $2,019,765 Less cost (1,500,000) NPV $ 519,765

b. Discount factor = $1,500,000 ÷ $289,286 = 5.1852 Discount factor of 5.1852 corresponds to ≈ 17%.

c. Cash flow x discount factor = $1,500,000 Cash flow x (6.9819) = $1,500,000 Cash flow = $214,841

d. $1,500,000 ÷ $289,286 = 5.1852 5.1852 is the discount factor for 11% and falls between the 11% discount factors corresponding to 8 and 9 years.

46. a. Year Revenue VC FC Net Cash Flow 1 - 4 $125,000 $ 75,000 $20,000 $ 30,000 5 - 8 175,000 105,000 20,000 50,000 9 - 10 100,000 60,000 20,000 20,000 Year Cash Flow PV Factor PV 0 $(145,000) 1.0000 $(145,000) 1 – 4 30,000 3.1699 95,097 5 - 8 50,000 2.1651 108,255 9 – 10 20,000 .8096 16,192 10 10,000 .3855 3,855 NPV $ 78,399 b. Year Revenue VC FC Net Cash Flow 1 - 4 $120,000 $ 78,000 $15,000 $27,000 5 - 8 200,000 130,000 17,500 52,500 9 - 10 103,000 66,950 25,000 11,050

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Year Cash Flow PV Factor PV 0 $(137,500) 1.0000 $(137,500) 1 – 4 27,000 3.1699 85,587 5 – 8 52,500 2.1651 113,668 9 – 10 11,050 .8096 8,946 10 23,500 .3855 9,059 NPV $ 79,760 c. The biggest factors are the increased level of variable costs, the additional working capital, the lower initial revenues, and the lower cost of production equipment. 47. a. Cash Cash Net Cumulative Year Receipts Expenses Inflows Cash Flows 1 $1,500,000 $1,315,000 $185,000 $ 185,000 2 1,600,000 1,280,000 320,000 505,000 3 1,860,000 1,449,000 411,000 916,000 4 2,560,000 1,984,000 576,000 1,492,000 5 3,200,000 2,320,000 880,000 2,372,000 6 3,200,000 2,320,000 880,000 3,252,000 Payback = 5 + (($3,200,000 - $2,372,000) ÷ $880,000) = 5.94 years b. Year Cash Flow PV Factor PV 0 $(3,200,000) 1.0000 $(3,200,000) 1 185,000 .9174 169,719 2 320,000 .8417 269,344 3 411,000 .7722 317,374 4 576,000 .7084 408,038 5 880,000 .6499 571,912 6 880,000 .5963 524,744 7 544,000 .5470 297,568 8 316,000 .5019 158,600 NPV $ (482,701) c. Year Net Income 1 $(215,000) 2 (80,000) 3 11,000 4 176,000 5 480,000 6 480,000 7 144,000 8 (84,000) $ 912,000

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Average annual income = $912,000 ÷ 8 = $114,000 Average Investment = (Cost + Salvage) ÷ 2 = ($3,200,000 + $0) ÷ 2 = $1,600,000 ARR = $114,000 ÷ $1,600,000 = 7.125%

d. Although there are no stated evaluation criteria for accounting rate of return or payback, the NPV criterion fails to meet the standard threshold of $0. Accordingly, unless there is a benefit of adding the new product line that has not yet been quantified, the product line should not be added.

48. a. Initial cost: t0 = $(730,000) + $170,000 = $(560,000) Annual cash flow: Additional revenue ($1.20 x 110,000) $132,000 Labor savings 30,000 Other operating savings ($192,000 - $80,000) 112,000 Total $274,000 NPV = $(560,000) + ($274,000 x 6.1446) = $1,123,620 b. Discount factor = $560,000 ÷ $274,000 = 2.0438

The IRR exceeds numbers reported in the present value appendix. By computer, the IRR is found to be 47.96%.

c. $560,000 ÷ $274,000 = 2.04 years d. ARR = ($274,000 - $31,000) ÷ (($560,000 + $0) ÷ 2) = 86.79% e. Incremental revenue ($132,000 x 10 years) $1,320,000 Labor cost savings ($30,000 x 10 years) 300,000 Savings in other costs ($112,000 x 10 years) 1,120,000 Less incremental cost (560,000) Incremental profit $2,180,000

Because the incremental profit is greater than $0, the firm should buy the new equipment.

(CMA adapted) 49. a. Incremental annual after-tax cash flows: Purchase Year 0 Purchase of new equipment $(300,000) One time production expense net of tax ($30,000 x .6) (18,000) Sale of old equipment net of tax ($5,000 x .6) 3,000 Total initial cash outflow $(315,000)

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Annual Operations Year 1 Year 2 Year 3 Year 4 Cash operating savings $ 90,000 $150,000 $150,000 $150,000 Less tax effect (40%) (36,000) (60,000) (60,000) (60,000) Cash savings after-tax 54,000 90,000 90,000 90,000 Depr. tax shield (see sched. below) 48,000 36,000 24,000 12,000 After-tax operating cash flows $102,000 $126,000 $114,000 $102,000

Depreciation Schedule Depreciable Base: $300,000

Life: Four-Year Limit Method: Sum-of-the-Years'-Digits

Year Rate Depreciation Depr. Shield 1 4/10 $120,000 $48,000 2 3/10 90,000 36,000 3 2/10 60,000 24,000 4 1/10 30,000 12,000 b. The company should accept the proposal since the NPV is positive. Year Cash Flow 12% PV Factor PV 0 $(315,000) 1.0000 $(315,000) 1 102,000 .8929 91,076 2 126,000 .7972 100,447 3 114,000 .7118 81,145 4 102,000 .6355 64,821 NPV $ 22,489 (CMA) 50. a. The benefits of a postcompletion audit program for capital expenditure

projects include these: • The comparison of actual results with projected results to validate

that a project is meeting expected performance or to take corrective action or terminate a project not achieving expected performance.

• An evaluation of the accuracy of projections from different departments.

• The improvement of future capital project revenue and cost estimates through analyzing variations between expected and actual results from previous projects and the motivational effect on personnel arising from the knowledge that a postinvestment audit

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will be done.

b. Practical difficulties that would be encountered in collecting and accumulating information include:

• Isolating the incremental changes caused by one capital project from all the other factors that change in a dynamic manufacturing and/or marketing environment.

• Identifying the impact of inflation on all costs in the capital project justification.

• Updating of the original proposal for approval of changes that may have occurred after the initial approval.

• Having a sufficiently sophisticated information accumulation system to measure actual costs incurred by the capital project.

• Allocating sufficient administrative time and expenses for the postcompletion audit.

(CMA adapted)