9-2

Jiambalvo Managerial Accounting

EXERCISES

E1.

Interest expense is not treated as a cash outflow because the “charge” for interest is included in the cost of capital (i.e., the hurdle or discount rate).

E2. The NPV is positive and Pauline should make the investment. Time 0 1 2 3 4 5 6 7 8

Cash Flow (25,000,000) 5,500,000 5,500,000 5,500,000 5,500,000 5,500,000 5,500,000 5,500,000 5,500,000

PV Factors 1.0000 0.8929 0.7972 0.7118 0.6355 0.5674 0.5066 0.4523 0.4039 NPV

1 2 3 4 5 6 7 8

Effect on Income 2,375,000 2,375,000 2,375,000 2,375,000 2,375,000 2,375,000 2,375,000 2,375,000

End of Year Investment 21,875,000 18,750,000 15,625,000 12,500,000 9,375,000 6,250,000 3,125,000 0

$(25,000,000) 4,910,950 4,384,600 3,914,900 3,495,250 3,120,700 2,786,300 2,487,650 2,221,450 $

2,321,800

ROI 0.109 0.127 0.152 0.190 0.253 0.380 0.760 division by zero not defined

Although the project has a positive NPV, if Pauline is overly focused on short-term performance, she may hesitate to make the investment, which has a relatively low ROI in the first year. Note that ROI increases dramatically as the book value of the investment decreases due to depreciation.

Chapter 9 Capital Budgeting Decisions

9-3

E3. According to Mignogna, “You can often determine the cash benefit of increases in capacity, production efficiency, and quality, as well as reductions in operating and maintenance costs attributable to an investment in new technology. However, seldom accounted for are the strategic benefits which result from such investments. With the assistance of the accompanying decisionmaking flow chart, let’s look at a few. First of all, is the investment required just to stay in game (for example, required for regulatory compliance)? If so, and assuming the game is worth being in, then you may not have any choice but to “just do it!” Next, have you considered the importance of the investment to remain competitive in your industry? Here, I am speaking of your ability to acquire, or at least defend, market share. While discounted cash flow analyses may include the benefits of reduced operating costs and so on, they seldom consider the opportunity cost of the lost business which results from your competitors’ ability to offer a higher quality at a reduced cost. In other words, there may be a very real cost attached to not pursuing an innovation. There are several other strategic considerations that are not particularly amenable to economic analyses. Will the investment add to or enhance your firm’s core competencies? Will it provide the capability to penetrate new markets with your product or service? Will expanded production capacity provide access to increased sales and more rapid learning curve progress which will ultimately lower costs? Are you in an industry where the market perceives technological leadership as important? You can probably think of others specific to your own situation. Such strategic benefits are seldom considered in discounted cash flow analyses of new technology. Remember, there’s a big difference between running the numbers and letting the numbers run you.”

9-4

Jiambalvo Managerial Accounting

E4. Company Charles Schwab

McDonalds Wal-Mart

E5.

E6.

Investment decision Should the company purchase additional servers and other equipment to enhance services related to the online business? Should the company purchase land, building, and equipment for a new restaurant? Should the company remodel it’s superstore on the west side of Chicago?

Cash Flow $100

Present Value Factor .6209

Total $62.09

Cash Flow $100

Present Value Factor 3.7908

Total $379.08

E7. The numbers decrease from left to right in a given row because cash received in the future is worth less the higher your required rate of return. The numbers decrease from top to bottom in a given column because cash received further in the future is less valuable today.

E8.

Cash Flow $200 500

Present Value Factor 3.7908 .6209

Total $ 758.16 310.45 $1,068.61

Chapter 9 Capital Budgeting Decisions

E9. Plan A Total $100,000.00 Plan B Cash Flow $ 10,000 100,000

Present Value Factor 6.7101 .4632

Plan C Cash Flow $20,000

Present Value Factor 6.7101

Total $ 67,101.00 46,320.00 $113,421.00

Total $134,202.00

Plan C should be selected as it has the highest present value.

E10.

Cash Flow ($10,000) 4,000

Present Value Factor 1.0000 3.0373

Total ($10,000.00) 12,149.20 $ 2,149.20

The net present value is positive so the project should be undertaken.

9-5

9-6

Jiambalvo Managerial Accounting

E11. The investment should not be undertaken because it has a negative NPV. Cash Flow $6,000.00 (3,500.00) 950.00 (1,800.00) 1,650.00

Present Value Factor

(20,000.00) 5,000.00

1.0000 .2697

5.2161

Total

$8,606.56 (20,000.00) 1,348.50 ($ 10,044.94)

E12. Machine A should be purchased because it has the highest positive NPV. Machine A Cash Flow $15,000.00 (50,000.00)

Present Value Factor 4.3553 1.0000

Machine B Cash Flow $20,000.00 (75,000.00)

Present Value Factor 4.3553 1.0000

Total $65,329.50 (50,000.00) $15,329.50

Total $87,106.00 (75,000.00) $12,106.00

Chapter 9 Capital Budgeting Decisions

9-7

E13. The investment should not be undertaken because the internal rate of return of 12% is less than the required rate of 18%. Initial outlay Annuity amount Outlay ÷ annuity amount Internal rate of return

E14. a. Initial outlay Annuity amount Outlay ÷ annuity amount Internal rate of return

$79,100.00 14,000.00 5.6500 12%

$79,137.00 22,500.00 3.5172 13%

b. Nadine should make the investment because its return of 13% is greater than the required return of 12%.

E15. Annual depreciation $200,000 ÷ 5 years

$40,000.00

Annual tax savings $40,000 × .40

$16,000.00

Present value of $16,000 per year for 5 years at 10% $16,000 × 3.7908

$60,652.80

9-8

E16.

Jiambalvo Managerial Accounting

Year 1 2 3 4

Income (Loss) ($100,000) (50,000) 120,000 200,000

The $100,000 loss in year 1 will offset income in year 3 resulting in a tax savings of $40,000 (i.e., $100,000 × 40% tax rate) in year 3. With respect to the $50,000 loss in year 2, $20,000 of it can be used to offset income in year 3 (resulting in a tax savings of $8,000 in year 3) and $30,000 of it can be used to offset income in year 4 (resulting in a tax savings of $12,000 in year 4). Cash Flow $40,000.00 8,000.00 12,000.00

Present Value Factor .6750 .6750 .5921

Total $27,000.00 5,400.00 7,105.20 $39,505.20

Chapter 9 Capital Budgeting Decisions

E17. The annual cash inflow is $5,700, calculated as follows: Revenue $15,500 Less: Cost other than depreciation 8,000 Depreciation 3,000 Income before taxes 4,500 Less taxes at 40% 1,800 Net income 2,700 Plus depreciation 3,000 Cash flow $5,700 The net present value is positive, so the smoker should be purchased. Cash Flow $5,700.00 (21,000.00)

Present Value Factor 4.5638 1.0000

Total $26,013.66 (21,000.00) $ 5,013.66

E18. The payback period is 8.2 years as follows: Cost Cash inflows Cost ÷ cash inflows

$41,000.00 5,000.00 8.2 years

E19. The accounting rate of return is 30%: Average income Average investment ($200,000 ÷ 2) Accounting rate of return

$30,000.00 100,000.00 30.00%

9-9

9-10

Jiambalvo Managerial Accounting

E20. As indicated, the NPV is close to zero ($145.00) at a rate of 14%. Thus, the IRR is approximately 14%. Given that the required rate of return is only 13%, the e-commerce business should be developed. PV at 13%

Cash Flow $(1,000,000) (500,000) 200,000 630,000 750,000 800,000

PV Factor 1.0000 0.8850 0.7831 0.6931 0.6133 0.5428

PV at 14%

Cash Flow $(1,000,000) (500,000) 200,000 630,000 750,000 800,000

PV Factor 1.0000 0.8772 0.7695 0.6750 0.5921 0.5194

PV at 15%

Cash Flow $(1,000,000) (500,000) 200,000 630,000 750,000 800,000

PV Factor 1.0000 0.8696 0.7561 0.6575 0.5718 0.4972

Total $(1,000,000) (442,500) 156,620 436,653 459,975 434,240 $ 44,988

Total $(1,000,000) (438,600) 153,900 425,250 444,075 415,520 $ 145

Total $(1,000,000) (434,800) 151,220 414,225 428,850 397,760 $ (42,745)

Chapter 9 Capital Budgeting Decisions

9-11

E21. As indicated below, the NPV is zero with a required rate of return of 9 percent. Thus, the IRR is 9 percent. PV at 9%

Cash Flow $(2,200,100) 200,000 400,000 600,000 800,000 1,000,000

PV Factor 1.0000 0.9174 0.8417 0.7722 0.7084 0.6499

Total $(2,200,100) 183,480 336,680 463,320 566,720 649,900 $ 0

E22. The online business may help the company manage a potentially stodgy image associated with its mall locations. Also, the online business may actually generate a number of large sales for the brick and mortar locations. Some customers will shop the Web site to make price and quality comparisons, but they will be unwilling to make, for example, a $5,000 purchase of a diamond ring over the Internet. Thus, after seeing merchandise on the Web site, they may visit one of Sherman’s mall stores to make a purchase. These potential benefits would be difficult to quantify.

E23. The annual value of the “soft” benefit must be at least $88,492.44 for the project to have a zero net present value. Given there is general agreement that the annual “soft” benefit will be at least $90,000, Pritchard should invest in the flexible manufacturing system. A. Present value needed to yield a zero NPV

$500,000.00

B. Present value of an annuity factor at 12%

5.6502

A ÷ B Required annual value of “soft benefit”

$88,492.44

9-12

Jiambalvo Managerial Accounting

PROBLEMS

P1. The original contract was worth $6,790,700 in present value terms while the new offer is worth $6,960,460. When the time value of money is taken into account, it is obvious that the new offer is not much better than the old one.

Time 0 1 2 3 4 5

Cash Flow $3,000,000 1,000,000 1,000,000 1,000,000 1,000,000 1,000,000

PV Factor 1.0000 0.9091 0.8264 0.7513 0.6830 0.6209

Time 1 2 3 4 5 5

Cash Flow 1,000,000 1,100,000 1,200,000 1,300,000 1,400,000 4,000,000

PV Factor 0.9091 0.8264 0.7513 0.6830 0.6209 0.6209

Total $3,000,000 909,100 826,400 751,300 683,000 620,900 $6,790,700

Total 909,100 909,040 901,560 887,900 869,260 2,438,600 $6,960,460

Chapter 9 Capital Budgeting Decisions

9-13

P2. a. Present value of ship in Caribbean/Alaska itinerary at 10% ($68,095,769 × 7.6061) $517,943,229 Present value of ship in Caribbean/Eastern Canada itinerary at 10% ($53,490,300 × 7.6061) $406,852,571 Present value of ship in Caribbean/Alaska itinerary at 15% ($68,095,769 × 5.8474) $398,183,200 Present value of ship in Caribbean/Eastern Canada itinerary at 15% ($53,490,300 × 5.8474) $312,779,180 The cost of the ship is only $180,325,005. Therefore, the NPV will be positive under all of the alternatives which provides strong evidence that the ship should be purchased. b. The NPV will be positive (suggesting that the ship should be purchased) whether the required return is 10 percent or 15 percent. c. The difference in present values is $111,090,658 ($517,943,229 $406,852,571). Thus, there is a high opportunity cost if the firm decides to operate the ship in a Caribbean/Eastern Canada itinerary.

9-14

Jiambalvo Managerial Accounting

P3.

Year 1 Revenue $12,000,000 Less amortization 12,000,000 Income before taxes 0 Less taxes 0 Net income 0 Add amortization 12,000,000 Cash flow $12,000,000

Time 0 1 2 3 4

Cash Flow ($16,000,000) 12,000,000 5,200,000 1,200,000 300,000

Year 2 $6,000,000 4,000,000 2,000,000 800,000 1,200,000 4,000,000 $5,200,000 PV Factor 1.0000 .9091 .8264 .7513 .6830

Year 3 $2,000,000 0 2,000,000 800,000 1,200,000 0 $1,200,000

Year 4 $500,000 0 500,000 200,000 300,000 0 $300,000

Total ($16,000,000) 10,909,200 4,297,280 901,560 204,900 $ 312,940

Since the NPV is positive, the company should produce the film.

Chapter 9 Capital Budgeting Decisions

9-15

P4. Cash flow per year: Revenue Less costs other than depreciation Depreciation Income before taxes Less taxes Net income Add depreciation Cash flow

$75,000 6,800 40,000 28,200 11,280 16,920 40,000 $56,920

Annuity factor equals cost divided by annual cash flow: ($200,000 ÷ $56,920)

3.5137

This implies an internal rate of return of approximately 13% (factor is 3.5172) Given the internal rate of return exceeds the required rate of 12%, the company should invest in the remodel.

9-16

Jiambalvo Managerial Accounting

P5. a. The net present value is positive ($43,496.60). Thus the company should invest in the paint and body shop. Net income Add depreciation Annual cash flow Cash Flow $121,000 (700,000)

$ 51,000 70,000 $121,000 Present Value Factor 6.1446 1.0000

Total $743,496.60 (700,000.00) $ 43,496.60

b. A present value of an annuity factor of 5.7851 implies an IRR of approximately 12%. Initial outlay Annuity amount

$700,000 121,000

Cost ÷ annuity

5.7851

Note—the annuity factor for 12% is 5.6502. c. The payback period is approximately 5.8 years: Initial outlay Annual cash flow Number of years to recover initial investment

$700,000 121,000

5.7851

d. The accounting rate of return is approximately 35%: Average income

$51,000

Average investment ($700,000 ÷ 2)

350,000

Accounting rate of return

14.57%

Chapter 9 Capital Budgeting Decisions

9-17

P6. a. Present value of Machine A

Labor saving Power saving Chemical saving Add. Main. Add. Misc. Total Cost Installation Residual value

Cash Flow $21,000 1,300 2,900 (1,000) (2,200) 22,000 (43,000) (4,500) 3,200

PV Factor

Total

2.9137 1.0000 1.0000 .5921 NPV

$ 64,101.40 (43,000.00) (4,500.00) 1,894.72 $18,496.12

b. Present value of Machine B

Labor saving Power saving Chemical saving Add. Main. Add. Misc. Total Cost Installation Residual value

Cash Flow $29,000 1,900 3,200 (1,200) (2,300) 30,600 (73,000) (5,000) 5,200

PV Factor

Total

2.9137 1.0000 1.0000 .5921 NPV

$ 89,159.22 (73,000.00) (5,000.00) 3,078.92 $14,238.14

c. Both NPVs are greater than zero, so both are acceptable investments. However, the company should purchase machine A since it has the highest NPV.

9-18

Jiambalvo Managerial Accounting

P7. Crown should invest in the new limousine since the NPV is positive. Net income Add depreciation Annual cash flow Cash Flow $29,790.00 20,000.00 (80,000.00)

$17,790 12,000 $29,790 Present Value Factor 3.4331 .5194 1.0000

Total $102,272.05 10,388.00 (80,000.00) $ 32,660.05

P8. Island Ferry should not invest in the boat because the NPV is negative. Revenue Less: Labor Fuel Maintenance Miscellaneous Depreciation Income before taxes Taxes Net income Depreciation Annual cash flow Cash Flow $136,100.00 62,000.00 (828,000.00)

$293,000 84,000 15,800 26,700 3,500 95,750 67,250 26,900 40,350 95,750 $136,100 Present Value Factor 4.9676 .4039 1.0000

Total $676,090.36 25,041.80 (828,000.00) ($126,867.84)

Chapter 9 Capital Budgeting Decisions

P9. a. Revenue (35,000 × $35) Less: Component cost Direct labor Depreciation Miscellaneous Advertising Income before taxes Taxes Net income Depreciation Annual cash flow Cash Flow $153,000.00 10,000.00 (310,000.00)

$1,225,000 300,000 400,000 60,000 180,000 130,000 155,000 62,000 93,000 60,000 $ 153,000

Present Value Factor 3.4331 .5194 1.0000

Total $525,264.30 5,194.00 (310,000.00) $220,458.30

b. The payback period is approximately 2 years: Initial outlay Annual cash flow

$310,000 153,000

Number of years to recover initial investment

2.026 years

c. The accounting rate of return is 60%: Average income Average investment ($310,000 ÷ 2) Accounting rate of return

$93,000

$155,000 60%

d. Given the positive NPV, company should invest in Autodial.

9-19

9-20

Jiambalvo Managerial Accounting

P10. Year 1 Income $45,000 Deprec. 50,000 Cash flow $95,000

2

3

4

5

6

7

48,750 52,688 56,822 61,163 65,721 70,507 50,000 50,000 50,000 50,000 50,000 50,000 98,750 102,688 106,822 111,163 115,721 120,507

Year 1. 2. 3. 4. 5. 6. 7.

Cash flow $95,000 98,750 102,688 106,822 111,163 115,721 120,507

Factor .8772 .7695 .6750 .5921 .5194 .4556 .3996

Total $ 83,334.00 75,988.13 69,314.40 63,249.31 57,738.06 52,722.49 48,154.60

7.

50,000

.3996

19,980.00

0.

- 400,000

1.0000

- 400,000.00

NPV

$ 70,480.99

Given the positive NPV, the company should invest in the new business.

Chapter 9 Capital Budgeting Decisions

9-21

P11. a. The cost of capital includes an allowance for expected inflation. Thus, in periods where expected inflation is high, the cost of capital is high, and firms demand a high return on their investments. b. Note that cash flows increase by 4% per year (except for the cash flow related to the depreciation tax shield). Year 1 Year 2 $575,000 $598,000

Cost savings Taxes on cost savings -201,250 -209,300 Tax savings related to depre. 140,000 140,000 Cash flow $513,750 $528,700 Year 1 2 3 4 5

Cash flow $513,750 528,700 544,248 560,418 577,235

Less cost of machine Net present value

Year 3 $621,920

Year 4 $646,797

Year 5 $672,669

-217,672

-226,379

-235,434

140,000 $544,248

140,000 $560,418

140,000 $577,235

Factor .9091 .8264 .7513 .6830 .6209

Total $ 467,050 436,918 408,894 382,765 358,405 2,054,032 2,000,000 $ 54,032

Given the positive NPV, the company should invest in the manufacturing equipment.

9-22

Jiambalvo Managerial Accounting

P12. Note that in problem 11, the NPV was only $54,032 using a 10% required rate of return. This suggests that to determine the IRR, we should start with a return larger than, but close to, 10 percent. Below, the cash flows are brought to present value using an 11% rate of return. Since the sum of the present values is approximately equal to the cost of the investment (a difference of $1,620), the internal rate of return is approximately 11%. Given that this is greater than the required return of 10%, the investment should be undertaken. Year 1. 2. 3. 4. 5.

Cash flow $513,750 528,700 544,248 560,418 577,235

Less cost of machine Net present value

Factor .9009 .8116 .7312 .6587 .5935

Total $ 462,837 429,093 397,954 369,147 342,589 2,001,620 2,000,000 $ 1,620

Chapter 9 Capital Budgeting Decisions

9-23

P13. Most likely, a higher required rate of return should be used reflecting the increased risk of the investment.

P14. a. Richards is evaluated and compensated based on ROI which has some measure of income in the numerator (and a measure of investment in the denominator). Thus, he will be highly focused on income. Some investment opportunities facing his division may increase shareholder wealth (as indicated by positive NPVs) but have a negative effect on short-run accounting income. If that will cause Richards to miss a bonus target, he may pass on these valuable investments. b. I believe this will mitigate the problem. If Richards owns a great deal of stock/and or options, he will have a strong incentive to work to increase the firm’s stock price. And stock prices are likely to be positively impacted when the firm takes on projects with positive NPVs.

9-24

Jiambalvo Managerial Accounting

P15. Revenue Less: Ingred. Salary Misc. Depre. Inc. before taxes Taxes Net income Depre. Cash flow

Year 1 $63,000

Year 2 $69,300

Year 3 $76,230

Year 4 $83,853

Year 5 $92,238

25,200 25,000 2,200 8,000 60,400 2,600 1,040 1,560 8,000 $ 9,560

27,720 27,000 2,400 8,000 65,120 4,180 1,672 2,508 8,000 $10,508

30,492 29,000 2,600 8,000 70,092 6,138 2,455 3,683 8,000 $11,683

33,541 31,000 2,800 8,000 75,341 8,512 3,405 5,107 8,000 $13,107

36,895 33,000 3,000 8,000 80,895 11,343 4,537 6,806 8,000 $14,806

Year 1. 2. 3. 4. 5.

Cash flow $ 9,560 10,508 11,683 13,107 14,806

Factor .8850 .7831 .6931 .6133 .5428

Total $ 8,460.60 8,228.81 8,097.49 8,038.52 8,036.70

5.

2,000

.5428

1,085.60

0.

-40,000

1.0000

- 42,000.00

NPV

($

52.28)

Using a rate of return of 13%, the NPV is approximately zero. Therefore, the IRR is approximately 13%. Melrose should investment in the delivery business given that the company’s required rate of return is only 10%.