Chapter 12

Cash Flow Estimation and Risk Analysis

LEARNING OBJECTIVES

After reading this chapter, students should be able to:

• Discuss difficulties and relevant considerations in estimating net cash flows, and explain the four major ways that project cash flow differs from accounting income.

• Define the following terms: relevant cash flow, incremental cash flow, sunk cost, opportunity cost, externalities, and cannibalization.

• Identify the three categories to which incremental cash flows can be classified.

• Analyze an expansion project and make a decision whether the project should be accepted on the basis of standard capital budgeting techniques.

• Explain three reasons why corporate risk is important even if a firm’s stockholders are well diversified.

• Identify two reasons why stand-alone risk is important.

• Demonstrate sensitivity and scenario analyses and explain Monte Carlo simulation.

• Discuss the two methods used to incorporate risk into capital budgeting decisions.

• List four different types of embedded real options, explain what a decision tree is, and provide an example of one.

• List the steps a firm goes through when establishing its optimal capital budget in practice.

LECTURE SUGGESTIONS

This chapter develops procedures for estimating and identifying relevant cash flows, discusses techniques used to measure and take account of project risk, introduces the concept of real options, and discusses general principles for determining the optimal capital budget. Assuming you are going to cover the entire chapter, the details of what we cover, and the way we cover it, can be seen by scanning Blueprints, Chapter 12. For other suggestions about the lecture, please see the “Lecture Suggestions” in Chapter 2, where we describe how we conduct our classes.

DAYS ON CHAPTER: 3 OF 58 DAYS (50-minute periods)

ANSWERS TO END-OF-CHAPTER QUESTIONS

12-1 Only cash can be spent or reinvested, and since accounting profits do not represent cash, they are of less fundamental importance than cash flows for investment analysis. Recall that in the stock valuation chapter we focused on dividends, which represent cash flows, rather than on earnings per share.

12-2 Capital budgeting analysis should only include those cash flows that will be affected by the decision. Sunk costs are unrecoverable and cannot be changed, so they have no bearing on the capital budgeting decision. Opportunity costs represent the cash flows the firm gives up by investing in this project rather than its next best alternative, and externalities are the cash flows (both positive and negative) to other projects that result from the firm taking on this project. These cash flows occur only because the firm took on the capital budgeting project; therefore, they must be included in the analysis.

12-3 When a firm takes on a new capital budgeting project, it typically must increase its investment in receivables and inventories, over and above the increase in payables and accruals, thus increasing its net operating working capital (NOWC). Since this increase must be financed, it is included as an outflow in Year 0 of the analysis. At the end of the project’s life, inventories are depleted and receivables are collected. Thus, there is a decrease in NOWC, which is treated as an inflow in the final year of the project’s life.

12-4 Simulation analysis involves working with continuous probability distributions, and the output of a simulation analysis is a distribution of net present values or rates of return. Scenario analysis involves picking several points on the various probability distributions and determining cash flows or rates of return for these points. Sensitivity analysis involves determining the extent to which cash flows change, given a change in one particular input variable. Simulation analysis is expensive. Therefore, it would more than likely be employed in the decision for the $200 million investment in a satellite system than in the decision for the $12,000 truck.

12-5 Postponing the project means that cash flows come later rather than sooner; however, waiting may allow you to take advantage of changing conditions. It might make sense, however, to proceed today if there are important advantages to being the first competitor to enter a market.

12-6 Timing options make it less likely that a project will be accepted today. Often, if a firm can delay a decision, it can increase the expected NPV of a project.

12-7 Having the option to abandon a project makes it more likely that the project will be accepted today.

SOLUTIONS TO END-OF-CHAPTER PROBLEMS

12-1 Equipment $ 9,000,000 NOWC Investment 3,000,000 Initial investment outlay $12,000,000

12-2 Operating Cash Flow: t = 1 Sales revenues $10,000,000 Operating costs 7,000,000 Depreciation 2,000,000 Operating income before taxes $ 1,000,000 Taxes (40%) 400,000 Operating income after taxes $ 600,000 Add back depreciation 2,000,000 Operating cash flow $ 2,600,000

12-3 Equipment’s original cost $20,000,000 Depreciation (80%) 16,000,000 Book value $ 4,000,000

Gain on sale = $5,000,000 - $4,000,000 = $1,000,000. Tax on gain = $1,000,000(0.4) = $400,000. AT net salvage value = $5,000,000 - $400,000 = $4,600,000.

12-4 WACC1 = 12%; WACC2 = 12.5% after $3,250,000 of new capital is raised.

Since each project is independent and of average risk, all projects whose IRR > WACC2 will be accepted. Consequently, Projects A, B, C, D, and E will be accepted and the optimal capital budget is $5,250,000.

12-5 Since Projects C and D are now mutually exclusive only one of them can be accepted. The project with the higher NPV should now be chosen. Therefore, Project D should be selected over Project C. The projects now selected are A, B, D, and E with an optimal capital budget of $4 million.

12-6 Risk-adjusted Projects Risk WACC IRR Decision A High 14.5% 14.0% Reject B Average 12.5 13.5 Accept C Average 12.5 13.2 Accept D Average 12.5 13.0 Accept E Average 12.5 12.7 Accept F Low 10.5 12.3 Accept G Low 10.5 12.2 Accept

On the basis of a risk-adjusted WACC, Projects B, C, D, E, F, and G will be accepted and Project A will be rejected. The firm’s optimal capital budget is $6 million.

12-7 Expected NPV = (0.3)(-$10,800) + (0.5)($23,400) + (0.2)($50,400) = -$3,240 + $11,700 + $10,080 = $18,540.

Since NPV is stated in thousands, E(NPV) = $18,540,000.

(NPV = [(0.3)(-$10,800 - $18,540)2 + (0.5)($23,400 - $18,540)2 + (0.2)($50,400 - $18,540)2]½ = [$258,250,680 + $11,809,800 + $203,011,920]½ = $21,750.23.

Since NPV is stated in thousands (NPV = $21,750,227.59.

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12-8 E(NPV) = 0.05(-$70) + 0.20(-$25) + 0.50($12) + 0.20($20) + 0.05($30) = -$3.5 + -$5.0 + $6.0 + $4.0 + $1.5 = $3.0 million.

(NPV = [0.05(-$70 - $3)2 + 0.20(-$25 - $3)2 + 0.50($12 - $3)2 + 0.20($20 - $3)2 + 0.05($30 - $3)2]½ = $23.622 million.

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12-9 a. 0 1 2 3 4 5 Initial investment ($250,000) Net oper. WC (25,000)

Cost savings $ 90,000 $ 90,000 $ 90,000 $ 90,000 $ 90,000 Depreciation 82,500 112,500 37,500 17,500 0 Oper. inc. before taxes $ 7,500 ($ 22,500) $ 52,500 $ 72,500 $ 90,000 Taxes (40%) 3,000 (9,000) 21,000 29,000 36,000 Oper. Inc. (AT) $ 4,500 ($ 13,500) $ 31,500 $ 43,500 $ 54,000 Add: Depreciation 82,500 112,500 37,500 17,500 0 Oper. CF $ 87,000 $ 99,000 $ 69,000 $ 61,000 $ 54,000

Return of NOWC $ 25,000 Sale of Machine 23,000 Tax on sale (40%) (9,200) Net cash flow ($275,000) $ 87,000 $ 99,000 $ 69,000 $ 61,000 $ 92,800

NPV = $37,035.13

Notes: aDepreciation Schedule, Basis = $250,000

MACRS Rate ( Basis = Year Beg. Bk. Value MACRS Rate Depreciation Ending BV 1 $250,000 0.33 $ 82,500 $167,500 2 167,500 0.45 112,500 55,000 3 55,000 0.15 37,500 17,500 4 17,500 0.07 17,500 0 $250,000

b. If savings increase by 20 percent, then savings will be (1.2)($90,000) = $108,000.

If savings decrease by 20 percent, then savings will be (0.8)($90,000) = $72,000.

(1) Savings increase by 20%:

0 1 2 3 4 5 Initial investment ($250,000) Net oper. WC (25,000)

Cost savings $108,000 $108,000 $108,000 $108,000 $108,000 Depreciation 82,500 112,500 37,500 17,500 0 Oper. inc. before taxes $ 25,500 ($ 4,500) $ 70,500 $ 90,500 $108,000 Taxes (40%) 10,200 (1,800) 28,200 36,200 43,200 Oper. Inc. (AT) $ 15,300 ($ 2,700) $ 42,300 $ 54,300 $ 64,800 Add: Depreciation 82,500 112,500 37,500 17,500 0 Oper. CF $ 97,800 $109,800 $ 79,800 $ 71,800 $ 64,800

Return of NOWC $25,000 Sale of Machine 23,000 Tax on sale (40%) (9,200) Net cash flow ($275,000) $ 97,800 $109,800 $ 79,800 $ 71,800 $103,600

NPV = $77,975.63

(2) Savings decrease by 20%: 0 1 2 3 4 5 Initial investment ($250,000) Net oper. WC (25,000)

Cost savings $ 72,000 $ 72,000 $ 72,000 $ 72,000 $ 72,000 Depreciation 82,500 112,500 37,500 17,500 0 Oper. inc. before taxes ($ 10,500)($ 40,500) $ 34,500 $ 54,500 $ 72,000 Taxes (40%) (4,200) (16,200) 13,800 21,800 28,800 Oper. Inc. (AT) ($ 6,300)($ 24,300) $ 20,700 $ 32,700 $ 43,200 Add: Depreciation 82,500 112,500 37,500 17,500 0 Oper. CF $ 76,200 $ 88,200 $ 58,200 $ 50,200 $ 43,200

Return of NOWC $25,000 Sale of Machine 23,000 Tax on sale (40%) (9,200) Net cash flow ($275,000) $ 76,200 $ 88,200 $ 58,200 $ 50,200 $ 82,000

NPV = -$3,905.37

c. Worst-case scenario: 0 1 2 3 4 5 Initial investment ($250,000) Net oper. WC (30,000)

Cost savings $ 72,000 $ 72,000 $ 72,000 $ 72,000 $ 72,000 Depreciation 82,500 112,500 37,500 17,500 0 Oper. inc. before taxes ($ 10,500)($ 40,500) $ 34,500 $ 54,500 $ 72,000 Taxes (40%) (4,200) (16,200) 13,800 21,800 28,800 Oper. Inc. (AT) ($ 6,300)($ 24,300) $ 20,700 $ 32,700 $ 43,200 Add: Depreciation 82,500 112,500 37,500 17,500 0 Oper. CF $ 76,200 $ 88,200 $ 58,200 $ 50,200 $ 43,200

Return of NOWC $30,000 Sale of Machine 18,000 Tax on sale (40%) (7,200) Net cash flow ($280,000) $ 76,200 $ 88,200 $ 58,200 $ 50,200 $ 84,000

NPV = -$7,663.52

Base-case scenario: This was worked out in part a. NPV = $37,035.13.

Best-case scenario: 0 1 2 3 4 5 Initial investment ($250,000) Net oper. WC ( 20,000)

Cost savings $108,000 $108,000 $108,000 $108,000 $108,000 Depreciation 82,500 112,500 37,500 17,500 0 Oper. inc. before taxes $ 25,500 ($ 4,500) $ 70,500 $ 90,500 $108,000 Taxes (40%) 10,200 (1,800) 28,200 36,200 43,200 Oper. Inc. (AT) $ 15,300 ($ 2,700) $ 42,300 $ 54,300 $ 64,800 Add: Depreciation 82,500 112,500 37,500 17,500 0 Oper. CF $ 97,800 $109,800 $ 79,800 $ 71,800 $ 64,800

Return of NOWC $20,000 Sale of Machine 28,000 Tax on sale (40%) (11,200) Net cash flow ($270,000) $ 97,800 $109,800 $ 79,800 $ 71,800 $101,600

NPV = $81,733.79 Prob. NPV Prob. ( NPV Worst-case 0.35 ($ 7,663.52) ($ 2,682.23) Base-case 0.35 37,035.13 12,962.30 Best-case 0.30 81,733.79 24,520.14 E(NPV) $34,800.21

(NPV = [(0.35)(-$7,663.52 - $34,800.21)2 + (0.35)($37,035.13 - $34,800.21)2 + (0.30)($81,733.79 - $34,800.21)2]½ (NPV = [$631,108,927.93 + $1,748,203.59 + $660,828,279.49]½ (NPV = $35,967.84.

CV = $35,967.84/$34,800.21 = 1.03.

12-10 a. Time Line (in millions of dollars): 0 1 2 20 | | | ( ( ( | -20 3 3 3

NPV = $2.4083 million.

b. Wait 1 year: NPV @ 0 1 2 3 21 Yr. 0 Tax imposed | | | | ( ( ( | 25% Prob. 0 -20 2.4 2.4 2.4 -$1.8512

Tax not imposed | | | | ( ( ( | 75% Prob. 0 -20 3.2 3.2 3.2 3.4841

Note though, that if the tax is imposed, the NPV of the project is negative and therefore would not be undertaken. The value of this option of waiting one year is evaluated as 0.25($0) + (0.75)($3.4841) = $2.6131 million. Since the NPV of waiting one year is greater than going ahead and proceeding with the project today, it makes sense to wait.

12-11 a. The net cost is $178,000:

Cost of investment at t = 0:

Base price ($140,000) Modification (30,000) Increase in NOWC (8,000) Cash outlay for new machine ($178,000)

b. The operating cash flows follow:

Year 1 Year 2 Year 3 After-tax savings $30,000 $30,000 $30,000 Depreciation tax savings 22,440 30,600 10,200 Net operating cash flow $52,440 $60,600 $40,200
Notes:

1. The after-tax cost savings is $50,000(1 — T) = $50,000(0.6) = $30,000.

2. The depreciation expense in each year is the depreciable basis, $170,000, times the MACRS allowance percentages of 0.33, 0.45, and 0.15 for Years 1, 2, and 3, respectively. Depreciation expense in Years 1, 2, and 3 is $56,100, $76,500, and $25,500. The depreciation tax savings is calculated as the tax rate (40 percent) times the depreciation expense in each year.

c. The terminal cash flow is $48,760:

Salvage value $60,000 Tax on SV* (19,240) Return of NOWC 8,000 $48,760

Remaining BV in Year 4 = $170,000(0.07) = $11,900.

*Tax on SV = ($60,000 - $11,900)(0.4) = $19,240.

d. The project has an NPV of ($19,549). Thus, it should not be accepted.

Year Net Cash Flow PV @ 12% 0 ($178,000) ($178,000) 1 52,440 46,821 2 60,600 48,310 3 88,960 63,320 NPV = ($ 19,549)

Alternatively, place the cash flows on a time line:

0 1 2 3 | | | | -178,000 52,440 60,600 40,200 48,760 88,960

With a financial calculator, input the appropriate cash flows into the cash flow register, input I = 12, and then solve for NPV = -$19,549.

12-12 a. The net cost is $126,000:

Price ($108,000) Modification (12,500) Increase in NOWC (5,500) Cash outlay for new machine ($126,000)

b. The operating cash flows follow:

Year 1 Year 2 Year 3 After-tax savings $28,600 $28,600 $28,600 Depreciation tax savings 13,918 18,979 6,326 Net operating cash flow $42,518 $47,579 $34,926

Notes:

1. The after-tax cost savings is $44,000(1 - T) = $44,000(0.65) = $28,600.

2. The depreciation expense in each year is the depreciable basis, $120,500, times the MACRS allowance percentages of 0.33, 0.45, and 0.15 for Years 1, 2, and 3, respectively. Depreciation expense in Years 1, 2, and 3 is $39,765, $54,225, and $18,075. The depreciation tax savings is calculated as the tax rate (35 percent) times the depreciation expense in each year.

c. The terminal cash flow is $50,702:

Salvage value $65,000 Tax on SV* (19,798) Return of NOWC 5,500 $50,702

BV in Year 4 = $120,500(0.07) = $8,435.

*Tax on SV = ($65,000 - $8,435)(0.35) = $19,798.

d. The project has an NPV of $10,841; thus, it should be accepted.

Year Net Cash Flow PV @ 12% 0 ($126,000) ($126,000) 1 42,518 37,963 2 47,579 37,930 3 85,628 60,948 NPV = $ 10,841

Alternatively, place the cash flows on a time line:

0 1 2 3 | | | | -126,000 42,518 47,579 34,926 50,702 85,628

With a financial calculator, input the appropriate cash flows into the cash flow register, input I = 12, and then solve for NPV = $10,841.

12-13 a. Expected annual cash flows:

Project A: Probable Probability × Cash Flow = Cash Flow 0.2 $6,000 $1,200 0.6 6,750 4,050 0.2 7,500 1,500 Expected annual cash flow = $6,750

Project B: Probable Probability × Cash Flow = Cash Flow 0.2 $ 0 $ 0 0.6 6,750 4,050 0.2 18,000 3,600 Expected annual cash flow = $7,650

Coefficient of variation:

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Project A:

[pic]

Project B:

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CVA = $474.34/$6,750 = 0.0703. CVB = $5,797.84/$7,650 = 0.7579.

b. Project B is the riskier project because it has the greater variability in its probable cash flows, whether measured by the standard deviation or the coefficient of variation. Hence, Project B is evaluated at the 12 percent cost of capital, while Project A requires only a 10 percent cost of capital.

NPVA = $6,750(PVIFA10%,3) - $6,750 = $6,750(2.4869) - $6,750 = $16,786.58 - $6,750 = $10,036.58 ( $10,037.

Alternatively, with a financial calculator, input the appropriate cash flows into the cash flow register, input I = 10, and then solve for NPV = $10,036.25.

NPVB = $7,650(PVIFA12%,3) - $6,750 = $7,650(2.4018) - $6,750 = $18,373.77 - $6,750 = $11,623.77 ( $11,624.

Alternatively, with a financial calculator, input the appropriate cash flows into the cash flow register, input I = 12, and then solve for NPV = $11,624.01. Project B has the higher NPV; therefore, the firm should accept Project B.

c. The portfolio effects from Project B would tend to make it less risky than otherwise. This would tend to reinforce the decision to accept Project B. Again, if Project B were negatively correlated with the GDP (Project B is profitable when the economy is down), then it is less risky and Project B's acceptance is reinforced.

12-14 If actual life is 5 years: Amount Amount Year PV before after Event Factor tax tax Occurs at 10% PV Outflows: Investment in new equipment $36,000 $36,000 0 1.0 $36,000 Total PV of outflows $36,000

Inflows: Operating cash flows excl. deprec. $12,000 $ 7,200 1-5 3.7908 $27,294 Depreciation 7,200 2,880 1-5 3.7908 10,918 $38,212

NPV = PV(Inflows) - PV(Outflows) = $38,212 - $36,000 = $2,212.

Alternatively, using a time line approach:

0 1 2 3 4 5 | | | | | | Investment outlay (36,000) Operating cash flows excl. deprec. (AT) 7,200 7,200 7,200 7,200 7,200 Depreciation savings 2,880 2,880 2,880 2,880 2,880 Net cash flow (36,000) 10,080 10,080 10,080 10,080 10,080

NPV10% = $2,211.13.

If actual life is 4 years: Amount Amount Year PV before after Event Factor tax tax Occurs at 10% PV Inflows: Operating cash flows excl. deprec. $12,000 $7,200 1-4 3.1699 $22,823 Depreciation 7,200 2,880 1-4 3.1699 9,129 Tax savings on loss at end of Year 4 7,200 2,880 4 0.6830 1,967 $33,919

NPV = $33,919 - $36,000 = -$2,081. Alternatively, using a time line approach:

0 1 2 3 4 | | | | | Investment outlay (36,000) Operating cash flows excl. deprec. (AT) 7,200 7,200 7,200 7,200 Depreciation savings 2,880 2,880 2,880 2,880 Tax savings on loss 2,880 Net cash flow (36,000) 10,080 10,080 10,080 12,960

NPV10% = -$2,080.68.

If actual life is 8 years:

Amount Amount Year PV before after Event Factor tax tax Occurs at 10% PV Inflows: Revenues $12,000 $7,200 1-8 5.3349 $38,411 Depreciation 7,200 2,880 1-5 3.7908 10,918 $49,329

NPV = $49,329 - $36,000 = $13,329.

Alternatively, using a time line approach:

0 1 5 6 7 8 | | ( ( ( | | | | Investment outlay (36,000) Operating cash flows excl. deprec. (AT) 7,200 7,200 7,200 7,200 7,200 Depreciation savings 2,880 2,880 Net cash flow (36,000) 10,080 10,080 7,200 7,200 7,200

NPV10% = $13,328.93.

If the life is as low as 4 years (an unlikely event), the investment will not be desirable. But, if the investment life is longer than 4 years, the investment will be a good one. Therefore, the decision will depend on the directors' confidence in the life of the tractor. Given the low proba-bility of the tractor's life being only 4 years, it is likely that the directors will decide to purchase the tractor.

12-15 a. NPV of abandonment after Year t:

Using a financial calculator, input the following: CF0 = -22500, CF1 = 23750, and I = 10 to solve for NPV1 = -$909.09 ( -$909.

Using a financial calculator, input the following: CF0 = -22500, CF1 = 6250, CF2 = 20250, and I = 10 to solve for NPV2 = -$82.64 ( -$83.

Using a financial calculator, input the following: CF0 = -22500, CF1 = 6250, Nj = 2, CF3 = 17250, and I = 10 to solve for NPV3 = $1,307.29 ( $1,307. Using a financial calculator, input the following: CF0 = -22500, CF1 = 6250, Nj = 3, CF4 = 11250, and I = 10 to solve for NPV4 = $726.73 ( $727.

Using a financial calculator, input the following: CF0 = -22500, CF1 = 6250, Nj = 5, and I = 10 to solve for NPV5 = $1,192.42 ( $1,192.

The firm should operate the truck for 3 years, NPV3 = $1,307.

b. No. Abandonment possibilities could only raise NPV and IRR. The firm’s value is maximized by abandoning the project after Year 3.

12-16 a. Time Line (in millions of dollars): 0 1 2 3 4 | | | | | -8 4 4 4 4

NPV = $4.6795 million.

b. Wait 2 years: Time Line (in millions of dollars): NPV @ 0 1 2 3 4 5 6 Yr. 0 | | | | | | | 10% Prob. 0 0 -9 2.2 2.2 2.2 2.2 -$1.6746

| | | | | | | 90% Prob. 0 0 -9 4.2 4.2 4.2 4.2 3.5648

If the cash flows are only $2.2 million, the NPV of the project is negative and, thus, would not be undertaken. The value of the option of waiting two years is evaluated as 0.10($0) + 0.90($3.5648) = $3.2083 million. Since the NPV of waiting two years is less than going ahead and proceeding with the project today, it makes sense to drill today.

SPREADSHEET PROBLEM

12-17 The detailed solution for the spreadsheet problem is available both on the instructor’s resource CD-ROM and on the instructor’s side of the Harcourt College Publishers’ web site: http://www.harcourtcollege.com/finance/concise3e.

CYBERPROBLEM

12-18 The detailed solution for the cyberproblem is available on the instructor’s side of the Harcourt College Publishers’ web site: http://www.harcourtcollege.com/finance/concise3e.

INTEGRATED CASE

Allied Food Products
Capital Budgeting and Cash Flow Estimation

12-19 AFTER SEEING SNAPPLE’S SUCCESS WITH NONCOLA SOFT DRINKS AND LEARNING OF COKE’S AND PEPSI’S INTEREST, ALLIED FOOD PRODUCTS HAS DECIDED TO CONSIDER AN EXPANSION OF ITS OWN IN THE FRUIT JUICE BUSINESS. THE PRODUCT BEING CONSIDERED IS FRESH LEMON JUICE. ASSUME THAT YOU WERE RECENTLY HIRED AS ASSISTANT TO THE DIRECTOR OF CAPITAL BUDGETING, AND YOU MUST EVALUATE THE NEW PROJECT. THE LEMON JUICE WOULD BE PRODUCED IN AN UNUSED BUILDING ADJACENT TO ALLIED’S FORT MYERS PLANT; ALLIED OWNS THE BUILDING, WHICH IS FULLY DEPRECIATED. THE REQUIRED EQUIPMENT WOULD COST $200,000, PLUS AN ADDITIONAL $40,000 FOR SHIPPING AND INSTALLATION. IN ADDITION, INVENTORIES WOULD RISE BY $25,000, WHILE ACCOUNTS PAYABLE WOULD GO UP BY $5,000. ALL OF THESE COSTS WOULD BE INCURRED AT t = 0. BY A SPECIAL RULING, THE MACHINERY COULD BE DEPRECIATED UNDER THE MACRS SYSTEM AS 3-YEAR PROPERTY. THE PROJECT IS EXPECTED TO OPERATE FOR 4 YEARS, AT WHICH TIME IT WILL BE TERMINATED. THE CASH INFLOWS ARE ASSUMED TO BEGIN 1 YEAR AFTER THE PROJECT IS UNDERTAKEN, OR AT t = 1, AND TO CONTINUE OUT TO t = 4. AT THE END OF THE PROJECT’S LIFE (t = 4), THE EQUIPMENT IS EXPECTED TO HAVE A SALVAGE VALUE OF $25,000. UNIT SALES ARE EXPECTED TO TOTAL 100,000 CANS PER YEAR, AND THE EXPECTED SALES PRICE IS $2.00 PER CAN. CASH OPERATING COSTS FOR THE PROJECT (TOTAL OPERATING COSTS LESS DEPRECIATION) ARE EXPECTED TO TOTAL 60 PERCENT OF DOLLAR SALES. ALLIED’S TAX RATE IS 40 PERCENT, AND ITS WEIGHTED AVERAGE COST OF CAPITAL IS 10 PERCENT. TENTATIVELY, THE LEMON JUICE PROJECT IS ASSUMED TO BE OF EQUAL RISK TO ALLIED’S OTHER ASSETS. YOU HAVE BEEN ASKED TO EVALUATE THE PROJECT AND TO MAKE A RECOMMENDATION AS TO WHETHER IT SHOULD BE ACCEPTED OR REJECTED. TO GUIDE YOU IN YOUR ANALYSIS, YOUR BOSS GAVE YOU THE FOLLOWING SET OF QUESTIONS.

TABLE IC12-1. ALLIED’S LEMON JUICE PROJECT

(TOTAL COST IN THOUSANDS)

END OF YEAR: 0 1 2 3 4

I. INVESTMENT OUTLAY EQUIPMENT COST INSTALLATION INCREASE IN INVENTORY INCREASE IN ACCOUNTS PAYABLE TOTAL NET INVESTMENT

II. OPERATING CASH FLOWS UNIT SALES (THOUSANDS) 100 PRICE/UNIT $ 2.00 $ 2.00 TOTAL REVENUES $200.0 OPERATING COSTS, EXCLUDING DEPRECIATION $120.0 DEPRECIATION 36.0 16.8 TOTAL COSTS $199.2 $228.0 OPERATING INCOME BEFORE TAXES $ 44.0 TAXES ON OPERATING INCOME 0.3 25.3 OPERATING INCOME AFTER TAXES $ 26.4 DEPRECIATION 79.2 36.0 OPERATING CASH FLOW $ 0.0 $ 79.7 $ 54.7

III. TERMINAL YEAR CASH FLOWS RETURN OF NET OPERATING WORKING CAPITAL SALVAGE VALUE TAX ON SALVAGE VALUE TOTAL TERMINATION CASH FLOWS

IV. NET CASH FLOWS NET CASH FLOW ($260.0) $ 89.7

V. RESULTS NPV = IRR = MIRR = PAYBACK =

A. DRAW A TIME LINE THAT SHOWS WHEN THE NET CASH INFLOWS AND OUTFLOWS WILL OCCUR, AND EXPLAIN HOW THE TIME LINE CAN BE USED TO HELP STRUCTURE THE ANALYSIS.

ANSWER: [SHOW S12-1 THROUGH S12-4 HERE.]

0 1 2 3 4 | | | | | CF0 CF1 CF2 CF3 CF4

TIME LINES ARE HELPFUL FOR SHOWING WHERE CASH FLOWS OCCUR. WHEN THE DATA ARE DEVELOPED, AND NUMBERS HAVE BEEN PUT ON THE TIME LINE, IT FACILITATES INPUTTING THE CASH FLOWS INTO A CALCULATOR TO CALCULATE THE NPV, IRR, MIRR, AND PAYBACK.

B. ALLIED HAS A STANDARD FORM THAT IS USED IN THE CAPITAL BUDGETING PROCESS; SEE TABLE IC12-1. PART OF THE TABLE HAS BEEN COMPLETED, BUT YOU MUST REPLACE THE BLANKS WITH THE MISSING NUMBERS. COMPLETE THE TABLE IN THE FOLLOWING STEPS:

1. FILL IN THE BLANKS UNDER YEAR 0 FOR THE INITIAL INVESTMENT OUTLAY.

ANSWER: [SHOW S12-5 HERE.] THIS ANSWER IS STRAIGHTFORWARD. NOTE THAT ACCOUNTS PAYABLE IS AN OFFSET TO THE INVENTORY BUILDUP, SO THE NET OPERATING WORKING CAPITAL REQUIREMENT IS $20,000, WHICH WILL BE RECOVERED AT THE END OF THE PROJECT’S LIFE. [SEE COMPLETED TABLE IN THE ANSWER TO B5.]

B. 2. COMPLETE THE TABLE FOR UNIT SALES, SALES PRICE, TOTAL REVENUES, AND OPERATING COSTS EXCLUDING DEPRECIATION.

ANSWER: THIS ANSWER REQUIRES NO EXPLANATION. STUDENTS MAY NOTE, THOUGH, THAT INFLATION IS NOT REFLECTED AT THIS POINT. IT WILL BE LATER. [THE COMPLETED TABLE IS SHOWN BELOW IN THE ANSWER TO B5.]

B. 3. COMPLETE THE DEPRECIATION DATA.

ANSWER: [SHOW S12-6 HERE.] THE ONLY THING THAT REQUIRES EXPLANATION HERE IS THE USE OF THE DEPRECIATION TABLES IN APPENDIX 12A. HERE ARE THE RATES FOR 3-YEAR PROPERTY; THEY ARE MULTIPLIED BY THE DEPRECIABLE BASIS, $240,000, TO GET THE ANNUAL DEPRECIATION ALLOWANCES:

(DOLLARS IN THOUSANDS)

YEAR 1 0.33 ( $240 = $ 79.2 YEAR 2 0.45 ( $240 = 108.0 YEAR 3 0.15 ( $240 = 36.0 YEAR 4 0.07 ( $240 = 16.8 1.00 $240.0

B. 4. NOW COMPLETE THE TABLE DOWN TO OPERATING INCOME AFTER TAXES, AND THEN DOWN TO NET CASH FLOWS.

ANSWER: [SHOW S12-7 HERE.] THIS IS STRAIGHTFORWARD. THE ONLY EVEN SLIGHTLY COMPLICATED THING IS ADDING BACK DEPRECIATION TO GET NET CF. [THE COMPLETED TABLE IS SHOWN BELOW IN THE ANSWER TO B5.]

B. 5. NOW FILL IN THE BLANKS UNDER YEAR 4 FOR THE TERMINAL CASH FLOWS, AND COMPLETE THE NET CASH FLOW LINE. DISCUSS NET OPERATING WORKING CAPITAL. WHAT WOULD HAVE HAPPENED IF THE MACHINERY WERE SOLD FOR LESS THAN ITS BOOK VALUE?

ANSWER: [SHOW S12-8 HERE.] THESE ARE ALL STRAIGHTFORWARD. NOTE THAT THE NET OPERATING WORKING CAPITAL REQUIREMENT IS RECOVERED AT THE END OF YEAR 4. ALSO, THE SALVAGE VALUE IS FULLY TAXABLE, BECAUSE THE ASSET HAS BEEN DEPRECIATED TO A ZERO BOOK VALUE. IF BOOK VALUE WERE SOMETHING OTHER THAN ZERO, THE TAX EFFECT COULD BE POSITIVE (IF THE ASSET WERE SOLD FOR LESS THAN BOOK VALUE) OR NEGATIVE.

TABLE IC12-1. ALLIED’S LEMON JUICE PROJECT
(TOTAL COST IN THOUSANDS)

INPUTS: PRICE: $2.00 k: 10.0% INFL: 0.0% VC RATE: 60.0% T-RATE: 40%

END OF YEAR: 0 1 2 3 4

I. INVESTMENT OUTLAY EQUIPMENT COST ($200) INSTALLATION (40) INCREASE IN INVENTORY (25) INCREASE IN ACCOUNTS PAYABLE 5 TOTAL NET INVESTMENT (260)

II. OPERATING CASH FLOWS UNIT SALES (THOUSANDS) 100 100 100 100 PRICE/UNIT $ 2.00 $ 2.00 $ 2.00 $ 2.00 TOTAL REVENUES $200.0 $200.0 $200.0 $200.0 OPERATING COSTS, EXCLUDING DEPRECIATION $120.0 $120.0 $120.0 $120.0 DEPRECIATION 79.2 108.0 36.0 16.8 TOTAL COSTS $199.2 $228.0 $156.0 $136.8 OPERATING INCOME BEFORE TAXES $ 0.8 ($ 28.0) $ 44.0 $ 63.2 TAXES ON OPERATING INCOME 0.3 (11.2) 17.6 25.3 OPERATING INCOME AFTER TAXES $ 0.5 ($ 16.8) $ 26.4 $ 37.9 DEPRECIATION 79.2 108.0 36.0 16.8 OPERATING CASH FLOW $ 0.0 $ 79.7 $ 91.2 $ 62.4 $ 54.7

III. TERMINAL YEAR CASH FLOWS

RETURN OF NET OPERATING WORKING CAPITAL 20.0 SALVAGE VALUE 25.0 TAX ON SALVAGE VALUE (10.0) TOTAL TERMINATION CASH FLOWS $ 35.0

IV. NET CASH FLOWS NET CASH FLOW ($260.0) $ 79.7 $ 91.2 $ 62.4 $ 89.7

CUMULATIVE CASH FLOW FOR PAYBACK: (260.0) (180.3) (89.1) (26.7) 63.0 COMPOUNDED INFLOWS FOR MIRR: 106.1 110.4 68.6 89.7 TERMINAL VALUE OF INFLOWS: 374.8

V. RESULTS NPV = -$4.0 IRR = 9.3% MIRR = 9.6% PAYBACK = 3.3 YEARS C. 1. ALLIED USES DEBT IN ITS CAPITAL STRUCTURE, SO SOME OF THE MONEY USED TO FINANCE THE PROJECT WILL BE DEBT. GIVEN THIS FACT, SHOULD THE PROJECTED CASH FLOWS BE REVISED TO SHOW PROJECTED INTEREST CHARGES? EXPLAIN.

ANSWER: [SHOW S12-9 HERE.] THE PROJECTED CASH FLOWS IN THE TABLE SHOULD NOT BE REVISED TO SHOW INTEREST CHARGES. THE EFFECTS OF DEBT FINANCING ARE REFLECTED IN THE COST OF CAPITAL, WHICH IS USED TO DISCOUNT THE CASH FLOWS.

C. 2. SUPPOSE YOU LEARNED THAT ALLIED HAD SPENT $50,000 TO RENOVATE THE BUILDING LAST YEAR, EXPENSING THESE COSTS. SHOULD THIS COST BE REFLECTED IN THE ANALYSIS? EXPLAIN.

ANSWER: [SHOW S12-10 HERE.] THIS EXPENDITURE IS A SUNK COST, HENCE IT WOULD NOT AFFECT THE DECISION AND SHOULD NOT BE INCLUDED IN THE ANALYSIS.

C. 3. NOW SUPPOSE YOU LEARNED THAT ALLIED COULD LEASE ITS BUILDING TO ANOTHER PARTY AND EARN $25,000 PER YEAR. SHOULD THAT FACT BE REFLECTED IN THE ANALYSIS? IF SO, HOW?

ANSWER: [SHOW S12-11 HERE.] THE RENTAL PAYMENT REPRESENTS AN OPPORTUNITY COST, AND AS SUCH ITS AFTER-TAX AMOUNT, $25,000(1 - T) = $25,000(0.6) = $15,000, SHOULD BE SUBTRACTED FROM THE CASH FLOWS THE COMPANY WOULD OTHERWISE HAVE.

C. 4. NOW ASSUME THAT THE LEMON JUICE PROJECT WOULD TAKE AWAY PROFITABLE SALES FROM ALLIED’S FRESH ORANGE JUICE BUSINESS. SHOULD THAT FACT BE REFLECTED IN YOUR ANALYSIS? IF SO, HOW?

ANSWER: [SHOW S12-12 HERE.] THE DECREASED SALES FROM ALLIED’S FRESH ORANGE JUICE BUSINESS SHOULD BE ACCOUNTED FOR IN THE ANALYSIS. THIS IS AN EXTERNALITY TO ALLIED--THE LEMON JUICE PROJECT WILL AFFECT THE CASH FLOWS TO ITS ORANGE JUICE BUSINESS. SINCE THE LEMON JUICE PROJECT WILL TAKE BUSINESS AWAY FROM ITS ORANGE JUICE BUSINESS, THE REVENUES AS SHOWN IN THIS ANALYSIS ARE OVERSTATED, AND THUS THEY NEED TO BE REDUCED BY THE AMOUNT OF DECREASED REVENUES FOR THE ORANGE JUICE BUSINESS. EXTERNALITIES ARE OFTEN DIFFICULT TO QUANTIFY, BUT THEY NEED TO BE CONSIDERED.

D. DISREGARD ALL THE ASSUMPTIONS MADE IN PART C, AND ASSUME THERE WAS NO ALTERNATIVE USE FOR THE BUILDING OVER THE NEXT 4 YEARS. NOW CALCULATE THE PROJECT’S NPV, IRR, MIRR, AND REGULAR PAYBACK. DO THESE INDICATORS SUGGEST THAT THE PROJECT SHOULD BE ACCEPTED?

ANSWER: [SHOW S12-13 THROUGH S12-17 HERE.] WE REFER TO THE COMPLETED TIME LINE AND EXPLAIN HOW EACH OF THE INDICATORS IS CALCULATED. WE BASE OUR EXPLANATION ON FINANCIAL CALCULATORS, BUT IT WOULD BE EQUALLY EASY TO EXPLAIN USING A REGULAR CALCULATOR AND EITHER EQUATIONS OR TABLES.

0 1 2 3 4 | | | | | (260) 79.7 91.2 62.4 89.7

NPV = -$4.0. NPV IS NEGATIVE; DO NOT ACCEPT.

IRR = [pic]

IRR = 9.3%. IRR IS LESS THAN COST OF CAPITAL; DO NOT ACCEPT.

MIRR: 0 1 2 3 4 | | | | | (260) 79.7 91.2 62.4 89.7 68.6 110.4 106.1 TERMINAL VALUE (TV) $374.8 PV OF TV $260 NPV $ 0

MIRR IS LESS THAN COST OF CAPITAL; DO NOT ACCEPT.

PAYBACK:

YEAR CASH FLOW CUMULATIVE CASH FLOW 0 ($260.0) ($260.0) 1 79.7 (180.3) 2 91.2 (89.1) 3 62.4 (26.7) 4 89.7 63.0

PAYBACK = 3 YEARS + $26.7/$89.7 = 3.3 YEARS. BASED ON THE ANALYSIS TO THIS POINT, THE PROJECT SHOULD NOT BE UNDERTAKEN. HOWEVER, THIS MAY NOT BE CORRECT, AS WE WILL SEE SHORTLY.

E. IF THIS PROJECT HAD BEEN A REPLACEMENT RATHER THAN AN EXPANSION PROJECT, HOW WOULD THE ANALYSIS HAVE CHANGED? THINK ABOUT THE CHANGES THAT WOULD HAVE TO OCCUR IN THE CASH FLOW TABLE.

ANSWER: [SHOW S12-18 AND S12-19 HERE.] IN A REPLACEMENT ANALYSIS, WE MUST FIND DIFFERENCES IN CASH FLOWS, i.e., THE CASH FLOWS THAT WOULD EXIST IF WE TAKE ON THE PROJECT VERSUS IF WE DO NOT. THUS, IN THE TABLE THERE WOULD NEED TO BE, FOR EACH YEAR, A COLUMN FOR NO CHANGE, A COLUMN FOR THE NEW PROJECT, AND FOR THE DIFFERENCE. THE DIFFERENCE COLUMN IS THE ONE THAT WOULD BE USED TO OBTAIN THE NPV, IRR, ETC.

F. ASSUME THAT INFLATION IS EXPECTED TO AVERAGE 5 PERCENT OVER THE NEXT 4 YEARS; THAT THIS EXPECTATION IS REFLECTED IN THE WACC; AND THAT INFLATION WILL INCREASE VARIABLE COSTS AND REVENUES BY THE SAME PERCENTAGE, 5 PERCENT. DOES IT APPEAR THAT INFLATION HAS BEEN DEALT WITH PROPERLY IN THE ANALYSIS? IF NOT, WHAT SHOULD BE DONE, AND HOW WOULD THE REQUIRED ADJUSTMENT AFFECT THE DECISION? YOU CAN MODIFY THE NUMBERS IN THE TABLE TO QUANTIFY YOUR RESULTS.

ANSWER: [SHOW S12-20 THROUGH S12-22 HERE.] IT IS APPARENT FROM THE DATA IN THE PREVIOUS TABLE THAT INFLATION HAS NOT BEEN REFLECTED IN THE CALCULATIONS. IN PARTICULAR, THE SALES PRICE IS HELD CONSTANT RATHER THAN RISING WITH INFLATION. THEREFORE, REVENUES AND COSTS (EXCEPT DEPRECIATION) SHOULD BOTH BE INCREASED BY 5 PERCENT PER YEAR. SINCE REVENUES ARE LARGER THAN OPERATING COSTS, INFLATION WILL CAUSE CASH FLOWS TO INCREASE. THIS WILL LEAD TO A HIGHER NPV, IRR, AND MIRR, AND TO A SHORTER PAYBACK. TABLE IC12-2 REFLECTS THE CHANGES, AND IT SHOWS THE NEW CASH FLOWS AND THE NEW INDICATORS. WHEN INFLATION IS PROPERLY ACCOUNTED FOR THE PROJECT IS SEEN TO BE PROFITABLE.

TABLE IC12-2. ALLIED’S LEMON JUICE PROJECT

(TOTAL COST IN THOUSANDS)

INPUTS: PRICE: $2.00 k: 10.0% INFL: 5.0% VC RATE: 60.0% T-RATE: 40%

END OF YEAR: 0 1 2 3 4

I. INVESTMENT OUTLAY EQUIPMENT COST ($200) INSTALLATION (40) INCREASE IN INVENTORY (25) INCREASE IN ACCOUNTS PAYABLE 5 TOTAL NET INVESTMENT (260)

II. OPERATING CASH FLOWS UNIT SALES (THOUSANDS) 100 100 100 100 PRICE/UNIT $2.100 $2.205 $2.315 $2.431 TOTAL REVENUES $210.0 $220.5 $231.5 $243.1 OPERATING COSTS, EXCLUDING DEPRECIATION $126.0 $132.3 $138.9 $145.9 DEPRECIATION 79.2 108.0 36.0 16.8 TOTAL COSTS $205.2 $240.3 $174.9 $162.7 OPERATING INCOME BEFORE TAXES $ 4.8 ($ 19.8) $ 56.6 $ 80.4 TAXES ON OPERATING INCOME 1.9 (7.9) 22.6 32.1 OPERATING INCOME AFTER TAXES $ 2.9 ($ 11.9) $ 34.0 $ 48.3 DEPRECIATION 79.2 108.0 36.0 16.8 OPERATING CASH FLOW $ 0.0 $ 82.1 $ 96.1 $ 70.0 $ 65.1

III. TERMINAL CASH FLOWS RETURN OF NET OPERATING WORKING CAPITAL 20.0 SALVAGE VALUE 25.0 TAX ON SALVAGE VALUE (10.0) TOTAL TERMINATION CASH FLOWS $ 35.0

IV. NET CASH FLOWS NET CASH FLOW ($260.0) $ 82.1 $ 96.1 $ 70.0 $100.1

CUMULATIVE CASH FLOW FOR PAYBACK: (260.0) (177.9) (81.8) (11.8) 88.3 COMPOUNDED INFLOWS FOR MIRR: 109.2 116.3 77.0 100.1 TERMINAL VALUE OF INFLOWS: 402.6

V. RESULTS NPV = $15.0 IRR = 12.6% MIRR = 11.6% PAYBACK = 3.1 YEARS

ALTHOUGH INFLATION WAS CONSIDERED IN THE INITIAL ANALYSIS, THE RISKINESS OF THE PROJECT WAS NOT CONSIDERED. THE EXPECTED CASH FLOWS, CONSIDERING INFLATION (IN THOUSANDS OF DOLLARS), ARE GIVEN IN TABLE IC12-2. ALLIED'S OVERALL COST OF CAPITAL (WACC) IS 10 PERCENT.

TABLE IC12-2. ALLIED’S LEMON JUICE PROJECT

(TOTAL COST IN THOUSANDS)

YEAR 0 1 2 3 4
INVESTMENT IN: FIXED ASSETS ($240) NET OPERATING WORKING CAPITAL (20)

UNIT SALES (THOUSANDS) 100 100 100 100
SALE PRICE (DOLLARS) $2.100 $2.205 $2.315 $2.431
TOTAL REVENUES $210.0 $220.5 $231.5 $243.1 CASH OPERATING COSTS (60%) 126.0 132.3 138.9 145.9
DEPRECIATION 79.2 108.0 36.0 16.8 OPER. INCOME BEFORE TAXES $ 4.8 ($19.8) $ 56.6 $ 80.4
TAXES ON OPER. INCOME (40%) 1.9 (7.9) 22.6 32.1 OPER. INCOME AFTER TAXES $ 2.9 ($11.9) $ 34.0 $ 48.3
PLUS DEPRECIATION 79.2 108.0 36.0 16.8
OPERATING CASH FLOW $ 82.1 $ 96.1 $ 70.0 $ 65.1
SALVAGE VALUE 25.0
TAX ON SV (40%) (10.0)
RECOVERY OF NOWC 20.0
NET CASH FLOW ($260) $ 82.1 $ 96.1 $ 70.0 $100.1

CUMULATIVE CASH FLOWS FOR PAYBACK: (260.0) (177.9) (81.8) (11.8) 88.3
COMPOUNDED INFLOWS FOR MIRR: 109.2 116.3 77.0 100.1
TERMINAL VALUE OF INFLOWS: 402.6

NPV AT 10% COST OF CAPITAL = $15.0
IRR = 12.6%
MIRR = 11.6%

YOU HAVE BEEN ASKED TO ANSWER THE FOLLOWING QUESTIONS.

G. 1. WHAT ARE THE THREE LEVELS, OR TYPES, OF PROJECT RISK THAT ARE NORMALLY CONSIDERED?

ANSWER: [SHOW S12-23 THROUGH S12-26 HERE.] HERE ARE THE THREE TYPES OF PROJECT RISK: 1. STAND-ALONE RISK IS THE PROJECT'S TOTAL RISK IF IT WERE OPERATED INDEPENDENTLY. STAND-ALONE RISK IGNORES BOTH THE FIRM'S DIVER-SIFICATION AMONG PROJECTS AND INVESTORS' DIVERSIFICATION AMONG FIRMS. STAND-ALONE RISK IS MEASURED EITHER BY THE PROJECT'S STANDARD DEVIATION ((NPV) OR ITS COEFFICIENT OF VARIATION OF NPV (CVNPV).

2. WITHIN-FIRM (CORPORATE) RISK IS THE TOTAL RISKINESS OF THE PROJECT GIVING CONSIDERATION TO THE FIRM'S OTHER PROJECTS, i.e., TO DIVERSIFICATION WITHIN THE FIRM. IT IS THE CONTRIBUTION OF THE PROJECT TO THE FIRM'S TOTAL RISK, AND IT IS A FUNCTION OF (A) THE PROJECT'S STANDARD DEVIATION OF NPV AND (2) THE CORRELATION OF THE PROJECTS' RETURNS WITH THOSE OF THE REST OF THE FIRM. WITHIN-FIRM RISK IS OFTEN CALLED CORPORATE RISK, AND IT IS MEASURED BY THE BETA OF THE PROJECT'S ROA VERSUS THE FIRM'S ROA.

3. MARKET RISK IS THE RISKINESS OF THE PROJECT TO A WELL-DIVERSIFIED INVESTOR. THEORETICALLY, IT IS MEASURED BY THE PROJECT'S BETA, AND IT CONSIDERS BOTH CORPORATE RISK AND STOCKHOLDER DIVERSIFICATION.

G. 2. WHICH TYPE IS MOST RELEVANT?

ANSWER: [SHOW S12-27 HERE.] BECAUSE MANAGEMENT'S PRIMARY GOAL IS SHAREHOLDER WEALTH MAXIMIZATION, THE MOST RELEVANT RISK FOR CAPITAL PROJECTS IS MARKET RISK. HOWEVER, CREDITORS, CUSTOMERS, SUPPLIERS, AND EMPLOYEES ARE ALL AFFECTED BY A FIRM'S TOTAL RISK. SINCE THESE PARTIES INFLUENCE THE FIRM'S PROFITABILITY, A PROJECT'S WITHIN-FIRM RISK SHOULD NOT BE COMPLETELY IGNORED.

G. 3. WHICH TYPE IS EASIEST TO MEASURE?

ANSWER: [SHOW S12-28 HERE.] BY FAR THE EASIEST TYPE OF RISK TO MEASURE IS A PROJECT'S STAND-ALONE RISK. THUS, FIRMS OFTEN FOCUS PRIMARILY ON THIS TYPE OF RISK WHEN MAKING CAPITAL BUDGETING DECISIONS. THIS FOCUS IS NOT THEORETICALLY CORRECT, BUT IT DOES NOT NECESSARILY LEAD TO POOR DECISIONS, BECAUSE MOST PROJECTS THAT A FIRM UNDERTAKES ARE IN ITS CORE BUSINESS.
G. 4. ARE THE THREE TYPES OF RISK GENERALLY HIGHLY CORRELATED?

ANSWER: [SHOW S12-29 HERE.] BECAUSE MOST PROJECTS THAT A FIRM UNDERTAKES ARE IN ITS CORE BUSINESS, A PROJECT'S STAND-ALONE RISK IS LIKELY TO BE HIGHLY CORRELATED WITH ITS CORPORATE RISK, WHICH IN TURN IS LIKELY TO BE HIGHLY CORRELATED WITH ITS MARKET RISK.

H. 1. WHAT IS SENSITIVITY ANALYSIS?

ANSWER: [SHOW S12-30 HERE.] SENSITIVITY ANALYSIS MEASURES THE EFFECT OF CHANGES IN A PARTICULAR VARIABLE, SAY REVENUES, ON A PROJECT'S NPV. TO PERFORM A SENSITIVITY ANALYSIS, ALL VARIABLES ARE FIXED AT THEIR EXPECTED VALUES EXCEPT ONE. THIS ONE VARIABLE IS THEN CHANGED, OFTEN BY SPECIFIED PERCENTAGES, AND THE RESULTING EFFECT ON NPV IS NOTED. (ONE COULD ALLOW MORE THAN ONE VARIABLE TO CHANGE, BUT THIS THEN MERGES SENSITIVITY ANALYSIS INTO SCENARIO ANALYSIS.)

H. 2. DISCUSS HOW ONE WOULD PERFORM A SENSITIVITY ANALYSIS ON THE UNIT SALES, SALVAGE VALUE, AND COST OF CAPITAL FOR THE PROJECT. ASSUME THAT EACH OF THESE VARIABLES DEVIATES FROM ITS BASE-CASE, OR EXPECTED, VALUE BY PLUS AND MINUS 10, 20, AND 30 PERCENT. EXPLAIN HOW YOU WOULD CALCULATE THE NPV, IRR, MIRR, AND PAYBACK FOR EACH CASE.

ANSWER: THE BASE CASE VALUE FOR UNIT SALES WAS 100; THEREFORE, IF YOU WERE TO ASSUME THAT THIS VALUE DEVIATED BY PLUS AND MINUS 10, 20, AND 30 PERCENT, THE UNIT SALES VALUES TO BE USED IN THE SENSITIVITY ANALYSIS WOULD BE 70, 80, 90, 110, 120, AND 130 UNITS. YOU WOULD THEN GO BACK TO THE TABLE AT THE BEGINNING OF THE PROBLEM, INSERT THE APPROPRIATE SALES UNIT NUMBER, SAY 70 UNITS, AND REWORK THE TABLE FOR THE CHANGE IN SALES UNITS ARRIVING AT DIFFERENT NET CASH FLOW VALUES FOR THE PROJECT. ONCE YOU HAD THE NET CASH FLOW VALUES, YOU WOULD CALCULATE THE NPV, IRR, MIRR, AND PAYBACK AS YOU DID PREVIOUSLY. (NOTE THAT SENSITIVITY ANALYSIS INVOLVES MAKING A CHANGE TO ONLY ONE VARIABLE TO SEE HOW IT IMPACTS OTHER VARIABLES.) THEN, YOU WOULD GO BACK AND REPEAT THE SAME STEPS FOR 80 UNITS--THIS WOULD BE DONE FOR EACH OF THE SALES UNIT VALUES. THEN, YOU WOULD REPEAT THE SAME PROCEDURE FOR THE SENSITIVITY ANALYSIS ON SALVAGE VALUE AND ON COST OF CAPITAL. (NOTE THAT FOR THE COST OF CAPITAL ANALYSIS, THE NET CASH FLOWS WOULD REMAIN THE SAME, BUT THE COST OF CAPITAL USED IN THE NPV AND MIRR CALCULATIONS WOULD BE DIFFERENT.) EXCEL AND LOTUS 1-2-3 ARE IDEALLY SUITED FOR SENSITIVITY ANALYSIS. IN FACT WE CREATED A SPREADSHEET TO OBTAIN THIS PROJECTS' NET CASH FLOWS AND ITS NPV, IRR, MIRR, AND PAYBACK. ONCE A MODEL HAS BEEN CREATED, IT IS VERY EASY TO CHANGE THE VALUES OF VARIABLES AND OBTAIN THE NEW RESULTS. THE RESULTS OF THE SENSITIVITY ANALYSIS ON THE PROJECT'S NPV ASSUMING THE PLUS AND MINUS 10, 20, AND 30 PERCENT DEVIATIONS ARE SHOWN BELOW. WE GENERATED THESE DATA WITH A SPREADSHEET MODEL.

1. THE SENSITIVITY LINES INTERSECT AT 0% CHANGE AND THE BASE CASE NPV, AT APPROXIMATELY $15,000. SINCE ALL OTHER VARIABLES ARE SET AT THEIR BASE CASE, OR EXPECTED, VALUES, THE ZERO CHANGE SITUATION IS THE BASE CASE.

2. THE PLOTS FOR UNIT SALES AND SALVAGE VALUE ARE UPWARD SLOPING, INDICATING THAT HIGHER VARIABLE VALUES LEAD TO HIGHER NPVs. CONVERSELY, THE PLOT FOR COST OF CAPITAL IS DOWNWARD SLOPING, BECAUSE A HIGHER COST OF CAPITAL LEADS TO A LOWER NPV.

3. THE PLOT OF UNIT SALES IS MUCH STEEPER THAN THAT FOR SALVAGE VALUE. THIS INDICATES THAT NPV IS MORE SENSITIVE TO CHANGES IN UNIT SALES THAN TO CHANGES IN SALVAGE VALUE.

4. STEEPER SENSITIVITY LINES INDICATE GREATER RISK. THUS, IN COMPARING TWO PROJECTS, THE ONE WITH THE STEEPER LINES IS CONSIDERED TO BE RISKIER.

THE SENSITIVITY DATA ARE GIVEN HERE IN TABULAR FORM (IN THOUSANDS OF DOLLARS):

CHANGE FROM RESULTING NPV AFTER THE INDICATED CHANGE IN:

BASE LEVEL UNIT SALES SALVAGE VALUE k

-30% ($36.4) $11.9 $34.1 -20 (19.3) 12.9 27.5 -10 (2.1) 13.9 21.1 0 15.0 15.0 15.0 +10 32.1 16.0 9.0 +20 49.2 17.0 3.3 +30 66.3 18.0 (2.2)

H. 3. WHAT IS THE PRIMARY WEAKNESS OF SENSITIVITY ANALYSIS? WHAT ARE ITS PRIMARY ADVANTAGES?

ANSWER: [SHOW S12-31 AND S12-32 HERE.] THE TWO PRIMARY DISADVANTAGES OF SENSITIVITY ANALYSIS ARE (1) THAT IT DOES NOT REFLECT THE EFFECTS OF DIVERSIFICATION AND (2) THAT IT DOES NOT INCORPORATE ANY INFORMATION ABOUT THE POSSIBLE MAGNITUDES OF THE FORECAST ERRORS. THUS, A SENSITIVITY ANALYSIS MIGHT INDICATE THAT A PROJECT'S NPV IS HIGHLY SENSITIVE TO THE SALES FORECAST, HENCE THAT THE PROJECT IS QUITE RISKY, BUT IF THE PROJECT'S SALES, HENCE ITS REVENUES, ARE FIXED BY A LONG-TERM CONTRACT, THEN SALES VARIATIONS MAY ACTUALLY CONTRIBUTE LITTLE TO THE PROJECT'S RISK. THEREFORE, IN MANY SITUATIONS, SENSITIVITY ANALYSIS IS NOT A PARTICULARLY GOOD INDICATOR OF RISK. HOWEVER, SENSITIVITY ANALYSIS DOES IDENTIFY THOSE VARIABLES THAT POTENTIALLY HAVE THE GREATEST IMPACT ON PROFITABILITY, AND THIS HELPS MANAGEMENT FOCUS ITS ATTENTION ON THOSE VARIABLES THAT ARE PROBABLY MOST IMPORTANT.

I. ASSUME THAT YOU ARE CONFIDENT ABOUT THE ESTIMATES OF ALL THE VARIABLES THAT AFFECT THE CASH FLOWS EXCEPT UNIT SALES. IF PRODUCT ACCEPTANCE IS POOR, SALES WOULD BE ONLY 75,000 UNITS A YEAR, WHILE A STRONG CONSUMER RESPONSE WOULD PRODUCE SALES OF 125,000 UNITS. IN EITHER CASE, CASH COSTS WOULD STILL AMOUNT TO 60 PERCENT OF REVENUES. YOU BELIEVE THAT THERE IS A 25 PERCENT CHANCE OF POOR ACCEPTANCE, A 25 PERCENT CHANCE OF EXCELLENT ACCEPTANCE, AND A 50 PERCENT CHANCE OF AVERAGE ACCEPTANCE (THE BASE CASE).

1. WHAT IS THE WORST-CASE NPV? THE BEST-CASE NPV?

ANSWER: [SHOW S12-33 AND S12-34 HERE.] WE USED A SPREADSHEET MODEL TO DEVELOP THE SCENARIOS (IN THOUSANDS OF DOLLARS), WHICH ARE SUMMARIZED BELOW:

CASE PROBABILITY NPV (000s) WORST 0.25 ($27.8) BASE 0.50 15.0 BEST 0.25 57.8

I. 2. USE THE WORST-, MOST LIKELY (OR BASE), AND BEST-CASE NPVs, WITH THEIR PROBABILITIES OF OCCURRENCE, TO FIND THE PROJECT'S EXPECTED NPV, STANDARD DEVIATION, AND COEFFICIENT OF VARIATION.

ANSWER: [SHOW S12-35 HERE.] THE EXPECTED NPV IS $14,968 (ROUNDED TO THE NEAREST THOUSAND BELOW).

E(NPV) = 0.25(-$27.8) + 0.50($15.0) + 0.25($57.8) = $15.

THE STANDARD DEVIATION OF NPV IS $30.3:

(NPV = [0.25(-$27.8 - $15)2 + 0.50($15 - $15)2 + 0.25($57.8 - $15)2]1/2 = [916]1/2 = $30.3,

AND THE PROJECT'S COEFFICIENT OF VARIATION IS 2.0:

CVNPV = [pic]

J. 1. ASSUME THAT ALLIED'S AVERAGE PROJECT HAS A COEFFICIENT OF VARIATION (CV) IN THE RANGE OF 1.25 TO 1.75. WOULD THE LEMON JUICE PROJECT BE CLASSIFIED AS HIGH RISK, AVERAGE RISK, OR LOW RISK? WHAT TYPE OF RISK IS BEING MEASURED HERE?

ANSWER: [SHOW S12-36 HERE.] THE PROJECT HAS A CV OF 2.0, WHICH IS MUCH HIGHER THAN THE AVERAGE RANGE OF 1.25 TO 1.75, SO IT FALLS INTO THE HIGH-RISK CATEGORY. THE CV MEASURES A PROJECT'S STAND-ALONE RISK--IT IS MERELY A MEASURE OF THE VARIABILITY OF RETURNS (AS MEASURED BY (NPV) ABOUT THE EXPECTED RETURN.

J. 2. BASED ON COMMON SENSE, HOW HIGHLY CORRELATED DO YOU THINK THE PROJECT WOULD BE WITH THE FIRM'S OTHER ASSETS? (GIVE A CORRELATION COEFFICIENT, OR RANGE OF COEFFICIENTS, BASED ON YOUR JUDGMENT.)

ANSWER: [SHOW S12-37 HERE.] IT IS REASONABLE TO ASSUME THAT IF THE ECONOMY IS STRONG AND PEOPLE ARE BUYING A LOT OF LEMON JUICE, THEN SALES WOULD BE STRONG IN ALL OF THE COMPANY'S LINES, SO THERE WOULD BE POSITIVE CORRELATION BETWEEN THIS PROJECT AND THE REST OF THE BUSINESS. HOWEVER, EACH LINE COULD BE MORE OR LESS SUCCESSFUL, SO THE CORRELATION WOULD BE LESS THAN +1.0. A REASONABLE GUESS MIGHT BE +0.7, OR WITHIN A RANGE OF +0.5 TO +0.9.

J. 3. HOW WOULD THIS CORRELATION COEFFICIENT AND THE PREVIOUSLY CALCULATED ( COMBINE TO AFFECT THE PROJECT'S CONTRIBUTION TO CORPORATE, OR WITHIN-FIRM, RISK? EXPLAIN.

ANSWER: IF THE PROJECT'S CASH FLOWS ARE LIKELY TO BE HIGHLY CORRELATED WITH THE FIRM'S AGGREGATE CASH FLOWS, WHICH IS GENERALLY A REASONABLE ASSUMPTION, THEN THE PROJECT WOULD HAVE HIGH CORPORATE RISK. HOWEVER, IF THE PROJECT'S CASH FLOWS WERE EXPECTED TO BE TOTALLY UNCORRELATED WITH THE FIRM'S AGGREGATE CASH FLOWS, OR POSITIVELY CORRELATED BUT LESS THAN PERFECTLY POSITIVELY CORRELATED, THEN ACCEPTING THE PROJECT WOULD REDUCE THE FIRM'S TOTAL RISK, AND IN THAT CASE, THE RISKINESS OF THE PROJECT WOULD BE LESS THAN SUGGESTED BY ITS STAND-ALONE RISK. IF THE PROJECT'S CASH FLOWS WERE EXPECTED TO BE NEGATIVELY CORRELATED WITH THE FIRM'S AGGREGATE CASH FLOWS, THEN THE PROJECT WOULD REDUCE THE TOTAL RISK OF THE FIRM EVEN MORE.

K. 1. BASED ON YOUR JUDGMENT, WHAT DO YOU THINK THE PROJECT'S CORRELATION COEFFICIENT WOULD BE WITH RESPECT TO THE GENERAL ECONOMY AND THUS WITH RETURNS ON "THE MARKET"?

ANSWER: IN ALL LIKELIHOOD, THIS PROJECT WOULD HAVE A POSITIVE CORRELATION WITH RETURNS ON OTHER ASSETS IN THE ECONOMY, AND SPECIFICALLY WITH THE STOCK MARKET. ALLIED FOOD PRODUCTS PRODUCES FOOD ITEMS, AND SUCH FIRMS TEND TO HAVE LESS RISK THAN THE ECONOMY AS A WHOLE--PEOPLE MUST EAT REGARDLESS OF THE NATIONAL ECONOMIC SITUATION. HOWEVER, PEOPLE WOULD TEND TO SPEND MORE ON NON-ESSENTIAL TYPES OF FOOD WHEN THE ECONOMY IS GOOD AND TO CUT BACK WHEN THE ECONOMY IS WEAK. A REASONABLE GUESS MIGHT BE +0.7, OR WITHIN A RANGE OF +0.5 TO +0.9.

K. 2. HOW WOULD CORRELATION WITH THE ECONOMY AFFECT THE PROJECT'S MARKET RISK?

ANSWER: [SHOW S12-38 HERE.] THIS CORRELATION WOULD NOT DIRECTLY AFFECT THE PROJECT'S CORPORATE RISK, BUT IT DOES, WHEN COMBINED WITH THE PROJECT'S HIGH STAND-ALONE RISK, SUGGEST THAT THE PROJECT'S MARKET RISK AS MEASURED BY ITS MARKET BETA IS RELATIVELY HIGH.

L. 1. ALLIED TYPICALLY ADDS OR SUBTRACTS 3 PERCENTAGE POINTS TO THE OVERALL COST OF CAPITAL TO ADJUST FOR RISK. SHOULD THE LEMON JUICE PROJECT BE ACCEPTED?

ANSWER: [SHOW S12-39 HERE.] SINCE THE PROJECT IS JUDGED TO HAVE ABOVE-AVERAGE RISK, ITS DIFFERENTIAL RISK-ADJUSTED, OR PROJECT, COST OF CAPITAL WOULD BE 13 PERCENT. AT THIS DISCOUNT RATE, ITS NPV WOULD BE -$2,226, SO IT WOULD NOT BE ACCEPTABLE. IF IT WERE A LOW-RISK PROJECT, ITS COST OF CAPITAL WOULD BE 7 PERCENT, ITS NPV WOULD BE $34,117, AND IT WOULD BE A PROFITABLE PROJECT ON A RISK-ADJUSTED BASIS.

L. 2. WHAT SUBJECTIVE RISK FACTORS SHOULD BE CONSIDERED BEFORE THE FINAL DECISION IS MADE?

ANSWER: [SHOW S12-40 HERE.] A NUMERICAL ANALYSIS SUCH AS THIS ONE MAY NOT CAPTURE ALL OF THE RISK FACTORS INHERENT IN THE PROJECT. IF THE PROJECT HAS A POTENTIAL FOR BRINGING ON HARMFUL LAWSUITS, THEN IT MIGHT BE RISKIER THAN FIRST ASSESSED. ALSO, IF THE PROJECT'S ASSETS CAN BE REDEPLOYED WITHIN THE FIRM OR CAN BE EASILY SOLD, THEN THE PROJECT MAY BE LESS RISKY THAN THE ANALYSIS INDICATES.

M. IN RECENT MONTHS, ALLIED’S GROUP HAS BEGUN TO FOCUS ON REAL OPTION ANALYSIS.

1. WHAT IS REAL OPTION ANALYSIS?

ANSWER: [SHOW S12-41 HERE.] REAL OPTIONS EXIST WHEN MANAGERS CAN INFLUENCE THE SIZE AND RISKINESS OF A PROJECT’S CASH FLOWS BY TAKING DIFFERENT ACTIONS DURING OR AT THE END OF A PROJECT’S LIFE. REAL OPTION ANALYSIS IN THE TYPICAL NPV CAPITAL BUDGETING ANALYSIS INCLUDES AN ANALYSIS FOR OPPORTUNITIES FOR MANAGERS TO RESPOND TO CHANGING CIRCUMSTANCES BECAUSE MANAGEMENT’S ACTIONS CAN INFLUENCE A PROJECT’S OUTCOME.

M. 2. WHAT ARE SOME EXAMPLES OF PROJECTS WITH EMBEDDED REAL OPTIONS?

ANSWER: [SHOW S12-42 HERE.] A PROJECT MAY CONTAIN ONE OR MORE DIFFERENT TYPES OF EMBEDDED REAL OPTIONS. EXAMPLES INCLUDE ABANDONMENT/SHUTDOWN OPTIONS, INVESTMENT TIMING OPTIONS, GROWTH/EXPANSION OPTIONS, AND FLEXIBILITY OPTIONS.

SOLUTION TO APPENDIX 12A PROBLEM

12A-1 Year MACRS S-L Dep ΔDep T(ΔDep) 0 $ 0 1 $10,000,000 $10,000,000 $ 0 0 2 18,000,000 10,000,000 8,000,000 2,800,000 3 14,000,000 10,000,000 4,000,000 1,400,000 4 12,000,000 10,000,000 2,000,000 700,000 5 9,000,000 10,000,000 (1,000,000) (350,000) 6 7,000,000 10,000,000 (3,000,000) (1,050,000) 7 7,000,000 10,000,000 (3,000,000) (1,050,000) 8 7,000,000 10,000,000 (3,000,000) (1,050,000) 9 7,000,000 10,000,000 (3,000,000) (1,050,000) 10 6,000,000 10,000,000 (4,000,000) (1,400,000) 11 3,000,000 0 3,000,000 1,050,000 PV @ 9% = $1,310,841

Therefore, the value of the firm would be increased by $1,310,841, each year, if it elected to use standard MACRS depreciation rates.

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12%

k = 12%

12%

12%

10%

10%

10%

10%

k = 10%

10%

10%

MIRR = 9.6%

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