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Chapter 13 Real Options and Other Topics in Capital Budgeting Learning Objectives After reading this chapter, the student should be able to:  Explain why conventional NPV analysis may not capture a project’s impact on the firm’s opportunities  Identify five different types of real options  Explain what an abandonment/shutdown option is, give an example of a project that includes this type of option, and explain what an option value is  Explain what a decision tree is and provide an example of one  Explain what an investment timing option is, and give an example of a project that includes one  Explain what a growth option is, and give an example of a project that includes one  Explain what a flexibility option is, and give an example of a project that includes one  Use the replacement chain and equivalent annual annuity methods to compare projects with unequal lives, and explain when you might use one method over the other  List the steps a firm goes through when establishing its optimal capital budget in practice Chapter 13: Real Options Learning Objectives 85 Lecture Suggestions This chapter covers some important but relatively technical topics Note too that this chapter is more modular than most, i.e., the major sections are discrete, hence they can be omitted without loss of continuity Therefore, if you are experiencing a time crunch, you could skip sections or even the entire chapter What we cover, and the way we cover it, can be seen by scanning the slides and Integrated Case solution for Chapter 13, which appears at the end of this chapter solution 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: OF 58 DAYS (50-MINUTE PERIODS) 86 Lecture Suggestions Chapter 13: Real Options Answers to End-of-Chapter Questions 13-1 a An abandonment option is the option to abandoning a project if operating cash flows turn out to be lower than expected This option can both raise expected profitability and lower project risk, because in the case of poor cash flows, the project can be ended and rather than continue realizing negative cash flows, fixed assets are sold and some cash is recovered b An investment timing option occurs when a firm has the option of delaying the start of a project until additional information can be obtained After the delay, if conditions for the project look unfavorable, the project will not be undertaken, while if conditions are favorable then the project proceeds as usual However, there are some drawbacks to relying on investment timing options First, the timing option should raise NPV because the probability of bad returns is less, but that NPV needs to be discounted back one additional year Second, there might be valuable first mover advantages to a project that will be lost if the project is delayed a year c Growth options exist if an investment creates the opportunity to make other potentially profitable investments that would not otherwise be possible A common example of a growth option occurs when a firm starts a project in a new country or market While the project is hoped to add value from its cash flows, it also has value because it opens the door to the firm to operate in the new country/market d Flexibility options permit the firm to alter operations depending on how conditions change during the project’s life Typically, inputs, outputs, or both can be changed easily to respond to market demands For example, instead of building an auto factory that builds a specific type of car (compact, SUV, etc.), a manufacturer can build a factory that allows the building of many types of cars Therefore, as market demand and consumer tastes change the firm can rapidly respond 13-2 Failure to recognize a growth option implies that a project with a negative conventional NPV was rejected despite have an embedded growth option whose consideration would cause the NPV to be positive As a result, failure to recognize the value of a growth option implies that the capital budget is below the optimal level since a value-adding project (albeit because of a real option) has been rejected This argument holds when considering failure to recognize all real options 13-3 It might be necessary for the firm to arrange things so that it has the possibility of abandonment when it is making the initial decision This might require contractual arrangements with suppliers, customers, and its union, and there might be some costs to getting the advanced permissions Any such costs could be compared with the value of the option as we calculated it, and this could enter into the initial decision In the case of investment timing options, the initial investment might grow if the project is delayed For any type of options, these additional costs must be considered in the analysis and the benefits of the “real option” must outweigh the associated costs 13-4 The replacement chain approach is a method of comparing projects with unequal lives that assumes that each project can be repeated as many times as necessary to reach a Chapter 13: Real Options Answers and Solutions 87 common life span As such, the NPVs over this life span are then compared, and the project with the higher common-life NPV is chosen 13-5 The equivalent annual annuity method calculates the annual payments a project would provide if it were an annuity When comparing projects of unequal lives, the one with the higher equivalent annual annuity should be chosen 13-6 Generally, the failure to employ replacement chain analysis or the equivalent annual annuity approach in such situations will bias the NPV against the shorter project because it “gets no credit” for profits beyond its initial life, even though it could possibly be “renewed” and thus provide additional NPV 13-7 For large, mature firms with good track records we can assume that all of its profitable projects can be financed, but this assumption is harder to make for smaller firms, new firms, and firms with dubious track records may have difficulties raising capital, even for projects that the firm concludes would have positive NPVs In such circumstances, the size of the firm’s capital budget may be constrained, a situation called capital rationing In such situations capital is limited, so it should be used in the most efficient way possible Procedures have been explored for allocating capital so as to maximize the firm’s aggregate NPV subject to the constraint that the capital rationing ceiling is not exceeded As a result the greater the capital budget, the greater the need for external financing, which raises the WACC 13-8 Capital rationing is a situation where a firm can raise only a specified, limited amount of capital regardless of how many good projects it has As a result, the firm must find the most efficient way of deploying that capital to its projects 88 Answers and Solutions Chapter 13: Real Options Solutions to End-of-Chapter Problems 13-1 a WACC = 11%; cash flows shown in millions 50% Prob -9 50% Prob | | | | | | NPV @ Yr $5.662 -6.556 Expected NPV = 0.5($5.662) + 0.5(-$6.556) = -$0.447 million b If the project is hugely successful, $10 million will be spent at the end of Year 2, and the new venture will be sold for $20 million at the end of Year 50% Prob | -9 | 50% Prob | -10 -4 | | +20 26 | NPV @ Yr $12.170 -6.556 Expected NPV = 0.5($12.170) + 0.5(-$6.556) = $2.807 million c Value of growth option: NPV with option NPV without option 13-2 a Project A: 10% | -10,000 $2.807 million - 0.447 million +$3.254 million | 6,000 | 8,000 Using a financial calculator, input the following data: CF = -10000, CF1 = 6000, CF2 = 8000, I/YR = 10, and then solve for NPVA = $2,066.12 Project B: 10% | -10,000 | 4,000 | 4,000 | 4,000 | 4,000 Using a financial calculator, input the following data: CF = -10000, CF1-4 = 4000, I/YR = 10, and then solve for NPVB = $2,679.46 Since neither project can be repeated, Project B should be selected because it has a higher NPV than Project A b To determine the answer to part b, we use the replacement chain (common life) approach to calculate the extended NPV for Project A Project B already extends out to years, so its NPV is $2,679.46 Chapter 13: Real Options Answers and Solutions 89 Project A: 10% | -10,000 | 6,000 | 8,000 -10,000 -2,000 | 6,000 | 8,000 Using a financial calculator, input the following data: CF = -10000, CF1 = 6000, CF2 = -2000, CF3 = 6000, CF4 = 8000, I/YR = 10, and then solve for NPV A = $3,773.65 Since Project A’s extended NPV = $3,773.65, it should be selected over Project B with an NPV = $2,679.46 c From part a, NPVA = $2,066.12 and NPVB = $2,679.46 Solving for PMT determines the EAA: Project A: N = 2, I/YR = 10, PV = -2066.12, FV = 0; solve for PMT = $1,190.48 Project B: N = 4, I/YR = 10, PV = -2679.46, FV = 0; solve for PMT = $845.29 Project A should be selected 13-3 14% | -190,000 | 87,000 | 87,000 | 87,000 Using a financial calculator, input the following data: CF = -190000; CF1-3 = 87000; I/YR = 14; and solve for NPV190-3 = $11,982 (for years) Extended NPV190-3 = $11,982 + $11,982/(1.14)3 = $20,070 14% | -360,000 | 98,300 | 98,300 | 98,300 | 98,300 | 98,300 | 98,300 Using a financial calculator, input the following data: CF = -360000; CF1-6 = 98300; I/YR = 14; and solve for NPV360-6 = $22,256 (for years) Both new machines have positive NPVs; hence the old machine should be replaced Further, since its NPV is greater, choose Model 360-6 13-4 First, solve for each project’s NPV Project A: CF0 = -20000, CF1 = 6000, Nj = 6, I/YR = 10; solve for NPV = $6,131.56 Project B: CF0 = -12000, CF1 = 6000, Nj = 3, I/YR = 10; solve for NPV = $2,921.11 The appropriate EAAs are: Project A: N = 6, I/YR = 10, PV = -6131.56, FV = 0; solve for PMT = $1,407.85 Project B: N = 3, I/YR = 10, PV = -2921.11, FV = 0; solve for PMT = $1,174.62 90 Answers and Solutions Chapter 13: Real Options Choose Project A, whose EAA = $1,407.85 13-5 The firm should accept Projects A, B, C, and D The firm’s optimal capital budget is $3,900,000 at a WACC of 10.8% and it requires the firm to issue new common stock 13-6 Since Plane A’s renewal investment changes the EAA method cannot be used, so the replacement chain method must be used Plane A: Expected life = years; cost = $100 million; NCF = $30 million; WACC = 12%; cost of renewing Plane A = $105 million A: | 12% | -100 10 | 30 | 30 | 30 | 30 | 30 -105 -75 | 30 | 30 | 30 | 30 30 Enter these values into the cash flow register: CF = -100; CF1-4 = 30; CF5 = -75; CF6-10 = 30 Then enter I/YR = 12, and press the NPV key to get NPVA = $9.93 million Plane B: Expected life = 10 years; cost = $132 million; NCF = $25 million; WACC = 12% B: | 12% | -132 10 | 25 | 25 | 25 | 25 | 25 | 25 | 25 | 25 | 25 25 Enter these cash flows into the cash flow register, along with the interest rate, and press the NPV key to get NPVB = $9.256 ≈ $9.26 million Project A is the better project and will increase the company's value by $9.93 million 13-7 A: | 10% | -10 | | | | -12 -8 | 4.2 | 4.2 4.2 | 4.2 Since Machine A’s renewal investment and cash flows change the EAA method cannot be used, so the replacement chain method must be used Machine A’s simple NPV is calculated as follows: Enter CF0 = -10 and CF1-4 = Then enter I/YR = 10, and press the NPV key to get NPVA = $2.679 million However, this does not consider the fact that the project can be repeated again Enter these values into the cash flow register: CF0 = -10; CF1-3 = 4; CF4 = -8; CF5-8 = 4.2 Then enter I/YR = 10, and press the NPV key to get extended NPVA = $3.58 million B: 10% Chapter 13: Real Options Answers and Solutions 91 | | | -15 | 3.5 | 3.5 | 3.5 | 3.5 | 3.5 3.5 3.5 | 3.5 Enter these cash flows into the cash flow register, along with the interest rate, and press the NPV key to get NPVB = $3.672 ≈ $3.67 million Machine B is the better project and will increase the company's value by $3.67 million, rather than the $3.58 million created by Machine A 13-8 First, solve for each project’s NPV Project X: CF0 = -100000, CF1 = 30000, CF2 = 50000, CF3 = 70000, I/YR = 12; solve for NPV = $16,470.0255 Project Y: CF0 = -70000, CF1 = 30000, Nj = 4, CF2 = 10000, I/YR = 12; solve for NPV = $26,794.749 The appropriate EAAs are: Project X: N = 3, I/YR = 12, PV = -16470.0255, FV = 0; solve for PMT = $6,857.28 Project Y: N = 5, I/YR = 12, PV = -26794.749, FV = 0; solve for PMT = $7,433.12 Choose Project Y 13-9 Cash flows shown in millions on time line: | 10% -20 7.5 7.5 7.5 | | | NPV = -$1.349 million Wait year; cash flows shown in millions on time line: Strong demand 50% Prob | Weak demand 50% Prob | 10% | -20 | 10 | 10 | 10 | -20 | | | NPV @ Yr $4.426 -6.878 However, if demand is weak, the project’s NPV is negative and therefore would not be undertaken The value of this option of waiting one year is evaluated as 0.5($0) + (0.5)($4.426) = $2.213 million Since the NPV of waiting one year is greater than going ahead and proceeding with the project today and greater than zero, it makes sense to wait 13-10 a NPV of abandonment after Year t: Using a financial calculator, input the following: CF = -22500, CF1 = 23750, and I/YR = 10 to solve for NPV1 = -$909.09 ≈ -$909 92 Answers and Solutions Chapter 13: Real Options Using a financial calculator, input the following: CF0 = -22500, CF1 = 6250, CF2 = 20250, and I/YR = 10 to solve for NPV2 = -$82.64 ≈ -$83 Using a financial calculator, input the following: CF = -22500, CF1 = 6250, Nj = 2, CF3 = 17250, and I/YR = 10 to solve for NPV3 = $1,307.29 ≈ $1,307 Using a financial calculator, input the following: CF = -22500, CF1 = 6250, Nj = 3, CF4 = 11250, and I/YR = 10 to solve for NPV4 = $726.73 ≈ $727 Using a financial calculator, input the following: CF = -22500, CF1 = 6250, Nj = 5, and I/YR = 10 to solve for NPV5 = $1,192.42 ≈ $1,192 The firm should operate the truck for years, NPV3 = $1,307 b No Abandonment possibilities could only raise NPV and IRR The value of the firm is maximized by abandoning the project after Year 13-11 a WACC1 = 12%; WACC2 = 12.5% Since each project is independent and of average risk, all projects whose IRR > WACC will be accepted Consequently, Projects A, B, C, D, and E will be accepted and the optimal capital budget is $5,250,000 After accepting projects A, B, and C, all of retained earnings will be used up and additional equity will be raised to fund the remaining projects, whose WACCs all exceed 12.5% b If Projects C and D are mutually exclusive, the firm will select Project D, because its NPV is greater than Project C’s NPV So, the optimal capital budget is $4 million, and consists of Projects A, B, D, and E c The appropriate costs of capital are 10.5% for low-risk projects, 12.5% for averagerisk projects, and 14.5% for high-risk projects Since Project A is high risk, it will be rejected (14% < 14.5%) Projects B, C, D, and E are all average risk and will be accepted since their returns exceed 12.5% Projects F and G are low risk and will both be accepted since their returns exceed 10.5% Therefore, the optimal capital budget is $6 million and consists of Projects B, C, D, E, F, and G 13-12 a | 10% | -8 4 4 | | | NPV = $4.6795 million b Wait years: 10% Prob | 90% Prob | 10% Chapter 13: Real Options | | -9 | 2.2 | 2.2 | 2.2 | 2.2 | | -9 | 4.2 | 4.2 | 4.2 | 4.2 NPV @ Yr -$1.6746 3.5648 Answers and Solutions 93 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 c The investment timing option has a value of $0 Since the difference between the project with the option and the project without the option is negative, $3.2083 million – $4.6795 million = -$1.4712 million, the option will not be exercised In other words, the costs of delaying the project outweigh the benefits gained by delaying and gathering more information d There is a danger that oil prices will decline causing the company to receive less revenue for the oil it extracts, and there is a danger that the company will lose market share or the chance to compete for new contracts as a result of waiting 13-13 a Cash flows if tax imposed: 12% | | -6,200,000 600,000 ••• 14 | 600,000 15 | 600,000 Using a financial calculator, input the following data: CF = -6200000; CF1-15 = 600000; I/YR = 12; and then solve for NPV = -$2,113,481.31 b Cash flows if tax not imposed: 12% | | -6,200,000 1,200,000 ••• 14 15 | | 1,200,000 1,200,000 Using a financial calculator, input the following data: CF = -6200000; CF1-15 = 1200000; I/YR = 12; and then solve for NPV = $1,973,037.39 c If they proceed with the project today, the project’s expected NPV = (0.5 × $2,113,481.31) + (0.5 × $1,973,037.39) = -$70,221.96 So, Nevada Enterprises would not it d Since the project’s NPV with the tax is negative, if the tax were imposed the firm would abandon the project Thus, the decision tree looks like this: 12% 50% Prob | | Taxes -6,200,000 6,600,000 No Taxes | 50% Prob -6,200,000 | 1,200,000 | | 1,200,000 ••• 15 | NPV @ Yr -$ 307,142.86 ••• | 1,200,000 1,973,037.39 Expected NPV $ 832,947.27 Yes, the existence of the abandonment option changes the expected NPV of the project from negative to positive Given this option the firm would take on the project because its expected NPV is $832,947.27 94 Answers and Solutions Chapter 13: Real Options e 50% Prob Taxes 12% | | NPV = ? -1,500,000 wouldn’t +300,000 = NPV @ t = No Taxes 50% Prob | NPV = ? | -1,500,000 +4,000,000 = NPV @ t = NPV @ Yr $ 0.00 2,232,142.86 Expected NPV $1,116,071.43 If the firm pays $1,116,071.43 for the option to purchase the land, then the NPV of the project is exactly equal to zero So the firm would not pay any more than this for the option Chapter 13: Real Options Answers and Solutions 95 Comprehensive/Spreadsheet Problems Note to Instructors: The solutions to these problems are not provided to students at the back of their text Instructors can access the Excel files on the textbook’s Web site or the Instructor’s Resource CD 13-14 See Problem 13-13 on the preceding two pages 13-15 a Without abandonment (Cost @ t = = -$10 million): | 9.0 | 9.0 | 9.0 40% Prob Average | 4.5 | 4.5 | 4.5 0.81 30% Prob Bad -1.5 | -1.5 | -1.5 -13.60 30% Prob Good 12% NPV @ Yr $11.62 Exp NPV = 0.3($11.62) + 0.4($0.81) + 0.3(-$13.60) = -$0.27 million Standard deviation = $9.81 million With abandonment (Cost @ t = = -$10 million): After the first year, the fixed assets will be depreciated by 1/3 of their value, meaning they are worth $6.67 million and can be retired/sold for $6.00 million The cash flow in the abandonment branch reflects the -$1.5 million operating cash flow plus the retirement of fixed assets (-$1.5 million + $6 million) | 9.0 | 9.0 | 9.0 40% Prob Average | 4.5 | 4.5 | 4.5 30% Prob Bad | 4.5 | | 30% Prob Good 12% NPV @ Yr $11.62 0.81 -5.98 Exp NPV = 0.3($11.62) + 0.4($0.81) + 0.3(-$5.98) = $2.01 million Standard deviation = $6.89 million When the abandonment option is factored in, the very large negative NPV under bad conditions is reduced, and the expected NPV becomes positive Also, the standard deviation and CV decline, indicating that the abandonment option lowers the project’s risk b NPV declines as the WACC increases, and it increases as the percentage of book at which the asset can be sold increases However, if the WACC is reasonably close to 96 Integrated Case Chapter 13: Real Options the estimated 12%, and the sale percentage is close to the estimated 90%, then the NPV will be comfortably positive Conclusion: When abandonment is recognized, the project is acceptable c Without abandonment, with growth (Cost @ t = = -$10 million) | 9.0 | 9.0 | 20.6 40% Prob Average | 4.5 | 4.5 | 4.5 0.81 30% Prob Bad -1.5 | -1.5 | -1.5 -13.60 30% Prob Good 12% NPV @ Yr $19.88 Exp NPV = 0.3($19.88) + 0.4($0.81) + 0.3(-$13.60) = $2.21 million Standard deviation = $13.02 million This growth option makes the project’s NPV positive, too Using a spreadsheet, the WACC at which NPV equals zero in this case is 23.11% So, we can be safe in saying that this project’s NPV is robust to changes in the WACC d Without abandonment, with investment timing (Cost @ t = = -$10 million) | 9.0 | 9.0 | 9.0 40% Prob Average | 4.5 | 4.5 | 4.5 0.81 30% Prob Bad | | 0 30% Prob Good 12% NPV @Yr $11.62 Exp NPV @ Year = 0.3($11.62) + 0.4($0.81) + 0.3(0) = $3.81 million Expected NPV today = $3.81/1.12 = $3.40 million Considering the project originally had a -$0.27 million NPV, the investment timing option adds $3.67 million of value to the project Chapter 13: Real Options Integrated Case 97 ... This chapter covers some important but relatively technical topics Note too that this chapter is more modular than most, i.e., the major sections are discrete, hence they can be omitted without... Chapter 2, where we describe how we conduct our classes DAYS ON CHAPTER: OF 58 DAYS (50-MINUTE PERIODS) 86 Lecture Suggestions Chapter 13: Real Options Answers to End-of-Chapter Questions 13- 1... than Project A b To determine the answer to part b, we use the replacement chain (common life) approach to calculate the extended NPV for Project A Project B already extends out to years, so its