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After reading this chapter, the student should be able to: • Use the replacement chain method to compare projects with unequal lives. • Explain why conventional NPV analysis may not capture a project’s impact on the firm’s opportunities. • Define the term option value, and identify four different types of embedded real options. • Explain what an abandonment option is, and give an example of a project that includes one. • 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. • List the steps a firm goes through when establishing its optimal capital budget in practice.
After reading this chapter, the student should be able to: • Use the replacement chain method to compare projects with unequal lives. • Explain why conventional NPV analysis may not capture a project’s impact on the firm’s opportunities. • Define the term option value, and identify four different types of embedded real options. • Explain what an abandonment option is, and give an example of a project that includes one. • 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. • List the steps a firm goes through when establishing its optimal capital budget in practice. Learning Objectives: 12 - 1 Chapter 12 Other Topics in Capital Budgeting LEARNING OBJECTIVES 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. 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: 2 OF 58 DAYS (50-MINUTE PERIODS) Lecture Suggestions: 12 - 2 LECTURE SUGGESTIONS 12-1 Generally, the failure to employ common life 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. 12-2 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. 12-3 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. 12-4 Having the option to abandon a project makes it more likely that the project will be accepted today. Answers and Solutions: 12 - 3 ANSWERS TO END-OF-CHAPTER QUESTIONS 12-1 a. Project A: 0 1 2 | | | -10,000 6,000 8,000 Using a financial calculator, input the following data: CF 0 = -10000, CF 1 = 6000, CF 2 = 8000, I = 10, and then solve for NPV A = $2,066.12. Project B: 0 1 2 3 4 | | | | | -10,000 4,000 4,000 4,000 4,000 Using a financial calculator, input the following data: CF 0 = -10000, CF 1-4 = 4000, I = 10, and then solve for NPV B = $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 must use the replacement chain (common life) approach to calculate the extended NPV for Project A. Project B already extends out to 4 years, so its NPV is $2,679.46. Project A: 0 1 2 3 4 | | | | | -10,000 6,000 8,000 6,000 8,000 -10,000 -2,000 Using a financial calculator, input the following data: CF 0 = -10000, CF 1 = 6000, CF 2 = -2000, CF 3 = 6000, CF 4 = 8000, I = 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. 12-2 WACC 1 = 12%; WACC 2 = 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. 12-3 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. Answers and Solutions: 12 - 4 SOLUTIONS TO END-OF-CHAPTER PROBLEMS 10% 10% k = 10% 12-4 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 only Project A will be rejected. The firm’s optimal capital budget is $6 million. 12-5 NPV 190-3 = $11,982 (for 3 years). Extended NPV 190-3 = $11,982 + $11,982/(1.14) 3 = $20,070. NPV 360-6 = $22,256 (for 6 years). Both new machines have positive NPVs; hence the old machine should be replaced. Further, since its NPV is greater, choose Model 360-6. 12-6 Plane A: Expected life = 5 years; Cost = $100 million; NCF = $30 million; COC = 12%. Plane B: Expected life = 10 years; Cost = $132 million; NCF = $25 million; COC = 12%. A: 0 1 2 3 4 5 6 7 8 9 10 | | | | | | | | | | | -100 30 30 30 30 30 30 30 30 30 30 -100 -70 Enter these values into the cash flow register: CF 0 = -100; CF 1-4 = 30; CF 5 = -70; CF 6-10 = 30. Then enter I = 12, and press the NPV key to get NPV A = $12.764 ≈ $12.76 million. B: 0 1 2 3 4 5 6 7 8 9 10 | | | | | | | | | | | -132 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 NPV B = $9.256 ≈ $9.26 million. Project A is the better project and will increase the company's value by $12.76 million. 12-7 A: 0 1 2 3 4 5 6 7 8 | | | | | | | | | -10 4 4 4 4 4 4 4 4 Answers and Solutions: 12 - 5 12% 12% 10% -10 -6 Machine A’s simple NPV is calculated as follows: Enter CF 0 = -10 and CF 1-4 = 4. Then enter I = 10, and press the NPV key to get NPV A = $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: CF 0 = -10; CF 1-3 = 4; CF 4 = -6; CF 5-8 = 4. Then enter I = 10, and press the NPV key to get Extended NPV A = $4.5096 ≈ $4.51 million. B: 0 1 2 3 4 5 6 7 8 | | | | | | | | | -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 NPV B = $3.672 ≈ $3.67 million. Machine A is the better project and will increase the company's value by $4.51 million. 12-8 a. 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 3.2 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. 12-9 a. NPV of abandonment after Year t: Using a financial calculator, input the following: CF 0 = -22500, CF 1 = 23750, and I = 10 to solve for NPV 1 = -$909.09 ≈ -$909. Using a financial calculator, input the following: CF 0 = -22500, CF 1 = 6250, CF 2 = 20250, and I = 10 to solve for NPV 2 = -$82.64 ≈ -$83. Answers and Solutions: 12 - 6 10% 12% k = 12% Using a financial calculator, input the following: CF 0 = -22500, CF 1 = 6250, N j = 2, CF 3 = 17250, and I = 10 to solve for NPV 3 = $1,307.29 ≈ $1,307. Using a financial calculator, input the following: CF 0 = -22500, CF 1 = 6250, N j = 3, CF 4 = 11250, and I = 10 to solve for NPV 4 = $726.73 ≈ $727. Using a financial calculator, input the following: CF 0 = -22500, CF 1 = 6250, N j = 5, and I = 10 to solve for NPV 5 = $1,192.42 ≈ $1,192. The firm should operate the truck for 3 years, NPV 3 = $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 3. 12-10 a. 0 1 2 3 4 | | | | | -8 4 4 4 4 NPV = $4.6795 million. b. Wait 2 years: 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. 12-11 a. 0 1 14 15 | | • • • | | -6,200,000 600,000 600,000 600,000 Using a financial calculator, input the following data: CF 0 = -6200000; CF 1-15 = 600000; I = 12; and then solve for NPV = -$2,113,481.31. Answers and Solutions: 12 - 7 10% 12% k = 10% b. 0 1 14 15 | | • • • | | -6,200,000 1,200,000 1,200,000 1,200,000 Using a financial calculator, input the following data: CF 0 = -6200000; CF 1-15 = 1200000; I = 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) = -$70,221.96. So, Nevada Enterprises would not do it. d. Since the project’s NPV with the tax is negative, if the tax were imposed the firm would abandon the project. Thus, the decision tree looks like this: NPV @ 0 1 2 15 Yr. 0 50% Prob. | | | • • • | Taxes -6,200,000 6,000,000 0 0 -$ 842,857.14 No Taxes | | | • • • | 50% Prob. -6,200,000 1,200,000 1,200,000 1,200,000 1,973,037.39 Expected NPV $ 565,090.13 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 $565,090.13. e. NPV @ 0 1 Yr. 0 50% Prob. | | Taxes NPV = ? -1,500,000 $ 0.00 +300,000 = NPV @ t = 1 No Taxes | | 50% Prob. NPV = ? -1,500,000 2,232,142.86 +4,000,000 = NPV @ t = 1 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. Answers and Solutions: 12 - 8 12% k = 12% k = 12% } wouldn’t do 12-12 The detailed solution for the spreadsheet problem is available both on the instructor’s resource CD-ROM and on the instructor’s side of South- Western’s web site, http://brigham.swlearning.com. Spreadsheet Problem: 12 - 9 SPREADSHEET PROBLEM 21st Century Educational Products Other Topics in Capital Budgeting 12-13 21ST CENTURY EDUCATIONAL PRODUCTS (21ST CENTURY) IS A RAPIDLY GROWING SOFTWARE COMPANY, AND CONSISTENT WITH ITS GROWTH, IT HAS A RELATIVELY LARGE CAPITAL BUDGET. WHILE MOST OF THE COMPANY’S PROJECTS ARE FAIRLY EASY TO EVALUATE, A HANDFUL OF PROJECTS INVOLVE MORE COMPLEX EVALUATIONS. JOHN KELLER, A SENIOR MEMBER OF THE COMPANY’S FINANCE STAFF, COORDINATES THE EVALUATION OF THESE MORE COMPLEX PROJECTS. HIS GROUP BRINGS THEIR RECOMMENDATIONS DIRECTLY TO THE COMPANY’S CFO AND CEO, KRISTIN RILEY AND BOB STEVENS, RESPECTIVELY. A. RIGHT NOW, KELLER’S GROUP IS LOOKING AT A VARIETY OF INTERESTING PROJECTS. FOR EXAMPLE, THE GROUP HAS BEEN ASKED TO CHOOSE BETWEEN THE FOLLOWING TWO MUTUALLY EXCLUSIVE PROJECTS: EXPECTED NET CASH FLOWS YEAR PROJECT S PROJECT L 0 ($100,000) ($100,000) 1 59,000 33,500 2 59,000 33,500 3 33,500 4 33,500 BOTH PROJECTS MAY BE REPEATED AND BOTH ARE OF AVERAGE RISK, SO THEY SHOULD BE EVALUATED AT THE FIRM'S COST OF CAPITAL, 10 PERCENT. WHICH ONE SHOULD BE CHOSEN? ANSWER: [SHOW S12-1 THROUGH S12-4 HERE.] PROJECT S: 0 1 2 3 4 | | | | | -100,000 59,000 59,000 59,000 59,000 -100,000 -41,000 Integrated Case: 12 - 10 INTEGRATED CASE 10% [...]...USING A FINANCIAL CALCULATOR, INPUT THE FOLLOWING DATA: CF0 = -100000; CF1 = 59000; CF2 = -41000; CF3-4 = 59000; I = 10; AND THEN SOLVE FOR NPV = $4,377.43 PROJECT L: 0 10% | -100,000 1 | 33,500 2 | 33,500 3 | 33,500 4 | 33,500 USING A FINANCIAL CALCULATOR, INPUT THE FOLLOWING DATA: CF0 = -100000; CF1-4 = 33500; I = 10; AND THEN SOLVE FOR NPV = $6,190.49 PROJECT L SHOULD BE CHOSEN SINCE IT HAS... NPV THAN PROJECT S B IN RECENT MONTHS, KELLER’S GROUP HAS BEGUN TO FOCUS ON REAL OPTION ANALYSIS 1 WHAT IS REAL OPTION ANALYSIS? ANSWER: [SHOW S12-5 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 INCLUDES IN THE TYPICAL NPV CAPITAL BUDGETING ANALYSIS AN ANALYSIS... GET MORE INFORMATION ABOUT THE MARKET RATHER THAN UNDERTAKING PROJECT L TODAY BECAUSE THE NPV IS $31,630.82 COMPARED TO $6,190.49, THE NPV OF DOING IT TODAY THE MORE VARIABLE THE CASH FLOWS (THE MORE UNCERTAINTY) THE LESS WILLING THE FIRM WILL BE TO INVEST IN THE PROJECT TODAY FACTORS THE FIRM SHOULD CONSIDER WHEN DECIDING WHEN TO INVEST: 1 DELAYING THE PROJECT MEANS THAT CASH FLOWS COME LATER RATHER... PROJECT’S COST OF CAPITAL IS THIS ASSUMPTION REASONABLE? HOW MIGHT THE ABANDONMENT OPTION AFFECT THE COST OF CAPITAL? Integrated Case: 12 - 15 ANSWER: [SHOW S12-17 HERE.] IT IS NOT REASONABLE TO ASSUME ABANDONMENT OPTION HAS NO EFFECT ON THE COST OF CAPITAL THAT THE HAVING THE ABILITY TO ABANDON A PROJECT REDUCES RISK; THEREFORE, REDUCING ITS COST OF CAPITAL F FINALLY, 21ST CENTURY IS ALSO CONSIDERING PROJECT... COST OF CAPITAL IS STILL 10 PERCENT WILL THIS INCREASED UNCERTAINTY MAKE THE FIRM MORE OR LESS WILLING TO INVEST IN THE PROJECT TODAY? Integrated Case: 12 - 12 ANSWER: [SHOW S12-10 AND S12-11 HERE.] 50% PROB 0 = 10% 1 k STRONG MKT | | 0 -100,000 2 | 53,500 3 | 53,500 4 | 53,500 5 | 53,500 NPV @ t = 1 $69,587.80 WEAK MKT 50% PROB | 13,500 | 13,500 | 13,500 | 13,500 -57,206.82 | 0 | -100,000 IN A WEAK... CHANGING CIRCUMSTANCES BECAUSE MANAGEMENT’S ACTIONS CAN INFLUENCE A PROJECT’S OUTCOME B 2 WHAT ARE SOME EXAMPLES OF PROJECTS WITH EMBEDDED REAL OPTIONS? ANSWER: [SHOW S12-6 HERE.] A PROJECT MAY CONTAIN ONE OR MORE DIFFERENT TYPES OF EMBEDDED REAL OPTIONS EXAMPLES INCLUDE ABANDON-MENT/SHUTDOWN OPTIONS, INVESTMENT TIMING OPTIONS, GROWTH/EXPANSION OPTIONS, AND FLEXIBILITY OPTIONS C TAKING REAL OPTIONS INTO... -$200,000 -100,000 -100,000 -100,000 CASH INFLOWS $ 0 180,000 180,000 180,000 NET CASH FLOWS -$200,000 80,000 80,000 80,000 Integrated Case: 12 - 13 1 THE PROJECT HAS AN ESTIMATED COST OF CAPITAL OF 10 PERCENT WHAT IS THE PROJECT’S NPV? ANSWER: [SHOW S12-12 HERE.] 0 10% | -200,000 1 | 80,000 2 | 80,000 3 | 80,000 USING A FINANCIAL CALCULATOR, INPUT THE FOLLOWING DATA: CF0 = -200000; CF1-3 = 80000; I... WILL NOT INCUR ANY OPERATING COSTS AFTER YEAR 1 THUS, IF THE COMPANY CHOOSES TO ABANDON THE PROJECT, ITS ESTIMATED CASH FLOWS ARE AS FOLLOWS: 60% PROB 0 | -200,000 1 | 150,000 40% PROB | -200,000 | -25,000 AGAIN, ASSUMING A COST OF 2 | 150,000 CAPITAL OF 10 3 | 150,000 PERCENT, PROJECT’S EXPECTED NPV IF IT ABANDONS THE PROJECT? WHAT IS THE SHOULD 21ST CENTURY INVEST IN PROJECT Y TODAY, REALIZING IT HAS... MARKET IS WEAK, THE YEARLY CASH FLOWS WILL BE ONLY $23,500 IF 21ST CENTURY CHOOSES TO WAIT A YEAR, THE INITIAL INVESTMENT WILL REMAIN $100,000 ASSUME THAT ALL CASH FLOWS ARE DISCOUNTED AT 10 PERCENT SHOULD 21ST CENTURY INVEST IN PROJECT L TODAY, OR SHOULD IT WAIT A YEAR BEFORE DECIDING WHETHER TO INVEST IN THE PROJECT? ANSWER: [SHOW S12-7 THROUGH S12-9 HERE.] 50% PROB 0 = 10% 1 k STRONG MKT | | 0 -100,000... TO BEING THE FIRST COMPETITOR TO ENTER A MARKET 3 WAITING MAY ALLOW YOU TO TAKE ADVANTAGE OF CHANGING CONDITIONS E 21ST CENTURY IS CONSIDERING ANOTHER PROJECT, PROJECT Y PROJECT Y HAS AN UP-FRONT COST OF $200,000 AND AN ECONOMIC LIFE OF THREE YEARS IF THE COMPANY DEVELOPS THE PROJECT, ITS AFTER-TAX OPERATING COSTS WILL BE $100,000 A YEAR; HOWEVER, THE PROJECT IS EXPECTED TO PRODUCE AFTER-TAX CASH INFLOWS . firm would not pay any more than this for the option. Answers and Solutions: 12 - 8 12% k = 12% k = 12% } wouldn’t do 12- 12 The detailed solution for the spreadsheet problem is available both on the. Solutions: 12 - 4 SOLUTIONS TO END-OF-CHAPTER PROBLEMS 10% 10% k = 10% 12- 4 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. 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