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CHAPTER 12 Other Topics in Capital Budgeting. Evaluating projects with unequal lives Identifying embedded options Valuing real options in projects. Evaluating projects with unequal lives. Projects S and L are mutually exclusive, and will be repeated. If k = 10%, which is better?
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CHAPTER 12Other Topics in Capital Budgeting Evaluating projects with unequal lives Identifying embedded options Valuing real options in projects
Evaluating projects with unequal lives Projects S and L are mutually exclusive, and will be repeated. If k = 10%, which is better? Expected Net CFs Year Project SProject L 0 ($100,000) ($100,000) 1 59,000 33,500 2 59,000 33,500 3 - 33,500 4 - 33,500
Solving for NPV, with no repetition • Enter CFs into calculator CFLO register for both projects, and enter I/YR = 10%. • NPVS = $2,397 • NPVL = $6,190 • Is Project L better? • Need replacement chain analysis.
Replacement chain • Use the replacement chain to calculate an extended NPVS to a common life. • Since Project S has a 2-year life and L has a 4-year life, the common life is 4 years. 0 1 2 3 4 10% -100,000 59,000 59,000 59,000 59,000 -100,000 -41,000 NPVS = $4,377 (on extended basis)
What is real option analysis? • Real options exist when managers can influence the size and riskiness of a project’s cash flows by taking different actions during the project’s life. • Real option analysis incorporates typical NPV budgeting analysis with an analysis for opportunities resulting from managers’ decisions.
What are some examples of real options? • Investment timing options • Abandonment/shutdown options • Growth/expansion options • Flexibility options
Illustrating an investment timing option • If we proceed with Project L, its annual cash flows are $33,500, and its NPV is $6,190. • However, if we wait one year, we will find out some additional information regarding output prices and the cash flows from Project L. • If we wait, the up-front cost will remain at $100,000 and there is a 50% chance the subsequent CFs will be $43,500 a year, and a 50% chance the subsequent CFs will be $23,500 a year.
Investment timing decision tree -$100,000 43,500 43,500 43,500 43,500 • At k = 10%, the NPV at t = 1 is: • $37,889, if CF’s are $43,500 per year, or • -$25,508, if CF’s are $23,500 per year, in which case the firm would not proceed with the project. 50% prob. -$100,000 23,500 23,500 23,500 23,500 50% prob. 0 1 2 3 4 5 Years
Should we wait or proceed? • If we proceed today, NPV = $6,190. • If we wait one year, Expected NPV at t = 1 is 0.5($37,889) + 0.5(0) = $18,944.57, which is worth $18,944.57 / (1.10) = $17,222.34 in today’s dollars (assuming a 10% discount rate). • Therefore, it makes sense to wait.
Issues to consider with investment timing options • What’s the appropriate discount rate? • Note that increased volatility makes the option to delay more attractive. • If instead, there was a 50% chance the subsequent CFs will be $53,500 a year, and a 50% chance the subsequent CFs will be $13,500 a year, expected NPV next year (if we delay) would be: 0.5($69,588) + 0.5(0) = $34,794 > $18,944.57
Factors to consider when deciding when to invest • Delaying the project means that cash flows come later rather than sooner. • It might make sense to proceed today if there are important advantages to being the first competitor to enter a market. • Waiting may allow you to take advantage of changing conditions.
0 1 2 3 k = 10% -$200,000 80,000 80,000 80,000 NPV = -$1,051.84 Abandonment/shutdown option • Project Y has an initial, up-front cost of $200,000, at t = 0. The project is expected to produce after-tax net cash flows of $80,000 for the next three years. • At a 10% discount rate, what is Project Y’s NPV?
Abandonment option • Project Y’s A-T net cash flows depend critically upon customer acceptance of the product. • There is a 60% probability that the product will be wildly successful and produce A-T net CFs of $150,000, and a 40% chance it will produce annual A-T net CFs of -$25,000.
Abandonment decision tree 150,000 150,000 150,000 • If the customer uses the product, NPV is $173,027.80. • If the customer does not use the product, NPV is -$262,171.30. • E(NPV) = 0.6(173,027.8) + 0.4(-262,171.3) = -1,051.84 60% prob. -$200,000 -25,000 -25,000 -25,000 40% prob. 0 1 2 3 Years
Issues with abandonment options • The company does not have the option to delay the project. • The company may abandon the project after a year, if the customer has not adopted the product. • If the project is abandoned, there will be no operating costs incurred nor cash inflows received after the first year.
NPV with abandonment option 150,000 150,000 150,000 • If the customer uses the product, NPV is $173,027.80. • If the customer does not use the product, NPV is -$222,727.27. • E(NPV) = 0.6(173,027.8) + 0.4(-222,727.27) = 14,725.77 60% prob. -$200,000 -25,000 40% prob. 0 1 2 3 Years
Is it reasonable to assume that the abandonment option does not affect the cost of capital? • No, it is not reasonable to assume that the abandonment option has no effect on the cost of capital. • The abandonment option reduces risk, and therefore reduces the cost of capital.
Growth option • Project Z has an initial up-front cost of $500,000. • The project is expected to produce A-T cash inflows of $100,000 at the end of each of the next five years. Since the project carries a 12% cost of capital, it clearly has a negative NPV. • There is a 10% chance the project will lead to subsequent opportunities that have an NPV of $3,000,000 at t = 5, and a 90% chance of an NPV of -$1,000,000 at t = 5.
NPV with the growth option $3,000,000 • At k = 12%, • NPV of top branch (10% prob) = $1,562,758.19 • NPV of lower branch (90% prob) = -$139,522.38 100,000 100,000 100,000 100,000 100,000 10% prob. -$1,000,000 -$500,000 100,000 100,000 100,000 100,000 100,000 90% prob. 0 1 2 3 4 5 Years
NPV with the growth option • If it turns out that the project has future opportunities with a negative NPV, the company would choose not to pursue them. • Therefore, the NPV of the bottom branch should include only the -$500,000 initial outlay and the $100,000 annual cash flows, which lead to an NPV of -$139,522.38. • Thus, the expected value of this project should be: NPV = 0.1($1,562,758) + 0.9(-$139,522) = $30,706.
Flexibility options • Flexibility options exist when it’s worth spending money today, which enables you to maintain flexibility down the road.