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Chapter 13. Identifying Embedded Options Valuing Real Options in Projects. Real Options and Other Topics in Capital Budgeting. What is real option analysis?.

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## Real Options and Other Topics in Capital Budgeting

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**Chapter 13**• Identifying Embedded Options • Valuing Real Options in Projects Real Options and Other Topics in Capital Budgeting**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?**• Growth/expansion options • Abandonment/shutdown options • Investment timing options • Flexibility options**Investment Timing Option**• Project X has an up-front cost of $100,000. The project is expected to produce after-tax cash flows of $33,500 at the end of each of the next four years (t = 1, 2, 3, and 4). The project has a WACC=10%. • The project’s NPV is $6,190. Therefore, it appears that the company should go ahead with the project. • However, if the company waits a year they will find out more about the project’s expected cash flows.**Investment Timing Option**• If they wait a year: • There is a 50% chance the market will be strong and the expected cash flows will be $43,500 a year for four years. • There is a 50% chance the market will be weak and the expected cash flows will be $23,500 a year for four years. • The project’s initial cost will remain $100,000, but it will be incurred at t = 1 only if it makes sense at that time to proceed with the project. • Should the company go ahead with the project today or wait for more information?**Investment Timing Decision Tree**• At WACC = 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. -$100,000 43,500 43,500 43,500 43,500 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% WACC). • Therefore, it makes sense to wait.**Issues to Consider with Investment Timing Options**• What is 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 > $18,945**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**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% WACC, 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**• If the customer uses the product, NPV is $173,027.80. • If the customer does not use the product, NPV is -$262,171.30. 150,000 150,000 150,000 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**• If the customer uses the product, NPV is $173,027.80. • If the customer does not use the product, NPV is -$222,727.27. 150,000 150,000 150,000 60% prob. -$200,000 -25,000 40% prob. 0 1 2 3 Years**Should an abandonment option affect a project’s WACC?**• Yes, an abandonment option should have an effect on the WACC. • The abandonment option reduces risk, and therefore reduces the WACC.**Growth Option**• Project Z has an initial 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, and has a WACC of 12%. 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**• At WACC = 12%, • NPV of top branch (10% prob) = $1,562,758.19 • NPV of lower branch (90% prob) = -$139,522.38 $3,000,000 100,000 100,000 100,000 100,000 100,000 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 the project’s future opportunities have a negative NPV, the company would choose not to pursue them. • The bottom branch only has the -$500,000 initial outlay and the $100,000 annual cash flows, which lead to an NPV of -$139,522. • 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.

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