Question

Problem 24-16 Abandonment and Expansion (LO5] We are examining a new project. We expect to sell 6,200 units per year at $76 net cash flow apiece for the next 10 years. In other words, the annual cash flow is projected to be $76 x 6,200 = $471,200. The relevant discount rate is 18 percent, and the initial investment required is $1,730,000. After the first year, the project can be dismantled and sold for $1,600,000. Suppose you think it is likely that expected sales will be revised upward to 9,200 units if the first year is a success and revised downward to 4,800 units if the first year is not a success. Suppose the scale of the project can be doubled in one year in the sense that twice as many units can be produced and sold. Naturally, expansion would be desirable only if the project is a success. This implies that if the project is a success, projected sales after expansion will be 18,400. Note that abandonment is still an option if the project is a failure. a. If success and failure are equally likely, what is the NPV of the project? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. What is the value of the option to expand? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) a. NPV Option value

Answer 1

1 Cash flows value after 1 years 2 Abandon value after 1 year 6,017,345.72 =PV(18%,9,-76*18400) 1,600,000.00 $ 7,617,345.72 =SUM(B1:B3) 0.5 IS 3,808,672.86 =+B5*B4 471,200.00 $ 4,279,872.86 =+B8+B7 4 Total 5 xProbability 6 7 PV of future cash flows at year 1 8 Add: year 1 cash flows 9 10 Expected value of project at Year 1 11 Less: 12 Initial investment 13 14 NPV 15 16 Gain from option to expand 17 xProbability 18 XPVIF(15%,1) 1,730,000.00 $ 1,897,010.90 +010/1.18-B12 3,008,672.86 =PV(18%,9,-76*9200) 0.5 0.8475 =1/1.18 20 Option value $ 1,274,861.38 +316*B17*B18

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