Problem
You are trying to decide whether to make an investment of $500 million in a new technology to produce Everlasting Gobstoppers.
There is a 60% chance that the market for these candies will produce profits of $100 million annually, a 20% chance the market will produce profits of $50 million, and a 20% chance that there will be no profits.
The size of the market will become clear one year from now. Currently, the cost of capital of the project is 11% per year.
There is a 20% chance that the cost of capital will drop to 9% in a year and stay at that level forever, and a 80% chance that it will stay at 11% forever. Movements in the cost of capital are unrelated to the size of the candy market.
Construct the decision tree that shows the choices you have to make to see if you make the investment either today or one year from now.
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Profits (million) |
Probability |
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Cost of Capital |
Probability |
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Investment (million) |
$500.00 |
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$100.00 |
60% |
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11.00% |
80% |
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$50.00 |
20% |
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9.00% |
20% |
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$0.00 |
20% |
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Firm Value |
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Expected |
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Value |
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| Decision tree ($ million): |
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To calculate the expected return on the investment opportunity, we need to construct the decision tree of outcome probabilities.
1. For the first possible outcome, in cell H15, by using cell references, input the first possible profit . In cell G15, by using cell references, input the probability that this outcome will occur .
2. For the second possible outcome, in cell H21, by using cell references, input the second possible profit . In cell G21, by using cell references, input the probability that this outcome will occur .
3. For the third possible outcome, in cell H27, by using cell references, input the third possible profit . In cell G27, by using cell references, input the probability that this outcome will occur .
4. Independent of the profits outcome, there are two possible costs of capital with their respective probabilities of occurrence. For the first possible profit outcome, in cell J14, by using cell references, input the probability that the first cost of capital will occur .
5. In cell J16, by using cell references, input the probability that the second cost of capital will occur .
6. For the second possible profit outcome, in cell J20, by using cell references, input the probability that the first cost of capital will occur .
7. In cell J22, by using cell references, input the probability that the second cost of capital will occur .
8. For the third possible profit outcome, in cell J26, by using cell references, input the probability that the first cost of capital will occur .
9. In cell J28, by using cell references, input the probability that the second cost of capital will occur .
10. For the first possible profit outcome, calculate the NPV of the investment opportunity for both possible costs of capital. In cell K13, by using cell references, calculate the NPV .
11. In cell K17, by using cell references, calculate the NPV .
12. For the second possible profit outcome, calculate the NPV of the investment opportunity for both possible costs of capital. In cell K19, by using cell references, calculate the NPV .
13. In cell K23, by using cell references, calculate the NPV .
14. For the third possible profit outcome, calculate the NPV of the investment opportunity for both possible costs of capital. In cell K25, by using cell references, calculate the NPV .
15. In cell K29, by using cell references, calculate the NPV .
16. Finally, in cell E21, by using cell references, calculate the expected value of the investment opportunity .