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# If the discount rate in not known with certainty, which project should the firm take as a function of the discount rate?

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A firm is considering two mutually exclusive projects. Both projects cost \$300,000 today. The first, the quick-payoff option, produces after-tax cash inflows of \$100,000 per year for each of the next four years (and nothing thereafter). The second, the slow-payoff option, produces after-tax cash inflows of \$50,000 per year for the next three years, and \$300,000 for year four (and nothing thereafter). Assume all cash flows occur at the end of the year, and that the two projects have identical risk. If the discount rate in not known with certainty, which project should the firm take as a function of the discount rate? In other words, give the preferred project for each relevant range of the potential discount rate.

#### Solution Preview

See the attached file.
Here we will calculate the NPV of both the projects under different discount rates.

Year Project 1 Project ...

#### Solution Summary

The solution determines which project the firm should take as a function of the discount rate not being known with certainty.

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