Question

Fitzgerald Industries has a new project available that requires an initial investment of $5.1 million. The project will provide unlevered cash flows of $855,000 per year for the next 20 years. The company will finance the project with a debt-value ratio of .4. The company’s bonds have a YTM of 7.6 percent. The companies with operations comparable to this project have unlevered betas of 1.04, .92, 1.19, and 1.14. The risk-free rate is 4.2 percent and the market risk premium is 6.7 percent. The tax rate is 25 percent. What is the NPV of this project?

Answer #1

The unlevered beta of the firm will be the average of the unlevered betas. Hence, unlevered beta = (1.04 + 0.92 + 1.19 + 1.14)/4 = 1.0725. Now assuming that the debt has beta = 0, the levered beta will be = Unlevered beta/equity percentage = 1.0725/0.6 = 1.7875. Now, we use CAPM to calculate cost of equity.

Re = Rf + Beta x (Rm-Rf) = 4.2 + 1.7875 x 6.7 = 16.17625%. The cost of debt is the YTM = 7.6% (before-tax). Hence, WACC = Rd x D/(D+E) x (1-T) + Re x E/(D+E) = 7.6 x 0.4 x 0.75 + 16.17625 x 0.6 = 11.98575%.

So, now the NPV equation will be:

NPV = -5.1 + 0.855 x (1/1.1198 + 1.1198^2 + ... + 1/1.1198^20) = $1.294389 million.

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