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Suppose that your firm consists of $50M in cash. Specifically, your firm consists of $10M in debt (issued in perpetuity) and $40M in equity.

Author:
January 11th, 2018

Suppose that your firm consists of $50M in cash. Specifically, your firm consists of $10M in debt (issued in perpetuity) and $40M in equity. You announce that you will take this $50M in cash and invest it into a project that will produce expected after-tax free cash flows of $12.5M in perpetuity. Assume a tax rate of 30 percent. You would like to value this project (and hence your firm) by utilizing the weighted average cost of capital with taxes.Assume throughout the problem that the correct expected return on equity is 20 percent and the correct expected return on debt is 5 percent.a) Based on the numbers given in the problem, calculate the WACC with taxes.b) Using the WACC with taxes, calculate the value of the firm.You might have noticed that the value of the firm that you calculated in (b) is inconsistent with the value of the firm you used to calculate the WACC with taxes ($50M) in part (a). That is, the WACC with taxes you used to value the firm is not internally consistent with the value of the firm used to calculate WACC with taxes. This is a problem when you use WACC with taxes to calculate the value of a project and the project in turn significantly affects the inputs for calculating WACC with taxes.c) What is the correct firm value and WACC with taxes?Hint: you will have to “guess” a value for the firm and calculate WACC with taxes (keep in mind that the value of debt will always equal $10M). Then, using this WACC with taxes, calculate the value of the firm by applying the WACC with taxes to the $12.5M perpetuity. If this calculated value equals your “guess”, then you have the correct value of the firm and WACC with taxes. If it does not equal your guess, you will have to try again until the calculated value equals your guess. Microsoft Excel, particularly the Solver function, might be useful when answering this question.

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