Question

Firm A has a beta of 1.3 and a debt-to-equity ratio of 0.4 and an interest rate of 9% on its debt. It has chosen Firm P as a proxy for a new line of business it is considering. Firm P has a beta of 1.6 and a debt to equity ratio of 0.8 and the expected return on the S&P 500 is 12% and the risk-free rate is 5.5%. The marginal tax rate is 40%.

A. Find the correct required return that the firm should use for its investment in the new line of business.
B. What are the dangers associated with its using is own beta in the calculation?

Answer 1

To answer this question, we need to have knowledge about levered and unlevered Beta. Unlevered means no leverage. Leverage means debt.

First we will find unlevered Beta of Firm A and then lever it back to the new line using D/E ration of Firm P.

Here T is tax rate, D/E is debt to equity ratio

T = 40%, D/E = 0.4, levered Beta = 1.3

Thus,

In new line,

here, unlevered beta = 1.048, T = 40% = 0.4 and D/E = 0.8

Thus,

This levered Beta will now on be just called Beta.

a) Required return in calculated using CAPM

CAPM:

rm = 12%, rf = 5.5% and Beta = 1.55

Thus,

Thus required return should be around 15.58% for its investment in the new line of business.

b) The danger is that the beta of 1.3 has debt factor associated with the Firm A which is in accordance with its old line of business. For the new line, the new D/E ratio needs to be taken into consideration for calculation purpose.

Since there is a change in business line, the overall debt and equity changes for the firm and hence the beta will also change. Thus, we need to first unlever the beta and then lever it back to the new line using its D/E ratio os 0.8.

This is the complete answer to your question. Please rate the answer and let me know if there is any doubt still persistant for this question. Thanks!