Question

Two firms are identical except for their capital structure. Company A is funded by 30% debt and
70% equity. Company B is funded by 40% debt and 60% equity.
(a) What are the relationships between their asset betas and equity betas? Fill in the blank.
Company A (“>”, “=”, or “<”) Company B
A’s Asset beta B’s Asset beta
A’s Equity beta B’s Equity beta
(b) Briefly explain your rationale for the answers provided in part (a) above.

Answer 1

A) Since both the firms are identical to each other except the capital structure then if we ignore the capital structure then the asset beta of Company A should be equal to Asset beta for Company B

Unlevered beta (asset beta) = Levered beta/(1 + (1-Tax rate)*(debt/equity))

The unlevered beta for both the companies should be equal.

The equity beta considers the impact of debt equity ratio is the capital structure. So higher the debt ratio as compared to equity the higher will be the beta.

Since the debt in the capital structure for company B is higher than for company A, the equity beta for company B should be higher than company A.

b). The rationale behind this is that when the company is fully equity funded and it has the same business risk then its beta of equity would be equal to unlevered beta or asset beta and since both the companies have same business risk, their asset beta should be same. Now as the debt increases in the capital structure the beta of the equity will increase (as the above formula shows), levered beta will increase. Higher the debt in the capital structure higher will be the equity beta.