Savvy Supermarkets is a chain of grocery stores that is currently financed with

Question

Savvy Supermarkets is a chain of grocery stores that is currently financed with 12.5% debt and 87.5% equity. The CEO of Savvy decides that the proportion of debt in the current capital structure is too low because investors in Savvy’s stock demand a higher rate of return. Savvy issues debt and pays out all proceeds as a special dividend to shareholders. The current rate of return on Savvy’s equity is 16%, only slightly higher than the 14% currently expected on the stock market index. Suppose the risk-free rate is 6% and Savvy has 10 million shares outstanding for a price of $18 per share. For answering the following questions, please assume the Modigliani and Miller assumptions are correct and the CAPM is valid.

a. What is the equity beta and the debt beta of Savvy if the debt has anexpected return of 6%?

b. What is the cost of capital of Savvy?

c. Suppose the CEO wishes to realize a target expected return of 20% throughleveraging and paying the proceeds as aspecial dividend. How much debtshould the company issue, assuming that all debt can be issued at an expectedreturn equal to the risk-free rate?

Explanation / Answer

a) E(R)=Rf+B*(Rm-Rf)

16%=6%+Beta*(14%-6%)

beta=1.25

b)cost of capital=(wt of debt*cost of debt)+(wt of equity*cost of equity)

=(12.5%*6%)+(87.5%*16%)

=14.75%

c)

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