Question

Savvy Supermarkets is a chain of grocery stores that is currently financed with 12.5% debt. 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, assume all assets are priced on the SML.

a) What is the equity beta of Savvy if the debt has an expected return of 6%?

b) What is the cost of capital of Savvy? Answer this question by using both methods, namely unlevering betas and the weighted average cost of capital.

c) 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. Suppose the CEO wishes to realize a target expected return on equity of 20% through leveraging and paying the proceeds as a special dividend. Savvy issues debt and pays out all proceeds as a special dividend to shareholders. How much debt should the company issue, assuming that all debt can be issued at an expected return equal to the risk-free rate? What is the cost of capital now?

Answer 1

a) Equity Beta

Rm = Return on Market = 14%

Re = Required return on Equity =16%

Rf = Risk free rate = 6%

Using SML

Re = Rf + ( Rm - Rf )B

16% = 6% + ( 14% - 6% )B

B = 1.25 ( Equity Beta )

b) Calculation of Cost of Capita, Using unleveraging Betas

BU = Unleveraged Beta

BU = Leveraged Beta OR Eqity Beta/ 1+ ( DEBT (1- TAX ) / Equity

Bu = 1.25 / 1+ 12.5/16 = 1.25/1.78125 =  0.70175 approx

Cost of Capital = Rf + Bu ( Rm - Rf) = 6% + 0.70175 ( 14% - 6% ) = 16.614%

Weighted Average Cost of Capital

WACC = E/V* Re + D/V* Rd* ( 1 - Tax )

E = Market value of Equity = 14%

D = Market value of Debt = 6%

V = E+ D = 14% + 6% = 20%

Re = Cost of Equity = 16 %

Rd = Cost of Debt = 12.5%

WACC = 14/20*16 + 6/20*6 = 13%