A firm currently has a debt-equity ratio of 1/2. The debt, which is virtually riskless, pays an interest rate of 6%. The expected rate of return on the equity is 12%. What would be the expected rate of return on equity if the firm reduced its debt-equity ratio to 1/3? Assume the firm pays no taxes.

Expected return on equity is 11.33%

Explanation:

Using Weighted Average Cost Capital without tax formula, overall rate of return is given by the formula:

WACC = (Ke*E/V) + (Kd*D/V)

Kd is the cost of debt at 6%

Ke is the cost of equity at 12%

D/E=1/2 which means debt is 1 and equity is 2

D/V=debt/debt+equity=1/1+2=1/3

E/V=equity/debt+equity=2/1+2=2/3

WACC = (12%*2/3) + (6%*1/3)

WACC=10%

If the firm reduces debt-equity ratio to 1/3,1 is for debt 3 is for equity

D/V=debt/debt+equity=1/1+3=1/4

E/V=equity/debt+equity=3/1+3=3/4

WACC=10%

10% = (Ke*3/4) + (6%*1/4)

10% = (Ke*3/4) + 1.5%

10%-1.5%=Ke*3/4

8.5%=Ke*3/4

8.5%=3Ke/4

8.5%*4=3 Ke

34%=3 Ke

Ke=34%/3

Ke=11.33%