Question

A firm is financed with debt that has a market beta of 0.3 and equity that has a market beta of 1.2. The risk-free rate is 3%, and the equity premium is 5%. The overall cost of capital for the firm is 8%. What is the firmʹs debt-equity ratio?

a) 28.6%

b) 25.0%

c) 74.8%

d) 25.2%

Answer 1

Risk free rate = 3%

Equity premium = 5%

Debt beta = 0.3

Equity beta = 1.2

Required rate of return for equity shall be = Risk free rate of return + (Beta * Equity premium)

=3% + (1.2 * 5%)

=9%

Other information about debt is not given. So Risk free rate will be required rate of return of Debt which is 3%

Assume weight of Equity = x, So weight of debt = (1-x)

Cost of capital = (Required rate of return of Equity * weight of Equity)+(Required rate of return of Debt * Weight of debt)

8 = (9 * x) + (3 *(1-x))

8 = 9x +3 - 3x

5 = 6x

x = 5/6 = 0.83333

So, Weight of equity = 0.83333

Weight of debt = 1-0.83333 = 0.16667

Debt-Equity ratio formula = Debt/Equity

0.166667/0.83333

=0.20

Cost of capital = Risk free rate of return * (Beta of company * Equity risk premium)

8 = 3 +(Beta * 5)

5 = 5*Beta

Beta = 1

Assume weight of Equity = x, So weight of debt = (1-x)

Beta formula = (Weight of Equity * Equity Beta)+(Weight of Debt * Debt equity)

1 = (1.2 * x) + (0.3 * (1-x)

1= 1.2x +0.3 - 0.3x

0.7 = 0.9x

x = 0.7/0.9 = 0.77778

So, weight of debt = 0.777778

weight of Equity = 1-0.777778 = 0.222222

Debt to Equity ratio = 0.222222/0.777778

= 28.6%

So, debt equity ratio is 28.6%