Question

1. Master Inc. Master has no debt and its cost of equity capital is 10%. The average debt-to-value for companies in Master's industry is 20%. What would its cost of equity capital be if it took on the average amount of debt for its industry, at a cost of debt capital of 5%? Assume perfect markets.

Answer 1

According to the Modigliani-Miller proposition-II (without taxes), Cost of equity is directly proportional to the company's leverage level. As the Debt increases in the Firm, Cost of equity also increases but the value of firm remain unchanged.

We can compute the Cost of equity of levered firm with following equation:

$r_E= r_a+\frac{D}{E}*(r_a-r_D)$

where,

rE = cost of equity levered

ra = cost of equity unlevered

D = Debt

E = Equity

rD = Cost of Debt

putting the values:

$r_E= 0.1+\frac{0.2}{0.8}*(0.1-0.05)$

$r_E= 0.1+\frac{0.2}{0.8}*(0.05)$

$r_E= 0.1+0.25*(0.05)$

$r_E= 0.1+0.0125$

$r_E= 0.1125$

$\bg_green \large r_E= 11.25\%$

Thus, Cost of levered Equity would be 11.25%

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.