Question

Roston Corporation has a debt-equity ratio of 3. The company’s weighted average cost of capital (WACC) is 11%. Its before-tax cost of debt is 13% and tax rate is 25%. The company uses Capital Asset Pricing Model (CAPM) to calculate its cost of equity. The risk-free rate of return is 5% and the market risk premium is 7%. Find out the beta of the company.

Answer 1

SOLUTION:-

The answer of this question can be solved by two steps:

Step 1:- calculation of cost of equity

  company’s weighted average cost of capital (WACC) = 11%

  before-tax cost of debt = 13%

After-tax cost of debt = 13% * (1-tax- rate)

= 13% * (1 - .25)

= 13% * .75

= 9.75%

Debt equity ratio = 3:1

   weight of debt =.75

weight of equity =.25

Let, Cost of capital be X

WACC= (weight of debt * after tax cost of bond) + (weight of capital * cost of capital)

11% = (.75 * 9.75%) + (.25 * X)

11% = 7.3125% + .25X

   3.6875%= .25X

   X= 3.6875% / .25

   X= 14.75%

  Cost of capital is 14.75%

Step 2:- calculation of beta of the company

Risk free rate of return = 5%

market risk premium = 7%

Cost of capital = 14.75% (from the above answer)

beta of the company ( = ?

  

Here the company uses Capital Asset Pricing Model (CAPM) to calculate its cost of equity. Therefore beta can be calculated using CAPM formula.

using CAPM we get

  Cost of capital =  Risk free rate of return + ( market risk premium)

By substituting the values we get,

14.75% = 5% + ( * 7%)

  14.75% = 5% + .07

7% * = 14.75% - 5%

7% * = 9.75%

= 9.75% / 7%

   = 1.3928

beta of the company = 1.3928