Question

5) EverShine was an unlevered company with beta of 1.25. It decided to borrow money and buyback stock with the proceeds. Cost of equity capital went up by 9% after levering to a debt to value ratio of 0.5. Debt is risk free. Tax rate is zero. Depreciation level is $ 50 Million per year. EBIT is $ 875 Million per year. How much is the market risk premium

Answer 1

market premium 0.072 -->7.2%

Step-by-step explanation:

We have to use the Modigliani-Miller proposition to solve for these amounts:

`\beta_l = \beta_u * [1 + (1 - t) * (D)/(E) ]\\\beta_l = 1.25 * [1 + (1 - 0) * 1 ]\\\\\beta_l = 1.25 * [1 + 1 ]\\\\\beta_l = 2.50`

Now, with the leverated beta we solve for the market premium using CAPM method

`Ke_l= r_f + \beta_l (r_m-r_f)`

`Ke_u= r_f + \beta_u (r_m-r_f)`

The difference between these rates is 9% and both have the risk free rate thus that is simplified leaving:

`Ke_l - Ke_u = r_f + \beta_u (r_m-r_f) - r_f - \beta_u (r_m-r_f)`

`0.09 = \beta_l * premium - \beta_u * premium`

`0.09 = (\beta_l - \beta_u) * premium`

`0.09 = (2.50 - 1.25) * premium`

premium = 0.09 / 1.25 = 0.072

Answer 2

The market risk premium is 7.2%.

Step-by-step explanation:

We are required to calculate the market risk premium (P).

Debt to value ratio = D/V = 0.5

Debt to equity ratio = D/E = 0.5 / (1 - 0.5) = 1

Unlevered beta = 1.25

Tax rate = t = 0%

Levered beta = Unlevered beta x [1 + (1 - t)] x D/E

= 1.25 x (1 + 1) x 1

= 2.5

We are informed that the cost of equity capital went up by 9% after levering to a debt to value ratio of 0.5. This implies the following:

(Levered beta - Unlevered beta) x Market risk premium = Change in cost of equity capital

⇒ (2.5 - 1.25) x P = 9%

⇒ 1.25 x P = 9%

⇒ P = 9% / 1.25

⇒ P = 7.2%

Therefore, the market risk premium is 7.2%.