Answer:
The market risk premium is 7.2%.
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%.
Answer:
market premium 0.072 -->7.2%
Explanation:
We have to use the Modigliani-Miller proposition to solve for these amounts:
[tex]\beta_l = \beta_u \times [1 + (1 - t) \times \frac{D}{E} ]\\\beta_l = 1.25 \times [1 + (1 - 0) \times 1 ]\\\\\beta_l = 1.25 \times [1 + 1 ]\\\\\beta_l = 2.50[/tex]
Now, with the leverated beta we solve for the market premium using CAPM method
[tex]Ke_l= r_f + \beta_l (r_m-r_f)[/tex]
[tex]Ke_u= r_f + \beta_u (r_m-r_f)[/tex]
The difference between these rates is 9% and both have the risk free rate thus that is simplified leaving:
[tex]Ke_l - Ke_u = r_f + \beta_u (r_m-r_f) - r_f - \beta_u (r_m-r_f)[/tex]
[tex] 0.09 = \beta_l \times premium - \beta_u \times premium[/tex]
[tex] 0.09 = (\beta_l - \beta_u) \times premium[/tex]
[tex] 0.09 = (2.50 - 1.25) \times premium[/tex]
premium = 0.09 / 1.25 = 0.072
