Question

Firm A and Firm B are totally identically firms except different financing strategies. Firm A does not have any leverage while Firm B has a 50% leverage ratio, debt/(debt+equity). Firm A has a beta of 0.7. The risk-free rate is 4% and the market risk premium is 3%. Assuming Firm B will never default under any possible scenario. What is the cost of equity for Firm B? There is no corporate tax or other frictions, and the market is perfect and satisfies all the assumptions of Modigliani-Miller Theorem.

Answer 1

The cost of equity for Firm B is 8.2%, calculated using the adjustment for leverage from the Modigliani-Miller proposition II without taxes in conjunction with the Capital Asset Pricing Model (CAPM).

Step-by-step explanation:

To calculate the cost of equity for Firm B, which has a 50% leverage ratio and a beta of 0.7, we can use the Modigliani-Miller proposition II without taxes. According to MM II, the cost of equity increases with leverage because the risk to equity holders increases when debt is introduced.

Firstly, we calculate the unlevered cost of equity for Firm A (which is identical to Firm B with no debt) using the Capital Asset Pricing Model (CAPM). Firm A's cost of equity (E(RA)) is given by:

E(RA) = Risk-free rate + BetaA * (Market Risk Premium)

E(RA) = 4% + 0.7 * 3% = 6.1%

Since Firm B has the same business risk as Firm A, its unlevered cost of equity is also 6.1%. We then adjust this cost of equity for the leverage using the following leverage adjustment formula:

Cost of Equity for Firm B (E(RB)) = E(RA) + (E(RA) - Risk-free rate) * (Debt/Equity ratio for Firm B)

Assuming Firm B will never default and there is no corporate tax or other frictions:

E(RB) = 6.1% + (6.1% - 4%) * (1)

E(RB) = 6.1% + 2.1% = 8.2%

The cost of equity for Firm B, therefore, is 8.2%.