Question

Greshak Corp. is analyzing its optimal capital structure. Currently, Greshak's capital structure includes 20% debt and the company is planning to double its debt capitalization. Assume that the current risk-free rate is 4.00% and the equity risk premium is 6.25%. If the company's cost of equity, which is based on the CAPM, is 12.50% and its tax rate is 40.00%, what would Greshak's estimated cost of equity (rounded) be if the company were to change its capital structure as indicated above? Make sure you use at least four (4) decimal places in calculations and answer.

Answer 1

As per CAPM,

Cost of equity = Risk free rate + [Market risk premium * Beta]

12.50% = 4.00% + [6.25% * Beta]

6.25% * Beta = 12.50% - 4.00%

Beta = 8.50% / 6.25% = 1.36

This is a levered beta. First, we need to find the unlevered beta and then relever the beta according to the new capital structure.

Unlevered Beta = Levered Beta / [1 + {(1 - t) * (D/E)}]

= 1.36 / [1 + {(1 - 0.40) * (0.2/0.8)}]

= 1.36 / [1 + 0.15] = 1.36 / 1.15 = 1.1826

Now, we have to relever the beta as per new capital structure.

Levered Beta = Unlevered Beta * [1 + {(1 - t) * (D/E)}]

= 1.1826 * [1 + {(1 - 0.40) * (0.4/0.6)}]

= 1.1826 * [1 + 0.4] = 1.1826 * 1.4 = 1.6557

New Cost of equity as per the new capital structure
= 4.00% + [6.25% * 1.6557] = 4.00% + 10.3478% = 14.3478%