A company has an equity beta of 1.4 with a debt to equity ratio of 0.6 and a 25% tax rate. The risk free rate is 4%, the equity risk premium 5% and pre-tax debt costs 6%. Compute the asset beta and the weighted average cost of capital.

A company has an equity beta of 1.4 with a debt to equity ratio of 0.6 and a 25% tax rate. The risk free rate is 4%, the equity risk premium 5% and pre-tax debt costs 6%. Compute the asset beta and the weighted average cost of capital.

Approach: Unlever the equity beta with the Hamada relation, then weight the cost of equity from the capital asset pricing model against the after-tax cost of debt at market weights.

8.56%. Unlevering with beta_A = beta_E/(1 + (1 - T)*D/E) gives 1.4/(1 + 0.75 * 0.6), so the asset beta is 1.4/1.45, or 0.97. The capital asset pricing model gives a cost of equity of 4% + 1.4 * 5%, which is 11%. With D/E of 0.6 the weights are E/V = 1/1.6, or 0.625, and D/V of 0.375, so the weighted average cost of capital is 0.625 * 11% + 0.375 * 6% * 0.75, which is 6.875% + 1.6875%, or 8.56%. The asset beta of 0.97 is the number to carry across to a comparable with different leverage, since the equity beta of 1.4 is a fact about this balance sheet rather than about the underlying business.

Follow-up: The comparable you are pricing runs a debt to equity ratio of 1.2. What equity beta and cost of equity do you assign it?

Key concepts: asset beta, weighted average cost of capital, capital asset pricing model, after-tax cost of debt.