LOS h: Compare and contrast models used to estimate the required rate of return to private company equity (for example, the CAPM, the expanded CAPM, and the build-up approach)

The required return on equity using the CAPM is: 3.5% + 1.4(6%) = 11.9%.

Note that the risk-free rate is the Treasury yield, not the returns for bonds in general.

Using the expanded CAPM, a small stock premium and company-specific risk premium are added: 11.9% + 4% + 3% = 18.9%.

Using the build-up method: the risk-free rate, the equity risk premium, the small stock premium, a company-specific risk premium, and an industry risk premium are added together: 3.5% + 6.0% + 4.0% + 3.0% + 2.0% = 18.5%. Note that the risk-free rate is the Treasury yield, not the returns for bonds in general.

Because the firm is being acquired, we assume the new owners will utilize an optimal capital structure and weights in the WACC calculation. The capital structure for public firms should not be used because public firms have better access to debt financing.

The WACC using the optimal capital structure factors in the debt to total cap, the cost of debt, the tax rate, and the given cost of equity:

[20% × 11% × (1-30%)] + [(1-20%) × 18.5%] = 16.3%.

If it is not possible to find comparable public firms with which to estimate beta by, the build-up method can be used for a private firm. It is similar to the expanded CAPM except that beta is not used. Implicitly, beta is assumed to be one. Both industry risk premiums and equity risk premiums are used. The risk-free rate, the equity risk premium, the small stock premium, a company-specific risk premium, and an industry risk premium are added together in the build-up method.