## Cost of Capital

The cost of capital is the rate of return that must be realized in order to satisfy investors. The cost of debt capital is the return demanded by investors in the firm’s debt; this return largely is related to the interest the firm pays on its debt. Managers used to believe that equity capital had no cost if no dividends were paid; however, equity investors incur an opportunity cost in owning the equity of the firm and they demand a rate of return comparable to what they could earn by investing in securities of comparable risk.
The return required by debt holders is found by applying the CAPM:
rD = rF + betadebt (rM– rF)
The required rate of return on assets can be found using the CAPM:
rA = rF + betaunlevered (rM– rF)
Using the CAPM, a firm’s required return on equity is calculated as:
rE = rF + betalevered (rM– rF)
Under the Modigliani-Miller assumptions of constant cash flows and constant debt level, the required ROE is
rE = rA + (1-t)(rA– rD)(D/E)
where t is the corporate tax rate.
The overall cost of capital is a weighted-average of the cost of its equity capital and the after-tax cost of its debt capital:
WACC = rE (E/VL) + rD (1 – t)(D/VL)
Assuming perpetuities for the cash flows, the WACC can be calculated as:
WACC = rA (1– t(D/VL))
Neglecting taxes, the WACC would be equal to the expected ROA because the WACC is the return on a portfolio of all the firm’s equity and debt, and such a portfolio essentially has claim to all of the firm’s assets.
Estimating Beta
In order to use the CAPM to calculate ROA or ROE, one needs to estimate the asset (unlevered) beta or the equity (levered) beta of the firm. The beta that often is reported for a stock is the levered beta for the firm. When estimating a beta for a particular line of business, it is better to use the beta of an existing firm in that exact line of business (a pure play) rather than an average beta of several firms in similar lines of business. Expressing the levered beta, unlevered beta, and debt beta in terms of the covariance of their corresponding returns with that of the market, one can derive an expression relating the three betas. This relationship between the betas is:
betalevered = betaunlevered (1 + (1– t) D/E)– betadebt(1 – t) D/E
betaunlevered = (betalevered + betadebt(1 – t) D/E) / (1 + (1– t) D/E)
The debt beta can be estimated using CAPM given the risk-free rate, bond yield, and market risk premium.