After determining the ERP, we must estimate the company's required rate of return to be used in calculating the WACC.

DDMs

Under the DDM, the value of a common stock is the present value of all future dividends. The required rate of return is the sum of the expected dividend yield (D₁/P₀) and the dividend growth rate g.

r_e = D₁/P₀ + g

If a stock does not pay dividend for some early years, investors expect at some point in the future the firm will start to pay dividends. Thus, valuation of stocks paying no dividends uses the same DDM approach, except that some of the early dividends are 0.

Bond Yield Plus Risk Premium

As a company's business risk rises it is immediately reflected in bond yields. This method uses normal spreads of equity returns over corporate bond yields, say around 3-4%.

r = R_D + Risk Premium

For example, suppose that ABC, Inc.'s interest rate on long-term debt is 10%. Assume the risk premium is 5%. ABC's cost of retained earnings is 10% + 5% = 15%.

It is challenging to estimate the risk premium. A company must trade debt securities to use this approach. Where a company has several traded debt securities with different features, there is no guidance on which bond yield to select.

CAPM

The required return on equity is estimated using the following equation:

Required return on share i = r_f + β_f (equity risk premium)

For example, firm A has a β_i of 0.6 for its stock. The risk-free rate, R_f, is 5%. The expected rate of return on the market, E(R_M), is 10%. The firm's cost of common equity is therefore calculated as 5% + (10% - 5%) x 0.6 = 8%.

Both the β_i and the equity risk premium need to be estimated.

To estimate β_i an analyst needs to make several choices:

• Which index should be used to represent the market portfolio? The S&P 500 is a traditional choice to represent U.S. equities.
• What should be the length of data period and the frequency of observations?

The Fama French Model

Fama and French started with the observation that two classes of stocks have tended to do better than the market as a whole: (i) small caps and (ii) stocks with a high book-value-to-price ratio (customarily called "value" stocks; their opposites are called "growth" stocks). They then added two factors to CAPM to reflect a portfolio's exposure to these two classes:

r = R_F + β_mkt (R_M - R_F) + β_S SMB + β_V HML

Here r is the portfolio's return rate, R_F is the risk-free return rate, and R_M is the return of the whole stock market. The "three factor" beta is analogous to the classical beta but not equal to it, since there are now two additional factors to do some of the work. SMB and HML stand for "small [cap] minus big" and "high [book/price] minus low"; they measure the historical excess returns of small caps and "value" stocks over the market as a whole.

The corresponding coefficients β_S and β_V take values on a scale of roughly 0 to 1: β_S = 1 would be a small cap portfolio, β_S = 0 would be large cap, β_V = 1 would be a portfolio with a high book/price ratio, etc.