As a funding source, debt and equity are priced quite differently. While debt relies heavily on default premiums being applied to a risk-free bond rate of interest (the premium usually dependent on the size of the debt compared to the size of the firm), equity isn't quite as well-defined. As a result, the cost of common equity is often inferred through assessing and comparing it to similar risk profiles, and trying to decipher the firm's relative sensitivity to systematic (market) risk.

The Capital Asset Pricing Model

One common tool used in assessing the cost of common equity is the capital asset pricing model (CAPM), which can be described via the following formula:

${\displaystyle E_{s}=R_{f}+\beta _{s}(R_{m}-R_{f})}$

What this formula is saying is essentially that the cost of equity is equal to the risk free rate of return plus a premium for the expected risk of investing in the organization's equity. The variable are defined as follows:

1. E_s - expected return for a security
2. R_f - expected risk-free return rate
3. β_s - sensitivity to market risk 
4. R_m - historical return of the stock market
5. (R_m – R_f) - risk premium of market assets over risk free assets

Other Tools to Value Equity

The cost of common equity is essentially the same thing as estimating the expected (or required) return to investors in the stock market. The idea is simply that the higher risk an organization is, the higher the corresponding return should be. As a result, there are countless stock price evaluation strategies and tactics one could use to estimate the cost of common equity from various perspectives. Two of these include the dividend discount model and the Fama-French three-factor model.

Dividend Discount Model

In short, this theory states that a given stock is worth the sum of its future dividend payments, discounted to their present value. This is therefore a model of deriving the present value of future dividend payments, calculated as follows (assuming no end date):

${\displaystyle P=\sum _{t=1}^{\infty }{D_{0}}{\frac {(1+g)^{t}}{(1+r)^{t}}}}$

In this calculation, P is the stock price while D is the dividend, g is the (constant) growth rate, and r is the constant cost of equity and t is time.

There are a few problems with this method, most notably that a steady and perpetual growth rate that is less than the cost of capital may not be reasonable. Similarly, this model is quite vulnerable to the growth rate. Also, not all stocks pay dividends.

Fama-French Three-Factor Model

Another valuation model was derived by Eugene Fama and Kenneth French with the intention to include company size and price-to-book ratio with overall market risk. You'll recognize the first half of this equation as the simple CAPM calculation, while the second half includes SMB (small minus big market capitalization) and HML (high minus low book-to-market ratio) multiplied by coefficients (from linear regression). While this all sounds a bit complicated, the basic premise is to offset the risk calculation with a stronger valuation for a firm's assets and scale:

${\displaystyle r=R_{f}+\beta _{3}(K_{m}-R_{f})+b_{s}\cdot {\mathit {SMB}}+b_{v}\cdot {\mathit {HML}}+\alpha }$

Conclusion

All and all, the valuation of common equity is always an estimation. As understanding the risk of a given organization within the stock market is intrinsically speculative, equity tends to be quite a bit more costly than debt. After all, when an organization goes bankrupt it is the debtors who are reimbursed first, preferred stock next, and common stock last. This is the riskiest position of an investment.