# Estimating the Cost of Common Stock

The cost of common equity is represented as re, and it is the rate of return required by the common shareholders.

The cost of common equity can be measured using the following methods:

1. Capital Asset Pricing Model (CAPM)

2. Dividend Discount Model

3. Bond Yield plus Risk Premium Method

Let's discuss each of these methods in some depth.

1. Capital Asset Pricing Model (CAPM)

The Capital Asset Pricing Model is a popular asset-pricing model in Finance. It is used to determine the expected rate of return of a risky asset. It says that the expected return on a risky asset is equal to the risk-free rate plus a risk premium.

The risk premium is a measure of non-diversifiable risk and is calculated using the asset’s Beta. CAPM considers only systematic risk (non-diversifiable risk) as the security specific risk (unsystematic risk) can be diversified away.

According to the CAPM model, the expected return on a security is given as follows:

$E(r)=R_{f}+\beta\left (E(R_{m}) - R_{f} \right )$

Where:

• E(Ri) is the expected return on the security
• Rf is the risk-free rate of return
• Β is the beta of the stock
• Rm is the expected return from the market

If the risk-free rate is 5.4%, the stock’s Beta is 1.5, and the expected market return is 8.4, then the stock is expected to return 9.9% (=5.4 + 1.5 * (8.4 – 5.4)).

If the actual returns offered by the stock are less than 9.9%, then you might want to avoid the investment.

As an alternative to CAPM, analysts may also use multi-factor models, such as Arbitrage Pricing Theory, to capture the risks not captured by the market portfolio alone.

2. Dividend Discount Model

The second approach for valuing common stock is the dividend discount model. According to the dividend discount model, the intrinsic value of a stock is equal to the present value of all the expected cash flows (dividends) from the stock.

The generic formula is as follows:

$V_{0}=\sum_{t=1}^{\infty }\left ( \frac{D_{t}}{\left ( 1+r_{e} \right )^{t}} \right )$

Where,

V0 is the present value of the stock D is the dividend received for each period t And re is the cost of equity

Considering a constant growth rate (g) of dividends for the life of the stock, the present value of the stock can be represented as follows.

$P_{0}=\frac{D_{1}}{r_{e}-g}$

This is called the Gordan Constant Growth formula. We can rewrite the formula to estimate the cost of equity.

$r_{e}=\frac{D_{1}}{P_{0}}+g$

So, an analyst will take the current stock price, estimate the dividends for the next year, and take the assumed growth rate to arrive at the cost of equity.

3. Bond Yield plus Risk Premium Approach

This approach assumes that the common equity is costlier than the debt, and estimates the cost of equity as a premium over the cost of debt.

We have already seen how to arrive at the before-tax cost of debt.

The cost of equity using this approach will be:

$r_{e}=r_{d}+ Risk\ Premium$

The risk premium represents the compensation for additional risk from equity. One of the ways to estimate this risk premium is to compare the historical spreads between the bond yields and stock yields. Generally, the risk premium is between 3 and 5%.