Cost of Common Stock Using the Capital Asset Pricing Model The investor’s required rate of return is compensation for both the time

Cost of Common Stock Using the Capital Asset Pricing Model The investor’s required rate of return is compensation for both the time

value of money and risk. To figure out how much compensation there should be for risk, we first have to understand what risk we are talking about.

As we saw in Chapter 10, the capital asset pricing model (CAPM) assumes an investor holds a diversified portfolio—a collection of invest- ments whose returns do not move in the same direction nor at the same time nor by the same amount. The result is that the only risk left in the portfolio as a whole is the risk related to movements in the market as a whole—market risk.

If we assume all shareholders’ hold diversified portfolios, the risk that is relevant in valuing a particular investment is the market risk of that investment. The greater the market risk, the greater the compensa- tion—meaning a higher yield—for bearing this risk. And the greater the yield, the lower the present value of the asset because expected future cash flows are discounted at a higher rate that reflects the higher risk.

The cost of common stock is the sum of the investor’s compensation for the time value of money and the investor’s compensation for the market risk of the stock:

Cost of common stock = Compensation for the time value of money

+ Compensation for market risk Let’s represent the compensation for the time value of money as the

expected risk-free rate of interest, r f . The risk-free rate of interest is the rate that is earned on an asset that has no risk. If a particular common

The Cost of Capital

stock has market risk that is the same as the risk of the market as a whole, then the compensation for that stock’s market risk is the market risk premium. The market’s risk premium is the difference between the

expected return on the market, r m , and the expected risk-free rate, r f :

Market risk premium = r m – r f

If the expected risk-free rate is 3% and the expected return on the mar- ket is 11%, the market risk premium is 8%.

But if a particular common stock has market risk that is different from the risk of the market as a whole, we need to adjust that stock’s market risk premium to reflect its different risk. Suppose the market risk premium is 8%. If a stock’s market risk is twice the whole market’s risk, the stock’s premium for its market risk is 2 × 8%, or 16%. If a stock’s market risk is half the risk of the market as a whole, the stock’s pre- mium for market risk is 0.5 × 8%, or 4%. What we are doing here is fine tuning the compensation investors will need to accept that stock’s market risk. We fine tune by starting with our benchmark of the risk of the market as a whole and adjust it to reflect the market’s premium for the stock’s relative market risk to come up with the stock’s premium.

Let β represent the adjustment factor. Then the compensation for market risk is:

Compensation for market risk = βr ( m – r f ) Because we know the compensation for the time value of money, r f ,

and now we know the compensation for market risk, we see that the

cost of common stock, r e , is:

(11-6) ■ The term ( r m – r f ) represents the risk premium required by investors for

r e = r f + βr ( m – r f )

bearing the risk of owning the market portfolio. ■ The multiplier, β, fine tunes this market risk premium to compensate for the market portfolio associated with the individual firm. β, com- monly referred to as beta, is a measure of the sensitivity of the returns on a particular security (or group of securities) to changes in the returns on the market—a measure of market risk.

A common stock having a β greater than 1.0 has more risk than the average security in the market. A common stock having a β less than 1.0 has less risk than the average security in the market.

THE FUNDAMENTALS OF VALUATION

Suppose a firm’s stock has a β of 2.0. This means its market risk is twice the risk of the average security in the market. If the expected risk- free rate of interest is 6% and the expected return on the market is

10%, the cost of common stock, r e , is:

r e = 0.06 + 2.0(0.10 – 0.06) = 0.14 or 14% In this example, the market risk premium is (10% – 6%) = 4%. A

market risk premium of 4% means that if you own a portfolio with the same risk as the market as a whole (that is, with a beta of 1.0), you would expect to receive a 10% return comprising: 6% to compensate you for the price of time and 4% to compensate you for the price of market risk. If you invest in a security with a β of 2.0, you would expect

a return of 14% comprising: 6% to compensate you for the price of time and 2.0 times 4% = 8% to compensate you for the price of that security’s particular risk.

The CAPM is based on two ideas that make sense: Investors are risk averse and they hold diversified portfolios. But the CAPM is not with- out its drawbacks. First, the estimates rely heavily on historical values— returns on the stock and returns on the market. These historical values may not be representative of the future, which is what we are trying to gauge. Also, the sensitivity of a firm’s stock returns may change over time; for example, when the firm changes its capital structure. Second, if the firm’s stock is not publicly-traded, there are no data sources even for historical values.