# Level 1 CFA® Exam:

Cost of Common Equity

From this lesson you will learn how to calculate the cost of common equity. Determining this kind of cost is usually more difficult than calculating the cost of debt or the cost of preferred stock.

The cost of common equity is the rate of return earned by common shareholders. There are several methods available for estimating the cost of common equity, e.g.:

- the capital asset pricing model (CAPM),
- the bond yield plus risk premium approach, and
- the dividend discount model (DDM).

In this lesson we will discuss only the first two methods, because using a dividend discount model to compute the cost of common equity is no longer required in level 1 exam. However you’ll read about dividend discount models including the Gordon growth model in the Equity Investments topic.

The capital asset pricing model (CAPM) is based on a principle which states that the expected rate of return is equal to the risk-free rate and a premium for bearing the stock's market risk:

\(E(R_{i})=R_{f}+\beta_{i}\times{[E(R_{m})-R_{f}]}\)

- \(E(R_{i})\) - expected return on a stock
- \(R_{f}\) - risk-free interest rate
- \(\beta_{i}\) - return sensitivity of stock "i" to changes in the market return
- \(E(R_{m})\) - expected return on the market
- \([E(R_{m})-R_{f}]\) - expected market risk premium

In other words, the expected rate of return equals the risk free rate added to beta times the expected return on the market minus the risk free rate.

Risk-free assets are assets that don’t involve default risk. A risk-free rate is determined using risk-free government debt instruments. Notice that if we consider a project that lasts for example 10 years, we have to use the rate of return on instruments with a ten-year maturity.

There is also the multifactor model. In the CAPM model, the expected rate of return on a security depends only on the expected rate of return on the market, and in the multifactor model it depends on more variables such as inflation rates, commodity prices, etc. The general formula for multifactor model looks as follows:

\(E(R) = R_{f}+\beta_{1}\times p_{1}\ +\beta_{2}\times p_{2}+\ldots\ +\beta_{j}\times p_{j}\)

- \(E(R)\) - expected return on a stock
- \(R_{f}\) - risk-free rate of interest
- \(\beta_{j}\) - stock's sensitivity to changes in the j-th factor
- \(p_{j}\) - factor risk premium (= expected risk premium for the j-th factor)

What is important in the CAPM model is the expected market risk premium that is an excess return over the risk free rate, required by investors in exchange for accepting the risk.

We can distinguish among three main methods of determining the expected market risk premium:

- the survey approach,
- the historical equity risk premium approach, and
- the dividend discount model.

(Currently, only the first 2 are discussed in the CFA level 1 curriculum).

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The second method for estimating the cost of common equity is the bond yield plus risk premium approach.

This approach is based on the assumption that the more risky the cash flows, the higher the cost of capital. In this approach you sum the cost of debt before tax and the risk premium resulting from the increased risk associated with the investment in the common equity of a company in relation to investment in bonds issued by the company:

\(r_{e}=r_{d} + p\)

- \(r_{e}\) - cost of common equity
- \(r_{d}\) - before-tax cost of debt
- \(p\) - risk premium

The risk premium compensates for the additional risk, which is present in the case of equity but does not occur in the case of bonds issued by the company. In developed markets, it is usually from 3 to 5%.

- The cost of common equity is the rate of return earned by common shareholders.
- Two methods available for estimating the cost of common equity are the capital asset pricing model (CAPM) and the bond yield plus risk premium approach.
- The capital asset pricing model (CAPM) is based on a principle which states that the expected rate of return is equal to the risk-free rate and a premium for bearing the stock's market risk.
- The bond yield plus risk premium approach is based on the assumption that the more risky the cash flows, the higher the cost of capital.