# 5. The Cost of Capital Part 2

Overview

To calculate the cost of equity for MarkerCo, we're going to use the Capital Asset Pricing Model (CAPM), a common but not uncontested technique among analysts.

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Summary

1. Lesson Goal (00:04)

The goal of this lesson is to use the Capital Asset Pricing Model to calculate the cost of equity.

2. Understanding Types of Risk (00:33)

The Capital Asset Pricing Model, or CAPM, is a model that can be used to calculate the cost of equity. CAPM assumes that any investment contains two types of risk: systematic risk and unsystematic risk. Systematic risk is risk associated with any investment, such as the risk of an economic recession. Unsystematic risk is risk that is specific to the investment in question, such as the effect of rising oil prices on an energy company.

3. Principles of CAPM (01:11)

CAPM calculates the cost of equity by considering three variables. First is the risk-free rate of return, representing the return required for accepting systematic risk. Second is the additional rate of return for investing in more volatile equity markets, representing the return required for unsystematic risk. Third is the volatility of the stock in question compared to the market, representing the return required for accepting uncertainty.

This produces the following formula for the cost of equity:

$$r_E = r_F + (r_M - r_F)\beta$$

In the formula above:

• $$r_E$$ is the cost of equity we want to calculate
• $$r_F$$ is the risk-free rate of return. This is typically the rate of return on 10-year government bonds
• $$r_M$$ is the expected return of the market as a whole
• $$\beta$$, or beta, represents the volatility of the stock in question compared to the market. If this value is greater than one, the stock is more volatile than the market, if it less than one, the stock is less volatile than the market.
4. Issues with CAPM (02:38)

There are some issues with CAPM. For example, the risk-free rate should theoretically be constant, but the rate on government bonds can change. The expected market return can also fluctuate significantly. Some analysts prefer to consider the Internal Rate of Return instead of using CAPM to calculate the cost of equity.

Transcript

In the previous lesson we examined the formula for the Weighted Average Cost of Capital, or WACC. We then focused on the hardest value in this formula to calculate, which is often the cost of equity. In this lesson, we're going to use the Capital Asset Pricing Model to calculate the cost of equity, and separately examine ways that analysts often get around using WACC by implenting IRR calculations when valuing a business. The Capital Asset Pricing Model is developed under the assumption that investments contain two types of risks. The first type of risk is systematic risk, which is risk that cannot be diversified away. This is risk from events such as recessions, interest rate hikes, etc that effect the whole market. The second type of risk is unsystematic risk, which is risk specific to individual investments, which can be diversified away. An example of unsystematic risk might be a rise in oil prices that affect a company like Exxon Mobil. To account for both types of risk, the CAPM Model adopts the following approach to calculating the cost of capital. It starts with the risk-free rate of return, which is assumed typically to be a 10-year government bond. This is essentially the systematic risk. It then calculates a premium to be paid by investing in the equity markets, and this additional premium is the expected return of the market, rM, minus the risk-free rate of capital, rF.

In step three, we apply a value called beta, to the market risk premium, and beta measures how the stock in question fluctuates compared to the market. If beta is less than one, this means that the stock price is less volatile than the market. And this would typically be the case for energy or water utilities, which are pretty stable businesses. If beta is greater than one, then the stock is more volatile than the market, and this would certainly be the case for a lot of technology or biotechnology stocks. Putting these steps together, we can develop a formula for the cost of equity, which is equal to the risk-free rate plus the market risk premium, which is the expected market return, minus the risk-free rate, multiplied by beta.

It's important to stress at this point that the Capital Asset Pricing Model is quite controversial. It's not used by every analyst, and it does have some obvious weaknesses. For example, the risk-free rate is based on long-term government bonds, which can of course change in price. What's more, the expected market return can also change very frequently. In the following chart, I showed the one year return on the S and P 500 since 2012, and as you can see, the one year return fluctuates dramatically from just under 30% to minus 7.5%.

As a consequence, many analysts have chosen to ignore the CAPM Model and focus instead on the Internal Rate of Return. As you may have seen in previous courses, the internal rate of return is an effective way of understanding the return on any money invested in either an asset or a company, and in the coming lessons I'll show you in our Excel model how to use both the Capital Asset Pricing Model and Internal Rate of Return when valuing a business.

Financial Modeling Essentials

Contents

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05:00

#### Exercise 4

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