# Chapter 15 : Cost of Equity & CAPM

Markets can remain irrational longer than you can remain solvent.

John Maynard Keynes

### An explanation of Capital Asset Pricing Model (CAPM)

Everything revolves around the question of values. The most important driver of values is the returns you expect in the stock that determines value.

Cost of Equity is an expected rate of return required by the investors to invest in the company's shares. The equity investors require:

• a Risk-Free Rate, plus

The Capital Asset Pricing Model (CAPM) explains the relationship between the systematic risk and the expected return on assets, particularly stocks. This model is used to compute the cost of equity and helps you value risky securities and evaluate expected returns on assets.

The formula for calculating the expected return of an asset given its risk is as follows:

ra = rf + [ βa x ( rm - rf ) ]

Where,
rf = Risk-Free Rate
βa = Beta of the security
rm = Expected Market Return

Simply,
Cost of Equity = Risk-Free Rate + Equity Risk Premium, where
Risk-Free Rate = Real Interest Rate + Expected Inflation Rate
Equity Risk Premium = Beta x (Expected Returns in the Market - Risk-Free Rate)

The Expected Returns in the Market represents the additional return expected by investors to invest in the equity market versus risk-free government bonds.

The Beta coefficient is the measure of volatility or systematic risk of the stock in comparison to the market as a whole. The individual stocks tend to be riskier or less risky than the market and the Beta measures this risk. Beta is easily obtainable from various financial online sites.

Beta is generally historic and does not reflect the changes in the business or the financial structuring that the company has undergone recently. One must always review the Beta with the following factors, such as

• Nature of its products and services (FMCG companies tend to have lower Beta), cyclical companies tend to have higher Beta
• Proportion of fixed to variable costs
• A higher operating profit margin for a company should relatively have a lower Beta
• A company with higher debt will have a higher Beta.

The expected return on equity varies across investor types. For example, venture capitalists would demand higher returns than stock market investors. Returns also depend on the lifecycle stage of a company.

In case if you find computing Beta and cost of equity under the Capital Asset Pricing Model (CAPM) cumbersome, then you may use a hurdle rate as cost of equity or expected market returns as cost of equity, or any other reference as the cost of equity.

### Example for Computing Cost of Equity of Black Bay Pizza

Continuing with the example of Black Bay Pizza, we now compute the Cost of Equity for Black Bay Pizza in Table 10,based on the following assumptions:

Assumptions

 Risk-Free Rate 6% Expected Inflation Rate 5% Expected Returns Over Inflation 7% Expected Market Returns 12% Beta 0.75%

ra = rf + [ βa x ( rm - rf ) ]

Where,
rf = Risk-Free Rate
βa = Beta of the security
rm = Expected Market Return

Thus, the computation of Cost of Equity is computed in Table 10 below:

Table 10 - Illustrative example of Computing Cost of Equity

 Risk-Free Rate + Beta x (Expected Market Returns - Risk-Free Rate) 6% + 0.75 x (12% - 6%) = 10.5%

Expected Market Returns (12%) in the above Example is inflation plus expected returns over inflation i.e. 5% + 7% (more on expected market returns in chapter 17).