M&A Fundamentals – Using the Capital Asset Pricing Model to Calculate Cost of Equity
The cost of equity (“Ke”) is a key component of the working average cost of capital (“WACC”) formula that M&A professionals use to calculate a discount rate when using a DCF present value model to prepare a valuation of an M&A target.
We explain the WACC calculation in another article from this M&A Fundamentals series: M&A Fundaments -Working Average Cost of Capital (WACC).
Most M&A professionals use the Capital Asset Pricing Model (CAPM) to calculate the cost of equity capital either for their own company, or in some circumstances for the M&A target. A separate cost of equity for the M&A target will be used when it operates in a market or region where the risk profile mandates a higher cost of capital.
We dig deeper into the circumstances where a cost of equity specific to the M&A target might be needed in our Advanced Business Valuation training course.
What is the Capital Asset Pricing Model?
The Capital Asset Pricing Model is widely used by financial analysts, investors, and M&A professionals to calculate the cost of equity capital. The concept was developed in the 1970s by Nobel laureate economist William Sharpe.
The starting point for the model is the insight that any investment in traded equities comes with two inherent types of risk:
Systematic risk is the risk to the whole market (or system) from external factors such as elections, wars, interest changes or the business cycle. As the total equity invested in the stock market is already diversified across all the different companies listed on the exchange, risk is already diluted to the maximum extent possible if investing in equities.
Unsystematic risk is the risk of investing in an individual stock listed on the stock exchange. The risk that comes from poor management, technological change, a risky financial structure, or a whole host of other factors. Just the kind of things an M&A professional would look for in due diligence. Changes in the share price of an individual company caused by these factors will not necessarily move in tandem with the overall market system. This is sometimes called the “specific risk” of the company.
If the unsystematic risk of a company is high investors, and after all M&A professionals are investing on behalf of the shareholders, will require a higher return on equity capital to invest in its shares.
What is the Formula for the Capital Asset Pricing Model?
The formula for calculating the cost of equity using CAPM is set out below.
Diagram 1: The CAPM Formula
Ke = Cost of equity
rf = Risk free rate
Β = The specific risk of the company.
rm = The overall stock market risk
rm-rf = The systematic risk of the stock market
In plain English the cost of equity (Ke) is the return on a risk-free investment (rf), plus the overall risk of investing in shares on a stock exchange (rm-rf) multiplied by the specific risk factor of the company (B).
Elements of the CAPM Formula
Cost of Equity (Ke)
The cost of equity Is the overall return investors require to invest in the company.
Risk Free Rate (rf)
The risk free Is the return an investor could achieve by investing in a risk-free security. For the purposes of the CAPM this is the redemption yield on a government bond with a maturity oof at least 15 years.
Overall Market Risk (rm)
The overall market risk is taken to be the annual returns on equity for a stock market over an extended period. In London, New York, and other long-established exchanges this analysis may be extended over 70 years or more.
Beta measure the volatility of an individual company’s stock in comparison to the overall volatility of the stock market on which it is traded. In simple It measures how much the price of share moves up and down compared with how much the entire stock market moves up and down. If the price of a share moves exactly in line with the market, then the beta is 1. A company with a share less volatile than the market would have a beta less than 1, and a company with a share more volatile than the market greater than 1.
Beta is calculated for every share on a stock exchange by a statistical analysis of individual, daily share price changes in comparison with the market’s daily movement over a defined period – usually a few weeks. M&A professionals can find the latest beta for an M&A target on the website for the stock exchange on which the company is traded.
How Would an M&A Professional Use the CAPM?
The chart below shows the steps an M&A professional would follow when calculating the cost of equity to use in the WACC calculation for an M&A target.
Diagram 2: CAPM Process Flowchart
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