Slightly wonkish blog post on equity returns ahead....

When valuing a privately held business, it is important to properly calculate the business’s total cost of capital in order to correctly capitalize or discount its cashflow. The basic premise of business valuation is that a business is worth the present value of its future cashflow, therefore discounting the future cashflow of the business at the appropriate discount rate is crucial.

What is the cost of capital for a business?

The weighted average cost of capital is the discount rate most often used to discount the future cashflow of a business. It reflects the time value of money and risk associated with the business’s future stream of unlevered cashflow (cashflow that accrues to equity holders and debt holders).

A business's capital structure is composed of its debt and its equity. Determining the company's total cost of capital basically entails taking its cost of debt (which is usually an interest rate) and its cost of equity (to be discussed below) and then taking the weighted average of the two based on the company's optimal capital structure (this is called the weighted average cost of capital, the WACC). Without getting too wonky (too late), it's very important to properly calculate this because the WACC is used to present value or capitalize the future cashlfows of the business, which is the key step in a business valuation.
So.... if your WACC is wrong then your business valuation conclusion can't be right. This post will look at the equity risk premium, which is a component of the total cost of equity which, in turn, is used to calculate the total cost of capital for a business.
Let's back up one step - what is the cost of equity??

The cost of equity is simply the return that equity investors expect to make on their investment in a business.
The higher the risk of the business cashflow to equity holders, the higher the cost of equity. Again, the cost of equity for a business plus its cost of debt together make up the business’ total capital cost, its WACC.

Ok.... so how is the cost of equity calculated?

There are a few ways a business valuator can calculate the cost of equity but some of the main ways are by using the:
• capital asset pricing model
• the build-up method
• arbitrage pricing theory
For this blog post we will stick to referring to the build-up method. It is easier to explain and can be more intuitive. The idea behind the build-up method is that the equity return required for a business is “built up” by layering on incremental elements of the cost of equity, as the following graphic illustrates:

As you can see, on the cost of equity side, we start off with the risk free rate (“RFR”) which is the return generated by investors in the market who invest in a risk-free investment (think government bonds), then we layer on the Equity Risk Premium (“ERP”), which is the incremental return that would be required over and above the risk free rate by investing in equities as a class (to be discussed below). Next is the industry risk adjustment, which is the incremental return for investing in a specific industry. The size premium is the incremental risk premium associated with the size of the business and company specific adjustment refers to the risk premium required to compensate equity investors for the incremental risk specific to the business.

What is the equity risk premium?

As stated above, the ERP is the return, over and above the risk free rate, that investors would need to justify their investment in equities as a class.
According to Modern Portfolio Theory, if you were theoretically able to invest in an investment that was comprised of the shares of all of the equity investments in the world, you would be able to eliminate the unsystematic risk, which is risk that is specific to the particular company. Basically the theory states that you can eliminate “specific risk” or diversifiable risk. The reason you can eliminate this risk is through diversification in a portfolio. Therefore if you are able to eliminate the specific risk through diversification then what you’d be left with is the return you’d require for investing in equities as a class.
One of the obvious problems with Modern Portfolio Theory (and it has its critics) is that you’re not able to invest in all of the equities in the world. To get around this constraint, finance professionals use stock indices as a proxy to represent a broad cross section of equity investments. In Canada we have the S&P TSX composite index which represents a broad cross section of equities in the Canadian market. This index measures the price movements of stocks as an index. The deficiency of this particular index is that it does NOT include the return from dividends. Therefore, many finance professionals, and this author, prefer to look to the S&P TSX composite total return index, which does include the impact of dividends on the index’s return.

Therefore…. if we know what the risk free rate might be (say, a government bond yield) then the difference between the expected equity return and the risk free rate is the equity risk premium, which is the premium required by equity investors for investing in equities as a class.

Equity Risk Premium = (return required to invest in equities) LESS (the risk free rate)
Basically, the equity risk premium is an estimate of how much of a return investors in equities require over and above the risk free rate to compensate them for investing in equities as a class. The equity risk premium is never really known with certainty because we don’t know what the expected return of equity is.  After all, in business valuation we are concerned about the future and less so about the past so the expected return is a tough one to calculate with precision. That said, the equity risk premium can be modeled a few ways but does require some assumptions.
Although there are many ways to estimate the equity risk premium, we will examine just a few intuitive ways here:
One approach that many well respected financial publications use is to survey leading economists on what they think the equity risk premium is. This is obviously a derivative approach since each economist would use their own models and inputs and bring their own biases and experiences to the table.  The published amount would be the average of these.

Look to historic data

The obvious benefit of using historic data is that it is known. The chart below shows the S&P TSX composite index total return index (which includes the impact of dividends on the return) and the 10 year government of Canada bond yield as at the end of each year for the last 20 years. The spread might be seen as a good proxy of the equity risk premium since an argument can be made that the equity risk premium will revert to its historic average over the long run. Using the geometric mean (which is the cumulative average) for the past 20 years of data in the table below suggests an equity risk premium of 3.87%.

There are criticisms of using historic data which are beyond the scope of this post. However many economists are proponents of using historic geometric means as a way of estimating the equity risk premium.

Dividend Discount Model (aka the Gordon Growth Model – named after the famous Canadian economist)

Another popular approach is to use the Gordon Growth Model to estimate the equity risk premium. The Gordon Growth Model (GGM) is used to calculate the value of an equity using its future dividends. The GGM formula can also be applied to a stock index to infer what the equity risk premium is.

The Gordon Growth Model is:

Value of an Equity=(future dividend) / (equity return – growth rate)

Rearranging the above formula and applying it to a stock index, we get the following:

Equity Return = Dividend Yield of index PLUS long term earnings growth rate

Subtracting the risk free rate would give us the equity risk premium:

Equity Risk Premium = Dividend Yield of the index PLUS long term earnings growth rate LESS risk free rate

The approach is mathematically sound but is open to criticism from analysts who would suggest that the future dividend yield cannot be known with certainty and that the long term earnings growth rate (often taken from macroeconomic data) is also a great unknown.

Use established published sources

Ibbotson associates created a niche by publishing stock and bond returns and premiums that the average person could not do. Over time their estimations have become generally well regarded. However, with readily available online data, powerful spreadsheets and statistical software tools, the cloak has been lifted and the calculation of equity risk premiums is no longer considered proprietary and above scrutiny. Ibbotson is a well respected organization but to be clear, they do NOT possess infallible insight into what the equity risk premium is.

The above are but a few of the approaches to calculating the equity risk premium. Other approaches include demand side approaches (market implied equity risk premium), many supply side approaches and other and can get quite technical. The reality is that the more complicated an approach is to calculate the equity risk premium does NOT mean that it is more sound. Proof of this is the disagreement among leading economists by several percentage points on what the equity risk premium is.
Whatever approach you use to value a business you will need to know what the equity risk premium is. Understanding the approach that was used in calculating it is important to having a defendable business value conclusion.