# Cost of Equity Formula Using DDM, CAPM, and Private Companies By | June 23, 2021

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From a company’s perspective, there are two methods for raising capital: debt and equity. Debt is usually less expensive than equity because the debtholder’s returns are fixed and finite. You can also deduct interest expenses from your tax burden, which is an advantage of using debt financing.

But there are many reasons a company would want to raise equity capital and therefore must understand their cost of equity. Investors will also likely conduct a similar analysis for different reasons, but it’s good to align cost of equity expectations.

Cost of equity means different things for different stakeholders. We will cover these differences shortly, but first, let’s define what this metric is.

## What Is the Cost of Equity?

Cost of equity is the return an investor expects to receive to compensate for the amount of risk inherent in the investment. From the company’s perspective, this is viewed as a cost because if the investment does not produce returns, the investor will likely sell, driving the value of the underlying investment down.

From the investor’s perspective, “cost of equity” is read, “expected return.” From the company’s perspective, it’s read, “expected growth.”

## How to Calculate Cost of Equity

There are two common ways to calculate the cost of equity, depending on how the underlying company returns on investment. The first, is the dividend capitalization model, which intuitively takes dividend yield into account when calculating cost of equity. The second, the capital asset pricing model or CAPM.

### Dividend Discount Model

The DDM formula for calculating cost of equity is the annual dividend per share divided by the current share price plus the dividend growth rate.

As you can probably guess, this method of calculating the cost of equity only works for investments that pay dividends.

Let’s cover an example of the dividend capitalization model. We will calculate the cost of equity before deciding whether to invest in Coca-Cola (KO), a company that has paid dividends since 1893.

Today, the annual dividend is \$1.68 per share and the stock currently trades around \$55. The dividend growth rate has been 3.60% per year for the last three years. Using this information, we can calculate the cost of equity:

Cost of Equity = \$1.68/\$55 + 3.60%

= 6.65%

This means that as an investor, you expect to receive an annual return of 6.65% on your investment.

### Capital Asset Pricing Model (CAPM)

The capital asset pricing model, or CAPM, is a method for evaluating the cost of equity for an investment that does not pay dividends. Instead, the CAPM formula considers the risk free rate, the beta, and the market return, otherwise known as the equity risk premium.

The risk free rate of return is what investors expect to receive when making an investment in something with essentially zero risk. Typically, investors use the yield of US treasury bonds as a proxy for the risk free rate because there is almost no risk of default.

Beta is a measure of correlation between a position and broader market moves. Beta can be positive or negative. If a position has a beta of one, it is perfectly correlated with the broader market and will tend to closely follow the price action. If beta is a negative one, it is perfectly inversely correlated with the market and prices will move in the exact opposite direction. Beta can be zero to indicate no correlation, or greater than one to express heightened volatility.

The market rate of return is the premium investors expect to receive above the risk free rate for assuming additional risk, hence its alias — equity risk premium.

### CAPM Example

In order to showcase the CAPM formula, we will use a company that does not pay a dividend, and has long defended their rationale for reinvesting retained earnings: Warren Buffett’s Berkshire Hathaway.

The current 10-year US treasury bond has a yield of 1.497%. The Beta for Berkshire Hathaway (BRK-B) is 0.90, in other words, very correlated with the stock market. The average market return over the last decade is 10%. Using this information:

Cost of Equity = 1.497% + 0.90(10% – 1.497%)

= 9.15%

Although the market has generally returned 10% on average annually, it’s common for investors to use a more conservative market return rate. Many investors will use NYU professor Aswath Damodaran’s calculation for implied equity risk premium, which is currently projected to be 4.24% in 2021. This would significantly impact our cost of equity calculation for Berkshire Hathaway.

Cost of Equity = 1.497% + 0.90(4.24%)

= 5.20%

This example highlights some of the shortcomings of using the CAPM model but can still be a good estimation of expected return on investment.

## How to Calculate the Beta of a Private Company

When analyzing the risk and potential return of a private company, we lack the availability of a beta in private markets. Similar to the comparable company analysis we discuss in our piece about calculating business valuations, in order to calculate beta, you’ll want to find an average of beta’s for complementary public companies.

For example, let’s say we wanted to calculate the cost of equity for Sky Systemz. They are a cloud POS and payment processing company competing with the likes of Square, Shopify, and LightSpeed.

Step 1

With the help of a tool like Yahoo! Finance, we can easily find the metrics for these publicly traded companies and calculate the average beta and D/E ratio:

Since Square’s D/E ratio is significantly higher than the others, we can discount that as an outlier and average the other two, to get a more realistic average of 7.33.

Step 2

The unlevered beta is calculated using the average beta and average debt-to-equity ratio from our analysis above, as well as the federal corporate tax rate of 21%.

2.29 / 1 + (1 – 0.21) * 7.33

2.29 / 6.79 = 0.33

Step 3

Using the unlevered beta calculated in step two, we can get to a levered beta:

0.33 * [1 + (1 – 0.21) * 7.33]

0.33 * 6.79 = 2.24

## Private Company Cost of Equity Example

Using our levered beta, we can now pull in our earlier variables to calculate the cost of equity for our private company example:

Aggressive Cost of Equity Calculation

Cost of Equity = 1.497% + 2.24(10% – 1.497%) = 20.54%

Conservative Cost of Equity Calculation

Cost of Equity = 1.497% + 2.24(4.24%) = 10.70%

This means that as investors in Sky Systemz, we would expect between a 10.70% and 20.54% return on our equity investment.

## Why Investors Should Calculate Cost of Equity

Cost of equity is an important metric that both businesses and their investors should understand and consider how the calculations reflect actual performance.

As investors, we must have conviction in our investments and not sell when the going gets tough, but we also must understand when ROI is simply not in the cards.

It’s obviously best to come to these conclusions before investing in the company, which is why we advocate you calculate a baseline expected return using the cost of equity formula detailed above as you do your diligence before investing in private companies