To calculate the cost of equity using the CAPM, you need the beta of the company.
The problem is that beta is a volatility measure based on the stock market. What if the company you’re evaluating isn’t publicly traded?
The answer is you “relever” the unlevered beta of a public benchmark similar to the company you’re evaluating, and plug that into the CAPM formula.
That’s the gist of it. Want a more comprehensive answer? Keep reading.
If you’re confused about how to calculate the cost of equity for unlisted companies, then this is for you.
By the end of this article, you’ll know the best way to estimate the required rate of return by shareholders of private businesses (according to the top business schools and private equity firms).
Ready? Let’s dive in:
What Is the Cost of Equity
The cost of equity is the required rate of return by shareholders in exchange for their investment in the company. The higher the risk associated with the operations of the business, the higher the cost of equity financing.
The most common way to calculate it is through the Capital Asset Pricing Model (CAPM).
The CAPM says the cost of equity of a company is the risk free rate plus a risk premium:
Where:
- rf (risk-free rate) is the theoretical rate of return of an investment with zero risk. In real life, you use the rate of return of government bonds of a country with a credit rating of AAA (as these carry a very small amount of risk). It includes the country risk premium, which is the difference between the risk-free rate and rate of return of government bonds of the country the company you’re evaluating operates in. What does this mean in practical terms? You can simply use the bonds of the firm’s country as the risk-free rate.
- (Erm – rf) is the market risk premium. This is the additional return an equity investor expects to receive for holding a portfolio of uncertain assets instead of risk-free assets. Erm is the expected rate of return for the market as a whole.
- β (Beta) is the volatility of the stock compared to the market as a whole. It is the covariance between the returns of the stock and the overall market, divided by the variance of the returns of the overall market. This means it only exists for publicly traded companies—precisely the problem we’re addressing in this post.
You can compare the cost of equity to the return on equity to determine if a company is creating value for its shareholders.
Additionally, the cost of equity is generally used in conjunction with the cost of debt to get the overall cost of capital (WACC, or Weighted Average Cost of Capital) and estimate the fair value of a company using the Discounted Cash Flow model (DCF valuation).
See also: CAPM vs WACC: Key Differences and How to Use Them
What Is Beta: The Obstacle
Beta is a measure of a stock’s volatility compared to the overall market. Analysts use it as a way of evaluating the risk of investing in a security.
By definition, the market has a beta of 1. This means stocks with betas above 1 are more volatile than their index, while stocks with lower betas are less volatile.
As you can see, beta depends on the data observed in the stock’s price movements relative to the stock market.
But what if the company you’re evaluating doesn’t trade publicly? How do you compute the cost of equity for a company that is not listed in an exchange?
First, you need to know about the different types of beta:
The levered beta (or equity beta) is the observed beta of the shares of the company. It considers both equity and debt financing to calculate the stock’s risk.
The formula for levered beta using the other classifications of beta is as follows:
Where:
- βU is the unlevered beta of the company (also called asset beta).
- βD is the beta of debt.
- D/E is the debt-to-equity ratio, which measures how much debt the firm owes in relation to its equity capital.
- t is the corporate tax rate. It is used to account for the tax savings of leverage.
The unlevered beta (βU) is a theoretical concept. It is the beta of the company if it had zero debt and was funded by equity only. To calculate the unlevered beta, use the following formula:
It is common to assume the beta of debt is zero. In this case, you can calculate the unlevered beta like this:
However, ignoring the beta of debt is only appropriate for established companies (with high market capitalization) such as Apple for example. Or good companies from AAA-rated countries.
What is the beta of debt?
The beta of debt is the risk associated with the company’s debt obligations. It measures the sensitivity of the returns on debt to changes in market returns.
It is usually a low number. Why? Because debt has priority claims in the case of bankruptcy, which means it is less risky than equity.
You calculate it by using the CAPM formula and equating it to the company’s cost of debt. Then, you extrapolate the implied beta of debt.
How to Calculate Cost of Equity for Private Companies
The cost of equity depends on the beta. And the beta depends on the returns of the stock you’re evaluating.
The share price of private companies is not observable however, which makes it difficult to calculate the beta and assess the risk of investing in these companies. This is our obstacle.
Fortunately, there’s a 5-step process you can follow to estimate the cost of equity of an unlisted company:
#1) Identify a Benchmark
The first step is to choose a benchmark.
A benchmark is something comparable to the company you’re analyzing. You have 3 options:
- A single listed public company with similar business operations, market position, size, enterprise value, capital structure, risks, and geographic location to your target.
- The industry average of listed companies in the same industry as your target company. This is more appropriate for industries where all companies are sensitive to the same market conditions.
- A select peer-group average. Similar to using the industry average, except you handpick a group of 3-7 companies that are the most similar to the one you’re evaluating. This approach is better when the unlisted company operates in a highly specialized market or has unique characteristics that aren’t common in the broader industry.
#2) Compute the Unlevered Beta of the Benchmark
Using the data of your chosen benchmark compute its unlevered beta.
If your benchmark is a single comparable company, you can compute its beta with the covariance and variance to get how much the stock deviates from the market.
It’s easy to find the beta of listed firms on financial websites such as Yahoo Finance, SeekingAlpha, and Finviz.
You’ll want to get the number from the site and then apply the formula to get the unlevered beta.
Similarly, if you choose a select group of peers as your benchmark, you can get the levered beta from these websites.
Then, you’ll want to “unlever” them individually (according to each company’s capital structure and effective tax rate) and calculate the average.
If your benchmark is the whole industry, it’s better to use Professor Damodaran‘s database. He’s an authority when it comes to information for valuation purposes.
You can find the average levered and unlevered beta by industry by going to the Homepage > Data > Current Data > Discount Rate Estimation.
Now, what do you do with this number?
#3) Assume the Unlevered Beta of the Company Equals the Benchmark
This is the key step. The main assumption.
We’re saying the unlevered beta of the chosen benchmark is the same as the unlevered beta of the target company.
But as long as the reasoning behind choosing your benchmark is on point, it is a reasonable and valid assumption.
#4) Compute the Levered Beta Using Data from the Company
The 4th step is to calculate the target company’s levered beta.
You may be wondering:
Why do I have to do this when I could simply use the levered beta of the benchmark directly?
Well, it’s because the levered beta reflects financial risk (different levels of leverage) and business risk. It changes in positive correlation with the amount of debt a company has.
Meanwhile, the unlevered beta only incorporates business risk. It strips off the debt component to isolate the risk attributed solely to company assets.
What you’re doing is isolating the risk of the operations from the financial risk from the capital structure (how the company funds its assets).
Companies in the same industry have similar operations—hence, similar business risk. But they don’t necessarily have the same ratio of equity and debt financing—hence, financial risk.
By “releveraging” the benchmark’s beta using the data of the company you’re evaluating, you’re incorporating its specific financial risk from its unique capital structure.
#5) Incorporate the Beta in the CAPM Formula
The last step is to simply use the final levered beta in the CAPM formula, giving you the cost of equity you can use in your financial modelling to estimate the fair market value of a private company.
Keep in mind the cost of equity for a private company is never an exact calculation and requires making assumptions.
Let’s go through a quick example to put these concepts in motion:
Calculating Cost of Equity for Private Company Valuation Example
Consider a construction firm based in Germany operating in Europe. It has a debt-to-equity ratio of 80% and an effective tax rate of 15%. It’s not listed on an exchange.
How do you estimate the required rate of return by the shareholders of this company?
The 10-year German government bonds have a yield of around 2%. This is the risk-free rate.
Damodaran also has information on the equity risk premium for each country. In the case of Germany, investors expect around 6% additional returns for putting their money in the market as opposed to government bonds (which are safer).
We can use the industry average as the benchmark. Since the company has operations all throughout Europe, you can go to Damodaran and see that the Engineering/Construction industry in this region has an average unlevered beta of 0.64.
Next, you relever that beta. This time using data from the company itself.
But before you do that, you need to calculate the beta of debt:
Now, the levered beta:
There you have it. We’ll assume a beta of 0.85 to calculate the cost of equity.
The final step is to plug everything into the CAPM formula:
In conclusion, the company has a cost of equity of 7.1%.
Hope this helps. Questions? Feedback? Leave them in the comments below.
