Morgan Stanley’s New York office recently asked this question during their 1st round interview for an investment banking summer internship:
“How do you calculate cost of equity?”
What is Cost of Equity?
Cost of equity is a concept that often comes up during investment banking interviews because you need to know the cost of equity before you can calculate the Weighted Average Cost of Capital (WACC).
The WACC is a popular concept for interviewers to test you on, because it’s arguably the most important assumption you need to make when you’re doing a Discounted Cash Flow (DCF).
DCFs are used as one of the primary ways of figuring out how much a business is worth, so it’s one of the most commonly used analyses in investment banking and also something that is frequently asked in interviews.
Long story short, if you don’t understand cost of equity, chances are high that your interview is not going to end well. So let’s dive into it to help you ace your next interview.
Calculating the Cost of Equity
The cost of equity formula is given by:
Cost of Equity = the Risk Free Rate + Beta x the Market Risk Premium
Let’s explain each of the variables in this formula:
1) Cost of Equity
The Cost of Equity is the return that an investor expects to get when they invest in the equity of a business.
One of the laws of investing is “higher risk, higher rewards; lower risk, lower rewards.” This basically means that for any logical investor, you’re going to have to promise them higher returns if you want them to take on a riskier investment.
Conversely, if the investment is safer, the investor would also be willing to accept lower returns. (Because think about it – if you only make investments that are highly risky but have low returns, you will probably go broke.)
And on the flip side, if you only make investments that are really safe but have high returns…
well, that would be impossible because if such an investment exists, then every other investor would want in on it and it would drive up the price of that investment, which would lower its returns.
An example of a low-risk investment would be buying the stock of Apple or Microsoft. These are two of the largest companies in the world, and they have tens of billions of dollars of cash on their balance sheet. In other words, their business prints money, and they’re not going out of business anytime soon.
On the other hand, an example of a high-risk investment would be Tesla.
If you sold your Apple stock and put that money into Tesla instead, you do so knowing that there’s a good chance that the Tesla stock price is a lot more volatile and could go down a lot faster than Apple stock would.
But you would only do that because you know that Tesla could also go up a lot faster than Apple could if everything goes well. So the cost of equity for Tesla should be higher than the cost of equity of Apple.
Hold that thought actually – I will prove this to you mathematically at the end of this article.
2) Risk-free rate
The risk-free rate is the theoretical rate of return of an investment with zero risk.
The closest thing to a risk-free investment would be loaning your money to the government because the government should always be able to pay you back no matter what, especially if you live in a first-world country with a stable economy.
For the risk-free rate, investment bankers in the US typically use the 10-year treasury yield, which is currently 4% as of the time of this writing.
3) Beta
Beta is a measure of the volatility of a stock compared to the market as a whole, typically represented by the S&P500 index.
- If a stock has a Beta of 1, that means that it moves in lockstep with the stock market.
- If the stock market goes up by 1%, the stock will also go up by 1%.
- If the stock market drops by 1%, the stock will also drop by 1%.
Along the same lines, if a company has a Beta of 2, then its stock price will move twice as much as the stock market. An increase of 1% in the S&P500 would cause a 2% increase in the company’s stock price, and the same if the market were to drop. (As of the time of this article, Tesla’s Beta is around 1.9, making it the highest Beta or most volatile large-cap stock out there.)
Last but not least, if a company has a Beta of less than 1, then its stock price will be less volatile than the stock market. For example, Walmart currently has a Beta of around 0.5, which means every 1% fluctuation in the market will only create a 0.5% change in Walmart’s stock price.
In case you are wondering, there are companies that have negative Betas, which means its stock price moves in the opposite direction relative to the stock market. These are typically stocks that tend to do well during a recession – so, for example, gold or gold stocks could have a negative Beta because investors flock to gold for safety when the stock market is doing poorly.
4) Market Risk Premium
The market risk premium is just the expected return you would get if you were to invest in the stock market as a whole, which again is typically represented by the S&P500 index, minus the risk-free rate, which we’ve already covered.
In other words, how much more returns would you expect to get if you were to invest in the S&P500, instead of something safe like US Treasury bills?
- The long-term average return of the S&P500 is about 10%.
- And as I mentioned earlier, the 10-year Treasury yield is currently 4%.
So the market risk premium is 10% minus 4%, which is 6%.
Let’s apply the numbers
Now that we understand each of these components, it’s easy to see why the cost of equity formula is the way it is:
Re = Rf + B x (Rm – Rf)
Essentially, the expected return you would get from investing in a stock is equal to the market risk premium multiplied by the stock’s volatility, and that’s how much more you would expect to make versus if you were to just invest in something that’s risk-free, like US government bonds.
Remember what I said earlier about “high risk, high returns; low risk, low returns”? This is captured by the Beta of the company.
For example, a higher risk stock like Tesla will be more volatile, which is why it has a Beta of 1.9. Assuming a risk-free rate of 4% and a market risk premium of 6%, the cost of equity would be 4% + 1.9 x 6%, or 15.4%.
On the other hand, a lower risk stock like Apple will be less volatile, which is reflected in its current Beta of 1.1.
That gives it a cost of equity of 4% + 1.1 x 6%, which is just 10.6%.
This means that investors expect to be compensated with returns that are 45% higher when they invest in Tesla’s stock versus Apple’s stock, due to the higher risk they’re taking on.
At this point, you should have a really good understanding of how cost of equity works. The next time you get asked this question in an interview, hopefully, you’ll ace it.
If you would like more hands-on and personalized coaching with your investment banking or private equity interviews from our team of coaches that includes the former global heads of recruiting at top investment banks like Goldman Sachs, Credit Suisse, UBS, and Lehman Brothers, then please don’t hesitate to reach out to our team.
And as always – remember – Nothing worthwhile comes easy, and nothing is more important than your future.
Keep Grinding!
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