This post is the final part of our Calculating the cost of capital series

**Is CAPM an appropriate tool for measuring the Cost of Equity, and are there any alternatives I can learn about to boost my Excel DCF Financial Modeling skills to prepare for Wall st?**

CAPM is by far the most common tool used in practice to assess the Cost of Equity when valuing a company. But, CAPM has its flaws too, which all Investment Bankers, Equity Analysts and the like need to be aware of. When we are valuing a company using a DCF model, how can CAPM fall short in properly assessing the Cost of Equity? Lets explore this:

CAPM utilises β, and the equation to calculate β (beta) is:

Without getting deep into mathematical definitions, the Variance of the market is a measure of how volatile or varied the distributions of returns from the market are, and the Covariance between the market and the stock in question is a measure of how closely the returns from the stock move in line with the returns from the market. The results of this equation are:

- If a stock moves in a particular direction when the market moves in that direction, Beta will be greater than 1 if the stock returns are more volatile than the market returns, and will be between 0 and 1 if the stock returns are less volatile than the market returns;
- If a stock return moves in a particular direction when the market return moves in the opposite direction, Beta will be less than -1 (greater in magnitude) if the return moves are more volatile than the market return moves, and will be between 0 and -1 if the stock return moves are less volatile than the market return moves;

So, what is the problem with Beta?

Firstly, a stock has many different Betas so an Analyst building a DCF model needs to decide which Beta to use. Beta is calculated by collecting a set of returns generated by the stock and the market, but these sets can be based on short time frames such as 30 days, or longer time frames such as 5 years, and they can be based on intervals between 1 second, 1 minute, 1 hour, 1 day or longer. This uncertainty is exacerbated by the fact that there is no standard that Corporate Finance, Equity Analyst or other Banking and Research Professionals use.

Secondly, a highly negative Beta can cause you to calculate the Cost of Equity as being below the Risk Free Rate, or even below 0% per annum (which is presently a good estimate of the Risk Free Rate in numerous locations around the world...). CAPM says that Ke = RFR + β X MRP (see last blog for explanation), so if our RFR = 5%, our MRP = 5% and our β = -1 or less, then we will calculate the Cost of Equity as being 0% or even negative! It is theoretically possible that an investor would demand an investment that is expected to generate a negative return, however the only time I have observed this was with US Treasuries during the height of the 2008-09 subprime crisis where for short period the yield turned negative on short-dated Treasuries. However these instruments are not equity instruments, and are often labelled as the specific embodiement of the Risk Free Asset, and further generally represent the Asset upon which all other Risky Assets need to generate a return premium to justify their existence. So the point to take away is that CAPM doesn't seem to effectively price the Cost of Equity for highly volatile investments whose returns are negatively correlated with the market return.

Thirdly, Beta has a potential feed-back loop in practice. What I mean by this is that you as an investor can effect the value of Beta by trying to measure Beta and act on your measurement. Let's run through an example to show you how this works. First, we see a set of data that compares movements in a stock price versus the market, and the resulting Beta and valuation based on the stock returning $1 in dividends and no growth:

From this example we determine that the Stock is worth $20 based on the Beta we calculate, so if we can purchase the stock for less than $20 including transaction fees we are getting appropriately compensated for the risk involved in the investment right? Well, Beta says no!!!

Let's now assume that we have to pay 4c in transaction costs to buy the stock,but we are lucky enough to be able to pick up the stock at $19.95 on market, so our all in cost of purchase is $19.99 for a discount to fair value of 1c (what a bargain...). What happens to our valuation when we update Beta for our transaction?

You can see our order for the stock on day 8 at what we thought was a bargain at $19.95, but what has happened is we have ended up paying a total of $19.99 for an investmant that, according to our calculation of value using CAPM is now worth only $16.81 due to us disturbing the stock price! Bear in mind that this example contains a small data sample with only 7 return data points, and additionally our market is displaying quite a high degree of price stability. However, this does illustrate the issue an investor faces when using Beta to determine the Cost of Equity, which is that you can affect your valuation on a company later either positively or negatively by trading based on your valuation, as you become a data point.

So what is an alternative to Beta that can help avoid these issues?

A well-used alternative to CAPM is the Build-Up method. The Build-Up method of calculating the Cost of Equity uses building blocks to get to a final Cost. Some more commonly used building blocks are:

- Risk Free Rate (Government Bond Rate);
- Debt Margin (what the Banks want in addition);
- Operating Risk Premium (can be reflected in the Debt margin, but charges for risks associated with management execution of business plans);
- Subordination or Financial Risk Premium (how much more should you be asking for based on the fact that debt gets paid first);
- Liquidity Premium (how easy or difficult it is to exit your position).

So the way we approach determining the Cost of Equity is to simply add the Required Return allocated to each of the identified factors. A worked example is as follows:

The key advantages of this method are that you actively identify which factors are contributing to your Cost of Equity and charge for those risks according to your view, and when you act on your view of the value of the company, your trades do not distort any factors that directly contribute to your valuation.

In conclusion, when you are building an Excel Financial Model it is worth considering using the Build-Up method in tandem or as a substitute for CAPM, especially if the purpose of your DCF valuation is to eventually take a trading position.