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

In our Primer, Level 1 and Level 2 Financial Modeling Courses, we teach students to use a variable Cost of Capital when building a valuation model of a company. The variability in the WACC and/or Cost of Equity (depending on the valuation technique) is largely influenced by the mix of Shareholders' Equity versus other more senior sources of Capital (eg. Debt, Convertible Notes, Preference Shares etc), which affects β (Beta) in the Cost of Equity Calculation. Focussing on the Cost of Equity, the other ways that it can vary are generally via a change in the Risk Free Rate or a change in the Market Risk Premium.

The most commonly used equation for determining the Cost of Equity is the Capital Asset Pricing Model (CAPM), which calculates the Cost of Equity as:

Ke = RFR + β X MRP

Where:

Ke = Cost of Equity

RFR = Risk Free Rate

β = Beta (levered)

MRP = Market Risk Premium

We teach more about all the components of CAPM in our Primer and Level 1 Courses, but you can see that there are three inputs, and all these inputs can change. In particular β can change based on the Capital Structure of a company, which is often forecast to change substantially when modelling a company on a stand-alone or acquisition transaction basis over a forecast period.

So intiuitively if you understand the components of CAPM it makes sense to have a variable Cost of Equity (and WACC) if you are forecasting a variable Capital Structure (which is almost all the time). Lets run through a worked example to demonstrate quickly the consequence of using a fixed Cost of Equity versus a Variable Cost of Equity to value a set of cash flows produced by a company:

The company in the example is drawing down additional debt each year which contributes to its Cash Flow to Equity, boosting the amount the company can pay its Equity Investors, but this comes at the cost of taking on additional Financial Leverage and the associated risks. However, our discount rate is determined at the start of the period (at 10%) when the Financial Leverage and associated risk is much lower.

Our terminal value in particular is affected by this assumption on the discount rate. In this example we have assumed no growth in cash flow after 2015, so the terminal value is simply calculated as the 2015 Cash Flow to Equity (125) divided by the Discount Rate in 2015 (10%). The question then is, would an investor be willing to accept the equivalent % returns for a cash flow subject to 100% Debt/Equity Leverage as seen in 2011, and for a cash flow subject to a 300% Debt/Equity leverage as seen in 2015. Answer: **unlikely...**

Lets look at the same cash flows and Leverage scenario, but with the Cost of Equity changing due to Beta increasing in line with the increase in Leverage (see our Primer and Level 1 Financial Modeling courses for specific equations on how to do this):

You can see that the Terminal Value in 2015 is worth 234 less if the Cost of Equity is varied based on the higher leverage in 2015, and our overall valuation on the company falls from 1042 to 858 (-17.7%).

One of the key tenants of Financial Theory is that the greater the risk of an investment, the greater the returns required by the investor. As such the variable Cost of Equity Approach makes sense. So why wouldn't you use a variable Cost of Equity given it seems to value a company more effectively?

The Answer is generally three-fold:

- In general, people first learn about discounted cash flow theory using simple examples where they are given one discount rate and a set of cash flows, and asked to find the net present value of the cash flows. This is drilled in by high volumes of practice and sinks in as "the way" to do things. Basically, people don't think enough about the complexity of real-life application of financial theory and how valuation involves a complex interaction between numerous moving parts that affect eachother.
- People have it drilled into their brains that assets have a single point estimate "intrinsic value" and are trained to believe that the ultimate pursuit of valuation exercises is to find this one magical number that is the correct answer. In practice valuation is not certain, and understanding the downside risk and potential upside to your base case valuation is what is important, however lots of practitioners are not consciously aware of this while performing valuations. Without labouring the point or getting into any deep and all-encompassing financial theory, we use monetary figures as a representation of value, but we also know that money itself does not have a stable value, so we should therefore understand that any value denominated in monetary terms is itself inherently unstable (if this is isn't clear don't worry, its not fundamental to this blog...).
- Finally, the Finance Industry generally is not set up to handle non-stationary valuations. The reasons analysts and students ultimately enrol in a Financial Modeling Training Course is to be able to get a job as an Investment Banker or Analyst of some sort. In these jobs you are serving clients that are often not particularly strong on their financial theory. So when a DCF model is built and then a presentation is made to a client it needs to be neat, and it can't have too many numbers flying all over the place otherwise it won't be effective in inspiring a client to do a deal. So having a single discount rate makes the presenation neater and easier to digest, and therefore is more common practice when presenting.

So how can you get around this predicament? We recommend that analysts creating a DCF valuation model that will be presented in one form or another to a client (that is not a financial genius) use a single discount rate in their presentations, but perform their DCF valuation initially using a variable discount rate. The way to reconcile the two is to use excel's goal seek function after you have settled on your base case valuation, to find a single discount rate that provides the same valuation. In our example above the appropriate rate would be 11.8%. This captures the risk of the increasing level of leverage for valuation purposes, but also is a lot easier to present and understand for a financially non-genius client.

So how do you find the goal seek function? For excel 2003 and excel 2007, hit **ALT + T**, **G** and it will bring up the Goal seek function. This function will find the value that a variable needs to be in order for an equation to provide a certain answer. This function is one of the more handy tools for an analyst to know about, so it is recommended you experiment with this and grasp its power!!