# A Crash Course in Discount Rates

A discount rate helps analysts and managers determine the value (or potential value) of an investment or portfolio. They’re an important part of the CFA® Level I exam. In this article, I’ll discuss

• what discount rates are,

• why it’s a crucial evaluation input (in my opinion), and

• various ways the discount rate is calculated (equity and firm).

Note that for this article, net present value is represented by NPV and is discussed briefly later in the post. Happy reading!

## What Is a Discount Rate?

In investing, the discount rate is a broad-spectrum term used to describe the rate of return an investor (corporate or individual) would expect by choosing to participate in a specific investment that will provide a positive NPV. There are various kinds of discount rates used in analysis, and I’ll classify them simply as either derived or calculated.

Derived discount rates are estimated from a bottom-up approach prior to commencement of any kind of evaluation (e.g., estimating cash flows). These include rates such as the cost of capital, weighted-average cost of capital (WACC), bank interest rates, cost of equity, etc. Calculated discount rates, on the other hand, include the internal rate of return (IRR) and its offshoots, like the modified internal rate of return (MIRR). These are calculated based on formulas after calculating cash flows.

To estimate a company’s profitability or value, cash flows are projected months or years into the future; this process helps capital budgeting. To bring these cash flows to today’s net values, or the NPV, things to consider include the cost of the capital, potential risks, opportunity cost(s), and the time value of money.

Let’s say you’re presented with two options for what to do with NGN 100,000:

• Option A - Leave it in a bank (interest rate = 5%)

• Option B - Invest it in a taxi business

To justify investing in the taxi business, the returns would have to be greater than 5% because there are a few extra things to consider, including the risks with the business, timing of the cash flows, and the opportunity cost.

## Why Is the Discount Rate So Important?

I consider the discount rate a central evaluation input because it helps determine the NPV, which accounts for the cash flows, the timing of the cash flows, and any risks associated with the investment decision.

In the example above, if the incremental risk associated with the taxi business accounts for 2% of the returns, the appropriate minimum discount rate to employ in this case would be 7% to cover the potential 5% interest you’re forgoing from the bank, and 2% to cover incremental risk associated with the taxi business.

## How to Estimate an Appropriate Discount Rate

The discount rate to apply depends on what it is you’re trying to value and the perspective you’re taking. Let’s now look at valuing a stock and valuing a firm or business, and review derived rates.

### Valuing a Stock or Equity

The general premise most analysts use for generating a valid discount rate is

Discount Rate (Rate of return) = Risk-free Rate + Risk Premium

The risk-free rate (Rf) is the rate on the most liquid government-issued security as it is assumed to have no risk and no “liquidity premium” attached to it. The most widely used is on-the-run long-term government debt. It’s important to note that the appropriate risk-free rate to use depends on the duration of your analysis. So if you’re looking at a 10-year horizon, look for 10-year on-the-run long-term government debt.

The risk premium (Rp), on the other hand, is essentially the return that the investors expect for taking the risk of investing in the stock. There are various ways of estimating the expected return used for equity investments, and they include the following:

• Market equity indices

• Capital asset pricing model (CAPM)

• Gordon growth model

• Multifactor models

• Build-up method

### Market Equity Indices

This is a relatively simple method of estimation because it uses the returns from known indices over long time spans. Examples are the S&P 500, Dow Jones Industrial, and FTSE 500, to name a few. This method assumes that the risks associated with investing in a stock or asset are priced into the index that has been chosen. There are, however, a number issues relating to this approach:

• It assumes returns don’t change over time.

• It potentially uses returns from only firms that exist in the market and ignores any other firm that may be closed but contributed historically (also called survivorship bias).

• Historical market events may not be relevant in the period used in the evaluation.

### CAPM

This is arguably the most popular discount rate estimator in many corporate entities. To calculate the discount rate based on this method, you need the following:

• Risk-free rate (Rf)

• Beta (β)—this is a measure of systematic risk of a stock relative to the market (i.e., the covariance between the stock and the stock market as a whole)

• Expected market return (Rm)—this can be the average return of a selected index or an “accepted return” based on consensus estimates

Together the discount rate (Er) is calculated as

Er = Rf + β(Rm - Rf)

The last portion of the equation (the β(Rm - Rf)) represents the risk premium for the investor. Even with its wide acceptance, the CAPM is still not really the best model when you consider every stock individually. There are small-, mid-, and large-cap stocks, so the risk premium may be “within range” but not accurate.

### Gordon Growth Model

From an equity perspective, this is a key model used to value stocks. To estimate the discount rate, you need the following:

• Forecasted dividend yield (D)

• Forecasted earnings growth rate (EGR)—this can be determined using consensus forecasts or estimates

Together, the equity return is calculated as

Er = D + EGR

It’s important to note that while this is a popular discounting method and may be quite suitable for assessing stocks in developed or mature markets, it may not be appropriate when evaluating stocks that are in fast-growing economies or that have a constant price-to-earnings ratio. The key reason for limitation is that the model assumes earnings and dividends grow at a constant rate. Furthermore, it assumes that the stock price grows at the same rate as earnings.

### Multifactor Models

The CAPM is considered a single-factor model, as it only considers a single risk source: market risk. Multifactor models, however, contain more sources of premium used in assessing the appropriate discount rate. Examples of multifactor models include

• the Fama–French model,

• the Pastor–Stambaugh model,

• macroeconomic models, and

• statistical models.

For instance, using the Pastor–Stambaugh model to estimate the discount rate, in addition to the requirements for the CAPM, you need the following:

• βsize:  The sensitivity of the security to movements in small stocks

• βvalue: The sensitivity of the security to movements in value stocks

• βliquidity: The sensitivity of the security to movements in illiquid stocks

The equation becomes

Er = Rf + β(Rm – Rf) + βsize(SMB) + βvalue(HML) + βliquidity(LIQ)

As you can see, there are more factors in the equation relative to the CAPM. The main issue with multifactor models, you may agree, is that they can become quite complex to use when you want to estimate the discount rate associated with a stock.

Overall, when analysing a stock, the decision on the discount rate depends on the level of accuracy you require. But as you can see, determining which method to use all comes down to the individual carrying out the analysis.

### Valuing a Firm or Business

Businesses raise capital by either issuing shares or stocks (these can either be preferred or ordinary) or debt (notes, corporate bonds, etc.). The costs of the funds raised from these sources are collectively referred to as “cost of capital” and represent the rate of return that the bondholders and stockholders expect to receive based on their capital contribution.

To properly value projects that companies engage in, they should, in my opinion, consider their cost of capital, the most appropriate discount rate to use being the WACC. To calculate the WACC, you need the following:

• Market value of debt (D) (but in many cases, the book value of debt can be used as a proxy)

• Market value of ordinary stock (E)

• Market value of preferred stock (P)

• Appropriate tax rate (T)

• Cost of debt (Cd)

• Cost of ordinary stock (Ce)

• Cost of preferred stock (Cp)

The equation then becomes

The expected returns from the investment should be greater than the WACC for the investment to be considered profitable. If Company A wants to acquire Company B, I would suggest that the WACC be used as a basis of estimating the NPV.