The 10 thousand dollar question for any absolute valuation analysis like the Discounted Cash Flow (DCF) Model, Residual Income Model, or Dividend Growth Model is: “What Discount Rate should I use?” An incorrect Discount Rate can drastically efffect your intrinsic valuations and ultimately your bottom line. Therefore, you should learn the principles of how to correctly Determine Discount Rates.
According to modern finance, there are a number of models that can be used to select for a Discount Rate. The following are some methods to use to determine a discount rate:
- Capital Asset Pricing Model (CAPM)
- Multifactor Models
- Fama-French Model
- Pastor-Stambaugh Model
- Macroeconomic Multifactor Models
- Build-Up Model
- Bond-Yield Plus Risk Premium Model
I would like to introduce you to two other Discount Rate Models:
- “Active Value Investing” (AVI) Discount Rate Model
- “Adept Analyst” Model: a modification of the AVI Discount Rate Model
Capital Asset Pricing Model (CAPM)
The CAPM estimates the required rate of return on equity using the following formula:
Required return on stock i = risk-free rate + (equity risk premium * Beta of i)
This is a classic model and is often taught in finance courses.
Multifactor Models generally have more explanatory power than CAPM (a single-factor model). The general form of an n-facto multifactor model is:
Required return = risk-free rate + (risk premium 1) + (risk premium 2) + … + (risk premium n)
Risk premium i = (factor sensitivity i) * (factor risk premium i)
The factor sensitivity is also called the factor beta. It is the asset’s sensitivity to a particular factor, all else being equal. The factor risk premium is the expected return above the risk-free rate from a unit sensitivity to the factor, while a zero sensitivity to all other factors.
The Fama-French Model is a multifactor model. It attempts to account for the higher returns generally associated with small-cap stocks. The model is:
Required return on stock i = risk-free rate + Beta of the market * (return of the market – risk-free rate) + Beta of small-cap * (return of small-cap – risk-free rate) + Beta of high book-to-market * (return of high book-to-market – return of low book-to-market)
(return of the market – risk-free rate) = return on a value-weighted market index minus the risk-free rate
(return of small-cap – risk-free rate) = small-cap return premium equal to the average return on small-cap portfolios minus the average return on large-cap portfolios
(return of high book-to-market – return of low book-to-market) = a value of return premium equal to the average return on high book-to-market portfolios minus the average returns on low book-to-market portfolios
The baseline value (expected value for the variable) for 1) Beta of the market is 1; the baseline values for 2) Beta of small-cap and 3) Beta of high book-to-market are 0.
The Pastor-Stambaugh Model adds a liquidity factor to the Fama-French Model. The baseline value for the Beta of the liquidity factor is 0. Less liquid assets should have a positive Beta, while more liquid assets should have a negative Beta.
Macroeconomic Multifactor Models
Macroeconomic Multifactor Models use factors that are associated with economic variables, which can be reasonably believed to affect cash flows and/or appropriate discount rates. Examples of some factors are:
- Confidence risk = unexpected change in the difference between the return of riskier corporate bonds and government bonds.
- Time horizon risk = unexpected change in the difference between the return of long-term government bonds and Treasury bills.
- Inflation risk = unexpected change in the inflation rate.
- Business cycle risk = unexpected change in the level of real business activity.
- Market timing risk = the equity market return that is not explained by the other 4 factors.
The Build-Up Model is like the risk premium approach. Generally, it is applied to closely held companies where Betas are not readily obtainable. A popular example is:
Required return = risk-free rate + equity risk premium + size premium + specific-company premium
Bond-Yield Plus Risk Premium Model
The Bond-Yield Plus Risk Premium Model is a Build-Up Model that is appropriate for companies with publicly traded debt. The method adds a risk premium to the yield to maturity (YTM) of the company’s long-term debt.
“Active Value Investing” (AVI) Discount Rate Model
In the great value investing book, “Active Value Investing” by Vitaliy Katsenelson, the author simplifies Discount Rate discussion by applying logic. He uses: 1) Business Risk Factor and 2) Financial Risk Factor to determine the appropriate Discount Rate.
Discount Rate = Basic Discount Rate * Business Risk Factor * Financial Risk Factor
You basically pick a Basic Discount Rate for the average stock, say 15%; apply a premium or discount for the type of business it is in (i.e. 1.20 for tech-stocks and 0.90 for Coca-Cola); and apply a premium or discount for how strong the balance sheet is (i.e. 1.50 for highly leveraged companies and 0.75 for more conservatively financed companies). You should use your investment judgment for the various risk factors.
“Adept Analyst” Model
“Adept Analyst” (AA) Model is a modification of the AVI Discount Rate Model. The AA Model adds a factor for country risk (i.e. 1.00 for U.S. stocks and 1.15 for less developed countries). You should use your investment judgment for the various risk factors.
Discount Rate = Basic Discount Rate * Business Risk Factor * Financial Risk Factor * Country Risk Factor
I favor the Adept Analyst Model because most quantitative models have (as Vitaliy Katsenelson explained in his book) a “false precision of math.” For example, Value Line Investment Survey, Yahoo! Finance, and Standard & Poor’s all have different Betas for the same stock because they each use different time periods. Hope you enjoyed this article and are now better equipped to Determine a Discount Rate.