Risk-Free Rate and Equity Risk Premium

1. Risk-Free Rate and Equity Risk Premium

Now, let's go through how we are going to obtain the last two components of the CAPM. The risk-free rate and the equity risk premium.

2. Risk-Free Rate

The CAPM requires the risk-free rate as an input. A risk-free security is an asset with zero beta. We can see this from the CAPM. If the asset's beta is 0, then the 2nd term on the right-hand-side of the CAPM, beta times Rm minus Rf, is equal to zero. So the asset's return equals the risk-free return. A common source for the risk-free rate is the yield on long-term US Treasury securities. Long-term can mean 10, 20, or 30 years. The risk-free rate can be obtained from the Federal Reserve Electronic Database or the Federal Reserve H 15 Selected Interest Rates database.

3. Equity Risk Premium

The last component of the CAPM is the Equity Risk Premium or ERP. The Equity Risk Premium measures the extra return that investors demand for putting their money in stocks compared to US Treasuries. The Equity Risk Premium is the market return less the US Treasury return. Since the US Treasury return can be of varying maturities, we should make sure that the term of the Risk-Free Rate is the same for the Rf and the Equity Risk Premium. For example, if we use a Risk-Free Rate of 10 years, we have to make sure the Equity Risk Premium is calculated using a 10-year US Treasury also. To calculate the ERP, we obtain a return series for the S&P 500 Index and, say, the 10-year US Treasury for at least 35 years. We then subtract the US Treasury yield from the S&P 500 Index return each year and average the annual differences. This annual difference is the historical Equity Risk Premium. The typical range of ERP is around 5 to 8 percent.

4. Let's practice!

Let's practice the material we just went through in the following exercise.

This exercise is part of the course

Equity Valuation in R

IntermediateSkill Level

4.9+

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Many individuals and institutions invest in equities. To do so effectively, the investor must have a solid understanding of how the value of the equity compares to the stock price. In this course, we focus on fundamental concepts of equity valuation. We begin with a discussion of time value of money and then move on to the first of two discounted cash flow methods we will discuss - the free cash flow to equity valuation model.

Exercise 1: Course Intro and Fundamental Valuation Exercise 2: Time Value of Money Exercise 3: Difference Between Valuing Enterprise and Equity Cash Flows Exercise 4: The Free Cash Flow to Equity Model Exercise 5: Calculating Operating Profit Exercise 6: Calculate Free Cash Flow to Equity Exercise 7: Calculating Terminal Value Exercise 8: Calculating Equity Value Exercise 9: Calculating Present Value of Free Cash Flow to Equity Exercise 10: Calculate Present Value of Terminal Value Exercise 11: Calculate Equity Value

One of the critical components of free cash flow to equity valuation is using reliable projections. In the first part of this chapter, we will discuss ways to analyze the projections to help us identify the right questions to ask. In the second part of this chapter, we will go through the second of our discounted cash flow models - the dividend discount model. In this approach, we discount expected dividends instead of free cash flows.

Exercise 1: Analyzing the Projections Exercise 2: Analyze Revenue Trends - Bar Chart Exercise 3: Analyze Revenue Trends - Regression Exercise 4: Perpetuity Growth Rate Exercise 5: Calculate Retention Ratio Exercise 6: Perpetuity Growth Rate Calculation Exercise 7: Dividend Discount Model Exercise 8: Valuing Preferred Stock Exercise 9: Valuation Assuming No Dividends For First Few Years Exercise 10: Valuation Assuming 2-Stages of Dividends

To be able to discount cash flows, we need a discount rate. For the free cash flow to equity and dividend discount model, the cost of equity is the appropriate discount rate. In this chapter, we will discuss how each of the components of the cost of equity are calculated.

Exercise 1: What is a discount rate?Exercise 2: Risk and Return Exercise 3: Calculating Returns Exercise 4: Estimating Beta Exercise 5: Unlevering Betas Exercise 6: Hamada vs. Fernandez Formula Exercise 7: Beta Unlevering Exercise Exercise 8: Beta Relevering Exercise Exercise 9: Risk-Free Rate and Equity Risk Premium

Current Exercise

Exercise 10: Obtain Risk-Free Rate Data Exercise 11: Calculate Historical Equity Risk Premium Exercise 12: Calculate the Cost of Equity

Relative valuation allows us to use the valuation of comparable companies to infer the value of our subject firm. In this chapter, we discuss how to identify comparable companies and how to calculate valuation multiples. We also show how to analyze the determinants of multiples.

Exercise 1: Relative Valuation Exercise 2: Identifying Comparable Firms Exercise 3: Valuation Multiples Exercise 4: Calculating Valuation Multiples Exercise 5: Calculating the Relevant Multiple Exercise 6: Implied Price Exercise 7: Analyzing Determinants of Multiples Exercise 8: Calculate ROE and P/B Exercise 9: Plot P/B vs. ROE Exercise 10: Strength of Relationship Exercise 11: Implied Price Using Regression Exercise 12: Difference in Implied Values

This chapter combines the lessons from Chapters 1 to 4 in a series of exercises. You will be asked to inspect the data and to value the firm using discounted cash flow and relative valuation approaches. At the end, you will combine the results in a summary table.

Exercise 1: Fundamental Valuation: Analyzing Projections Exercise 2: Visually Inspecting the Data Exercise 3: Using Regression to Test the Projections Exercise 4: Fundamental Valuation: Implementation Exercise 5: Cost of Equity Exercise 6: Calculate Value During Projection Period Exercise 7: Calculate the Terminal Value Exercise 8: Equity Value Per Free Cash Flow to Equity Model Exercise 9: Equity Value per Dividend Discount Model Exercise 10: Relative Valuation Exercise 11: Equity Value Per Price-to-Earnings Multiples Exercise 12: Combine valuation into a summary table Exercise 13: Congratulations!