LOS b: Explain the equity risk premium and its use in required return determination, and demonstrate the use of historical and forward-looking estimation approaches.

Q1. Equity analyst Yasmine Cordova of Substantial Securities is trying to determine the investment appeal of shares of Maxwell Mincemeat, a small food company. Cordova has assembled the following data about the company:

• Internal rate of return: 9.4%.
• Maxwell’s 20-year bond yield to maturity: 7.9%.
• Maxwell’s two-year bond yield to maturity: 6.1%.
• Treasury bill yield: 3.4%.
• Maxwell’s estimated beta: 2.1.
• Maxwell’s 20-year bonds are priced at $102.65.
• Maxwell’s two-year bonds are priced at $101.47.
• Estimated return of Russell 2000 Index: 12.3%.
• Substantial’s credit analyst estimates that Maxwell’s equity warrants a premium of 4.9% over its bonds.

Cordova wants to make sure her estimates are accurate, so she decides to calculate the estimated required return in two ways. She opts for the bond-yield plus risk premium method and the capital asset pricing model. To check her work, she wants to compare the estimates derived under each method. The difference between the required returns is closest to:

A)   9.29%.

B)   5.30%.

C)   5.89%.

Q2. The equity risk premium is the difference between:

A)   the required equity return and the risk-free return.

B)   the estimated equity return and the risk-free return.

C)   estimated equity returns and estimated bond returns.

Q3. An analyst attempting to derive the equity risk premium for a stock starting from the required return for that stock would find which of the following statistics least useful?

A)   The stock’s beta.

B)   Historical 10-year Treasury bond rates.

C)   The stock’s estimated return.

Q4. Ben Jacobs, CFA, is attempting to calculate a historical equity risk premium. His first estimate uses geometric mean equity returns and long-term bond yields. His second estimate uses arithmetic mean returns and short-term bond yields. The effect of the changes in methodology in the second estimate, relative to the first, will:

A)   both decrease the size of the risk premium.

B)   both increase the size of the risk premium.

C)   have offsetting effects.

LOS b: Explain the equity risk premium and its use in required return determination, and demonstrate the use of historical and forward-looking estimation approaches. fficeffice" />

Q1. Equity analyst Yasmine Cordova of Substantial Securities is trying to determine the investment appeal of shares of Maxwell Mincemeat, a small food company. Cordova has assembled the following data about the company:

• Internal rate of return: 9.4%.
• Maxwell’s 20-year bond yield to maturity: 7.9%.
• Maxwell’s two-year bond yield to maturity: 6.1%.
• Treasury bill yield: 3.4%.
• Maxwell’s estimated beta: 2.1.
• Maxwell’s 20-year bonds are priced at $102.65.
• Maxwell’s two-year bonds are priced at $101.47.
• Estimated return of Russell 2000 Index: 12.3%.
• Substantial’s credit analyst estimates that Maxwell’s equity warrants a premium of 4.9% over its bonds.

Cordova wants to make sure her estimates are accurate, so she decides to calculate the estimated required return in two ways. She opts for the bond-yield plus risk premium method and the capital asset pricing model. To check her work, she wants to compare the estimates derived under each method. The difference between the required returns is closest to:

A)   9.29%.

B)   5.30%.

C)   5.89%.

Correct answer is A)

The capital asset pricing model uses the following equation:

Required return = risk-free rate + beta × equity risk premium

To calculate the required return under CAPM, use the Russell 2000 index return, the beta, and the risk-free rate.

Required return = 3.4% + 2.1 × (12.3% ? 3.4%) = 22.09%.

The bond-yield model uses the following equation:

Required return = yield to maturity on long-term bonds + risk premium.

Required return = 7.9% + 4.9% = 12.8%.

The difference between the two estimated required returns is 9.29%.

Q2. The equity risk premium is the difference between:

A)   the required equity return and the risk-free return.

B)   the estimated equity return and the risk-free return.

C)   estimated equity returns and estimated bond returns.

Correct answer is A)

The equity risk premium reflects the return in excess of the risk-free rate that investors require for holding stocks. It is derived by subtracting the risk-free return from the required return.

Q3. An analyst attempting to derive the equity risk premium for a stock starting from the required return for that stock would find which of the following statistics least useful?

A)   The stock’s beta.

B)   Historical 10-year Treasury bond rates.

C)   The stock’s estimated return.

Correct answer is C)

The required return for a stock is equal to the risk-free return plus beta times the equity risk premium. An analyst starting from the required return would need beta and a risk-free rate. Historical 10-year T-bond rates can be used as an estimate of the risk-free rate. Since the analyst is starting with the required return, estimated returns are not needed.

Q4. Ben Jacobs, CFA, is attempting to calculate a historical equity risk premium. His first estimate uses geometric mean equity returns and long-term bond yields. His second estimate uses arithmetic mean returns and short-term bond yields. The effect of the changes in methodology in the second estimate, relative to the first, will:

A)   both decrease the size of the risk premium.

B)   both increase the size of the risk premium.

C)   have offsetting effects.

Correct answer is B)

Switching from a geometric mean to an arithmetic mean will increase the mean equity return. All else being equal, that will increase the estimated risk premium. When the yield curve slopes upward, short-term bonds yield less than long-term bonds. Thus, the equity risk premium estimate will be larger when short-term bond rates are used.

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