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# Capital Asset Pricing Model, ROE

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1. The capital asset pricing model (CAPM) contends that there is systematic and unsystematic risk for an individual security. Which is the relevant risk variable and why is it relevant? Why is the other risk variable not relevant?

2 a. You expect an RFR of 10 percent and the market return (RM) of 14 percent. Compute the expected return for the following stocks, and plot them on an SML graph.

Stock Beta E ( Ri )
U 0.85
N 1.25
D -0.20

b. You ask a stockbroker what the firm's research department expects for these three stocks. The broker responds with the following information:

Stock Current Price Expected Price Expected Dividend
U 22 24 0.75
N 48 51 2.00
D 37 40 1.25

Plot your estimated returns on the graph from Part a, and indicate what actions you would take with regard to these stocks. Explain your decisions.

3. Describe the components of business risk, and discuss how the components affect the variability of operating earnings (EBIT).

4. The Shamrock Vegetable Company has the following results:

Net sales \$6,000,000
Net total assets 4,000,000
Depreciation 160,000
Net income 400,000
Long-term debt 2,000,000
Equity 1,160,000
Dividends 160,000
a. Compute Shamrock's ROE directly. Confirm this using the three components.
b. Using the ROE computed in Part (a), what is the expected sustainable growth rate for Shamrock?
c. Assuming the firm's net profit margin went to 0.04, what would happen to Shamrock's ROE?
d. Using the ROE in Part (c), what is the expected sustainable growth rate? What if dividends were only \$40,000?

#### Solution Preview

Chapter 8, question 3, page 232;
11. The capital asset pricing model (CAPM) contends that there is systematic and unsystematic risk for an individual security. Which is the relevant risk variable and why is it relevant? Why is the other risk variable not relevant?

The relevenat risk is the systematic risk as it cannot be diversified away.
An investor can diversify away the unsystematic risk of securities by constructing a portfolio of securities.
Systematic risk are economy-wide risks such as inflation, exchange rate and interest rate volatility that all companies face. These risks threaten each company. Therefore, this risk cannot be avoided, regardless of how diversified a portfolio the investor holds.
Market rewards investors for taking systematic risk and not unsystematic risk as unsystematic risk can be diversified away.

Problems 2, 5 pages 233-234
a. You expect an RFR of 10 percent and the market return (RM) of 14 percent. Compute the expected return for the following stocks, and plot them on an SML graph.

CAPM (Capital Asset Pricing Model) equation is:
r A= r f + &#946;A (r m - r f)

risk free rate=RFR= r f = 10%
return on market portfolio= r m = 14%

Stock Beta E ( Ri )
U 0.85 13.40% =10.%+0.85*(14.%-10.%)
N 1.25 15.00% =10.%+1.25*(14.%-10.%)
D -0.2 9.20% =10.%+-0.2*(14.%-10.%)

Beta R
Risk free rate 0 10%
Market 1 14%
U 0.85 13.40%
N 1.25 15.00%
D -0.2 9.20%

b. You ask a stockbroker what the firm's research department expects for these three stocks. The broker responds with the following information:

Stock Current Price Expected Price Expected Dividend Expected Return
U 22 24 0.75 12.50% ={(0.75 + 24 ) / 22 }-1
N 48 51 2 10.42% ={(2 + 51 ) / 48 }-1
D 37 40 1.25 11.49% ={(1.25 + 40 ) / 37 }-1

Plot your estimated returns on the graph from Part a, and indicate what actions you would take with regard to these stocks. Explain your decisions.

Stock Beta Required Return Expected Return Under/ Over ...

#### Solution Summary

Answers questions on CAPM, Return on Equity (ROE).

\$2.19