# Capital Asset Pricing Model, ROE

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?

please see the attachment.

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#### Solution Preview

Please see attached file

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 + βA (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).

Finance: Millman EBIT, ROE, capital structure, Jones recapitalization, Tapley stock price

See the attached file.

1. Millman Electronics will produce 60,000 stereos next year. Variable costs will equal 50% of sales, while fixed costs will total $120,000. At what price must each stereo be sold for the company to achieve an EBIT of $95,000?

$6.57 $6.87 $7.17 $7.47 $7.77

2. Firms A and B are identical except for their level of debt and the interest rates they pay on debt. Each has $2 million in assets, $400,000 of EBIT, and has a 40% tax rate. However, firm A has a debt-to-assets ratio of 50% and pays 12% interest on its debt, while Firm B has a 30% debt ratio and pays only 10% interest on its debt. What is the difference between the two firms' ROEs?

1.25% 1.91% 2.23% 2.64% 2.86%

3. The firm's target capital structure is consistent with which of the following?

Maximum earnings per share (EPS).

Minimum cost of debt (rd).

Highest bond rating.

Minimum cost of equity (rs).

Minimum weighted average cost of capital (WACC).

4. Jones Co. currently is 100% equity financed. The company is considering changing its capital structure. More specifically, Jones' CFO is considering a recapitalization plan in which the firm would issue long-term debt with a yield of 9% and use the proceeds to repurchase common stock. The recapitalization would not change the company's total assets nor would it affect the company's basic earning power, which is currently 15%. The CFO estimates that the recapitalization will reduce the company's WACC and increase its stock price. Which of the following is also likely to occur if the company goes ahead with the planned recapitalization?

The company's net income will increase.

The company's earnings per share will decrease.

The company's cost of equity will increase.

The company's ROA will increase.

The company's ROE will decrease.

5. Tapley Inc. currently has assets of $5 million, zero debt, is in the 40% federal-plus-state tax bracket, has a net income of $1 million, and pays out 40% of its earnings as dividends. Net income is expected to grow at a constant rate of 5 percent per year, 200,000 shares of stock are outstanding, and the current WACC is 13.40%.

The company is considering a recapitalization where it will issue $1 million in debt and use the proceeds to repurchase stock. Investment bankers have estimated that if the company goes through with the recapitalization, its before-tax cost of debt will be 11%, and its cost of equity will rise to 14.5%.

a. What is the stock's current price per share (before the recapitalization)?

b. Assuming the company maintains the same payout ratio, what will be its stock price following the recapitalization?