# Required return, portfolio beta,stock price, dividend yield

1. Magee Company's stock has a beta of 1.20, the risk-free rate is 4.50%, and the market risk premium is 5.00%. What is Magee's required return?

10.25%

10.50%

10.75%

11.00%

11.25%

2. Parr Paper's stock has a beta of 1.40, and its required return is 13.00%. Clover Dairy's stock has a beta of 0.80. If the risk-free rate is 4.00%, what is the required rate of return on Clover's stock? (Hint: First find the market risk premium.)

8.55%

8.71%

8.99%

9.14%

9.33%

3. Suppose you hold a diversified portfolio consisting of $10,000 invested equally in each of 10 different common stocks. The portfolio's beta is 1.120. Now suppose you decided to sell one of your stocks that has a beta of 1.000 and to use the proceeds to buy a replacement stock with a beta of 1.750. What would the portfolio's new beta be?

0.982

1.017

1.195

1.246

1.519

4. A mutual fund manager has a $20.0 million portfolio with a beta of 1.50. The risk-free rate is 4.50%, and the market risk premium is 5.50%. The manager expects to receive an additional $5.0 million which she plans to invest in a number of stocks. After investing the additional funds, she wants the fund's required return to be 13.00%. What must the average beta of the new stocks added to the portfolio be to achieve the desired required rate of return?

1.12

1.26

1.37

1.59

1.73

5. A stock is expected to pay a dividend of $1 at the end of the year. The required rate of return is rs = 11%, and the expected constant growth rate is 5%. What is the current stock price?

$16.67

$18.83

$20.00

$21.67

$23.33

6. A stock just paid a dividend of $1. The required rate of return is rs = 11%, and the constant growth rate is 5%. What is the current stock price?

$15.00

$17.50

$20.00

$22.50

$25.00

7. The Lashgari Company is expected to pay a dividend of $1 per share at the end of the year, and that dividend is expected to grow at a constant rate of 5% per year in the future. The company's beta is 1.2, the market risk premium is 5%, and the risk-free rate is 3%. What is the company's current stock price?

$15.00

$20.00

$25.00

$30.00

$35.00

8. An increase in a firm's expected growth rate would normally cause its required rate of return to

Increase.

Decrease.

Fluctuate.

Remain constant.

Possibly increase, decrease, or have no effect.

9. If a company's dividend is $2.12 and the price of the company's stock is $40 what is the stock's dividend yield?

5.0%

5.1%

5.3%

5.6%

5.8%

10. A share of common stock has just paid a dividend of $2.00. If the expected long-run growth rate for this stock is 7%, and if investors require a(n) 11% rate of return, what is the price of the stock?

$47.50

$49.00

$50.50

$52.00

$53.50

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#### Solution Preview

Formula - Required rate of return = risk free rate + Beta*market risk premium

Formula - Market risk premium = required market return - risk free rate

Formula - Stock price = Expected divdend/(required return- constant growth rate)

1. Magee's Required return = 4.5% + 1.2*5% = 4.5%+6 = ...

#### Solution Summary

The solution computes required return, portfolio beta, current stock price, and dividend yield in order to solve the problems, providing the answer as well as how it was obtained.

Portfolio Required Return, CAPM, Beta, Inonconstant Growth

PORTFOLIO REQUIRED RETURN Suppose you are the money manager of a $4 million investment fund. The fund consists of four stocks with the following investments and betas:

Stock Investment Beta

A $400,000 1.50

B 600,000 (0.50)

C 1,000,000 1.25

D 2,000,000 0.75

CAPM AND REQUIRED RETURN Bradford Manufacturing Company has a beta of 1.45, while Farley Industries has a beta of 0.85. The required return on an index fund that holds the entire stock market is 12.0%. The risk-free rate of interest is 5%. By how much does Bradford's required return exceed Farley's required return?

PORTFOLIO BETA A mutual fund manager has a $20 million portfolio with a beta of 1.5. The risk-free rate is 4.5%, and the market risk premium is 5.5%. The manager expects to receive an additional $5 million, which she plans to invest in a number of stocks. After investing the additional funds, she wants the fund's required return to be 13%. What should be the average beta of the new stocks added to the portfolio?

NONCONSTANT GROWTH VALUATION Hart Enterprises recently paid a dividend, D0, of $1.25. It expects to have nonconstant growth of 20% for 2 years followed by a constant rate of 5% thereafter. The firm's required return is 10%.

a. How far away is the terminal, or horizon, date?

b. What is the firm's horizon, or terminal, value?

c. What is the firm's intrinsic value today, P0?

CORPORTATE VALUATION Smith Technologies is expected to generate $150 million in free cash flow next year, and FCF is expected to grow at a constant rate of 5% per year indefinitely. Smith has no debt or preferred stock, and its WACC is 10%. If Smith has 50 million shares of stock outstanding, what is the stock's value per share?

PREFERRED STOCK RETURNS Bruner Aeronautics has perpetual preferred stock outstanding with a par value of $100.The stock pays a quarterly dividend of $2, and its current price is $80.

a. What is its nominal annual rate of return?

b. What is its effective annual rate of return?

NONCONSTANT GROWTH Assume that it is now January 1, 2009. Wayne-Martin Electric Inc. (WME) has developed a solar panel capable of generating 200% more electricity than any other solar panel currently on the market. As a result, WME is expected to experience a 15% annual growth rate for the next 5 years. Other firms will have developed comparable technology at the end of 5 years, and WME's growth rate will slow to 5% per year indefinitely. Stockholders require a return of 12% on WME's stock. The most recent annual dividend (D0), which was paid yesterday, was $1.75 per share.

a. Calculate WME's expected dividends for 2009, 2010, 2011, 2012 and 2013

b. Calculate the value of the stock today, P0. Proceed by finding the present value of the dividends expected at the end of 2009, 2010, 2011, 2012, and 2013 plus the present value of the stock price that should exist at the end of 2013. The year-end 2013 stock price can be found by using the constant growth equation. Notice that to find the December 31, 2013, price, you must use the dividend expected in 2014, which is 5% greater than the 2013 dividend.

c. Calculate the expected dividend yield (D1/P0), capital gains yield, and total return (dividends yield plus capital gains yield) expected for 2009. (Assume that P0=P0 amd recognize that the capital gains yield is equal to the total return minus the dividend yield.) Then calculate these same three yields for 2014.

d. How might an investor's tax situation affect his or her decision to purchase stocks of companies in the early stages of their lives, when they are growing rapidly, versus stocks of older, more mature firms? When does WME's stock become "mature "for purpose of this question?

e. Suppose your boss tells you she believes that WME's annual growth rate will be only 12% during the next 5 years and that the firm's long-run growth rate will be only 4%. Without doing any calculations, what general effect would these growth rate changes have on the price of WME's stock?

f. Suppose your boss also tells you that she regards WME as being quite risky and that she believes the required rate of return should be 14%, not 12%. Without doing any calculations, determine how the higher required rate of return would affect the price of the stock, the capital gains yield, and the dividend yield. Again, assume that the long-run growth rate is 4%.