# Portfolio Required Return, CAPM, Beta, Inonconstant Growth, Valuation, Preferred Stock

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%.

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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 1.5

B $600,000 -0.5

C $1,000,000 1.25

D $2,000,000 0.75

NOTE: Double click the table(s) to see the formulas used.

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 non-constant 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?

The terminal date is the date after which all factors would be constant. From the above question, you will observe that constant growth rate would occur after 2 years, so therefore the terminal date is just 2 years from the present.

b. What ...

#### Solution Summary

Portfolio required return, CAPM, beta and inonconstant growth are examined.