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P8–9 Rate of return, standard deviation, and coefficient of variation Mike is searching for a stock to include in his current stock portfolio. He is interested in Hi-Tech, Inc.; he has been impressed with the company’s computer products and believes that Hi-Tech is an innovative market player. However, Mike realizes that any time you consider a technology stock, risk is a major concern. The rule he follows is to include only securities with a coefficient of variation of returns below 0.90. Mike has obtained the following price information for the period 2012 through 2015. Hi-Tech stock, being growth-oriented, did not pay any dividends during these 4 years.
Stock price
Year Beginning End
2012 14.36 21.55
2013 21.55 64.78
2014 64.78 72.38
2015 72.38 91.80
a. Calculate the rate of return for each year, 2012 through 2015, for Hi-Tech stock.
b. Assume that each year’s return is equally probable, and calculate the average return over this time period.
c. Calculate the standard deviation of returns over the past 4 years. (Hint: Treat these data as a sample.)
d. Based on b and c, determine the coefficient of variation of returns for the security.
e. Given the calculation in d, what should be Mike’s decision regarding the inclusion of Hi-Tech stock in his portfolio?
P8–14 Portfolio analysis: You have been given the expected return data shown in the first table on three assets—F, G, and H—over the period 2016–2019.
Expected return
Year Asset F Asset G Asset H
2016 16% 17% 14%
2017 17 16 15
2018 18 15 16
2019 19 14 17
Using these assets, you have isolated the three investment alternatives shown in the following table.
Alternative Investment
1 100% of asset F
2 50% of asset F and 50% of asset G
3 50% of asset F and 50% of asset H
a. Calculate the expected return over the 4-year period for each of the three alternatives.
b. Calculate the standard deviation of returns over the 4-year period for each of the three alternatives.
c. Use your findings in parts a and b to calculate the coefficient of variation for each of the three alternatives.
d. On the basis of your findings, which of the three investment alternatives do you recommend? Why?
P8-27 Portfolio return and beta Jamie Peters invested $100,000 to set up the following portfolio 1 year ago.
Asset Cost Beta at purchase Yearly income Value today
A $20, 000 0.80 $1,600 $20,000
B $35,000 0.95 $4,000 $36,000
C $30,000 1.50 - $34,500
D $15,000 1.25 $ 375 $16,500
a. Calculate the portfolio beta on the basis of the original cost figures.
b. Calculate the percentage return of each asset in the portfolio for the year.
c. Calculate the percentage return of the portfolio on the basis of original cost, using income and gains during the year.
d. At the time Jamie made his investments, investors were estimating that the market return for the coming year would be 10%. The estimate of the risk-free rate of return averaged 4% for the coming year. Calculate an expected rate of return for each stock on the basis of its beta and the expectations of market and risk-free returns.
e. On the basis of the actual results, explain how each stock in the portfolio performed relative to those CAPM-generated expectations of performance. What factors could explain these differences?
P9–5: The cost of debt Gronseth Drywall Systems, Inc., is in discussions with its investment bankers regarding the issuance of new bonds. The investment banker has informed the firm that different maturities will carry different coupon rates and sell at different prices. The firm must choose among several alternatives. In each case, the bonds will have a $1,000 par value and flotation costs will be $30 per bond. The company is taxed at a rate of 40%. Calculate the after-tax cost of financing with each of the following alternatives
Alternative Coupon rate Time to maturity (yrs) Premium or discount
A 9% 16 $250
B 7 5 $0
C 6 7 par
D 5 10 -75
P9–7 Cost of preferred stock Taylor Systems has just issued preferred stock. The stock has a 12% annual dividend and a $100 par value and was sold at $97.50 per share. In addition, flotation costs of $2.50 per share must be paid. a. Calculate the cost of the preferred stock. b. If the firm sells the preferred stock with a 10% annual dividend and nets $90.00 after flotation costs, what is its cost?
P9–9 Cost of common stock equity: CAPM J&M Corporation common stock has a beta, b, of 1.2. The risk-free rate is 6%, and the market return is 11%.
a. Determine the risk premium on J&M common stock.
b. Determine the required return that J&M common stock should provide.
c. Determine J&M’s cost of common stock equity using the CAPM
P9–10 Cost of common stock equity Ross Textiles wishes to measure its cost of common stock equity. The firm’s stock is currently selling for $57