**Solutions of Problems**

$ 10.00

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 |

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 |

Asset |

Expected |

return, r |

Risk (standard |

deviation), sr |

V 8% 5% |

W 13 10 |

Using these assets, you have isolated the three investment alternatives shown in the |

following table. |

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 1,400 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 (years) |

Premium |

or discount |

A 9% 16 $250 |

B 7 5 50 |

C 6 7 par |

D 5 10 2 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 $57.50. The firm expects to pay |

a $3.40 dividend at the end of the year (2016). The dividends for the past 5 years |

are shown in the following table. |

Year Dividend |

2015 $3.10 |

2014 2.92 |

2013 2.60 |

2012 2.30 |

2011 2.12 |

After underpricing and flotation costs, the firm expects to net $52 per share on a |

new issue. |

a. Determine the growth rate of dividends from 2011 to 2015. |

b. Determine the net proceeds, Nn, that the firm will actually receive. |

c. Using the constant-growth valuation model, determine the cost of retained earnings, rr. |

d. Using the constant-growth valuation model, determine the cost of new common |

stock, rn. |

P9–17 Calculation of individual costs and WACC Dillon Labs has asked its financial manager |

to measure the cost of each specific type of capital as well as the weighted average |

cost of capital. The weighted average cost is to be measured by using the following |

weights: 40% long-term debt, 10% preferred stock, and 50% common stock equity |

(retained earnings, new common stock, or both). The firm’s tax rate is 40%. |

Debt The firm can sell for $980 a 10-year, $1,000-par-value bond paying annual |

interestat a 10% coupon rate. A flotation cost of 3% of the par value is required |

in addition to the discount of $20 per bond. |

Preferred stock Eight percent (annual dividend) preferred stock having a par |

value of $100 can be sold for $65. An additional fee of $2 per share must be paid |

to the underwriters. |

Common stock The firm’s common stock is currently selling for $50 per share. |

The dividend expected to be paid at the end of the coming year (2016) is $4. Its |

dividend payments, which have been approximately 60% of earnings per share in |

each of the past 5 years, were as shown in the following table. |

Year Dividend |

2015 $3.75 |

2014 3.50 |

2013 3.30 |

2012 3.15 |

2011 2.85 |

It is expected that to attract buyers, new common stock must be underpriced |

$5 per share, and the firm must also pay $3 per share in flotation costs. Dividend |

payments are expected to continue at 60% of earnings. (Assume that rr= rs.) |

a. Calculate the after-tax cost of debt. |

b. Calculate the cost of preferred stock. |

c. Calculate the cost of common stock. |

d. Calculate the WACC for Dillon Labs. |

**Category:**Business, General Business

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