# Solutions Of Problems

**Solutions Of Problems**

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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

**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), **s*r*

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, *N**n*, that the firm will actually receive.

**c. **Using the constant-growth valuation model, determine the *cost of retained earnings, r**r*.

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

*stock, r**n*.

**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*

*interest*at 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 *r**r*= *r**s*.)

**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.