FIN 350 Week 7 Module 7 Practice Problems
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- Do all work in Excel. Do not submit Word files or *.pdf files.
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- Place each problem on a separate spreadsheet tab.
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- Follow the directions in the “Guidelines for Developing Spreadsheets.”
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
- Calculate the rate of return for each year, 2012 through 2015, for Hi-Tech stock.
- Assume that each year’s return is equally probable, and calculate the average return over this time period.
- Calculate the standard deviation of returns over the past 4 years. (Hint: Treat these data as a sample.)
- Based on b and c, determine the coefficient of variation of returns for the security.
- 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.
Year Asset F Asset G Asset H
2016 16% 17% 14%
2017 17 16 15
2018 18 15 16
2019 19 14 17
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.
- Calculate the expected return over the 4-year period for each of the three alternatives.
- Calculate the standard deviation of returns over the 4-year period for each of the three alternatives.
- Use your findings in parts a and b to calculate the coefficient of variation for each of the three alternatives.
- 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
- Calculate the portfolio beta on the basis of the original cost figures.
- Calculate-the percentage return of each asset in the portfolio for the year.
- Calculate the percentage return of the portfolio on the basis of original cost, using income and gains during the year.
- 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.
- 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.
- Calculate the cost of the preferred stock.
- If the firm sells the preferred stock with a 10% annual dividend and nets $90.00 after flotation costs, what is its cost? fin 350 week 7
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%.
- Determine the risk premium on J&M common stock.
- Determine the required return that J&M common stock should provide.
- 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.
After underpricing and flotation costs, the firm expects to net $52 per share on anew issue.
- Determine the growth rate of dividends from 2011 to 2015.
- Determine the net proceeds, Nn, that the firm will actually receive.
- Using the constant-growth valuation model, determine the cost of retained earnings, rr.
- 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 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.
It is …..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 …..to continue at 60% of earnings. (Assume that rr = rs.)
- Calculate the after-tax cost of debt.
- Calculate-the cost of preferred stock.
- Calculate-the cost of common stock.
- Calculate the WACC for Dillon Labs.
FIN 350 Week 7 Module 7 Discussion Question 1
Diversification occurs when stocks with low correlations of returns are placed together in a portfolio. Identify at least one type of firm that might exhibit low correlations of returns with the overall stock market? Explain why the correlations of these firms are expect to be low.
FIN 350 Week 7 Module 7 Discussion Question 2
In general, the cost of debt capital is lower than the cost of equity capital. For this reason, it might be expected that firms with high debt ratios would have a lower weighted average cost of capital. Explain at least one reason why this is not the case.