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Risk and Return and Cost of Capital Problems week 5P8–1 Rate of return Douglas Keel, a financial analyst for Orange Industries, wishes to estimatethe rate of return for two similar-risk investments, X and Y. Douglas’s researchindicates that the immediate past returns will serve as reasonable estimates offuture returns. A year earlier, investment X had a market value of $20,000, and investmentY had a market value of $55,000. During the year, investment X generatedcash flow of $1,500, and investment Y generated cash flow of $6,800. The currentmarket values of investments X and Y are $21,000 and $55,000, respectively.a. Calculate the expected rate of return on investments X and Y using the most recentyear’s data.b. Assuming that the two investments are equally risky, which one should Douglasrecommend? Why?P8–4 Risk analysis Solar Designs is considering an investment in an expanded productline. Two possible types of expansion are being considered. After investigating thepossible outcomes, the company made the estimates shown in the following table.Expansion A Expansion BInitial investment $12,000 $12,000Annual rate of returnPessimistic 16% 10%Most likely 20% 20%Optimistic 24% 30%a. Determine the range of the rates of return for each of the two projects.b. Which project is less risky? Why?c. If you were making the investment decision, which one would you choose? Why?What does this decision imply about your feelings toward risk?d. Assume that expansion B’s most likely outcome is 21% per year and that allother facts remain the same. Does your answer to part c now change? Why?P8–14 Portfolio analysis You have been given the expected return data shown in the firsttable on three assets—F, G, and H—over the period 2016–2019. Expected returnYear Asset F Asset G Asset H2016 16% 17% 14%2017 17 16 152018 18 15 162019 19 14 17Using these assets, you have isolated the three investment alternatives shown in thefollowing table Alternative Investment1 100% of asset F2 50% of asset F and 50% of asset G3 50% of asset F and 50% of asset Ha. Calculate the expected return over the 4-year period for each of the threealternatives.b. Calculate the standard deviation of returns over the 4-year period for each of thethree alternatives.c. Use your findings in parts a and b to calculate the coefficient of variation foreach of the three alternatives.d. On the basis of your findings, which of the three investment alternatives do yourecommend? Why?P8–23 Portfolio betas Rose Berry is attempting to evaluate two possible portfolios, whichconsist of the same five assets held in different proportions. She is particularly interestedin using beta to compare the risks of the portfolios, so she has gathered thedata shown in the following table.Portfolio weightsAsset Asset beta Portfolio A Portfolio B 1 1.30 10% 30% 2 0.70 30 10 3 1.25 10 20 4 1.10 10 20 5 0.90 40 20Totals 100% 100%a. Calculate the betas for portfolios A and B.b. Compare the risks of these portfolios to the market as well as to each other.Which portfolio is more risky?P9–1 Concept of cost of capital Mace Manufacturing is in the process of analyzing itsinvestment decision-making procedures. Two projects evaluated by the firm recentlyinvolved building new facilities in different regions, North and South. The basicvariables surrounding each project analysis and the resulting decision actions aresummarized in the following table.Basic variables North SouthCost $6 million $5 millionLife 15 years 15 yearsExpected return 8% 15%Least-cost financingSource Debt EquityCost (after-tax) 7% 16%DecisionAction Invest Don’t investReason 8% . 7% cost 15% , 16% costa. An analyst evaluting the North facility expects that the project will be financedby debt that costs the firm 7%. What recommendation do you think this analystwill make regarding the investment opportunity?b. Another analyst assigned to study the South facility believes that funding for thatproject will come from the firm’s retained earnings at a cost of 16%. What recommendationdo you expect this analyst to make regarding the investment?c. Explain why the decisions in parts a and b may not be in the best interests of thefirm’s investors.d. If the firm maintains a capital structure containing 40% debt and 60% equity,find its weighted average cost using the data in the table.e. If both analysts had used the weighted average cost calculated in part d, what recommendationswould they have made regarding the North and South facilities?f. Compare and contrast the analyst’s initial recommendations with your findingsin part e. Which decision method seems more appropriate? Explain why.P9–2 Cost of debt using both methods Currently, Warren Industries can sell 15-year,$1,000-par-value bonds paying annual interest at a 12% coupon rate. As a resultof current interest rates, the bonds can be sold for $1,010 each; flotation costs of$30 per bond will be incurred in this process. The firm is in the 40% tax bracket.a. Find the net proceeds from sale of the bond, Nd.b. Show the cash flows from the firm’s point of view over the maturity of the bond.c. Calculate the before-tax and after-tax costs of debt.d. Use the approximation formula to estimate the before-tax and after-tax costs of debt.e. Compare and contrast the costs of debt calculated in parts c and d. Which approachdo you prefer? Why?P9–17 Calculation of individual costs and WACC Dillon Labs has asked its financial managerto measure the cost of each specific type of capital as well as the weighted averagecost of capital. The weighted average cost is to be measured by using the followingweights: 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 annualinterest at a 10% coupon rate. A flotation cost of 3% of the par value is requiredin addition to the discount of $20 per bond.Preferred stock Eight percent (annual dividend) preferred stock having a parvalue of $100 can be sold for $65. An additional fee of $2 per share must be paidto the mon 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. Itsdividend payments, which have been approximately 60% of earnings per share ineach of the past 5 years, were as shown in the following table.Year Dividend2015 $3.752014 3.502013 3.302012 3.152011 2.85It 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. Dividendpayments 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. ................
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