Homework 10 AND 11 - homewirk 10 and 11 PDF

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HOMEWORK 10: 1) What are the portfolio weights for a portfolio that has 142 shares of Stock A that sell for $45 per share and 122 shares of Stock B that sell for $30 per share? STOCK A: .6358 STOCK B:.3642 The portfolio weight of an asset is the total investment in that asset divided by the total portfolio value. First, we will find the portfolio value, which is: Portfolio value = 142($45) + 122($30) Portfolio value = $10,050 The portfolio weight for each stock is the dollar value of the investment in that stock divided by the portfolio value, or: WeightA = 142($45)/$10,050 WeightA = .6358 WeightB = 122($30)/$10,050 WeightB = .3642

2) You own a portfolio that has $3,000 invested in Stock A and $4,000 invested in Stock B. If the expected returns on these stocks are 8 percent and 11 percent, respectively, what is the expected return on the portfolio? 9.71%

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5) You own a stock portfolio invested 30 percent in Stock Q, 20 percent in Stock R, 35 percent in Stock S, and 15 percent in Stock T. The betas for these four stocks are .85, 1.18, 1.02, and 1.20, respectively. What is the portfolio beta? 1.03 The beta of a portfolio is the sum of the weight of each asset times the beta of each asset. So, the beta of the portfolio is: βP = .30(.85) + .20(1.18) + .35(1.02) + .15(1.20) βP = 1.03

6) A stock has a beta of 1.18, the expected return on the market is 12 percent, and the risk-free rate is 4 percent. What must the expected return on this stock be? 13.44

7) A stock has an expected return of 13 percent, the risk-free rate is 7 percent, and the market risk premium is 8 percent. What must the beta of this stock be? .75 We are given the values for the CAPM except for the β of the stock. We need to substitute these values into the CAPM, and solve for the β of the stock. One important thing we need to realize is that we are given the market risk premium. The market risk premium is the expected return of the market minus the risk-free rate. We must be careful not to use this value as the expected return of the market. Using the CAPM, we find:

E(Ri) = .13 = .07 + .08βi βi = (.13 − .07)/.08 βi = .75

8) A stock has an expected return of 12 percent, its beta is 1.30, and the riskfree rate is 5 percent. What must the expected return on the market be? 10.39 Here we need to find the expected return of the market using the CAPM. Substituting the values given, and solving for the expected return of the market, we find: E(Ri) = .12 = .05 + [E(RM) − .05](1.30) E(RM) = .1038, or 10.38%

9) Stock Y has a beta of .9 and an expected return of 12.6 percent. Stock Z has a beta of .6 and an expected return of 8.9 percent. What would the riskfree rate have to be for the two stocks to be correctly priced? 1.50% We need to set the reward-to-risk ratios of the two assets equal to each other, which is: (.126 – Rf)/.9 = (.089 – Rf)/.6 We can cross multiply to get: .6(.126 – Rf) = .9(.089 – Rf) Solving for the risk-free rate, we find: .0756 – .6Rf = .0801 – .9Rf Rf = .0150, or 1.50%

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12) Suppose the risk-free rate is 3.9 percent and the market portfolio has an expected return of 10.6 percent. The market portfolio has a variance of .0352. Portfolio Z has a correlation coefficient with the market of .25 and a variance of .3255 According to the capital asset pricing model, what is the expected return on Portfolio Z? 8.99

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HOMEWORK 11: 1) The Nixon Corporation’s common stock has a beta of 1.7. If the risk-free rate is 4.8 percent and the expected return on the market is 10 percent, what is the company’s cost of equity capital? 13.64% With the information given, we can find the cost of equity using the CAPM. The cost of equity is: RS = .048 + 1.7(.10 – .048) RS = .1364, or 13.64%

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3) Mullineaux Corporation has a target capital structure of 60 percent common stock and 40 percent debt. Its cost of equity is 11.7 percent, and the cost of debt is 6.4 percent. The relevant tax rate is 22 percent. What is the company’s WACC? 9.02% Using the equation to calculate the WACC, we find: RWACC = .60(.117) + .40(.064)(1 − .22) RWACC = .0902, or 9.02%

4) Miller Manufacturing has a target debt-equity ratio of .75. Its cost of equity is 11.7 percent and its cost of debt is 6.4 percent. If the tax rate is 22 percent, what is the company’s WACC? 8.83% Here we need to use the debt-equity ratio to calculate the WACC. Doing so, we find: RWACC = .117(1/1.75) + .064(.75/1.75)(1 – .22) RWACC = .0883, or 8.83%

5) Fama’s Llamas has a weighted average cost of capital of 8.5 percent. The company’s cost of equity is 12.1 percent, and its cost of debt is 6.7 percent. The tax rate is 25 percent. What is the company’s debt-equity ratio? Here we have the WACC and need to find the debt-equity ratio of the company. Setting up the WACC equation, we find: RWACC = .0850 = .121(S/V) + .067(B/V)(1 – .25) Rearranging the equation, we find: .0850(V/S) = .121 + .067(.75)(B/S) Now we must realize that the V/S is just the equity multiplier, which is equal to: V/S = 1 + B/S .0850(B/S + 1) = .121 + .0503(B/S) Now we can solve for B/S as: .03475(B/S) = .036 B/S = 1.0360

6) Kose, Inc., has a target debt-equity ratio of 1.59. Its WACC is 7.8 percent, and the tax rate is 24 percent. If the company’s cost of equity is 14 percent, what is its pretax cost of debt? 5.13% If instead you know that the aftertax cost of debt is 6.2 percent, what is the cost of equity? 10.34 a. Using the equation to calculate WACC, we find: RWACC = .078 = (1/2.59)(.14) + (1.59/2.59)(1 – .24)RD RB = .0513, or 5.13% b. Using the equation to calculate WACC, we find: RWACC = .078 = (1/2.59)RE + (1.59/2.59)(.062) RS = .1034, or 10.34%

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a. If the firm's rate of return is used as the benchmark, then a project with a return that is lower than the firm's cost of capital will be rejected while a project with a return higher than the firm's cost of capital will be accepted. So, Project W would be rejected, Project X would be rejected, Project Y would be accepted, and Project Z would be accepted. b. Using the CAPM to consider the projects, we need to calculate the expected return of each project given its level of risk. This expected return should then be compared to the expected return of the project. If the return calculated using the CAPM is lower than the project expected return, we should accept the project; if not, we reject the project. After considering risk via the CAPM: E[W] E[X] E[Y] E[Z]

= .053 + .65(.123 – .053) = .0985 > .095, so reject W = .053 + .74(.123 – .053) = .1048 < .107, so accept X = .053 + 1.33(.123 – .053) = .1461 > .142, so reject Y = .053 + 1.44(.123 – .053) = .1538 < .173, so accept Z

c. Project W would be correctly rejected, Project X would be incorrectly rejected, Project Y would be incorrectly accepted, and Project Z would be correctly accepted.

8) Suppose your company needs $12 million to build a new assembly line. Your target debt-equity ratio is .4. The flotation cost for new equity is 8 percent and the flotation cost for debt is 5 percent. Your boss has decided to fund the project by borrowing money because the flotation costs are lower and the needed funds are relatively small. a What is your company’s weighted average flotation cost, assuming all equity . is raised externally? 7.14% b What is the true cost of building the new assembly line after taking flotation . costs into account? 12,972,679 a. The weighted average flotation cost is the weighted average of the flotation costs for debt and equity, so: fT = .05(.40/1.4) + .08(1/1.4) fT = .0714, or 7.14% b. The total cost of the equipment including flotation costs is: Amount raised (1 – .0714) = $12,000,000 Amount raised = $12,000,000/(1 – .0714) Amount raised = $12,923,077 Even if the specific funds are actually being raised completely from debt, the flotation costs, and hence true investment cost, should be valued as if the firm’s target capital structure is used.

9) Och, Inc., is considering a project that will result in initial aftertax cash savings of $1.81 million at the end of the first year, and these savings will grow at a rate of 1 percent per year indefinitely. The company has a target debt-equity ratio of .75, a cost of equity of 12.1 percent, and an aftertax cost of debt of 4.9 percent. The cost-saving proposal is somewhat riskier than the usual projects the firm undertakes; management uses the subjective approach and applies an adjustment factor of +2 percent to the cost of capital for such risky projects. What is the maximum initial cost the company would be willing to pay for the project? 18,075,000 Using the debt-equity ratio to calculate the WACC, we find:

RWACC = (.75/1.75)(.049) + (1/1.75)(.121) RWACC = .0901, or 9.01%

Since the project is riskier than the company, we need to adjust the project discount rate for the additional risk. Using the subjective risk factor given, we find:

Project discount rate = 9.01% + 2% Project discount rate = 11.01%

We would accept the project if the NPV is positive. The NPV is the PV of the cash outflows plus the PV of the cash inflows. Since we are seeking the cost, we just need to find the PV of inflows. The cash inflows are a growing perpetuity. If you remember, the equation for the PV of a growing perpetuity is the same as the dividend growth equation, so:

PV of future CF = $1,810,000/(.1101 – .01) PV of future CF = $18,074,179.74

The project should only be undertaken if its cost is less than $18,074,179.74 since costs less than this amount will result in a positive NPV.

10 )Schultz Industries is considering the purchase of Arras Manufacturing. Arras is currently a supplier for Schultz and the acquisition would allow Schultz to better control its material supply. The current cash flow from assets for Arras is $6.8 million. The cash flows are expected to grow at 5 percent for the next five years before leveling off to 2 percent for the indefinite future. The costs of capital for Schultz and Arras are 9 percent and 7 percent, respectively. Arras currently has 3 million shares of stock outstanding and $25 million in debt outstanding. What is the maximum price per share Schultz should pay for Arras? 44.45 We are given the total cash flow for the current year. To value the company, we need to calculate the cash flows until the growth rate levels off at a constant perpetual rate. So, the cash flows each year will be: Year 1: $6,800,000(1 + . 05) Year 2: $7,140,000(1 + . 05) Year 3: $7,497,000(1 + . 05) Year 4: $7,871,850(1 + . 05) Year 5: $8,265,442(1 + . 05) Year 6: $8,678,715(1 + . 02)

= $7,140,000 = $7,497,000 = $7,871,850 = $8,265,442 = $8,678,715 = $8,852,289

We can calculate the terminal value in Year 5 since the cash flows begin a perpetual growth rate. Since we are valuing Arras, we need to use the cost of capital for that company since this rate is based on the risk of Arras. The cost of capital for Schultz is irrelevant in this case. So, the terminal value is: TV5 = CF6/(RWACC – g) TV5 = $8,852,289/(.07 – .02) TV5 = $177,045,778 Now we can discount the cash flows for the first 5 years as well as the terminal value back to today. Again, using the cost

of capital for Arras, we find the value of the company today is: V0 = $7,140,000/(1 + .07) + $7,497,000/(1 + .07) 2 + $7,871,850/(1 + .07)3 + $8,265,442/(1 + .07)4 + ($8,678,715 + 177,045,778)/(1 + .07)5 V0 = $158,371,505 The market value of the equity is the market value of the company minus the market value of the debt, or: S = $158,371,505 – 25,000,000 S = $133,371,505 To find the maximum offer price, we divide the market value of equity by the shares outstanding, or: Share price = $133,371,505/3,000,000 Share price = $44.46...