Ross Westerfield Jordan Essentials of Corporate Finance Third Edition

Problem List Click on a Problem number to jump to the slide Problem List Click on a Problem number to jump to the slide. Click on Return to Problem List to select a different Problem. Chapter 7 Problem 2 Problem 4 Problem 11 Problem 13 Chapter 8 Problem 1 Problem 7 Problem 10 Problem 13 Chapter 9 Problem 2 Problem 9 Problem 13 Problem 14 Chapter 10 Problem 1 Problem 9 Problem 21 Problem 25 Chapter 11 Problem 2 Problem 6 Problem 7 Problem 11 Chapter 12 Problem 3 Problem 6 Problem 12 Problem 15

Chapter 7 Equity Markets and Stock Valuation

Problem 7-2 The next dividend payment by BJG, Inc., will be $2 per share. The dividends are anticipated to maintain a 6 percent growth rate forever. If BJG stock currently sells for $35 per share, what is the required return? R = (D1 / P0) + g R = ($2.00 / $35.00) + .06 R = .1171 or 11.71% Return to Problem List

Problem 7-4 Motorheadache Corporation will pay a $4.00 per share dividend next year. The company pledges to increase it dividend by 4 percent per year indefinitely. If you require a 13 percent return on your investment, how much will you pay for the company’s stock today? P0 = D1 / (R – g) P0 = $4.00 / (.13 - .04) P0 = $44.44 Return to Problem List

Problem 7-11 Rebecca, Inc. has a new issue of preferred stock they call 20/20 preferred. The stock will pay a $20 dividend per year but the first dividend will not be paid for 20 years. If you require a 9 percent return on this stock, how much should you pay today? P19 = D20 / R = $20 / .09 = $222.22 P0 = P19 / (1 + R)19 Po = $222.22 / (1.09)19 P0 = $43.22 Return to Problem List

Problem 7-13 Metallica Bearings, Inc., is a young start-up company. No dividends will be paid over the next six years because the firm needs to plow back its earnings to fuel growth. The company will then pay an $8 per share dividend and will increase the dividend by 5 percent per year thereafter. If the required return on this stock is 16 percent, what is the current share price? P6 = D7 / (R – g) = $8.00 / (.16 - .05) = $72.73 P0 = P6 / (1 + R)6 = $72.73 / (1.16)6 P0 = $29.85 Return to Problem List

Chapter 8 Net Present Value and Other Investment Criteria

Problem 8-1 What is the payback period for the following set of cash flows? Year Cash Flows 0 –$2,500 1 300 2 1,500 3 900 4 300

After year 2, cash inflows = $300 + 1,500 = $1,800 Payback period = 2 + $700/$900 = 2.78 years Return to Problem List

Problem 8-7 A project that provides $900 for eight years costs $4,000 today. Is this a good project if the required return is 8 percent? What of it’s 24 percent? At what discount rate would you be indifferent between accepting the project and rejecting it? At 8%: NPV = –$4,000 + $900 [1 – 1/1.088]/.08 NPV = –$4,000 + $5,171.98 NPV = $1,171.98

At 24%: NPV = –$4,000 + $900 [1 – 1/1.248]/.24 NPV = –$4,000 + $3,079.10 NPV = –$920.90

NPV = 0 = –$4,000 + $900 {[1 – 1/(1+IRR)t] / IRR} Using a financial calculator or by trial and error, IRR = 15.29% Return to Problem List

Problem 8-10 Darby & Davis, LLC, has identified the following two mutually exclusive projects: Year Cash Flow (A) Cash Flow(B) 0 –$17,000 –$17,000 1 8,000 2,000 2 7,000 5,000 3 5,000 9,000 4 3,000 9,500 a. What is the IRR for each of these projects. If you apply the IRR decision rule, which project should the company accept? Is this decision necessarily correct? b. If the required return is 11 percent, what is the NPV for each of these projects? Which project will you choose if you apply the NPV decision rule? c. Over what range of discount rates would you choose Project A? Project B?At what discount rate would you be indifferent between these two projects?

a. For Project A: NPV = 0 = –$17,000 + $8,000/(1+IRR) + $7,000/(1+IRR)2 + $5,000/(1+IRR)3 + $3,000/(1+IRR)4 Solving with a financial calculator or by trial and error: IRR = 15.86% For Project B: NPV = 0 = –$17,000 + $2,000/(1+IRR) + $5,000/(1+IRR)2 + $9,000/(1+IRR)3 + $9,500/(1+IRR)4 IRR = 14.69%

b. For Project A: NPV = –$17,000 + $8,000/1.11+ $7,000/1.112 + $5,000/1.113 + $3,000/1.114 NPV = –$17,000 + 18,520.71 NPV = $1,520.71 For Project B: NPV = –$17,000 + $2,000/1.11 + $5,000/1.112 + $9,000/1.113 + $9,500/1.114 NPV = –$17,000 + $18,698.58 NPV = $1,698.58

c. Crossover rate, subtracting Project B from Project A: 0 = $6,000/(1+R) +$2,000/(1+R)2 – $4,000/(1+R)3 – $6,500/(1+R)4 Solving, we find R = 12.18% At discount rates above 12.18% choose Project A; for discount rates below 12.18% choose Project B; indifferent between A and B at a discount rate of 12.18%. Return to Problem List

Problem 8-13 What is the profitability index for the following set of cash flows if the relevant discount rate is 10 percent? What of the discount rate is 15 percent? If it is 22 percent? Year Cash Flow 0 – $5,000 1 3,000 2 2,000 3 1,200 At 10 percent: PI = [$3,000/1.10 + $2,000/1.102 + $1,200/1.103] / $5,000 PI = $5,281.74 / $5,000 PI = 1.056

At 15 percent: PI = [$3,000/1.15 + $2,000/1.152 + $1,200/1.153] / $5,000 PI = $4,910.00 / $5,000 PI = 0.982 At 22 percent: PI = [$3,000/1.22 + $2,000/1.222 + $1,200/1.223] / $5,000 PI = $4,463.59 / $5,000 PI = 0.893 Return to Problem List

Chapter 9 Making Capital Investment Decisions

Problem 9-2 Speedy Racer Corp. currently sells 18,000 motor homes per year at $40,000 each, and 6,000 luxury motor coaches per year at $55,000 each. The company wants to introduce a new portable camper to fill out its product line; it hopes to sell 12,000 of these campers per year at $10,000 each. An independent consultant has determined that if Speedy Racer introduces the new campers, it should boost sales of the existing motor homes by 5,000 units per year, and reduce the sales of its motor coaches by 2,000 units per year. What is the amount to use as the annual sales figure when evaluating this project? Why?

Sales of camper = 12,000($10,000) = $120 million Sales of motor home = 5,000($40,000) = $200 million Lost sales of luxury motor coach = 2,000($55,000) = $110 million The additional motor home sales are relevant as is the erosion of the motor coach sales. Net sales = $120M + $200M – $110M = $210M Return to Problem List

Problem 9-9 D. Ervin, Inc. is considering a new three-year expansion project that requires an initial fixed asset investment of $1.5 million. The fixed asset will be depreciated straight-line to zero over its three-year life, after which it will be worthless. The project is estimated to generate $1,750,0000 in annual sales, with costs of $575,00. If the tax rate is 35 percent, what is the OCF for this project?

OCF = EBIT + Depreciation – Taxes OCF = $675,000 + 500,000 – 236,250 Sales $1,750,000 Costs 575,000 Depreciation 500,000 EBIT 675,000 Taxes 236,250 Net income $ 438,750 OCF = EBIT + Depreciation – Taxes OCF = $675,000 + 500,000 – 236,250 OCF = $938,750 Return to Problem List

Problem 9-13 Kaleb’s Korndogs is looking at a new sausage system with an installed cost of $485,000. This cost will be depreciated straight-line to zero over the project’s five-year life, at the end of which the sausage system can be scrapped for $60,000. The sausage system will save the firm $123,000 per year in pretax operating costs, and the system requires an initial investment in net working capital of $27,000. If the tax rate is 34 percent and the discount rate is 10 percent, what is the NPV of this project?

Annual depreciation = $485,000/5 = $97,000 Aftertax salvage value = $60,000(1 – .34) = $39,600 Costs $123,000 Depreciation 97,000 EBIT 26,000 Taxes 8,840 Net income $ 17,160

OCF = $26,000 + 97,000 – 8,840 = $114,160 NPV = –$485,000 – $27,000 + $114,160 [1 – 1/1.105]/.10 + [($39,600 + $27,000)/1.105 NPV = –$37,890.42 Return to Problem List

Problem 9-14 Your firm is contemplating the purchase of a new $650,000 computer-based order entry system. The system will be depreciated straight-line to zero over its five-year life. It will be worth $150,000 at the end of that time. You will save $300,000 before taxes per year in order processing costs and you will be able to reduce working capital by $63,000 (this is a one-time reduction). If the tax rate is 35 percent, what is the IRR for this project?

Annual depreciation = $650,000/5 = $130,000 Aftertax salvage value = $150,000(1 – .35) = $97,500 Costs $ 300,000 Depreciation 130,000 EBIT 170,000 Taxes 59,500 Net income $ 110,500

0 = –$650,000 + 63,000 + 240,500 {1–[1/(1+IRR)5]/IRR} OCF = $170,000 + 130,000 – 59,500 = $240,500 0 = –$650,000 + 63,000 + 240,500 {1–[1/(1+IRR)5]/IRR} + [($39,600 + $27,000)/(1+IRR)5 Using a financial calculator or by trial and error: IRR = 30.70% Return to Problem List

Chapter 10 Some Lessons from Capital Market History

Problem 10-1 Suppose a stock had an initial price of $63 per share, paid a dividend of $1.25 per share during the year, and had an ending share price of $52. Calculate the percentage total return. R = (P1 – P0 + D1) / P0 R = ($52 – 63 + 1.25) / $63 R = –15.48% Return to Problem List

Problem 10-9 You’ve observed the following returns on Belmont Data Corporation’s stock over the past five years: 9 percent, –10 percent, 2 percent, 25 percent and 17 percent. a. What was the average return on Belmont’s stock over this five-year period? b. What was the variance of Belmont’s returns over this period? The standard deviation? a. Avg. return = (.09 – .10 + .02 + .25 + .17)/5 Avg. return = .086 or 8.6%

b. Variance = [(.09 – .086)2 + (–.10 –.086)2 + (.02 – .086)2 + (.25 – .086)2 + (.17 – .086)2] / (5 – 1) Variance = 0.01823 Standard deviation = (Variance)1/2 Standard deviation = (0.01823)1/2 Standard deviation = 0.1350 or 13.50% Return to Problem List

Problem 10-21 A stock had annual returns of 8 percent, –6 percent, 14 percent, 24 percent, 16 percent and 12 percent each for he past six years. What is the average return and standard deviation for this stock? a. Avg. return = (.08 – .06 + .14 + .24 + .16 + .12)/6 Avg. return = .1133 or 11.33%

Standard deviation = (Variance)1/2 Standard deviation = (0.01003)1/2 + (.14 – .1133)2 + (.24 – .1133)2 + (.16 – .1133)2 + (.12 – .1133)2] / (6 – 1) Variance = 0.01003 Standard deviation = (Variance)1/2 Standard deviation = (0.01003)1/2 Standard deviation = 0.1001 or 10.01% Return to Problem List

Problem 10-25 You bought one of Tappan Manufacturing Co.’s 9 percent coupon bonds one year ago for $1,002.50. The bonds make annual payments and mature six years from now. Suppose you decide to sell your bonds today, when the required return on the bonds is 10 percent. If the inflation rate was 3.5 percent over the past year, what would be your total real return on the investment? P1 = $1,000/(1.10)6 + $90[(1 – 1/1.106)/.10] P1 = $956.45

R = ($956.45 – 1,002.50 + 90) / $1,002.50 R = .0438 (1 + R) = (1 + r)(1 + h) 1 + .0438 = (1 + r)(1 + .065) (1.0438/1.065) – 1 = r r = –.0199 or –1.99% Return to Problem List

Chapter 11 Risk and Return

Total portfolio value = $600 +$1,400 = $2,000 wA = $600/$2,000 = .30 Problem 11-2 You own a portfolio that has $600 invested in Stock A and $1,400 invested in Stock B. If the expected returns on these stocks are 14 percent and 22 percent, respectively, what is the expected return on the portfolio? Total portfolio value = $600 +$1,400 = $2,000 wA = $600/$2,000 = .30 wB = $1,400/$2,000 = .70 E[RP] = .30(.14) + .70(.22) = .196 or 19.6% Return to Problem List

E[R] = .30(–.08) + .60(.14) + .10(.30) E[R] = .09 or 9.00% Problem 11-6 Based on the following information, calculate the expected return. State of Probability of State Rate of Return Economy of Economy if State Occurs Recession .30 –.08 Normal .60 .14 Boom .10 .30 E[R] = .30(–.08) + .60(.14) + .10(.30) E[R] = .09 or 9.00% Return to Problem List

Problem 11-7 Based on the following information, calculate the expected return and standard deviation for the two stocks. State of Probability of State Rate of Return if State Occurs Economy of Economy Stock A Stock B . Recession .15 .06 –.20 Normal .65 .07 .13 Boom .20 .11 .33

For Stock A: E[RA] = .15(.06) + .65(.07) + .20(.11) = .0765 Variance = .15(.06 – .0765)2 + .65(.07 – .0765)2 + .20(.11 – .0765)2 = .00293 Standard deviation = (Variance)1/2 Standard deviation = (.00293) Standard deviation = .0171 or 1.71%

Standard deviation = (Variance)1/2 Standard deviation = (.024245) For Stock B: E[RA] = .15(–.20) + .65(.13) + .20(.33) = .1205 Variance = .15(–.20 – .1205)2 + .65(.13 – .1205)2 + .20(.33 – .1205)2 = .024245 Standard deviation = (Variance)1/2 Standard deviation = (.024245) Standard deviation = .1557 or 15.57% Return to Problem List

Problem 11-11 You own a stock portfolio invested 20 percent in Stock Q, 20 percent in Stock R, 10 percent in Stock S and 50 percent in Stock T. The betas for these four stocks are 1.4,.6,1.5, and 1.8, respectively. What is the portfolio beta? p = .2(1.4) + .2(.6) + .1(1.5) + .5(1.8) = 1.45 Return to Problem List

Chapter 12 Cost of Capital

Problem 12-3 Stock in Sampras Industries has a beta of 1.05. The market risk premium is 8 percent and T-bills are currently yielding 5.5 percent. Sampras’s most recent dividend was $2.20 per share, and dividends are expected to grow at a 4 percent annual rate indefinitely. If the stock sells for $32 per share, what is you best estimate of Sampras’s cost of equity?

Using CAPM RE = .055 + 1.08(.08) = .1390 Using the DDM RE = (.1390 + .1115) / 2 = .1253 or 12.53% Return to Problem List

Problem 12-6 PC, Inc., is trying to determine its cost of debt. The firm has a debt issue outstanding with seven years to maturity that is quoted at 87 percent of face value. The issue makes semiannual payments and has an embedded cost of 6.5 percent annually. What is PC’s pretax cost of debt? If the tax rate is 38 percent, what is the aftertax cost of debt?

$870 = $1000/(1+R)14 + $32.50{[1 – 1/(1+R)14]/R} Using a financial calculator, or by trial and error: R = 4.52 % Pretax cost of debt = YTM = 4.52%  2 = 9.05% Aftertax cost of debt = YTM(1 – tax rate) Aftertax cost of debt = 9.05%(1 - .38) Aftertax cost of debt = 5.61% Return to Problem List

Problem 12-12 Merton has 8.2 million shares of common stock outstanding. The current share price is $52, and the book value per share is $4. Merton also has two bond issues outstanding. The first bond issue has a face value of $70 million, an 8 percent coupon, and sells for 103 percent of par. The second issue has a face value of $50 million, a 7.5 percent coupon and sells for 98 percent of par. The first issue matures in 10 years, the second in 6 years.

a . What are Merton’s capital structure weights on a book value basis? b. What are Merton’s capital structure weights on a market value basis? c. Which are more relevant, the book or market value weights?

a. BVE = 8,200,000($4) = $32,800,000 BVD = $70,000,000 + 50,000,000 = $120,000,000 V = $32,800,000 + 120,000,000 = $152,800,000 wE = $32,800,000 / $152,800,000 = 0.215 wD = $120,000,000 / $152,800,000 = 0.785

b. MVE = 8,200,000($52) = $426,400,000 MVD = 1.03($70,000,000) + 0.98($50,000,000) = $121,100,000 V = $426,400,000 + 121,100,000 = $547,500,000 wE = $426,400,000 / $547,500,000 = 0.779 wD = $121,100,000 / $547,500,000 = 0.221 c.The market value weights are more relevant because they represent a more current valuation of debt and equity. Return to Problem List

CS: 60,000 shares outstanding, selling for $75 per share; the Problem 12-15 Given the following information for Janicek Power Co., find the WACC. Assume the company’s tax rate is 35 percent. Debt: 5,000 8 percent coupon bonds outstanding, $1,000 par value, ten years to maturity, selling for 96 percent of par. CS: 60,000 shares outstanding, selling for $75 per share; the beta is 1.10. PS: 9,000 shares of 5.5 percent preferred stock outstanding, currently selling for $60 per share. Mkt.: 8 percent market risk premium and a 6 percent risk-free rate.

MVD = 5,000($1,000)(.96) = $4,800,000 MVE = 60,000($75) = $4,500,000 MVP = 9,000($60) = $540,000 V = $4,800,000 + 4,500,000 + 540,000 = $9,840,000 wD = $4,800,000 / $9,840,000 = .488 wE = $4,500,000 / $9,840,000 = .457 wP = $540,000 / $9,840,000 = .055

$960 = $1000/(1+R)14 + $40{[1 – 1/(1+R)14]/R} Using a financial calculator, or by trial and error: R = 4.30 % Pretax cost of debt = YTM = 4.30%  2 = 8.60% Aftertax cost of debt = YTM(1 – tax rate) = 8.60%(1 - .35) = 5.59%

WACC = (RD  wD) + (RE  wE) + (RP  wP) RE = .06 + 1.010(.08) = .1480 or 14.80% RP = $5.50 / $60 = .0917 or 9.17% WACC = (RD  wD) + (RE  wE) + (RP  wP) WACC = (.0559  .488) + (.1480  .457) + (.0917  .055) WACC = .1000 or 10.00% Return to Problem List