Corporate Finance, Fall 03 Exam #2 review questions (full solutions at end of document)

Corporate Finance, Fall 03 Exam #2 review questions (full solutions at end of document) 1. Portfolio risk & return. Idaho Slopes (IS) and Dakota Steppes (DS) are both seasonal businesses. IS is a downhill skiing facility, while DS is a tour company that specializes in walking tours and camping. The returns on each company over the next year is expected to be: Economy Idaho Slopes Dakota Steppes Strong Downturn -10% 2% Mild Downturn -4% 7% Slow Growth 4% 6% Moderate Growth 12% 4% Strong Growth 20% 4% a) Find the mean and variance of returns for each company. b) Find the covariance and correlation of returns for the two companies. c) If IS and DS are combined in a portfolio with 50% invested in each, find the portfolio expected return and standard deviation. IS = 4.4 DS = 4.6 s 2 IS = 0.011584 s 2 DS = 0.000304 s DS =.000056 r IS,DS = 0.0298 r p = 4.5 s P =.05477 2) CAPM Kindercare Inc. has a beta of 1.20. The risk free rate is 6% and the expected return on the market portfolio is 14.5%. The company presently pays an annual dividend of $5 per share, and investors expect it to experience a growth in dividends of 1% per annum for many years to come. a. What is the stock s present market price per share, assuming the required rate of return is determined by the CAPM? b. Consider an alternative investment in the stock of Maxicare Inc. Maxicare has an expected return of 15% and a beta of 1.5. Should you purchase this stock? (why or why not?) a. P = 33.22 b. dont buy Maxicare. 3) CAPM The risk-free rate is 5.5%, and the market portfolio has an expected return of 14%. The market portfolio has a standard deviation of 10%. Stock Z has a correlation coefficient with the market of 0.2 and a standard deviation of 12%. According to the CAPM, what is the expected rate of return on stock Z? r z = 7.54% 4. Cost of capital

Hook Corp. has $100 million face value of outstanding debt with a coupon of 10% and a yield to maturity of 8% (annualized). The bonds make semi-annual payments, and have 10 years to maturity. The company also has 1 million shares of common stock with book value per share of $35 and a market value per share of $50. The current beta of the stock is 1.5. The treasury Bill rate is 5%, and the market risk premium is 8.5%. The company is in the 40% tax bracket. What is the company s current weighted average cost of capital? r WACC = 8.76% 5. Risk & Return: Estimating beta. You wish to estimate the beta of your company by looking at comparable firms. You have gathered the data on the firms indicated below. If you are currently all-equity financed and face a tax rate of 35%, what would be an appropriate estimate for your beta? Firm Beta D/E X 1.2 0.33 Y.8 0.25 Z 1.3 0.40 b unlev =.907 6. Cost of capital a. Einstein Bagels is considering expanding into the gourmet coffee business. The coffee business is expected to be 20% of the overall firm value in 1998, and the average beta of comparable coffee firms is 1.30; the average debt/equity ratio for these firms is 60%. The marginal corporate tax rate is 36%. Einstein's equity beta at the end of 1997 was 0.90, and the company's debt/equity ratio was 80%. If Einstein maintains its current debt equity ratio, what will its equity beta be in 1998? b. After the expansion, Einstein's cost of debt will be 11%. If the Treasury bond rate is 7%, and the historical market risk premium is 5.5%, find Einstein's weighted average cost of capital. a. New Einstein levered beta = 1 b. WACC = 10.07% 7. Capital Structure: Modigliani Miller Theorems Assume you are in a Modigliani Miller world with corporate taxes but no costs of financial distress. GTE has perpetual EBIT of $8 million per year and an all equity discount rate (r 0 ) of 12%. GTE has $15 million of debt outstanding at a cost 8%, and its corporate tax rate is 34%. a) What is GTE s value? b) What is GTE s cost of equity? a. V L = $49.1 b. R S = 13.16%

8. Capital Structure Theory a. Assume you are in a Modigliani Miller world (MM propositions I and II hold). AB Corporation is unlevered and is valued at $640,000. AB is currently deciding whether including debt in their capital structure would increase their value. Under consideration is issuing $300,000 in new debt with an 8% interest rate. AB would repurchase $300,000 of stock with the proceeds of the debt issue. There are currently 32,000 shares outstanding and their effective marginal tax bracket is zero. (i) What will the firm value be after the change? (ii) What will the share price be and how many shares will be outstanding after the change? b. Now assume you are in a Modigliani Miller world with corporate taxes added. CD Corp. is all equity financed with 5,000 shares outstanding worth $7 each. They are planning on issuing $10,000 of new perpetual debt at the 8% market rate of interest. The effective tax rate is 25%. What is the market value of the firm s outstanding equity after they make the debt for equity exchange? a.i. New firm value: $640,000 (MM Prop I) a. ii. Number of shares outstanding = 17,000, Share price = $20/share b. E = 27,500 9. Capital Structure. You have been asked by AB Corporation to evaluate its capital structure. The company currently has 20 million shares outstanding trading at $20 per share. In addition, it has $250 million public debt outstanding, rated AA and with a yield to maturity of 8%. The beta for the company is 1.0, the current Treasury bond rate is 6%, and the market risk premium is 5.5%. The tax rate is 40%. AB Corporation is proposing to borrow an additional $150 million to use as follows: - Repurchase $30 million worth of stock - Pay $80 million in dividends - Invest $40 million in a project with a NPV of $30 million. The additional borrowing will cause the bond rating to fall to BBB, which currently carries a yield to maturity of 10%. How will the firm s cost of capital change with this additional borrowing? (hint: to simplify your calculations, assume the total firm value used in computing WACC does not have to consider the change in firm value due solely to the change in total cost of capital) Current WACC = 8.92% New WACC = 9.11%

10. Capital Structure. GE Corp. is examining its capital structure with the intent of arriving at an optimal debt ratio. It currently has no debt and has a beta of 1.5. The riskless interest rate is 9%, and the risk premium is 8.3%. Your research indicates that the debt rating will as follows at different debt levels: D/(D+E) Rating Interest rate 0% AAA 10% 10% AA 10.5% 20% A 11% 30% BBB 12% 40% BB 13% 50% B 14% 60% CCC 16% 70% CC 18% 80% C 20% 90% D 25% The firm currently has 1 million shares outstanding at $ 20 per share. (Tax rate = 40%) What is the firm's optimal debt ratio? Beta with no debt is 1.50. D E Beta Cost of Cost of WACC equity debt 0.5 0.5 2.40 0.2892 0.14 0.1866 optimal 11. Long term financing. You are analyzing a convertible preferred stock, with the following characteristics for the security: There are 50,000 preferred shares outstanding, with a face value of $100 and a 6% preferred dividend rate. The firm has straight preferred stock outstanding, with a preferred dividend rate of 9%. The preferred stock is trading at $105. Estimate the preferred stock and equity components of this preferred stock. Value of Straight Preferred Stock portion of Convertible = 66.67 Value of Conversion Portion = 38.33 12. Measuring Risk. Chrysler, the automotive manufacturer, had a beta of 1.05 in 1995. It had $13 billion in debt outstanding in that year, and 355 million shares trading at $50 per share. The firm had a cash balance of $8 billion at the end of 1995. The marginal tax rate was 36% a. Estimate the unlevered beta of the firm. b. Estimate the effect of paying out a special dividend of $5 billion on this unlevered beta. c. Estimate the beta for Chrysler after the special dividend. a. b Utotal =.715 b. b U,auto =.966 New b U = 0.853 c. New b L = 1.41

13. Cost of capital The Limited Group s assets have a total market value of $1,000 million. $600 million of the asset value is in the company's clothing division, which has an unlevered beta of 1.2. The other $400 million of the asset value is in the company's specialty retailing division. The company s equity (levered) beta is 1.8. The company s current outstanding debt is worth $250 million. $200 million of this debt is allocated to the clothing division. The rest of the debt is in the specialty retail division. The company has just announced the acquisition of RK Shoes, a small footwear company. RK is a private company and has no debt in its capital structure. The Limited s investment bankers estimate that RK has a beta of 1.5. The Limited is going to raise the necessary $50 million for the acquisition by issuing new debt. This new debt, as well as the newly acquired assets, will be allocated to The Limited s specialty retailing division. What are The Limited s divisional asset (unlevered) betas after the acquisition? What will the beta be for the company s stock after the acquisition? Assume that The Limited has a 40% tax rate. b unlevered,clothing = 1.2 b U,new SR = 1.90 New levered beta: b L = = 1.86 14. Risk & Return You run a regression of XYZ stock returns against the market returns using monthly observation over a five-year period. You had an intercept of 0.20% and a slope of 1.20. Over this time period, XYZ s stock return had an annualized standard deviation of 40% whereas the market standard deviation was only 20%. The risk free rate has been 6% on average over the last five years, and currently it is at 7%. The historical risk premium has been 8.5%. The annualized dividend per share currently is $2.00, and the stock is currently selling at $50. There are 100,000 shares outstanding. (a) What proportion of XYZ risk is diversifiable? (b) What would you expect XYZ s stock price to be one year from today? (c) XYZ currently has $5 million in debt outstanding and its marginal tax rate is %40. XYZ is planning on selling one of its divisions for $5 million. This division has an asset beta of 0.5. XYZ will use the proceeds from the sale to pay $3 million as dividends to its stockholders. The rest will be used to retire debt. What will the beta be after this restructuring? (a) 1 - R 2 = 0.64 (b) P 1 = $56.6 (c) b AFTER = 1.9 diversifiable risk

full solutions 1) Portfolio risk and return IS = (-10-4+4+12+20)/5 = 4.4 DS = (2+7+6+4+4)/5 = 4.6 s 2 IS =.2{(-.10-.044) 2 +(-.04-.044) 2 +(.04-.044) 2 +(.12-.044) 2 +(.2-.044) 2 } = 0.011584 s 2 DS =.2{(.02-.046) 2 +(.07-.046) 2 +(.06-.046) 2 +(.04-.046) 2 +(.04-.046) 2 } = 0.000304 s DS = {(-.10-0.44)(.02-.046)+ (-.04-0.44)(.07-.046)+ (.04-0.44)(.06-.046)+ (.12-0.44)(.04-.046)+ (.20-0.44)(.04-.046)} =.000056 r IS,DS = (.000056)/(.011584) (.000304) = 0.0298 r p =.5*4.4+.5*4.6=4.5 s P = {.5 2 *.00304 +.5 2 *.011584 + 2*.5*.5*.000056} 1/2 =.05477 2) CAPM r m =.145 r f =.07 b k = 1.2 E(r k ) =.06 + 1.2(.145-.06) =.162 P = (5*1.01)/(.162-.01) = 33.22 b. E(r MX ) =.15 b MX = 1.5 1 st. Compare risk reward ratios: Market (r m -r f )/ b m =.085 Kindercare (r K -r f )/ b K = (.162-.06)/1.2 =.085 Maxicare (r MK -r f )/ b MX = (.15-.06)/1.5 =.06 expected return is too low relative to systematic risk, dont buy Maxicare. Or, 2 nd from CAPM: E(r MX ) =.06 + 1.5*(.145-.06) =.1875 Since return is lower than that predicted by CAPM (below security market line), don t buy it. 3) CAPM s zm =r zm s z s m =.2*.1*.12 =.0024 b Z =s zm /s 2 m =.0024/.1 2 =.24 r z =.055+.24*(.14-.055) =7.54%

4. Cost of capital D: $100M. FV, 10% coupon rate, semi-annual pmts. 10 yrs to maturity, YTM 8% MV DEBT = $5/0.04 [1-1/1.04 20 ] + $100/(1.04) 20 = 113.59M MV EQUITY = (1 M)( $50) = $ 50 M MV FIRM = 113.59 + 50 = 163.59 b = 1.5 T-Bill rate = 5% Risk-premium = 8.5 % T = 40% r e = 5% + (1.5)(8.5%) = 17.75% r WACC = (50/163.59) * (17.75%) + (113.59/163.59) * (1-0.4) * (8%) = 8.76% 5. Risk & Return: Estimating beta. ave beta = 1.1 ; ave D/E =.327 b unlev = 1.1/[1+.327(1-.35)] =.907 6. Cost of capital a. Unlever coffee beta: 1.3/(1+(1-.36).6)=.9393 Unlever Einstein beta:.9/(1+(1-.36).8) =.595 New Einstein unlevered beta: 80%*.595 + 20%*.9393 =.66386 New Einstein levered beta:.66(1+(1-.36).8)=1 b. cost of capital: r d =.11 r e =.07 + 1*.055 =.125 D/V =.8/1.8 =.444 E/V = 1/1.8 =.556

WACC =.8/1.8*.11*(1-.36) + 1/1.8*.125 = 10.07% 7. Capital Structure: Modigliani Miller Theorems a. V L = V U + T C B = EBIT(1-T C )/r 0 + T C B = $8(.66)/.12 +.34*$15 = $49.1 b. R S =r 0 +B/S(r 0 -r B )(1-T C ) =.12 + [15/( 49.1-15)]*(.12-.08)*.66 = 13.16% 8. Capital Structure Theory a. i. New firm value: $640,000 (MM Prop I) ii. Share price = 640,000/32,000 = $20/share Number of shares repurchased = 300,000/20 = 15,000 Capital structure = D + E = 300,000 + 340,000 MVE = 340,000 Number of shares outstanding = 32,000-15,000 = 17,000 Share price = $20/share b. Original firm value = 5,000*7 = 35,000 Tax shield = T c B =.25(10,000) = 2,500 New firm value = 37,500 37,500 = D+E = 10,000 + E ; E = 27,500 9. Capital Structure. Current value of equity = $400 million Current value of debt = $250 million Cost of equity =.06 + 1.0*.055 = 11.5% Cost of debt = 8% Current WACC = 250/650*8%*(1-.4) + 400/650*11.5% = 8.92% NPV of project accrues to equity, so Equity = $400 $30 - $80 + $30 = $320 Debt = $250 + $150 = $400 New D/E ratio = 400/320 Unlevered beta = 1/(1+0.6*250/400) = 0.727 New levered beta = 0.727*(1+0.6*400/320)) = 1.27 New cost of equity =.06 + 1.27*.055 = 13% New WACC = 400/720*10%*(1-.4) + 320/720*13% = 9.11% 10. Capital Structure. Beta with no debt is 1.50. Need to calculate new beta as D/E changes. D E Beta Cost of Cost of WACC equity debt 0 1 1.50 0.2145 0.10 0.2145 0.1 0.9 1.60 0.2228 0.11 0.2068

0.2 0.8 1.73 0.2332 0.11 0.1997 0.3 0.7 1.89 0.2465 0.12 0.1942 0.4 0.6 2.10 0.2643 0.13 0.1898 0.5 0.5 2.40 0.2892 0.14 0.1866 optimal 0.6 0.4 2.85 0.3266 0.16 0.1882 0.7 0.3 3.60 0.3888 0.18 0.1922 0.8 0.2 5.10 0.5133 0.20 0.1987 0.9 0.1 9.60 0.8868 0.25 0.2237 11. Long term financing. Value of Straight Preferred Stock portion of Convertible = 6/.09 = $ 66.67! Perpetual Life Value of Conversion Portion = $ 105 - $ 66.67 = $ 38.33 12. Measuring Risk. Before Cash 8 billion D=13 billion Auto 22.75 E=17.75 billion billion b unlevered = 1.05/[1+13/17.75*(1-.36)] =.715 b cash = 0 b U =.715 = b U,auto *22.75/30.75 + b cash *8/30.75 b U,auto =.966 After Cash 3 billion Auto 22.75 billion D=13 billion E=12.75 billion New b U = b U,auto *22.75/25.75 + b cash *3/25.75 = 0.853 New b L = 0.853*[1+13/12.75*(1-.36)] = 1.41 13. Cost of capital b Levered,CLOTHING+SR = 1.8 b unlevered,clothing = 1.2 b RK = 1.5 BEFORE A: $600M D: $200M (Clothing division) E: $400M

A: $400M (SR division) D: $50 E: $350 AFTER A: $600M D: $200M (Clothing division) E: $400M A: $450M (SR division) D: $100 E: $350 b L = b U * 1+ (1 T) D E 250 1.8 = b U,COTHING+SR * 1 + 0.6 b U,CLOTHING+SR = 1.50 before. 750 b U,CLOTHING+SR = 1.5 = 600/1000 * 1.2 + 400/1000 * b U,SR ; b U,SR = 1.95 After, b U,new SR = 400/450 * 1.95 + 50/450 * 1.5 = 1.90 So asset beta for new SR division = 1.90; asset beta for clothing division equals original 1.2 New levered beta:, b U,new total = 600/1050 * 1.2 + 450/1050 * 1.9 = 1.50 300 b L = 1.50 * 1 + 0.6 = 1.86 750 14. Risk & Return a = 0.30%, b= 1.20 R i = r f + B(r m - r f ) = (1-B) r f + Br m s xyz = 0.4, s m = 0.2 r f = 6% (historical) (7% now) r f - r m = 8.5% D = $2/share P o = $50 n = 100,000 shares (a) R 2 = b 2 s m 2 /s xyz 2 = 1.2 2 (0.2) 2 /(0.4) 2 = 0.36 systematic

1 - R 2 = 1-0.36 = 0.64 diversifiable risk (b) r xyz = 7% + 1.2(8.5%) = 17.2% (P 1 + 2 50) / 50 = 17.2 % P 1 = $56.6 (c) Before A = $10 M D = $5 M E = 100,000 * 50 = $5 M b E = 1.2 ; 1.2 = b u * [ 1 + 0.6 (5/5) ] b u = 0.75 b u = 0.75 = 1/2 (0.5) + 1/2 b u, 2 b u,2 = 1 After A = $5 M D = $3M E = $2 M b AFTER = (1) * [1 + 0.6(3/2) ] = 1.9

additional problems done in class: Quick Mart is a small convenience store thinking of adding a donut shop in the store to serve their commuting customs breakfast. They have complied the following information on companies in the donut business: Comparable firm Beta Debt/Equity ratio Krispy Crème 1.2 0.2 Dunkin Donut 1.7 0.5 H&H 1.3 0.75 The appropriate corporate tax rate is 34%, and Quick Mart s management has set a target D/E ratio of.3 for the donut project. The market risk premium is 6%, and the risk free rate is 5%. a. Estimate an unlevered beta using the comparable firms. b. Estimate the levered beta for the new project. c. Estimate the cost of equity for the donut shop. Solution Average beta=1.4 Average D/E=0.4833 Unlevered beta=1.4/(1+(1-0.34)*0.4822)=1.0614 1.0614*(1+(1-0.34)*0.3)=1.2716 0.05+1.2716*0.06=0.1263

Measuring risk You have run a regression of AB Corp s stock returns against the market and determined its equity beta is 1.5. The company has, in market value terms, $500 million of debt and $500 million of equity. The company currently has two divisions. Division A, which has a market value of $600 million, produces disk drives and you find 5 listed companies on the NYSE which made only disk drives. These companies have an average beta of 1.31 and an average debt equity ratio of 20%. Division B produces memory chips and you cannot find any comparable companies. Assume all companies face a tax rate of 50%. a. What is the asset (unlevered) beta for division B? b. If the company divests itself of Division B and increases its debt equity ratio to 2, what would the company s beta be? Solution β L,AB =1.5 A=600 D=500 B=400 E=500 β L,Acomps =1.31 D/E of Acomps =0.2 β U,Acomps =1.31/[1+(1-0.5)*0.2]=1.31/1.1=1.19 β U,AB =1.5/[1+(1-0.5)*1]=1 1=β U,AB =600/1000*β U,A +400/1000*β U,B =0.6*1.19+0.4*β U,B β U,B =0.715 β L,A =β U,A *[1+(1-0.5)*2]=1.19*2=2.38