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Sheet1 Spring 1998 Problem 1 Bond Rating = BBB Interest Rate = 9.00% After-tax Cost of Debt = 5.40% Unlevered Beta = 1.06/(1+(1-0.4)(.1111)) = 0.993756211 Beta at 25% D/E Ratio = 0.99(1+0.6(.25)) = 1.142819643 Cost of Equity = 7% + 1.14 (5.5%) = 13.27% Cost of Capital = 5.40% (.2) + 13.27% (.8) = 11.70% Problem 2 Change in Firm Value = (250 + 50) (.11-.10)(1.05)/(.10-.05) = 63 Change in stock price = 63/10 = $ 6.30 ($10.50 if you assume buyback at current price) Problem 3 (100/250) (2) + (150/250) (X) = 5 Solve for X, X = 7 years Spring 1999 Problem 1 Value of Bank Loan = 4 (PVA,7%,5) + 50/(1.07)^5 = $52.05 Value of Bonds Outstanding = $50.00 PV of Operating Leases = 10 (PVA,7%,7) = $53.89 Market Value of Outstanding Debt= $155.94 Market Value of Equity = 15* 10 = $150.00 Debt Ratio = 155.94/(150+155.94) = 50.97% Cost of Equity = 6% + 1.2 (5.5%) = 12.60% Cost of Capital = 12.60%(.49) + 7% (1-.4)(.51) = 8.32% Adjusted EBIT = 40 + 53.89*0.7 = $43.77 Adjusted BV of Capital = 50 + (50 + 50 + 53.89) = 203.89 Adjusted Return on Capital = 43.77 (1-.4)/203.89 = 12.88% Problem 2 Change in Firm Value = 3 * 10 = $30.00 Firm Value (Chg in WACC) (1.05)/(WACC(after)-.05) = 250 (Chg in WACC)(1.05)/(.10 -.05)= 30 Chg in WACC = 0.57% WACC before = 10.57% Ke (.8) + 8%(1-.4) (.2) = 10.57% Cost of Equity before transaction = (.1057-.0096)/.8 = 12.01% Problem 3 Value of firm before expansion = 300 + 70*10 = 1000 Duration of assets after expansion = 7.5 (1000/1250) + 1 (250/1250) = Weighted Duration of Assets has to be equal to 6.2years (200/550)(1) + (100/550)(4) + (250/550) (X) = 6.2 Solve for X X = 11.24 years Page 1 Sheet1 Spring 1999 (A) Problem 1 PV of operating leases = $ 1,408 Straight Debt portion of convertible debt = $ 1,798 Total Debt = $ 3,206 Equity Value of stock = $ 3,000 Value of conversion option = 2500-1798= $ 702 Value of Equity = $ 3,702 Cost of Equity = 5.5% + 1.25(6.3%) = 13.375% Cost of Debt (after-tax) = 7.5%(1-.4)= 4.50% Cost of Capital = 13.375% (3702/6908) + 4.50% (3206/6908) = 9.26% Problem 2 Change in Firm Value = 500 5000 (.10 - WACC after)/WACC after = 500 Solve for WACC after, WACC after = 500/5500 = 9.09% Cost of Equity after = 5.5% + 1 (6.3%) = 0.118 11.8(X) + 5% (1-X) = 9.09% Solve for X, X = (9.09-5)/6.8 = 60% Debt to Capital ratio = 40% Problem 3 Cody's should have long term debt: Negative coefficient suggests duration of 7.5 years BAM should have floating rate debt: Oper income tends to move with inflation Spring 2000 Problem 1 a. False. It has to be weighed off against the increase in both costs b. True. It will reduce the marginal tax advantage of debt c. True. The net operating loss carry forward will reduce the tax benefit of the debt. (No matter how the the argument is structured, the firm without net operating losses will be able to borrow more money and get a larger tax savings. The NOL will reduce the income available from which interest expenses can be deducted. d. False. If you are more uncertain about future investment needs, you will value flexibility more and borrow less. Problem 2 Current cost of capital = Cost of equity (because firm has no debt) = 9.20% Change in firm value = .1375 = (Cost of capital before - Cost of capital after)/Cost of capital after 0.1375 = (0.092 - Cost of capital after)/Cost of Capital after Solving, Cost of capital after = 0.092/(1+.1375) = 8.09% Cost of equity after = 10.48% Cost of debt after = 4.5% 10.48% (1-X) + 4.5% (X) = 8.09% Solving for X, X = 40% Page 2 Sheet1 Problem 3 Duration of assets = 7 Existing Debt = 1 (duration of this debt = 4 years) New Debt = 3 (1/(1+3)) (4) + (3/(1+3)) X = 7 ! Since the asset mix does not change, the duration remains 7. Solving Duration of new debt = 8 Proportion on new debt that has to be 2 year debt = 25% (.25(2) + .75(10) = 8) Spring 2001 Problem 1 a. Current Cost of Equity = 10.72% ! 5% + 1.04*5.5% ! If you decide to use the effective tax Current cost of debt = 3.90% has to be that you do not have enoug Current cost of capital = 8.47% ! 10.72% (.67) + 3.9% (.33) However, this will mean that the effec If you did this, I gave you full credit. b. New debt to capital ratio = 50% New debt to equity ratio = 100.00% ! I gave full credit if you read the incre Unlevered Beta = 0.8 of the existing interest rate (I did take New Beta = 1.28 if you read it as 25% New cost of equity = 12.0400% ! You lost a point if you did not unleve New after-tax cost of debt = 4.05% New Cost of capital= 8.05% c. Number of shares bought back = 21.7391304 ! Since the price at which you were bu c. Change in annual financing cost = $6.37 cannot divide by the total number of s Change in firm value = $79.13 Change per share = $0.59 ! Transfer of wealth to stockholders s Problem 2 Market value of the firm = 2000 ! 1000/.5 Dollar debt at optimal of 25% = 500 ! Don't increase the size of the firm. Otherwise, asset Duration of debt at optimal Let X be the proportion of the debt that is 5-year debt at optimal X (4) + (1-X) (8) = 7 X = .25 The firm has to have $ 125 million in 5-year debt and $ 375 million in 10-year debt It needs to pay off $ 275 million of 5-year debt and $ 225 million of 10 year debt. Spring 2002 Problem 1 Part a: Current cost of capital Beta = 1.15 Math error: -0.5 Cost of equity = 9.85% forgot to after-tax cost of debt: -0.5 Cost of capital = 9.23% ! Debt ratio = 10% Part b: New cost of capital Unlevered beta = 1.078125 ! Forgot to adjust cost of equity : - New levered beta = 1.35535714 ! Don't forget to unlever and relever ! Math errors: -0.5 New cost of equity = 10.67% New cost of capital = 8.73% Page 3 Sheet1 Part c Borrow money over next 5 years and pay dividends Its stockholders like dividends, because it has paid large dividends in the past Its projects earn less than its cost of capital Problem 2 Cost of capital before = 9.00% Cost of capital after 8.00% Change in firm value = 824 ! Forgot to consider the effect of growth : -1 point Increase in dollar debt to get to 25% = 1000 Number of shares bought back = 12.5 Number of shares left = 37.5 ! Did not adjust the number of shares for buybac Increase in value per share = 21.9733333 ( Remember that you cannot divide by 50 if you a Problem 3 a. Long term, Dollar, Fixed Rate, Straight ! Heavy infrastructure: Long term ! U.S. operations: Dollar ! No pricing power: Fixed ! Low growth: Straight b. Long term, Mixed Currency, Floating Rate, Straight ! Brand Name: Long term ! Worldwide operations: Mixed Currency ! Pricing power: You can pass inflation through… ! High margins and cashflows : Straight (Some o c. Short term, Dollar, Fixed Rate, Convertible ! Speedy Obsolescence: Short term ! U.S. operations: Dollar ! High Uncertainty: Floating (but Competitive Ind ! High growth: Convertible Spring 2003 Problem 1 Current cost of capital = 9% Current debt ratio = 0.25 Current after-tax cost of debt = 0.036 Current cost of equity = 0.108 Current beta = 1.45 Unlevered beta = 1.21 New levered beta = 2.30 ! Debt = 3000; Equity = 2000; Stock buyback reduces the value Cost of equity = 14.18% New cost of capital = 8.19% Change in firm value $393.82 ! (.09 - .0819) (4000)/.0819 ! If you had the NPV of the new in Number of shares = 100 Price at which bought back = $33.00 Number bought back = 30.3030303 ! 1000/33 Number remaining = 69.6969697 Page 4 Sheet1 Change in value per share = $4.35 ! (393.82 - (33-30) (30.30))/69.70 Price per share after transaction = $34.35 Problem 2 Duration of existing debt = 2.00 Duration of new debt = 6.50 Currency break down Dollar debt = 50% Euro debt = 50% ! $1 billion of Euro debt needed to get to $ 1 billion (1/3 of total debt) Spring 2004 Problem 1 New beta = 1.12 Cost of equity = 0.093984 Interest coverage ratio = 3.75 Rating = BB+ Cost of debt = 0.06 After-tax cost of debt = 0.036 Cost of capital = 7.08% Problem 2 a. Value of firm = 1050 ! 80*10+250 Cost of capital = 10% Cashflow last year = 50 1050 = 50 (1+g)/ (Cost of capital -g) Expected growth rate= 0.05 1050 = 50 (1+g)/(.10-g) b. Increase in value from recapitalization Annual cost at current cost of capital = 105 Annual cost at new cost of capital = 94.5 Annual savings = 10.5 PV at expected growth rate = 262.5 c. If investors are rational, savings will accrue to all stockholders Increase in value per share = 3.28125 New stock price = 13.28125 Number of shares bought back = 18.8235294 Number of shares left = 61.1764706 Problem 3 6 (150/500) + 8 (100/500) + X (250/500) = 10 Solving for X, Duration of new bond = 13.2 Since the firm has little pricing power, you would go with fixed rate debt Since half of its revenues come from the EU region, half of its total debt of $ 500 million should be in Euros Hence the firm should use 100% Fixed rate, Euro debt Page 5 Sheet1 Spring 2005 Problem 1 Value of unlevered firm = 1000 !100 *10 !This firm has no debt. This is the With $250 million in debt, used to buy back stock Value of levered firm = 1025 ! 100 *10.25 Tax benefit from additional debt = 100 ! Tax rate * Dollar Debt Value of levered firm = Value of unlevered firm + Tax benefit - (Probability of bankruptcy * Cost of bankruptcy) 1025 = 1000 + 100 - (X* .30*1000) Probability of bankruptcy = 25% Problem 2 Current market value of equity = 4000 Market value of debt = 1000 Value of firm = 5000 Cost of capital = 10.44% = Cost of equity (.80) + 4.2% (.20) Cost of equity = 0.12 Current beta = 1.75 After debt is repaid New beta = 1.52173913 New cost of equity = 11.09% ! Equal to cost of capital New firm value = $4,708.24 ! Change in firm value = (.1044-.1109) 5000/.1109 Problem 3 a. Current asset duration = 0.75(10) + 0.25 (5) = 8.75 b. Expected asset duration if tourism business doubles = (0.75/1.25)(10) + (0.5/1.25) (5) = To solve for duration of new debt (.5/.75)*6+(.25/.75)*X = 8 ! New debt issue = 0.25 Duration of new debt = 12 Fall 2006 Problem 1 a. Cost of equity = 4.5% + 1.00*4% = 8.50% Cost of capital = 8.5% (.9) + 5% (.1) = 8.15% b. With change in tax status and leverage Unlevered beta = 0.9 ! 1/ (1+(1-0)(1/9)) New levered beta = 1.44 ! 0.9 (1+(1-.4)(50/50)) Cost of equity = 10.26% Cost of capital = 6.93% ! 10.26% (.5)+6%(1-.4)(.5) c. Change in firm value, assuming 3% growth rate Savings in costs each year = $12.20 ! 1000 (.0815-.0693) Increase in firm value = $310.43 ! 12.20/(.0693-.03) Firm value after transaction = $1,310.43 Page 6 Sheet1 Price paid on transaction For equity = 11.5*90= $1,035.00 For debt = $100.00 Total price paid = $1,135.00 Value gained in transaction = $175.43 Prtoblem 2 Duration of assets after divestiture = 8.25 Duration of debt after transactiion Let the proportion of 10-year bonds after the repayment be X X(10) + (1-X) (2) = 8.25 Solving for X, X= 0.78125 Dollar debt after repayment = 8 -4 = 4 ! Repaid $ 4 billion of debt 10-year bonds after the repayment = 3.125 2-year bonds after the repayment = 0.875 Repaid amounts 10-year bonds = 2.875 2-year bonds = 1.125 Spring 2007 Problem 1 8.44% a. Cost of capital at existing debt ratio = ! 13%(.4)+9%(1-.4)(.6) b. Beta at current cost of equity = 2 ! (13-5)/4 Unlevered beta = 1.0526 New Debt to Equity Ratio = 42.86% ! (600-300)/(400+300) Levered Beta = 1.3233083 New cost of equity 10.29% New cost of capital 8.29% Problem 2 a. Change in firm value = $11.11 ! (80+20)(.10-.09)/.09 b. Number of shares bought back = 6 $6.00 Share of firm value to buy back shares ! 6* $1/share $5.11 Share of firm value to remaining shares Number of shares remaining 14 ! 20-6 Value increase per remaining share$0.37 Problem 3 Duration of existing assets = 8 ! 2(5/20)+10(15/20) Duration of existing debt = 8 Duration after transaction 6.8 ! 2(5/12.5)+10(7.5/12.5) To estimate the duration of the new debt 8(5/10) + X(5/10) = 6.8 Duration of new debt = 5.6 Spring 2008 Page 7 Sheet1 Problem 1 Old debt to equity = 0% Current beta = 1.00 ! Cost of equity is 9%; Rf =5% and Risk premium =4% New debt to equity = 42.86% ! 600/1400; Debt used to buy back stock New beta = 1.2571 New cost of equity = 10.03% New after-tax cost of debt = 3.60% Debt Ratio = 30.00% ! 600/ (600 +1400) Cost of capital = 8.100% Problem 2 Current cost of capital = 12% New cost of capital = 10.00% Market value of firm = 1000 ! 200 + 800 Annual cost savings = 20 PV of savings (with g=4%) = 333.333333 ! 20/ (.1-.04): Okay if you used (1+g) New firm value = 1333.33333 b. Value of firm = 1333.33333 - Debt = 500 ! Paid off $ 300 million out of $ 800 million Value of equity = 833.333333 Number of shares = 30 Value per share = $27.78 Here is anyother way to get to the same solution Increase in firm value = $333.33 Discount on stock offered = $100.00 ! The discount on the private placement Remaining value savings = $233.33 / Number of shares= $30.00 Increase in value per share= $7.78 Added tos hare price = $27.78 Problem 3 Existing assetsNew Business Value of business 100 50 Duration of assets 7.5 3 Weighted duration = 6 ! 7.5(100/150)+3 (50/150) Existing debt New debt Value 25 50 Duration 5X Solving for duration of new debt 5 * (25/75) + X (50/75) = 6 Duration of new debt = 6.50 Spring 2009 Problem 1 a. Existing cost of capital Weoight Estimated value Cost Risk measure Debt 600 0.6 6.00% BB Equity 400 0.4 17.68% 2.28 Capital 1000 10.67% Page 8 Sheet1 b. New cost of capital New debt ratio = 30.00% New D/E ratio = 0.4285714 Unlevered beta = 1.2 New levered beta = 1.5085714 Weight Cost Risk Measure Debt 30.00% 3.90% A Equity 70.00% 0.1305143 1.5085714 10.31% Problem 2 Current cost of equity = Current cost of capital = 10.00% If investors are rationa, all shares get an equal portion of increase in firm value Increase in firm value = 100 ! Since investors are rational, all shares gain $1.00. Solving for cost of capital after, (Cost of capital before - Cost of capital after)*Existing firm value/ Cost of capital after =100 (.10-Cost of Capital after)*1000/ cost of capital after = 100 Cost of capital after = 9.09% Beta after = 1.4 ! Lever the beta, using new debt/equity ratio Cost of equity after= 12.400% 12.4% (.6) + X(1-.4) (.4) = .0909 Pre-tax cost of debt = 6.88% I kept the firm value constant at 1000 in the example above. If you use 1100 as firm value, the answers will b D/E ratio after = 0.5714286 Beta after = 1.3428571 Cost of equity after = 12.06% 12.06% (700/1100) + X (1-.4) (400/1100)= .0909 Pre-tax cost of debt = 6.49% Problem 3 Weighted duration of assets after cash is used = 8.4 ! Weighted average of just operating asset Duration of the debt has to be equal to this after the debt is paid off: (since cash is being used for retiring deb X (10) + (1-X) (0) = 8.4 84% of the debt has to be 10-year zero coupon debt. Total debt outstanding after debt retirement = 1300 ! Debt outstnading before - Debt repaid !0-year zero coupon debt = 1092 ! 84% of outstanding debt 10-year coupon debt to be paid off = 108 ! Long term debt repaid Short trm debt to be paid off = 92 ! Short term debt repaid Page 9 Sheet1 Alternatively, you can assume that the bank debt is at market value Market Value of Debt = 153.94 If you do this, the cost of debt will be a weighted average of 7% and 8%, the cost of debt will be around 7.5%. 29.925 6.2 Page 10 Sheet1 Common errors 1. Reversed the cost of capital before and after in firm value change calculation. 2. Computed change in firm value incorrectly 3. Did not use after-tax cost of debt 4. Other math errors. Page 11 Sheet1 32.6086956 Common errors 1. Misread the problem to read change by instead of change to. ange, the duration remains 7. 2. Tried to change asset duration (why?) 3. Set up new debt incorrectly (had two unknowns with one equation) 25(2) + .75(10) = 8) 4. Other errors. If you decide to use the effective tax rate, the rationale as to be that you do not have enough operating income to cover your interest expenses. owever, this will mean that the effective tax rate should be 10% in part b (since debt is doubled) you did this, I gave you full credit. I gave full credit if you read the increase as 0.25% f the existing interest rate (I did take off half a point 78.2608696 you read it as 25% You lost a point if you did not unlever and relever betas Since the price at which you were buying back the stock was given, you annot divide by the total number of shares outstanding. Transfer of wealth to stockholders selling back stock = (11.50-10)*21.739 ax cost of debt: -0.5 Forgot to adjust cost of equity : -1 Math errors: -0.5 Page 12 Sheet1 ! Closely held, outperformed: Not target of a takeover - No immediacy ! ROC < Cost of capital : Don't invest ! History of paying dividends: Pay more dividends the number of shares for buyback : -1 at you cannot divide by 50 if you are buying back at the current price) ucture: Long term 0.25 points off for each mistake erations: Mixed Currency You can pass inflation through… Hence, floating rate debt and cashflows : Straight (Some of you made the argument for convertible because of intangibility of asset, but the cashflows are predictable escence: Short term nty: Floating (but Competitive Industry: Fixed - So, I gave credit for both) Stock buyback reduces the value of equity If you had the NPV of the new investment, you can add that on. Page 13 Sheet1 billion (1/3 of total debt) d be in Euros Page 14 Sheet1 This firm has no debt. This is the unlevered firm value. 1. Tried to force cost of capital approach through: -2 to -3 2. Wrong bankrupcty cost: -0.5 to -1 3. Other errors: -0.5 to -1 !Note that the stock price increases on the announcement to reflect what the firm will be worth after the transaction t of bankruptcy) 1. Error in estimating current cost of equity: -0.5 2. Did not unlever beta: -0.5 3. Estimated new cost of equity wrong: -0.5 4. Used old cost of equity instead of capital in computing firm value ch 5. Did not compute PV of annual savings: -0.5 6. Did not compute increase in firm value at all: -1 4-.1109) 5000/.1109 Current Balance Sheet 1. Weighted businesses incorrectly: -0.5 Transporation 0.75 Debt 0.5 2. Did not compute new weights after bu Tourism 0.25 Equity 0.5 3. Did not compute new dollar debt corre 4. Mixed up asset and debt durations: -1 New Balance Sheet Transporation 0.75 Debt 0.75 ! Issued 0.25 of debt to fund doubling of Tourism 0.5 Equity 0.5 ! Mechanical errors: -0.5 ! Tax effect: -0.5 ! Unlevered with tax rate: -0.5 ! Relevered with wrong debt to equity: -0.5 ! Forgot to tax effect cost of debt: -0.5 ! Wrong debt ratio: -0.5 ! Okay if you used (1+g) in numerator ! Change in firm value incorrect: -1 to -1.5 Page 15 Sheet1 ! Gan/Loss on Sale: -1 to -1.5 ! Duration for assets computed incorrectly: -1.5 to -2 ! Dolalr debt after restructuring incorrect: -1 ! Breakdown of debt after restructuring: -1 to -1.5 Page 16 Sheet1 Grading Guidelines 1. Did not adjust the cost of equity at all: -1.5 points 2. Error in beta estimation: -0.5 to -1 point 3. Weights incorrect: -0.5 point 4. Forgot to after-tax cost of debt: -0.5 point 1. Cost savings per year incorrect: -0.5 point 2. PV of savings incorrect: -1 point 3. Math errors: -0.5 point each 1. Divided by existing number of shares: -1 point 2. Error in computing per share value: -.5 to -1 point 1. Asset duration incorrect: -0.5 to -1.5 points (depending) 2. Debt duration incorrect: -0.5 to -1 point 3. Math error: -0.5 point ! Wrong cost of debt : -.5 ! Math error: -.5 Page 17 Sheet1 ! Wrong debt ratio: -0.5 to -1 ! Forgot to unlever and relever beta: -1 ! Used Debt to capital ratio to lever beta: -0.5 ! Wrong cost of cebt : -.5 ! Firm value computed incorrectly: -1 ! Did not lever beta: -1 ors are rational, ! Error in setting up new WACC: -.5 to -1 after =100 w debt/equity ratio irm value, the answers will be different. ! Computed beta of assets including cash: -1 verage of just operating assets debt) s being used for retiring(Cash is used up after the transaction) Did not comptue the new debt level right: -1 Other math errors: -.5 point ading before - Debt repaid tanding debt Page 18 Sheet1 Page 19 Sheet1 Page 20 Sheet1 Page 21 Sheet1 sset, but the cashflows are predictable and brand name has high marketable value) Page 22 Sheet1 Page 23 Sheet1 l approach through: -2 to -3 e worth after the transaction cost of equity: -0.5 y wrong: -0.5 ead of capital in computing firm value change: -0.5 ual savings: -0.5 n firm value at all: -1 . Weighted businesses incorrectly: -0.5 . Did not compute new weights after business changed: -0.5 . Did not compute new dollar debt correctly: -0.5 . Mixed up asset and debt durations: -1 Issued 0.25 of debt to fund doubling of tourism business Page 24

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Net Operating Loss Carry Forward document sample

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