Chapter 16 In Class Problems - Solutions

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Solutions for Chapter 16 In-class Practice Problems 1. You own 25% of Unique Vacations, Inc. You have decided to retire and want to sell your shares in this closely held, all equity firm. The other shareholders have agreed to have the firm borrow $1.5 million to purchase your 1,000 shares of stock. What is the total value of this firm today if you ignore taxes? Price per share = $ 1,500,000 1,000 = $ 1,500 Current noof shares = 1,000 0.25 = 4,000 [ ( 4,000 − 1000 ) ∗ $ 1,500 ] + $ 1,500,000 = $ 6,000,000 ∨ simply 4,000 ∗ $ 1,500 = $ 6,000,000 2. Your firm has a debt-equity ratio of .75. Your pre-tax cost of debt is 7% and your required return on assets is 15%. What is your cost of equity if you ignore taxes? r E = r A + ( r A − r D ) D E = 0.15 + ( 0.15 − 0.07 ) 0.75 1 = 0.21 = 21% 3. Bigelow, Inc. has a cost of equity of 13.56% and a pre-tax cost of debt of 7%. The required return on the assets is 11%. What is the firm’s debt-equity ratio based on MM Proposition II with no taxes? r E = 0.1356 = r A + ( r A − r D ) D E = 0.11 + ( 0.11 − 0.07 ) D E → D E = 0.64 4. Gail’s Dance Studio is currently an all equity firm that has 80,000 shares of stock outstanding with a market price of $42 a share. The current cost of equity is 12% and the tax rate is 34%. Gail is considering adding $1 million of debt with a coupon rate of 8% to her capital structure. The debt will be sold at par value. What is the levered value of the equity? V L = V U + D T C =( 80,000 ∗ $ 42 )+ ( 1,000,000 ∗ 0.34 ) = 3,700,000 V L = FirmValue = V E + V D → V E = $3.7m − $1m = $2.7m 5. Hey Guys!, Inc. has debt with both a face and a market value of $3,000. This debt has a coupon rate of 7% and pays interest annually. The expected earnings before interest and taxes is $1,200, the tax rate is 34%, and the unlevered cost of capital is 12%. What is the firm’s cost of equity? V U = EBIT ( 1 − T C ) R U = 1,200 ∗ ( 1 − 0.34 ) 0.12 = $ 6,600 V L = V U + D T C = 6,600 + ( 3,000 ∗ 0.34 ) = $ 7,620 V L = FirmValue = V E + V D →V E = V L − V D = $ 7,620 − $ 3,000 = $ 4,620

r E = r U + ( r U − r D ) D E ( 1 − T c ) = 0.12 + ( 0.12 − 0.07 ) 3,000 4,620 ∗( 1 − 0.34 )= 0.1414 = 14.14% 6. Bertha’s Boutique has 2,000 bonds outstanding with a face value of $1,000 each and a coupon rate of 9%. The interest is paid semi-annually. What is the amount of the annual interest tax shield if the tax rate is 34%? Annual Intrerest tax Shield = D ∗ R D ∗ T c → ( 2000 ∗ 1,000 )∗ 0.09 ∗ 0.34 = 61,200 7. A firm has debt of $5,000, equity of $16,000, a cost of debt of 8%, a cost of equity of 12%, and a tax rate of 34%. What is the firm’s weighted average cost of capital? WACC = E V r E + D V r D ( 1 − T C ) = 16,000 21,000 ∗ 12% + 5,000 21,000 ∗ 8% ∗ ( 1 − 0.34 ) = 10.40% 8. If a firm is unlevered and has a cost of equity capital 12%, what would its cost of equity be if its debt-equity ratio became 2? The expected cost of debt is 8%. r E = r A + ( r A − r D ) D E ∗( 1 − T c )= 0.12 + ( 0.12 − 0.08 ) 2 1 = 0.20 = 20% 9. A firm has zero debt in its capital structure. Its overall cost of capital is 9%. The firm is considering a new capital structure with 40% debt. The interest rate on the debt would be 4%. Assuming that the corporate tax rate is 34%, what would its cost of equity capital with the new capital structure be? r E = r A + ( r A − r D ) D E ∗ ( 1 − T c ) = 0.09 + ( 0.09 − 0.04 ) ∗ 0.4 0.6 ∗( 1 − 0.34 )= 0.112 = 11.2% 10. Consider two firms, U and L, both with $100,000 in assets. Firm U is unlevered, and firm L has $40,000 of debt that pays 5% interest. There are two investors, Mike and Steve, who own 20% of firm L each. Mike believes that leverage works in his favor. Steve says that this is an illusion, and that with the possibility of borrowing on his own account at 5% interest, he can replicate Mike's payout from firm L. Given a level of operating income of $5000, show the specific strategy that Steve has in mind. Mikeis entitled ¿ 0.2 ( $ 5000 − $ 2000 )= $ 6000.2 ∗( Operatingincome − Interest expense ) Steveliquidateshis position ( 20% of L’ s equity )∧ receives 20% ∗( 100,000 − 40,000 )= $ 12,000 Steve borrows $ 8,000 at 5% interest ( 20% of Firm L' s Debt )∧ pays $ 400 ∈ interest . Stevethen purchases 20% of FirmU ∧ pays 20% ∗( 100,000 )= $ 20,000 Steveisnow entitled ¿ receive 20% ∗( $ 5000 )= $ 1000 ¿ firmU ’ searnings. Steve' stotal payout is $ 1000 − $ 400 = $ 600 , ∨ Mike' s payout . 11. The Nantucket Nugget is unlevered and is valued at $640,000. Nantucket is currently deciding whether including debt in its capital structure would increase its value. The current cost of equity is 12%. Under consideration is issuing $300,000 in new debt with an 8% interest rate. Nantucket would repurchase $300,000 of stock with the

proceeds of the debt issue. There are currently 32,000 shares outstanding and effective marginal tax bracket is zero. What will Nantucket's new WACC be? New FirmValue : $ 640,000 +( .0 )( $ 300,000 )= $ 640,000 Capital Structure = D + E = 300,000 + 340,000 r E ¿ 0.12 +( 300 / 340 )∗( 0.12 − 0.08 )= 0.12 + 0.0353 = 0.1553 = 15.53% WACC =( 300 / 640 )∗( 0.08 )+( 340 / 640 )∗( 0.1553 )= 0.0375 + 0.0825 = 0.12 = 12% The value of the firm stays at $ 640,000 ( MM I ) ,the cost of levered equity rises ¿ 15.53% ∧ the WACC remainsat 12% . 12. ( WACC ) The Nantucket Nugget is unlevered and is valued at $640,000. Nantucket is currently deciding whether including debt in its capital structure would increase its value. The current of cost of equity is 12%. Under consideration is issuing $300,000 in new debt with an 8% interest rate. Nantucket would repurchase $300,000 of stock with the proceeds of the debt issue. There are currently 32,000 shares outstanding and its effective marginal tax bracket is 34%. What will Nantucket's new WACC be? New FirmValue : $ 640,000 +( .34 )( $ 300,000 )= $ 742,000 Capital Structure = D + E = $ 300,000 + $ 442,000 r E = 0.12 +( 300 / 442 )∗( 0.12 − 0.08 )∗( 1 − 0.34 )= 0.12 + 0.0179 = 0.1379 = 13.79% WACC =( 300 / 742 )∗( 0.08 )∗( 1 − 0.34 )+( 442 / 742 )∗( 0.1379 )= 0.0213 + 0.0821 = 0.1034 = 10.34 % The value of the firm increases ¿ $ 742,000 ( ¿ Valueof the Tax Shield ) ,increasingthe relative weight of equity ∧ the cost of levered equityrises ¿ 13.79% ∧ the WACC falls ¿ at 10.34% whichisconsistent withthe increase ∈ firm value .

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13. ( BREAK-EVEN EPS EBIT ) Solin Inc. has 2,000,000 shares outstanding, $4,000,000 of debt at 5% interest and is subject to 35% tax rate. An additional $1,000,000 has to be raised, and the following alternatives are available:  Common shares  The company can issue equity at $5 a share  200,000 new shares.  Debt  Debt can be issued at 5% again. (Solin does not use debt to repurchase shares.) Compute EPS asafunction of EBIT for both alternatives ∧ derivethe break even point . You need to equalize the EPS values under both “shares” and “debt” capital structures to find the break-even EBIT. EPS shares = ( EBIT − Interest )( 1 − T c ) ¿ of sharesoutstanding = [ EBIT − ( 4,000,000 ∗ 0.05 ) ] ∗( 1 − 0.35 ) 2,000,000 + 200,000 EPS debt = ( EBIT − Interest )( 1 − T c ) ¿ of shares outstanding = [ EBIT − ( 5,000,000 ∗ 0.05 ) ]∗( 1 − 0.35 ) 2,000,000 EPS shares = EPS debt → [ EBIT − ( 4,000,000 ∗ 0.05 ) ] ∗ 0.65 2,200,000 = [ EBIT − ( 5,000,000 ∗ 0.05 ) ]∗ 0.65 2,000,000 ( EBIT − 200,000 ) ∗ 0.65 2,200,000 = ( EBIT − 250,000 ) ∗ 0.65 2,000,000 →EBIT = $ 750,000 EPS shares = EPS debt = $ 0.1625 Numerator representsthe aftertax earnings,whiledenominator ¿ of sharesoutstanding . ¿ findthebreakeven point ,equatethe EPS for the twoalternatives ∧ solvefor the EBIT . If EBIT < $ 750,000 ,commonshares wouldbe favoured ,but if EBIT > $ 750,000 debt wouldbe favoured .

14. Homemade Leverage Example: • You have 150 shares of an all-equity firm. • There are 9,000 shares outstanding. • EBIT = $40,000 and P 0 = $42 • Company is considering a new capital structure with 40% debt at 8% interest rate. Ignore taxes. a) Calculate the current and proposed capital structures. Current Cap. Structure : Proposed Cap. Structure : Assets Debt (0) Assets Debt (378,000*0.4) = 151,200 378,000 378,000 Equity Equity 9000*42=378,000 226,800 Firm will use debt in order to repurchase shares. 151,200 42 = 3600 shareswill berepurchased b) What’s the CF to you (as a S/H of 150 shares) under both capital structures? Current (unlevered) Proposed (levered) EBIT = $40,000 EBIT = $40,000 Int = 0 Int = (151,200*0.08) = $12,096 Tax = 0 Tax = 0 EPS = ¿ ¿ of shares = 40,000 9000 = $ 4.444444 EPS = ¿ ¿ of shares = 40,000 − 12,096 9000 − 3600 = $ 5.167407 CF to you  150 shares * 4.44 EPS = $666.667 CF to you  150 shares * 5.17 EPS = $775.11 c) Assume that the firm keeps the current all-equity capital structure, and you’d like to have the proposed one. Can you use the homemade leverage to replicate the payoff of proposed capital structure? CF unl = $666.667  You have this. CF lv = $775.11  You’d like to have this.

Increase leverage  You own stock of unlevered firm + Borrow & purchase more = Levered CF. You need to replicate the capital structure of the levered firm in your personal portfolio. Debt = 151,200 Equity = $226,800  Debt Equity = 151,200 226,800 = 2 3  this D/E ratio will be applied in your own portfolio. Personal equity = 150 *42 = $6300 Personal debt = 6300 * 2 3 = 4200 So, you need to borrow $4,200 and pay 8% interest for this loan just like the firm. You will purchase additional stocks with this loan  4200 42 = 100 shareswillbe purchased. Now, you own 150 + 100 = 250 shares of the unlevered firm and $4,200 of personal debt. CF to you  250 * 4.444444 = $1111.11 Interest on debt  4,200 * 0.08 = $336 Net CF to you  1110 – 336 = $775.11 You have successfully replicated the payoff of the investor who invests in the levered firm by staying in the unlevered firm and mimicking the levered firm’s capital structure in your personal portfolio. d) Now assume that you own 150 shares in the company that follows the proposed capital structure, that is levered and following a D/E ratio of 2/3. Can you use the homemade leverage to replicate the payoff of current capital structure (unlevered firm’s capital structure)? CF unl = $666.667  You’d like to have this. CF unl = $775.11  You have this. Decrease leverage in your personal portfolio  You own stock of levered firm + Sell & Lend = Un Levered CF. You need to replicate the capital structure of the unlevered firm in your personal portfolio.  Debt Equity = 151,200 226,800 = 2 3  this D/E ratio will be applied in your own portfolio. Personal levered investment value = 150 *42 = $6300, only the equity portion of proposed cap. Structure. Personal lending should be  6300 * 2 5 = $ 2520 of your levered investment value. So, you need to sell $2520 worth of stocks and lend it to earn 8% interest. $ 2520 42 = 60 sharesneed ¿ be sold . After that, you’ll be left with 150-60=90 shares, each of which will bring $5.1674 EPS. You’ll make the following CF from earnings  90 * $5.1674 = $465.06 You’ll also make an interest income of  $2520 * 8% = $201.60 So, you’ll have a total CF of $465.06 + $201.60 = $666.66 You have successfully replicated the payoff of the investor who invests in the unlevered firm by staying in the levered firm and mimicking the unlevered firm’s capital structure in your personal portfolio.

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15. MM Arbitrage Example 1: The Veblen Company and the Knight Company are identical in every respect except that Veblen is not levered. Financial information for the two firms appears in the following table. All earnings streams are perpetuities, and neither firm pays taxes . Both firms distribute all earnings available to common stockholders immediately. Veblen Knight Operating Cash Flow 400,000 400,000 Year-end interest on debt ----- 72,000 Market Value of stock 3,600,000 2,532,000 Market Value of debt ----- 1,200,000 a) What will the annual cash flow be to an investor who purchases 5% of Knight's equity? Our investor will switch from Knight’s equity to that of Veblen. How much is she going to need extra? Cash flow from Knight to shareholder = 0.05*($400,000 – 72,000) = $16,400 Selling 5% of Knight’s equity, you have: Knight inv . = 0.05 ∗( $ 2,532,000 )= $ 126,600 Purchasing 5% of Veblen, you need: Vebleninv . = 0.05 ∗( $ 3,600,000 )= $ 180,000 Investor will need to borrow: Amount ¿ borrow = $ 180,000 – 126,600 = $ 53,400 An investor who owns 5% of Knight’s equity will be entitled to 5% of the firm’s earnings available to common stock holders at the end of each year. While Knight’s expected operating income is $400,000, it must pay $72,000 to debt holders before distributing any of its earnings to stockholders. So, the amount available to this shareholder will be:

CF ¿ who ∋ 5% of Knight = 0.05 ∗( 400,000 − 72,000 )= $ 16,400 b) What is the annual net cash flow to the investor if 5 percent of Veblen's equity is purchased instead? Assume that borrowing occurs so that the net initial investment in each company is equal. The interest rate on debt is 6 percent per year. Veblen will distribute all of its earnings to shareholders, so the shareholder will receive: Cashflow ¿ Veblen ¿ shareholder = 0.05 ∗( $ 400,000 )= $ 20,000 However, to have the same initial cost, the investor has borrowed $53,400 to invest in Veblen, so interest must be paid on the borrowings. The net cash flow from the investment in Veblen will be: Net cash flow ¿ Veblen = $ 20,000 – 0.06 ∗( $ 53,400 )= $ 16,796 For the same initial cost, the investment in Veblen produces a higher dollar return . c) Given the two investment strategies in (a), which will investors choose? Both of the two strategies have the same initial cost. Since the dollar return to the investment in Veblen is higher, all investors will choose to invest in Veblen over Knight. The process of investors purchasing Veblen’s equity rather than Knight’s will cause the market value of Veblen’s equity to rise and/or the market value of Knight’s equity to fall. Any differences in the dollar returns to the two strategies will be eliminated, and the process will cease when the total market values of the two firms are equal. 16. MM Arbitrage Example 2 There are two firms, U and L, having the same EBIT of $20,000. They are identical in every respect except firm L has a debt of $100,000 at 7% rate of interest. The cost of equity of firm U is 10% and that of firm L is 11.5%. Assume that you own 10% of shares of the firm L. Show how the arbitrage principle will be applied in this setting. Also assume that all earnings streams are perpetuities. There are no taxes and both firms distribute all earnings available to common stockholders. Value of Equity = V U , Equity = EBIT − Interest Cost of Equity = 20,000 − 0 0.10 = $ 200,000 for firmU . Since firmU has nodebt V U = V U ,Equity = $ 200,000 Value of Equity = V L, Equity = EBIT − Interest Cost of Equity = 20,000 −( 100,000 ∗ 0.07 ) 0.115 = $ 113,043 for firm L. V L = V D + V L, Equity = 100,000 + 113,043 = $ 213,043 Firm U(unlevered) Firm L(Levered) EBIT $20,000 $20,000 Debt ---- $100,000 R E 10% 11.5%

Youhave 10% of shares ∈ firm Lso your net worth ∈ firm L→ 10% ∗ 113,043 = $ 11,304.30 Step I : She sellsher equity ∈ firm L,she ’ ≪ receive 10% ∗ $ 113,043 = $ 11,304.30 Step II : She’ ≪ borrow 10% of L’ sdebt 10% ∗ 100,000 = $ 10,000 at acost of 7% Step III : She ’ ≪ purchase 10% of firm U for 10% ∗ $ 200,000 = $ 20,000 Step IV : Profit ¿ this switch = ( $ 11,304.30 + $ 10,000 ) − $ 20,000 = $ 1,304.30 , ∨ ¿ Step I : She sellsher equity ∈ firm L,she ’ ≪ receive 10% ∗ $ 113,043 = $ 11,304.30 Step II : She’ ≪ borrow asmuch ( ¿ % ) as L’ sdebt D E = 100,000 113,043 ∗ 11,304.30 = $ 10,000 at 7 % . Step III : She ’ ≪ purchase 10% of firm U for 10% ∗ $ 200,000 = $ 20,000 Step IV : Profit ¿ this switch =( $ 11,304.30 + $ 10,000 )− $ 20,000 = $ 1,304.30 Here , youinvest $ 20,000 ∧ receivea 10% return ∈ firmU ∧ pay your interest expenses ( 10,000 ∗ 7% ) . So,the net proceeds ¿ this switch ¿ firm L ¿ firm U ∧ addingasmuch equity asdebt you have ∈ firm Lcanbe calculated as ( 20,000 ∗ 0.1 ) – 700 = $ 1300 There also ∃ a surplusof $ 21,304.30 − $ 20,000 = $ 1,304.30 ¿ short, youhavereached ¿ abetter position bymoving ¿ firm L ¿ firm U ∧ introducing as muchleverageas equity ¿ your portfolio.That is , younot only kept the sameamount of ownership , 10% ,thistime ∈ firm U ,but also maintaineda surplusof $ 1,304.30 CF before 10% [ 20,000 – ( 100,000 ∗ 7 % ) ]= $ 1,300 CF after 10% ( 20,000 ) – ( 10,000 ∗ 7 % )= $ 1,300 Althoughthere willbea surplusof $ 1,304.30 ,CashFlows for theinvestor arethe same ∈ both positions. 17. MM Arbitrage Example 3 Company U and company L are identical in every respect except company U is unlevered and company L has $2,000,000 perpetual debt with an interest rate of 6%. Both companies are expecting to have an EBIT of $500,000 in perpetuity and all earnings will be immediately distributed to common shareholders. The cost of equity Company U is 12% and the cost of equity for company L is 15%. Assume that all Modigliani and Miller assumptions are satisfied (individuals can borrow or lend at the same rate as the corporations). a) Calculate the value of firm U. V U = EBIT R A = 500,000 0.12 = $ 4,166,667 b) Calculate the total value of firm L and its equity portion.

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V L = EBIT − ∫ Expense R E + debt = 500,000 −( 2,000,000 ∗ 6 % ) 0.15 + 2,000,000 = $ 4,533,333 Equity portionisthe first partof the equation  500,000 −( 2,000,000 ∗ 6% ) 0.15 = $ 2,533,333 c) Assuming an investor who owns 15% of firm L’s equity; show that if she will be able to increase her wealth using the MM arbitrage argument. Also, show that future expected cash flows cash flows are not affected. She’ ≪ switchher investment position ¿ L ¿ U : Step I : She sellsher equity ∈ firm L,she ’ ≪ receive 15% ∗ $ 2,533,333 = $ 380,000 Step II : She’ ≪ borrow 15% of L’ sdebt 15% ∗ 2,000,000 = $ 300,000 at acost of 6% . Step III : She ’ ≪ purchase 15% of firm U for 15% ∗ $ 4,166,667 = $ 625,000 Step IV : Profit ¿ this switch =( $ 380,000 + $ 300,000 )− $ 625,000 = $ 55,000 , ∨ ¿ Step I : She sellsher equity ∈ firm L,she ’ ≪ receive 15% ∗ $ 2,533,333 = $ 380,000 Step II : She’ ≪ borrow asmuch ( ¿ % ) as L’ sdebt D E = 2,000,000 2,533,333 ∗ 380,000 = $ 300,000 at 6% . Step III : She ’ ≪ purchase 15% of firm U for 15% ∗ $ 4,166,667 = $ 625,000 Step IV : Surplus ( profit ) ¿ thisswitch =( $ 380,000 + $ 300,000 )− $ 625,000 = $ 55,000 CF before 15% ( 500,000 – ( 2,000,000 ∗ 6 % ))= $ 57,000 CF after 15% ( 500,000 ) – ( 300,000 ∗ 6 % )= $ 57,000 18.MM Arbitrage Example 4 Company U and company L are identical in every respect except company U is unlevered and company L has $3,000,000 perpetual debt with an interest rate of 4%. Both companies are expecting to have an EBIT of $500,000 in perpetuity and all earnings will be immediately distributed to common shareholders. The Company U has 400,000 shares outstanding and the current shares price is $20. Company L has 600,000 shares outstanding and the current share price is $10. Assume that all Modigliani and Miller assumptions are satisfied (individuals can borrow or lend at the same rate as the corporations). a) Calculate the cost of equity for each firm. V U = 400,000 ∗ 20 = 8,000,000 = EBIT R E = 500,000 R E →R E = 6.25%

V L, E = 600,000 ∗ 10 = 6,000,000 = EBIT − interest expense R E = 500,000 −( 3,000,000 ∗ 0.04 ) R E = 380,000 6,000,000 → R b) Assuming an investor owning 10% of firm L’s equity, show if she will be able to increase her wealth using the MM arbitrage argument. Also, show that future expected cash flows cash flows are not affected. Assume that she will be able to borrow at 4% as the firms. She’ll switch her investment position from L to U: Step I : If she sellsher equity ∈ firm L, she’ ≪ receive 10% ∗ $ 6,000,000 = $ 600,000 Step II : She’ ≪ borrow 10% of L’ sdebt 10% ∗ 3,000,000 = $ 300,000 at acost of 4 % . Step III : She ’ ≪ purchase 10% of firm U for 10% ∗ $ 8,000,000 = $ 800,000 Step IV : Profit ¿ this switch =( $ 600,000 + $ 300,000 )− $ 800,000 = $ 100,000 , ∨ ¿ Step I : If she sellsher 10% of equity ∈ firm L,she’ ≪ receive 10% ∗ $ 6,000,000 = $ 600,000 Step II : She’ ≪ borrow asmuch ( ¿ % ) as L’ sdebt D E = 3,000,000 6,000,000 ∗ 600,000 = $ 300,000 at 4% . Step III : She ’ ≪ purchase 10% of firm U for 10% ∗ $ 8,000,000 = $ 800,000 Step IV : Profit ¿ this switch =( $ 600,000 + $ 300,000 )− $ 800,000 = $ 100,000 CF before 10% ( 500,000 – ( 3,000,000 ∗ 4% ))= $ 38,000 CF after 10% ( 500,000 ) – ( 300,000 ∗ 4% )= $ 38,000 19. MM Propositions 1&2 (With and Without Taxes) Example Company U and company L are identical in every respect except company U is unlevered and company L has $1,000,000 perpetual debt with an interest rate of 4%. Both companies are expecting to have an EBIT of $600,000 in perpetuity and all earnings will be immediately distributed to common shareholders. Company U has a cost of equity of 12%. Assume that all Modigliani and Miller assumptions are satisfied. Firm U(unlevered) Firm L(Levered) EBIT $600,000 $600,000 Debt ---- $1,000,000 R E 12%

a) Calculate the value of each firm according to MM proposition I without taxes. V U = EBIT R A = 600,000 0.12 = $ 5,000,000  V U = V L = $ 5,000,000 b) Calculate the cost of equity (R E ) for the firm L according to MM proposition II without taxes. r E = r A + ( r A − r D ) D E = 0.12 + ( 0.12 − 0.04 ) 1,000,000 4,000,000 = 0.14 = 14% c) Calculate the WACC for each firm according to MM Proposition I without taxes. For firmU →WACC = R E = 0.12 and For firm L→WACC = ¿ 0.12 Underthe conditions of MM I without taxes,WACC isconstant . d) Calculate the value of each firm according to MM proposition I with taxes. T C = 20% . V U = EBIT ( 1 − T C ) R A = 600,000 ( 1 − 0.2 ) 0.12 = 4,000,000 V L = V U + DT C = 4,000,000 + ( 1,000,000 ∗ 0.2 ) = 4,200,000 e) Calculate the cost of equity (R E ) for the firm L according to MM proposition II with taxes. r E = r U + ( r U − r D ) D E ( 1 − T C )= 0.12 + ( 0.12 − 0.04 ) 1,000,000 3,200,000 ( 1 − 0.2 )= 0.14 = 14 % f) Calculate the WACC for firm L according to MM Proposition II with taxes. WACC = E V r E + D V r D ( 1 − T C ) = 3,200,000 4,200,000 14% + 1,000,000 4,200,000 4% ( 1 − 0.2 ) = 11.43% ¿ ,V L = EBIT ( 1 − T c ) WACC = 600,000 ( 1 − 0.2 ) WACC = 4,200,000 →WACC = 11.43% g) Calculate the value of each firm if the corporate tax rate is 20%, personal equity income tax rate is 18% and the personal debt income tax rate is 30% according to MM proposition I. V U = EBIT ( 1 − T C ) ( 1 − T S ) R A = 600,000 ∗( 1 − 0.2 )( 1 − 0.18 ) 0.12 = 3,280,000 V L = V U + D ( 1 − ( 1 − T C ) ( 1 − T S ) ( 1 − T D ) )= 3,280,000 + 1,000,000 ( 1 − ( 1 − 0.2 ) ( 1 − 0.18 ) ( 1 − 0.3 ) )= 3,342,857.14 20. Capital Structures and Homemade Leverage Berfin Inc. has 2,000,000 shares outstanding and you own 2,500 shares of this company, which has a dividend payout ratio of 100% and an expected perpetual EBIT of $800,000 per year. The company is considering converting its current all-equity capital structure to one with 1,200,000 shares outstanding and $4,000,000 in debt. The proceeds from raising debt will be used to repurchase shares. There are no taxes and the cost of debt is 6%. a) What is your cash flow under the current capital structure?

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EPS = $ 800,000 2,000,000 = $ 0.40 CF ¿ youas aninvestor with 2,500 shares→$ 0.40 ∗( 2,500 )= $ 1,000 b) What would be your cash flow under the proposed levered capital structure? If the firm switches ¿ the leveredCapital Structure→ Net Income = $ 800,000 − 0.06 ( 4,000,000 )= $ 560,000 Shares ¿ berepurchased = $ 4,000,000 ( 2,000,000 − 1,200,000 ) = $ 5 per share EPS = 560,000 1,200,000 = $ 0.466667 CF ¿ youas aninvestor with 1000 shares→CF = $ 0.466667 ∗( 2,500 )= $ 1,166.67 c) What is the D/E ratio under the proposed levered capital structure? Price per share→ P = Amount of debt raised ¿ of sharesrepurchased = 4,000,000 ( 2,000,000 − 1,200,000 ) = $ 5 V = $ 5 ∗ ( 2,000,000 ) = $ 5 ∗ ( 1,200,000 ) + 4,000,000 = $ 10,000,000 D E = 4,000,000 6,000,000 D = 2 3 → 40% debt ∧ 60% equity d) Assume the company applies the levered capital structure and investors can borrow and lend at an interest rate of 6%. Would it be possible to replicate the cash flow she would have received as if the company had an unlevered capital structure? (That is, the cash flow she received in part a) Theinvestor needs ¿ replicate the capital structureof thelevered firm ∈ her own portfolio. That is ,she needs ¿ sell 40% of her equity ∈ the levered firm ∧ lend the proceeds ¿ receive 6% of interest . Step I : ¿ replicate the portfolioshe needs ¿ sell→ 0.40 ∗ ( 2,500 ) = 1,000 shares Step II : Proceeds ¿ Selling 1000 Shares = $ 5 ∗( 1,000 )= $ 5,000 Step III : Lend the proceeds ¿ receive 6% of interest income→$ 5,000 ∗ 0.06 = $ 300 Step IV : Calculatethe dividendincome she ' ≪ receive → = $ 0.466667 ∗ ( 2,500 − 1,000 ) = $ 700 StepV : HertotalCF willbe→ 300 + 700 = $ 1,000 So,she hasreplicatedthe cash flow that she wouldhave receivedif thecompany hadanunlevered ca 21. Klassen Corporation is an all equity firm with 170,000 shares outstanding. It is considering changing its capital structure to include debt. If it does, its shares will reduce to 90,000 and it will incur interest of $100,000. Given this information, calculate the indifference EBIT.

EBIT 170,000 = EBIT −( 100,000 ) 90,000 → Break − even EBIT = $ 212,500 22. Martha's Grapevines, Inc. has an EBIT of $46,000, no debt, a 34% tax rate, and a 15% cost of capital. What will the value of the firm be if Martha's Grapevines issues $75,000 in debt? V u = EBIT ∗( 1 − T c ) R A = 46,000 ∗( 1 − 0.34 ) 0.15 = $ 202,400 V L = V U + D T c = 202,400 + ( 75,000 ∗ 0.34 ) = $ 227,900 23. Hanover Tech is currently an all equity firm that has 130,000 shares of stock outstanding with a market price of $36 a share. The current cost of equity is 14% and the tax rate is 35%. The firm is considering adding $1.5 million of debt with a coupon rate of 7% to its capital structure. The debt will be sold at par value. What is the levered value of the equity? V u = 130,000 ∗ 36 = $ 4,680,000 V L = V U + DT c = 4,680,000 + ( 1,500,000 ∗ 0.35 ) = $ 5,205,000 Debt is $1.5 million of this amount, so the remaining must be the equity  V L, E = $ 5,205,000 − $ 1,500,000 = $ 3,705,000 24. Thompson & Jones has earnings before interest and taxes of $149,000. Both the book and the market value of debt is $265,000. The unlevered cost of equity is 13.5% while the pre-tax cost of debt is 9%. The tax rate is 34%. What is Thompson & Jones' weighted average cost of capital? V u = EBIT ∗( 1 − T c ) R A = 149,000 ∗( 1 − 0.34 ) 0.135 = $ 706,370.4 V L = V U + D T c = $ 706,370.40 + ( 265,000 ∗ 0.34 ) = $ 796,470.40 Debt is $265,000 of this amount, so the remaining must be the equity  V L, E = $ 796,470.40 − $ 265,000 = $ 531,470.40

First, we need to calculate the cost of equity for the levered firm: r E = r U + ( r U − r D ) D E ( 1 − T C )= 0.135 + ( 0.135 − 0.09 ) 265,000 531,470.40 ( 1 − 0.34 )= 0.14.98 = 14.98% Then, we can calculate the WACC: WACC = E V r E + D V r D ( 1 − T C ) = 531,470.40 796,470.40 ∗ 14.98% + 265,000 796,470.40 ∗ 9% ∗ ( 1 − 0.34 ) = 11.97 % Thanks to Frankie Liang for the correction . 25. Al's Pub has debt with both a book and a market value of $120,000. This debt has a coupon rate of 9% and pays interest annually. The expected earnings before interest and taxes are $42,600, the tax rate is 34%, and the unlevered cost of capital is 11%. What is the firm's cost of equity? V u = EBIT ∗( 1 − T c ) R A = 42,600 ∗( 1 − 0.34 ) 0.11 = $ 255,600 V L = V U + DT c = $ 255,600 + ( 120,000 ∗ 0.34 ) = $ 296,400 V L, E = $ 296,400 − $ 120,000 = $ 176,400 r E = r U + ( r U − r D ) ∗ D E ∗ ( 1 − T C ) = 0.11 + ( 011 − 0.09 ) ∗ 120,000 176,400 ∗ ( 1 − 0.34 ) = 11.89% →r U = 11.89 % or V L = ¿¿ R E = 11.89 % →T hisist he costof equity for t helevered firm.

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