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Applied Corporate Finance Practice Problems January 25, 2024 Please read these instructions before working on the problems or contacting me with ques- tions 1. These are practice problems that will resemble the problems on the Midterm and Final 2. I do not recommend starting these until 1-2 weeks before the midterm. It is better to focus on understanding the concepts discussion in lecture. 3. If you understand the key concepts of the course, these problems and those in the lecture notes - you will almost certainly do well on the exams • There is a difference between understanding versus simply following the solution steps • It is better to devote time to understand these questions well versus trying to do as many problems as possible. For this reason, please do not ask me for more practice problems. More practice problems will not help you. 4. The tutors will hold extra office hours to answer your questions on these problems prior to the midterm 5. There are many more practice problems in the lecture notes 6. There will be no formula sheet provided on any exam 7. Long problems 1 - 9 and short problems 1 - 4, 7, 9 - 11 cover the material for the midterm 8. All of the problems cover the material for the final 9. There are many more problems in this document then I would reasonably expect you to complete in one exam 10. Some problems may be a bit longer than those I would give on the exam - you will have enough time to complete any exam I give you 11. The answers I provide in the quantitative questions often contain much more explanation than would be needed on the exam so that you can understand the solutions. On the actual exam I prefer more succinct answers 12. Real options practice problem are contained in the lecture notes 1

Problem 1. Two firms, U and L, are identical except for their capital structure. Both will earn $ 150 in a boom and $ 50 in a slump. Each year there is a 50% chance of each event. U is entirely equity-financed, and therefore shareholders receive the entire income. Its shares are valued at $ 500. L has issued $ 400 of risk-free debt at an interest rate of 10%, and therefore $ 40 of L’s income is paid out as interest. There are no taxes or other market imperfections so investors can borrow and lend at the risk-free rate of interest. (a) What is the value of L’s stock? (b) Now show that M&M’s proposition II holds (i.e., show the relationship between the expected return of your investments with identical payoffs is the one predicted by Proposition II). Solution. (a) Because the firms are identical except for the financial structure, according to M&M, the total value of these companies must be the same. Thus L’s stock is worth $500 - $400 = $100. (b) Proposition II states that r E = r U + D E ( r U - r D ) For U, the expected return on assets is: (0 . 5 × 50 + 0 . 5 × 150) / 500 = 20%. Thus for both companies r U = 20%. For L, the expected return on equity is: . 5(50 - 40) + . 5(150 - 40) 100 = 60% This is exactly what we calculate, using the Proposition II formula: r E = . 20 + 4( . 20 - . 10) = 60% Problem 2. A firm is currently partially financed with zero-coupon debt that promises to repay bondholders $ 100 at maturity. These bonds mature one year from today at t = 1. The firm is in a very risky industry, so its assets will be worth $ 200 next year with probability 1/3, $ 100 next year with probability 1/3, and $ 50 next year with probability 1/3. The existing debt-holders were very trustful of management, so they did not insist on any clauses governing issuance of additional debt; however, the firm is planning on issuing new debt that is senior to the old debt (i.e., in bankruptcy the new debt-holders are first in line to get their cash back). This new debt promises to pay these new debt-holders $ 50 at maturity. Assume for simplicity that interest rates are zero and thus that the value of a claim today at t = 0 is equal to the expected payoff to the claimholder at t = 1. (a) What will the new debt sell for? (b) Assuming that the proceeds from the new debt issue are used to pay a special dividend to shareholders, after the debt is issued what will be the value of (i) the old debt, (ii) the new debt, and (iii) equity? Has total firm value changed? Who is made better off or worse off from the transaction? Solution. (a) Since the new debt is senior to the old debt and the firm will have at least $ 50 to repay next year for sure, the new debt is risk-free. Since interest rates are zero, a risk-free promise to pay back $ 50 next year has a present value of $ 50 today. (b) Before the change Asset Value 200 100 50 Expected Value: 350 3 Old Debt 100 100 50 Expected Value: 250 3 Equity 100 0 0 Expected Value: 100 3 2

After the change Asset Value 200 100 50 Expected Value: 350 3 New Debt 50 50 50 Expected Value: 150 3 Old Debt 100 50 0 Expected Value: 150 3 Equity 50 0 0 Expected Value: 50 3 Total firm value is constant at 350 3 . Old debt value goes down, so they are worse off. Equity decreases in value by 100 3 - 50 3 = 50 3 but they also get a special dividend of 50; hence they are better off by 50 - 50 3 . Problem 3. Sharp needs to spend $ 150 million at year 0 to develop a new financial calculator. The demand for calculators is uncertain at year 0. At year 1, however, Sharp will learn whether the demand for the Financial Calculator is high (probability 3/7) or low (probability 4/7). To continue operations, and after learning the demand, Sharp must decide whether to spend an additional $ 200 million at year 1. If Sharp decides to continue operations, the Financial Calculator will produce at year 2 a CF of $ 1,000 million if demand is high and of $ 300 million if demand is low. There are no taxes, investors are risk-neutral and that the risk-free rate of zero. Assume that Sharp wants to raise the $ 150 million of year 0 by issuing senior debt that matures in year 2. (a) Calculate the face value of the senior debt (b) Calculate the value of equity and the value of firm at t = 0 (right after raising the $ 150 million in senior debt) (c) Assume that in the case of low demand, debt-holders could get together and renegotiate the face value of the debt. By how much should they reduce the face value of debt? Solution. (a) Since the investors are risk neutral and the risk free rate is zero, the current value of the debt is equal to the expected payment to the debt holders in year 2. If Sharp wants to raise $ 150 million, the face value of the debt has to be at least $ 150 million. However, with a face value of debt of $ 150 million shareholders will not invest $ 200 million in the case of low demand, i.e., 300 - 150 - 200 < 0 This means that debt holders will not be paid in the case of low demand and hence, their payment in the case of high demand (with probability 3/7) has to be higher than $ 150 million to compensate for the default in the low demand state. Therefore: Value of Senior Debt (at t=0) = (3 / 7)Face Value of Debt 150 = (3 / 7)Face Value of Debt = ⇒ Face Value of Debt = 150 × (7 / 3) = $350 M (b) Since equity holders will not invest in year 1 in the case of low demand: (i.e., 300 - 350 - 200 < 0) equity holders only be paid in the case of high demand. The value of the equity at t=0 is therefore: E = 3 / 7(1000 - 350 - 200) = 193 Note that the equity-holders must pay 350 to the senior debt-holders and must also invest an additional 200 at t=1 to continue the project. And hence, the value of the firm is: V = D + E = 150 + 193 = 343 3

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(c) In the case of low demand, shareholders will not be willing to invest the additional $ 200 million because the most of cash-flow at t=2 will go to the debt-holders. Nevertheless, notice that at t=1, investing in the case of low demand is a positive NPV project (i.e., 300–200 > 0). Therefore, debt-holders must reduce the face value of debt to the point where shareholders will be willing to invest at t=1 (i.e., will at least break even): 300 - New FVD - 200 = 0 , = ⇒ New FVD = 100 By reducing the face value of debt to $ 100 million, shareholders will invest (i.e., shareholders can now recover their $ 200 million investment) and debt holders will hence receive $ 100 million. Problem 4. Fountain Corporation economists estimate that the probability of a good business environment next year is equal to the probability of a bad environment. Knowing this, the managers of Fountain must choose between two mutually exclusive projects. Suppose the payoff from the chosen project is the only future cash flow expected by the firm. Fountain is obliged to make a $ 500 payment to its bondholders next year. Here is a description of the projects: Low Risk Project Probability Payoff Value of Stock Value of Bonds Recession .5 500 0 500 Boom .5 700 200 500 High Risk Project Probability Payoff Value of Stock Value of Bonds Recession .5 100 0 100 Boom .5 800 300 500 Which project will the stockholders prefer? Which project maximizes the value of the firm? Why are these answers different? Solution. Expected payoff to shareholders from low risk project: ( . 5 × 0) + ( . 5 × 200) = $100. Expected payoff to shareholders from high risk project: ( . 5 × 0) + ( . 5 × 300) = $150. Clearly shareholders prefer the high risk project because of its higher expected payoff. Expected value of firm from low risk project: ( . 5 × 500) + ( . 5 × 700) = $600. Expected value of firm from high risk project: ( . 5 × 100) + ( . 5 × 800) = $450. The low risk project maximizes the total value of the firm. What is going on here is that the high risk project is good for shareholders and bad for bondholders. The benefit to shareholders for choosing the high risk project over the low risk project is smaller than the cost to bondholders from this choice. Since shareholders do not care about the returns to bondholders, they will pick the higher risk project even though this choice does not maximize firm value. In an efficient market, bondholders will anticipate this risk taking behavior and will pay less for the bonds when they are issued relative to what they would pay if they knew the firm would take the low risk project. Thus, the shareholders ultimately pay for the fact that they will take the high risk project Problem 5. Gator Software has just completed an RD project that required borrowing senior debt with a face value of $ 70 million from a bank. This R&D effort has resulted in an investment opportunity that will cost an additional $ 100 million and will result in a cash flow of $ 90 million with probability .5 and $ 210 million with probability .5. The firm has no cash on hand and no other assets except for this investment opportunity. Assume risk-neutrality, a zero interest rate, no direct bankruptcy costs, and no taxes. (a) Could the firm fund the investment opportunity with an equity issue? (b) Could the firm fund the investment opportunity with an issue of junior debt? 4

Solution. (a) Given that $ 70 million has been promised to senior debtholders, total equity value will be 210 - 70 = $140 if the project is a funded and is a success and it will be 90 - 70 = $20 if the project is funded and it is less successful. Thus, if the project is funded, total equity value after raising the funds will be ( . 5 × 140) + ( . 5 × 20) = $80. Since you can’t sell any more than 100% of the firm, you cannot raise more than $ 80 in an equity sale. Thus, the project cannot be funded. (b) Following the same math as in part (a), given that $ 70 million has been promised to senior debtholders, for any face value of junior debt of $ 140 or more, the total amount of repayment that can be expected by bondholders is $ 140 with probability .5 and $ 20 with probability .5. Thus the most bondholders can be promised is an expected value of ( . 5 × 140) + ( . 5 × 20) = $80. They will not be willing to contribute $ 100 for a claim worth only $ 80. The project cannot be funded. Problem 6. Emruss Industries has no cash flow this year, but it expects to have a cash flow of $ 3 million next year if the firm is able to lower its costs, and a cash flow of $ 1 million next year if the firm is unable to lower its costs. There will be no cash flows after next year. There is a .5 probability that the firm will be able to lower its costs next year, and a .5 probability that they will be unable to lower their costs. The firm can be liquidated immediately for $ 2.4 million. The firm has both junior debt and senior debt outstanding. If Emruss does not pay the $ 300,000 due immediately, it will be forced into liquidation (i.e. Chapter 7) and the liquidation proceeds will be distributed according to the Absolute Priority Rule (APR). Assume that the appropriate discount rate is 0%. Due Immediately Due Next Year Senior Debt 300,000 2,000,000 Junior Debt 0 400,000 Suppose the management of Emruss asks the junior debtholders for $ 300,000 in exchange for a junior bond that promises repayment of $ 500,000 in one year. The $ 300,000 proceeds from this deal will be used to pay the senior debt that is due immediately. Will the junior debtholders agree to this deal? Will Emruss management be willing to offer this deal? Will the senior debtholders be happy if the junior debtholders accept this offer? Solution. If the firm files Chapter 7, the senior debtholders will have a claim of 300 , 000 + 2 , 000 , 000 = $2 , 300 , 000 and the junior debtholders will have a claim of $ 400,000. If the firm is liquidated for $ 2,400,000, the senior debtholders are first in line according to APR and they should get fully repaid their $ 2,300,000. The junior debtholders will only get $ 100,000. Case 1: Junior Debtholders If junior debtholders do not accept the deal, the firm will be liquidated, and they will get $ 100,000. If they accept the deal what do they get? 50% of the time the firm will have $ 3.0 million next year. After the senior debtholders are repaid there will still be enough to fully repay the junior debtholders their original $ 400,00 claim plus their new $ 500,000 claim. Thus they get $ 900,000 with probability 0.5. 50% of the time the firm will only have $ 1.0 million next year and the junior debtholders will get nothing. Thus the junior debtholders have the choice of taking the sure $ 100,000 or else paying $ 300,000 for a claim that entitles them to an expected payoff of . 5 × 900 , 000 = $450 , 000. Thus if they accept the deal they will get a package with a value of 450 , 000 - 300 , 000 = $150 , 000. Since this package has a higher value than the sure $ 100,000 payoff, they should accept the deal. Case 2: Management/Equity This is simple. If they don’t offer this deal they will get nothing in liquidation. If they do offer the deal they have a 50% chance of a $ 100,000 payoff ($3 . 0 million - $2 million - $400 , 000 - $500 , 000). Thus they clearly do better by offering the deal versus not offering the deal. Case 3: Senior Debtholders If the deal does not go through the firm is liquidated and senior debtholders get fully repaid their $ 2,300,000. If the deal does go through they get: $ 300,000 repayment immediately, 5

50% chance of full repayment of $ 2,000,000, 50% chance of partial repayment of $ 1,000,000. This implies a total expected payoff of $ 1,800,000. Since $1 , 800 , 000 < $2 , 300 , 000, senior debtholders do not like the deal. Intuitively we knew the senior debtholders would not like this deal. Since $ 2.4 million liquidation value > $ 2 million continuation value, value is destroyed if the deal goes through and the firm is not liquidated. If value is destroyed while at the same time equity and junior debtholders are better off, it must be the senior debtholders who are worse off. Problem 7. The current stock price of Spartan airlines is $ 40. If Spartan issues equity, Spartan’s manage- ment anticipates that the market will react negatively and that Spartan will only be able to sell the new shares for $ 35 per share. However, Spartan airlines management knows that if they do not issue equity their stock will soon go up to its fair fundamental value of $ 50 per share. Management knows this because they have inside information that future earnings will be higher than the market expects. Currently Spartan has 100,000 shares outstanding. Spartan is considering investing in a new airplane that will cost them $ 350,000. They anticipate that the present discounted value of increased earnings from purchasing the new plane is $ 450,000. (a) If Spartan had the cash available to purchase the new plane, should it make the purchase? (b) If Spartan needs to finance the purchase of the new plane with equity, will it make sense for them to purchase the plane? (Take the perspective of a long-term shareholder who owns the stock at the time of the decision and holds it for the foreseeable future.) Solution. (a) If the plane costs $ 350,000 and results in a cash flow worth $ 450,000 then the NPV of the investment is + $ 100,000. Clearly Spartan should buy the plane. (b) If the firm does not purchase the airplane, the stock will soon go up to its fair value of $ 50. If they purchase the airplane, soon the market will realize that the firm’s existing assets are worth 50 × 100 , 000 = $5 , 000 , 000, and the new airplane will be valued by the market at $ 450,000. Currently there are 100,000 shares outstanding. If they purchase the new plane, they will need to sell 350 , 000 / 35 = 10 , 000 new shares. Thus, after the issue there will be 110,000 shares outstanding. The long-run stock price if they purchase the plane will be: (5 , 000 , 000 + 450 , 000) / 110 , 000 = $49 . 54. Since this number is less than $ 50 it does not make sense to purchase the plane. Shareholders will be better off without the purchase. To see this another way, once the cash is raised in the equity issue, the NPV of the project is + $ 100,000 from part (a). The process of selling equity entails selling shares for $ 35.00 that are actually worth $ 49.54, entailing a loss of 49 . 54 - 35 . 00 = $14 . 54 per share. Since they sell 10,000 shares, the total loss on the financing is 14 . 54 × 10 , 000 = $145 , 400 which exceeds the $ 100,000 NPV from the project. Again, we see that the project should not be taken. Problem 8. A firm’s existing assets either have a high value of $ 170 million (the undervalued firm) or a low value of $ 70 million (the overvalued firm). The firm’s manager knows the value of her firm’s assets, but the market does not. The market assesses that there is a 50% chance the firm has high value assets and a 50% chance the firm has low value assets. Regardless of the value of the firm’s current assets, the manager and the market are both aware that the firm has the opportunity to invest $ 15 million in a new project that will generate a cash flow with a present value of $ 30 million. The firm currently has 900,000 shares outstanding. The firm does not have the internal cash to fund the project, and thus if they want to fund the project they must conduct an equity issue immediately. In the long-run (i.e., next year) the markets will learn whether the firm was the undervalued or overvalued. Assume that managers act to maximize the long-run value of existing shareholder’s claims when making the equity issue/investment decision. a) Show that there is an equilibrium where both the manager of the undervalued firm and the overvalued firm both will issue equity to invest in the project. In this equilibrium how many shares will be sold? At what price will they be sold? 6

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b) Show that there is an equilibrium where only the overvalued firm issues equity. In this equilibrium how many shares will be sold? At what price will they be sold? Solution. a) Suppose that the market believes that both firm types will issue equity. After the equity sale the undervalued firm type is worth 170 + 30 = 200 M and the overvalued firm type is worth 70 + 30 = 100 M . Thus, the market would believe that the firm they are investing in is worth, on average, ( . 5 × 200) + ( . 5 × 100) = 150 M . If the firm is selling equity, the new equity investors will assume they are purchasing a piece of a $ 150M pie. Since they are being asked for $ 15M, they must receive 1/10 of the firm’s equity in return, since (1 / 10) × 150 M = 15 M . If the firm has 900,000 shares currently outstanding, they must print up and sell 100,000 more shares in the equity issue (if x is number of shares, x must satisfy x = 1 10 (900 + x )). Since firm is raising $ 15 million via the sale of 100,000 shares, the pricing of the shares must be $ 150 in the equity sale. To verify that this is an equilibrium, we must check that both firm types will in fact be willing to issue equity if they anticipate that the market will price the equity in the manner outlined above. The undervalued firm type could choose not to issue equity, in which case its aggregate equity value will eventually increase to $ 170M, and its longrun share price will therefore increase to 170 M/ 900 , 000 = $188 . 88. If it issues equity along the lines outlined above, the firm must sell 10% of the shares to raise the equity funds, thus leaving the original equityholders with a claim worth . 90 × (170 + 30) = $180 M . Thus, since 180 M > 170 M , the long-run aggregate equity value of original shareholders is greater under the scenario where the firm issues equity. To see this another way, note that the long-run stock price of the undervalued firm after the equity issue and after the market realizes the firm was undervalued will be equal to (total asset value/total shares outstanding) = (170M + 30M)/(900,000 + 100,000) = $ 200. Since 200 > 188 . 88, we see again that the shareholders of the undervalued firm will in fact be better off if the firm issues equity and invests. The overvalued firm type could also choose not to issue equity, in which case his aggregate equity value will eventually decrease to $ 70 million, and his long-run share price will decrease to 70 M/ 900 , 000 = $77 . 77. If it issues equity along the lines outlined above, the firm must sell 10% of the shares to raise the equity funds, thus leaving the original equityholders with a claim worth . 90 × (70 + 30) = $90 M . Thus, since 90 M > 70 M , the long-run aggregate equity value of initial shareholders is greater under the scenario where the firm issues. To see this another way, note that the long-run stock price of the overvalued firm after the equity issue and after the market realizes the firm was overvalued will be equal to (total asset value/total shares outstanding) = (70M + 30M)/(900,000 + 100,000) = $ 100. Since 100 > 77 . 77, we see again that the shareholders of the overvalued firm will in fact be better off if the firm issues equity and invests. In conclusion, if the market believes both firm types will issue equity, it will in fact be the case that both firm types will choose to issue equity. In this case the asymmetric information problem is sufficiently small that it does not affect equity issue decisions. b) Suppose that the market believes that only the overvalued firm type will issue equity. Under this set of beliefs, the market would believe that the firm they are investing in is worth 70 + 30 = 100 M . If the firm is selling equity, the new equity investors will assume they are purchasing a piece of a $ 100M pie. Since they are being asked for $ 15M, they must receive 15% of the firm’s equity in return, since . 15 × 100 M = 15 M . If the firm has 900,000 shares currently outstanding, it must print up and sell 158,824 more shares in the equity issue (if x is number of shares, x must satisfy x = . 15(900 + x ), which gives the 158,824 shares). Since firm is raising 15 million via the sale of 158,824 shares, the pricing of the shares in the equity sale must be 15 , 000 , 000 / 158 , 824 = $94 . 44. To verify that this is an equilibrium, we must check that only the overvalued firm type will actually be willing to issue equity given the anticipated market behavior outlined above (i.e., the new equity will only fetch a price of $ 94.44) If the undervalued firm type chooses not to issue equity, his aggregate equity value will eventually increase to $ 170M, and his long-run share price will increase to 170 M/ 900 , 000 = $188 . 88. If it issues equity along the lines outlined above, the firm must sell 15% of the shares to raise the equity funds, thus leaving the original equityholders with a claim worth . 85 × (170 + 30) = $170 M . Since the initial shareholders in the undervalued firm will get a claim worth $ 170M under either scenario, the 7

undervalued firm manager should be indifferent between issuing and not issuing. We will assume that the firm therefore will not issue equity. The overvalued firm type could also choose not to issue equity. Under this choice, in the long- run its aggregate equity value will eventually decrease to $ 70M, and its share price will decrease to 70 M/ 900 , 000 = $77 . 77. If the firm issues equity along the lines outlined above, the firm must sell 15% of the shares to raise the equity funds, thus leaving the original equityholders with a claim worth . 85 × (70 + 30) = $85 M . Thus, since 85 M > 70 M , the long-run aggregate equity value of original shareholders is greater under the scenario where they do issue. To see this another way, note that the long-run stock price of the overvalued firm after the equity issue and after the market realizes the firm was overvalued will be equal to (total asset value/total shares outstanding) = (70M + 30M)/(900,000 + 158,824) = $ 94.44. Since 94 . 44 > 77 . 77, we see that the shareholders of the overvalued firm will in fact be better off if the firm issues equity and invests. In conclusion, if the market believes that only the overvalued firm issues equity, it will in fact be the case that only the overvalued firm will prefer to issue equity. In this case the asymmetric information problem is sufficiently severe that it affects equity issue decisions Problem 9. A firm’s existing assets (not including future investment opportunities) either have a high value of $ 800 million (the high type firm) or a low value of $ 400 million (the low type firm). The firm has 100 million shares outstanding. The firm’s manager knows the value of her firm’s assets, but the market does not. The market will find out the firm’s type next period after annual earnings figures are released. The market assesses that there is a 50% chance the firm has high value assets and a 50% chance the firm has low value assets. Whatever the firm’s type, the market knows that 10% of a firm’s existing assets are held in cash, and this cash can be used either to distribute to shareholders or to invest in new projects. Since this is a booming industry, the market anticipates that each dollar of internal cash that is plowed into new investment projects will generate a future cash flow stream with a present value of two dollars. Managers care about maximizing a weighted average of today’s stock price and tomorrow’s stock price. In particular, they maximize: (.5 x today’s price) + (.5 x tomorrow’s price). The market observes the firm’s repurchase decision, but they observe nothing else (i.e., they do not know the firm’s asset value or cash on hand). Suppose the low type firm pursues a strategy of repurchasing no shares and the high type firm pursues a strategy of repurchasing $ 40.001 million worth of shares. Is this an equilibrium? If so, show how many shares will be repurchased and outline the price of the high-type and low type firms before the announcement, immediately after the announcement, and next period. [Note: To check if it is an equilibrium you need to confirm whether the proposed market belief (i.e., the high-type firm repurchases shares and the low-type doesn’t) is indeed the behavior that the firms find in their best interest to follow.] Solution. To check that the situation is an equilibrium, we need to confirm that the proposed market belief (i.e., the high-type firm repurchases shares and the low-type doesn’t) is indeed the behavior that the firms find in their best interest to follow. In this case, the low type simply cannot repurchase that amount (it does not have enough cash to do it) so we do not need to check potential deviation from the low-type firm. However, does the good type firm want to repurchase $ 40.001? (Next, I simplify the computations by considering that they buy $ 40 million in shares rather than $ 40.001). a) If it does its market value today would be: 720 + 40 + 80 = $840 M (i.e., $ 720M of the value of the illiquid assets, $ 40M due to the cash that will be used to repurchase and $ 80M as a consequence of the investment of the remaining $ 40M that will produce $ 80M) So the price per share will be $ 8.4 (today) and $ 8.4 next year and hence $ 8.4 on average. (The price per share does not change when shares are repurchased—you may want to check this, dividing the value of the assets by the number of shares). Add number of shares they purchase b) If the firm does not repurchase the shares, then the high-type firm will be thought by the market to be low and be assigned today a value per share of 440/100 = $ 4.4. However, after making the investment (now for a total of $ 80 if the firm is high type and no shares are repurchased) the share price of the high-type firm will reach $ 8.8 in the future. Hence, if the high-type does not repurchase, its average 8

share price would be (8 . 8 + 4 . 4) / 2 = $6 . 6, which is less than $ 8.4. Conclusion: The high-type rather repurchases the shares, which confirms that the proposed situation is indeed an equilibrium. What would happen to share prices? • Before the announcement: $6 . 4(= 0 . 5 × 8 . 4 + 0 . 5 × 4 . 4) • Immediately after the announcement: – If the firm announce to repurchase it jumps to $ 8.4 – If the firm doesn’t announce the repurchase it jumps to $ 4.4 • Next period no changes in prices will occur (i.e., they stay at $ 8.4 and $ 4.4 respectively). Problem 10. DMT is considering replacing one of its existing machines. The new machine costs $ 2,300,000 and it would be sold for $ 400,000 after 7 years. During those 7 years, the new machine would be depreciated at the rate of $ 250,000 per year. The old machine has a current book and a market value of $ 1,000,000. The old machine would also last for another 7 years, and after that it would be worth $ 100,000. During those 7 years the old machine would be depreciated at the rate of $ 100,000 per year. The new machine would produce annual sales of $ 1,500,000 and variable cost would amount to 15% of those sales. Alternatively, the old machine would produce annual sales of $ 1,000,000 and variable cost would amount to 10% of those sales. These sales and costs would occur at year-end during the 7 years that the machine would be operating. DMT’s equity has a beta of 1.6, a D/V ratio of 30%, and pays a 5% rate on its debt. Assume that the market risk premium is 7%, the risk free rate is 3% and that the tax rate is 35%. Should DMT go ahead and replace the machine? Solution. First, calculate Incremental Free Cash flows • Year 0: Incremental FCF (year 0) = -2300K + 1000K = - $ 1300K – Note: The salvage value of the old machine is not taxed because the salvage value is equal to the book value. • Year 1-6: Incremental FCF = [EBITD (1-t) + Depreciation × t] New Machine - [EBITD (1-t) + Depreciation × t]Old Machine = [1500K(1-0.15)(1-0.35) + 250K × 0.35] – [1000K(1-0.1)(1-0.35) + 100K × 0.35] = $ 296.25K • Year 7: Incremental FCF = = 296.25 K + (400K + (550K-400K) × 0.35) – ( 100K + (300K-100K) × 0.35 ) = 296.25K + 452.5K- 170K = $ 578.75K Note: We have depreciated the new machine with value $ 2,300,000 at the rate of $ 250,000 per year, so in year-7 the un-depreciated capital is $550 , 000(= 2300 K –(250 K × 7)). In this case, we obtain a tax shield of $52 , 500(= 0 . 35 × (550 , 000 - 400 , 000). Similarly, if we keep the old machine with value $ 1,000,000 depreciated at the rate of $ 100,000 per year, in year-7 the un-depreciated capital is $300 , 000(= 1000 K –(100 K × 7)). Hence, we get a tax shield of $70 , 000(= 0 . 35 × (300 , 000 - 100 , 000)) Second, calculate discount rate. Cost of equity: R E = R F + β E ( R M - R F ) = 0 . 03 + 1 . 6 × 0 . 07 = . 1420 Cost of Capital: WACC = 0 . 1420 × 0 . 7 + 0 . 05 × (1 - 0 . 35) × 0 . 3 = 0 . 1092 Using this discount rate (10.92%) we obtain the following Incremental NPV: NPV = - 1300 + 296 . 5 0 . 1092 1 - 1 (1 . 1092) 6 + 578 . 75 (1 . 1092) 7 = 236 . 3607 K > 0 Since the incremental NPV is positive, DMT should replace the machine. 9

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Problem 11. Lyreco is a firm with two divisions in different lines of business: office equipment and clothing. An analyst has run a regression of monthly returns on Lyreco’s equity against returns on the SP 500 index over the last three years with the following result: r Lyreco = - 0 . 32% + 1 . 3 r S & P 500 Currently, Lyreco has an EBITDA of $ 300 million and a (EV/EBITDA) ratio of 8. The book value of Lyreco’s debt is $ 700 million and the book value of its equity is $ 800 million. Lyreco’s debt is virtually risk-free, has a target D/E ratio of 30% and its marginal tax rate is 40%. The office equipment division has an estimated market value of $ 1,000 million and while the division is not publicly traded, there are two comparable publicly traded firms with the following information: Equity Beta D/E Office Depot 1.9 25% Stylo 1.6 35% The clothing division has an estimated value of 12 times its current EBIT (which is the average multiple for the clothing industry). The target D/E in the clothing industry is 25% and debt is virtually risk-free. While from 2009 to 2012 government bonds yielded an annual return of 4%, the current yield on government bonds is only 3%. Most analysts estimate the market risk premium to be 5%. Answer the following questions a) Calculate the WACC for the clothing division? b) If you expect the EBIT of the clothing division to have a stable growth rate of 3%, what is the return on capital that you are assuming in perpetuity by using a multiple of 12 times its current EBIT? Solution. Something important to note throughout the problem is that because the debt is approximately risk-free, it has a beta of zero. a) Calculate the WACC for the clothing division First, unlever the beta of Lyreco • The market value of Lyreco: EV = 300 × 8 = $2 , 400 M • The book value of debt: D = $700 M β E 1 + (1 - t ) D E = 1 . 3 1 + (1 - 0 . 4) 700 2 , 400 - 700 = 1 . 042 Second find the unlevered beta of the office equipment division: Equity Beta D/E Unlevered Beta Office Depot 1.9 25% 1.65 Stylo 1.6 35% 1.32 Average 1.49 Third, find the unlevered beta of the clothing division β Lyreco U = 1 , 000 2 , 400 β OfficeEq. U + 2 , 400 - 1 , 000 2 , 400 β Clothing U , = ⇒ 1 . 042 = 1 , 000 2 , 400 1 . 49 + 2 , 400 - 1 , 000 2 , 400 β Clothing U , = ⇒ β Clothing U = 0 . 723 Fourth, relever the beta of the clothing division at its target D/E of 25%: β Clothing E = β Clothing U 1 + (1 - t ) D E = 0 . 724 × (1 + (1 - 0 . 4) × . 25) = 0 . 831 10

Fifth, calculate the cost of equity r Clothing E = r F + β Clothing E ( r M - r F ) = 0 . 03 + 0 . 831 × 0 . 05 = 7 . 16% Sixth, calculate the WACC D E = 0 . 25 , = ⇒ D V = 0 . 2 Hence, WACC = r E × E V + r D (1 - t ) D V = 0 . 0716 × . 8 + 0 . 03 × (1 - 0 . 4) × 0 . 2 = 6 . 09% b) V alue 0 = EBIT 1 (1 - t ) × (1 - RR ) r - g = EBIT 0 × (1 + g )(1 - t ) × (1 - RR ) r - g , = ⇒ V alue 0 EBIT 0 = 12 = (1 - 0 . 4) × (1 + 0 . 03) × (1 - RR ) 0 . 0609 - 0 . 03 , = ⇒ RR = 40% Second, you need to calculate the return on capital (i.e., ROC) consistent with the growth and rein- vestment rate: g = RR × ROC, = ⇒ 0 . 03 = 0 . 4 × ROC, = ⇒ ROC = 7 . 5% 1 Sample Short Questions Problem 1. Why issuing debt is considered a signal of firm quality? Solution. Because issuing debt (i) is costly due to the cost of financial distress and (ii) is costlier for the “bad firm” since the “good firm” has a higher probability of being able to pay back the debt. Problem 2. Debt-overhang is in essence a renegotiation problem. Explain why. Solution. In debt overhang firms cannot raise new funds (and hence pass up positive NPV projects) because the existing debt-holders would capture most of the cash flows generated by those projects. If a firm, however, could restructure its capital structure (e.g., renegotiate reduction on the face value of debt or debt-equity exchanges etc.) this would allow the firm to compensate new investors for the funds invested in the firm. Problem 3. “If debt is risk-free, equity does bear financial risk.” Do you agree? Explain your answer. Solution. The statement is true. Financial risk is NOT caused by the probability of default but by the priority of debt over equity. Problem 4. “According to MM, firms should be indifferent between issuing fixed rate debt or floating debt.” Explain why. Solution. Under the MM assumptions, whether firm issue fixed rate debt or floating debt does not affect the value of the firm. Shareholders are indifferent to the interest rate risk exposure of the firm because they can always trade in the market and achieve their desired risk exposure (i.e., “homemade interest rate risk exposure”). 11

Problem 5. Expensive-Red and Mad-Blue are both publicly traded companies. Expensive-Red is a com- pany that sells luxury products and does particularly well during booms. In particular, Expensive-Red will generate a one-time cash flow of $ 10 million in one year if the economy is in a boom, which will happen with probability 0.7. (Otherwise, if the economy is in recession, Expensive-Red will not generate any cash flows.) Mad-Blue will generate a one-time cash flow of $ 10 million in one year if its “mad scientist” gets inspired, which will happen with probability 0.7. (Otherwise, if the “mad scientist” does not get inspired, Mad-Blue will not generate any cash flows). Assume each firm is all equity financed. Which company is likely to have a higher market value? Explain your answer. Solution. Expensive-Red is likely to have a lower market value. While both companies have the same expected cash-flows, Expensive-Red’s cash-flows are positively correlated with the economy and hence, Expensive-Red has a positive beta. Therefore, Mad-Blue’s cash flow should be discounted at the risk free rate while Expensive-Red’s cash flow should be discounted at a rate higher than the risk-free rate. Problem 6. “GE has many profitable businesses. This allows GE to finance new ventures by issuing debt at a very low rate. Therefore, GE will have a lower WACC than competing businesses.” True/False; briefly explain your answer. Solution. False. The WACC depends on the use of the resources; it reflects the risk of the project that you are investing in. Problem 7. “Because covenants restrict firms from taking certain actions they make firms worse off.” True/False; briefly explain your answer. Solution. False. The covenants actually raise the value of the firm by forcing them to commit to actions that do not destroy firm value. Without covenants, bondholders would price in the actions firms take which would ultimately lower overall firm value. Problem 8. Explain the main problem with using a firm-wide WACC for evaluating new projects? Solution. Firms will tend to forego relatively safe projects and take on relatively risky projects when they should not because they are not adjusting the discount rate to reflect the riskiness of the individual project. Problem 9. The CFO of a firm tells the CEO ”interest rates have gone down, this means we should buy back our bonds and issue new bonds at a lower interest rate” Is CFO correct? Solution. No, the price of the existing bonds will be higher after interest rates have gone done. Buying the existing bonds at a fair price and then issuing new bonds at a fair price will not be advantageous to the firm at all. Problem 10. Maverick Inc. announced the firing of their CEO, after which its stock price declined by 5%. Does this mean the firing the CEO was a bad decision? Explain why? Solution. No, by firing the CEO the market may be realizing that there are other issues at the firm (perhaps the CEO has been doing a bad job managing projects). Hence, even if firing the CEO is the correct decision, the stock price may drop because the market learns about these other potential issues. Problem 11. The CEO of a firm says “issuing new bonds that are senior to existing bondholders and paying out a dividend cannot create value for equity holders because value is only created through NPV positive projects”. The CFO responds “No, in this case issuing bonds can create value for our equity holders by diluting existing debtholders” Who is correct? The CFO or the CEO? Solution. The CFO. Even if the firm is not investing in an NPV positive project, by issuing debt and paying out the proceeds as a dividend to shareholders, this raises the value of equity at the expense of old debtholders. 12

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