CH-14 Capital Structure and Leverage – Practical Financial Management : Book Guide

CHAPTER 14 CAPITAL STRUCTURE AND LEVERAGE FOCUS Capital structure can influence the value of a firm. Our focus is on understanding why that's true and what we can and can't do with the knowledge. The ideas are developed through a detailed illustration that shows the performance and risk implications of financial leverage. Later in the chapter we explore the theoretical approach to the same issue and see that the conclusions reached are similar. Along the way we examine the concept of operating leverage and see how it interacts with financial leverage. PEDAGOGY The ideas behind capital structure and leverage are taught on two levels, the practical and the theoretical. A practical understanding is developed using an example illustrating how leverage helps reported financial performance if the firm is doing well, but hurts it if operating results are poor. We then describe how this effect influences risk-averse investors in their quest for returns. The pedagogical challenge of capital structure is presenting the MM theory in a way the average person can understand. The theory's math is difficult and its notation is unusual, creating two factors that combine to bewilder most students immediately. Nevertheless, the theory is an important pillar in the structure of finance, and should be at least appreciated by anyone seriously in the field. The presentation of the subject is one of the defining features of this book. The ideas are developed slowly, beginning with notation. Students are brought to an appreciation of what MM accomplished and why it's important without advanced mathematics. At the end they can hold their own in a discussion of the independence theory, arbitrage, and the effects of taxes and bankruptcy costs. Their understanding is graphic and intuitive rather than mathematically rigorous, but it's all most will ever need. TEACHING OBJECTIVES Students should gain an understanding of the interrelations among capital structure, financial results, stock market prices and risk. They should also be able to quantify and roughly measure the risk and performance implications of policy decisions regarding capital and cost structure. OUTLINE I BACKGROUND Terms are defined and the idea that capital structure can influence financial performance is introduced. A. The Central Issue Can capital structure influence stock price and the market value of the firm? Further, is there an optimal structure that maximizes value? B. Risk in the Context of Leverage Redefining risk as variation in EBIT and EPS. C. Leverage and Risk - Two Kinds of Each Operating and financial leverage, business and financial risk. Understanding the nature of each. II. FINANCIAL LEVERAGE A. The Effect of Financial Leverage How financial leverage amplifies performance as measured by ROE and EPS - developed through a detailed illustration. When leverage helps and when it hurts. B. Financial Leverage and Financial Risk Tying leverage to the notion of risk as variation in performance. C. Putting the Ideas Together - The Effect on Stock Price How investors react to performance variations and the effect on stock prices. The practical difficulty of finding an optimal capital structure. D. The Degree of Financial Leverage (DFL) - A Measurement The DFL concept. Using DFL to predict results and measure risk. E. EBIT-EPS Analysis Using leverage concepts to determine an appropriate capital structure given management's expectations about EBIT. III. OPERATING LEVERAGE A. Terminology and Definitions Cost structure - fixed and variable, defining operating leverage as the use of fixed costs. B. Breakeven Analysis and Diagrams The breakeven technique graphically and algebraically C. The Effect of Operating Leverage Using breakeven concepts to understand how operating leverage affects EBIT when volume changes. D. The Degree of Operating Leverage (DOL) - A Measurement The DOL concept. Using DOL to predict results and measure risk. E. Comparing Operating and Financial Leverage A detailed comparison of the concepts showing similarities and differences. F. The Compounding Effect of Operating and Financial Leverage The effect of the two leverages is multiplicative. Acting together they can make a company very risky. G. The Degree of Total Leverage (DTL) concept and application. IV. CAPITAL STRUCTURE THEORY Financial theory approaches the capital structure issue differently but arrives at basically the same result. A. Background - The Value of the Firm Understanding the theory's notation B. The Early Theory by Modigliani and Miller The basic MM model, its restrictive assumptions, and its results. C. Relaxing the Assumptions - More Insights The effect of including taxes and bankruptcy costs. The MM approach arrives at the same result as the intuitive approach for somewhat different reasons. D. An Insight into Mergers and Acquisitions The value added by financial leverage as a justification for paying premiums in acquisitions. E. Estimating the Optimal Capital Structure – The Levered Beta QUESTIONS 1. The user of leverage might be thought of as taking advantage of the provider. Between stockholders and bondholders, who is the user and who is the provider? Give a word explanation or illustration that might support this view. What does the used party get in return? ANSWER: Stockholders use leverage provided by bondholders. The stockholders, through management, undertake projects using both their own and bondholder's money. The rewards of success accrue mainly to stockholders, while the penalty for total failure is shared by both. This seeming unfairness is the sense in which the user of leverage takes advantage of the provider. However, bondholders are protected against moderate failure, which mainly hurts stockholders. This is because interest payments must be made regardless of profitability. This safety under a wide range of poor performance short of disaster is what bondholders get in return for providing leverage. 2. The central issue underlying the study of leverage is whether or not it influences stock price and whether there's an optimal structure. But the whole idea seems kind of fuzzy and uncertain. Why are people so interested? (Hint: Think of management's goals and of the world of mergers.) ANSWER: A great deal of money can be made very quickly if a change in leverage can have an immediate and substantial impact on stock price. In merger situations, acquiring firms often borrow the money to purchase firms being acquired. If the resulting increase in leverage of the combined organization has a positive effect on stock price, the stockholders of both companies can get rich virtually overnight. 3. Relate business and financial risk as defined in this chapter to the risks described in Chapter 9. ANSWER: The risks discussed in this chapter relate to variations in a firm's financial results. Business risk is variation in EBIT. Financial risk is the increase in variation found between EBIT and EPS and ROE if financial leverage is present. In other words, these risks are found within the firm's financial statements. The concepts in Chapter 9 were broader in that they addressed an investor's return. That return can be influenced by recorded financial results as well as by other things that don't show up on a company's books. For example, an economic recession depresses stock prices and therefore investor returns, but may not influence profitability as seen in EBIT, ROE or EPS. The risks in Chapter 9 include the risks discussed here. 4. Why are ROE and EPS such important measures of performance to investors? ANSWER: ROE is an indication of the total performance of a company including both operating and financing issues. Since people invest only for money, the return on what's invested is of fundamental importance. EPS taken along with stock price gives an indication of the same thing, just how much is a firm making relative to the price of a share? EPS is also important because it tends to drive stock price through the P/E ratio. Hence, it can be an indication of future price appreciation. 5. Both business risk and financial risk would exist with or without either type of leverage. Leverage just makes them more significant. Are these statements true or false? Explain. ANSWER: False. Business risk is variation in EBIT. It is increased but not caused by operating leverage. Some business risk exists in virtually all companies even in the complete absence of leverage. However, financial risk is the additional variation in EPS over that of EBIT that comes as a result of debt (financial leverage). Without financial leverage there is no financial risk. 6. Briefly explain the pros and cons of financial leverage. In other words, what are its benefits, and what are the costs that come along with those benefits? ANSWER: Financial leverage makes good results measured in terms of EPS and ROE better. Hence in good times it can enhance financial performance and thereby tends to increase stock price. However, it can also exaggerate poor performance making a moderately poor showing in bad times much worse. Leverage adds to the variability of financial performance, which is the essence of risk. Hence financial leverage adds risk, which tends to depress stock price. This increased risk is the cost of leverage. 7. Explain in words the ROCE test for the advisability of adding leverage. That is, what is the test really telling us? When will it indicate a company is doing the wrong thing? ANSWER: The ROCE test measures the firm's operating ability to earn a return on invested money against the cost of borrowing. If the ROCE is higher than the cost of borrowed funds (both after tax) the firm will profit to the extent of the difference on whatever money it borrows. However, leverage adds risk, and the ROCE doesn't test for that. Hence if borrowing is already high, it may be unwise to borrow more even if the ROCE is above the cost of debt. 8. The risk added by financing is small and insignificant relative to the inherent risk in most businesses. Is that statement true or false? Discuss. ANSWER: The statement is generally true in good times if, in addition, the use of leverage is low or moderate. However, it is false when debt levels are high. Then debt can create financial risk that exceeds business risk several times over. 9. Describe generally how leverage affects stock prices. What forces are at work, driven by what effects? ANSWER: If business is good and the ROCE exceeds the after-tax cost of capital, additional leverage enhances ROE and EPS. These measures are watched by investors and the improvement can have a positive effect on stock price. At the same time, however, increased leverage makes those measures more volatile in response to changes in the business's operating results. That implies a riskier business. Risk levels are also watched by investors and have a negative impact on price. Which effect dominates depends on how much leverage exists and the current business climate. 10. Explain the difference between a fixed and a variable cost. How do these concepts change as the time horizon lengthens? In other words, are the same things fixed over a 5-year planning period that are fixed in a typical 1-year period? What about a 10-year period? What's the relevant period when we're talking about operating leverage? ANSWER: A fixed cost remains constant when production levels change. A variable cost increases or decreases in direct proportion to changes in production. The longer the planning period the more things are variable. For example the costs associated with a factory are fixed in the 1-year time frame. Over a 10-year period, however, a new factory can be built so the costs associated with it can be considered variable. The discussion of operating leverage is made in the context of a relatively short period of time. Hence only direct inputs are variable. 11. Why do labor-intensive processes involve less operating leverage than automated processes? What fixed costs are associated with automation? Why can't those costs be eliminated by just selling the machinery? ANSWER: High operating leverage implies a preponderance of fixed cost. Labor isn't a fixed cost, because people can be fired if business turns down. The main fixed cost associated with automation is depreciation associated with the equipment. If the equipment is leased, the payments can be fixed if the lease can't be broken. If the equipment is acquired with borrowed money, the interest on the loan is a fixed cost. Idle machinery can be sold, but generally at a big loss. If the equipment is highly specialized, there may be no market for it. 12. Explain the idea of breakeven analysis in a brief paragraph. ANSWER: Breakeven analysis finds the production and sales level required for the company to just survive. At the breakeven volume, all costs are covered by revenue, but nothing is left over for profit. The firm just "breaks even" in terms of profit and loss. 13. Describe the concept of the breakeven point in words by using the concept of contribution and fixed costs. (Short answer.) ANSWER: Each unit sold contributes the difference between price and variable cost to profit and overhead. This amount is called the "contribution". At the breakeven point the total contribution from all units sold just equals the firm's fixed costs. 14. Summarize the effect of operating leverage on EBIT. ANSWER: More operating leverage enhances EBIT at points above breakeven, but makes it worse when operating below breakeven. Hence, it makes EBIT more volatile with changes in volume. 15. The Braithwaite Tool Co. is considering a major modernization and automation of its plant using borrowed funds. Fully discuss a serious financial negative that could result from the project. ANSWER: The automation of the plant will make Braithwaite more capital intensive, add fixed costs, and increase operating leverage. This will increase the volatility of EBIT as the level of sales changes. By financing the project with borrowed money, the firm will add debt to its capital structure increasing financial leverage. This makes EPS and ROE more volatile as EBIT changes. The net result of these effects is multiplicative. Therefore, changes in sales may produce very large changes in EPS and ROE after the project is implemented. This is likely to make the company more risky in the eyes of investors and may have a detrimental effect on its stock price. 16. Explain the idea of bankruptcy costs. Why are they important to investors? When do investors start to worry about them? ANSWER: Bankruptcy costs are the expenses incurred as a result of the administration of a firm's failure. They are not losses associated with the business deterioration that causes the bankruptcy. Rather they're the costs of the legal and administrative system and the loss incurred if assets need to be sold cheaply. Bankruptcy costs are important to investors because they represent potential investment losses. When times are good and the firm's debt level is relatively low, investors don't think much about bankruptcy costs. They start to worry, however, when failure looks possible. They become especially concerned when debt levels are high due to financial risk. 17. Briefly describe the result of MM's original restrictive model. Why was it important in spite of its serious restrictions? ANSWER: MM's original model implied that the firm's value is independent of capital structure. Although this view was already held by many others, MM described a logical way in which the behavior of investors could make it happen. The theory showed that the effect of capital structure on price and value is due to market imperfections like taxes and bankruptcy costs rather than to the basic interaction between investors and companies. 18. Briefly summarize the operating income argument that was supported by the original MM result. ANSWER: A firm's value is nothing more than the present value of its expected future income stream. If expected income doesn't change, a rational market will hold the firm's total value constant regardless of how the income is divided between debt and equity investors. Essentially the argument says that you can't make something out of nothing. I.e., you can't create additional value out of a fixed income stream by changing the way it's divided between debt and equity. 19. Outline the arbitrage process proposed by MM that supports the operating income argument. What is the arbitrage between? ANSWER: If increasing a firm's use of leverage created value, stockholders could profit by selling its appreciated shares, borrowing money, and buying the unappreciated shares of a similar but unleveraged firm. This would put downward pressure on the price of the leveraged firm and upward pressure on the price of the unleveraged firm driving the two together. (Actually, keeping them from being different.) The arbitrage is between stocks of leveraged and unleveraged firms. 20. Explain in words how the tax system favors debt financing. ANSWER: Payments to investors are either interest on debt or dividends on equity. Interest payments are tax deductible, while dividends are not. To the extent income is paid in interest rather than as a dividend, it generates a tax savings. That savings is kept by the company without affecting investors. Hence it's cheaper to pay a debt investor than to pay the same amount to an equity investor. The government effectively splits the bill for debt funds. 21. In a short paragraph, describe the result of adding taxes to the MM model. ANSWER: When taxes are added to the MM model, an annual tax savings equal to the tax rate times the firm's total debt is created. The present value of the perpetuity of that stream of savings is an addition to the value of the firm. This value increment increases steadily as more debt is added. It belongs entirely to stockholders, since bondholder returns are fixed. Therefore, in the absence of other refinements, the MM model with taxes implies that the firm should borrow as much as possible right up to 100% of capital. 22. In another short paragraph, describe the effect of adding bankruptcy costs to the MM model with taxes. ANSWER: Including bankruptcy costs in the MM model mitigates the value enhancing effect of taxes by recognizing that more leverage increases risk. Since risk lowers value through its effect on the required returns of equity investors, it offsets the benefit of the tax shield associated with more debt. The two effects taken together mean that as leverage is added, value increases, reaches a maximum, and then decreases 23. Compare the implications of the MM model with taxes and bankruptcy costs to the things we discovered by studying the Arizona Hot Air Balloon Corporation. ANSWER: The bottom line is about the same. Adding debt to an unleveraged firm can initially increase value and stock price, but eventually detracts from both. This means an optimal point must exist for every firm with respect to the amount of leverage it uses. Neither approach tells us how to find the optimum. The reasons for the model's conclusions are somewhat different. The MM model bases the beneficial effect of leverage on the favorable tax treatment of interest. The intuitive approach, on the other hand, is based on the idea that a profit is available if a firm can earn more using borrowed money than it pays for that use. Both approaches conclude that a little leverage is good, but a lot is generally bad. BUSINESS ANALYSIS 1. The Armageddon Corp is in big trouble. Sales are down and profits are off. On top of that, the firm's credit rating has been reduced so it's facing very high interest rates on anything it borrows in the future. Current long-term borrowing represents 60% of capital but at fixed interest rates, so it won't be affected. The firm's major stockholder, the Apocalypse Group, has scheduled a conference with management to discuss the company's problems. Everyone is very nervous about this conference, and the executive team is meeting to decide what to tell Apocalypse. Charlie Gladhand, the director of marketing, came into the meeting wearing a wide grin. He explained that he'd read an article about leverage that contained the solution to the company's problem. The article told of several successful firms that had, to the delight of their owners, become more successful by borrowing money. Charlie suggests that Armageddon dazzle the Apocalypse Group by borrowing heavily in the next few days before the conference. Critique Charlie's idea. ANSWER: Charlie doesn't understand what he read. Increasing leverage only helps when (1) times are good, and (2) when there isn't much debt to begin with. Armageddon is doing poorly, so more debt would make returns worse. But it would also add risk. With the existing debt level at 60%, an addition would be dangerously risky even in the best of times. In this situation it would probably be a disaster. 2. You're interested in investing in the Peters Company, which has shown a remarkable increase in EPS over the last three years. You investigate and find that the company's debt-to-equity ratio has increased dramatically over the same period and is now four to one. How does this information affect your feelings about Peters as an investment? ANSWER: Peters’ high EPS is based partly on its use of leverage, which seems to have become excessive. This situation implies high risk in that a modest business downturn is likely to cause a precipitous drop in EPS and probably stock price. This should dampen investor interest somewhat. 3. You're the CFO of Axelrod Trucking, a privately held firm whose owner, Joe Axelrod, is interested in selling the company and retiring. He therefore wants to pump up its value by any means possible. Joe read an article about leverage in a business magazine the other day, and has sent you a memo directing that you restructure the firm's capital to the "optimum" in order to maximize the company's value. Prepare a brief response to Joe's memo. ANSWER: Joe: Optimizing a company's value by borrowing is a good idea in theory, but it's hard to put it into practice with any precision. If a firm is doing well, more debt enhances financial results in terms of ROE and EPS. However, if the company is doing poorly, it makes results worse. That means increasing the use of debt (known as leverage) makes results more volatile or risky. Better results tend to enhance value, but riskiness tends to detract from it. The problem is that no one knows exactly how to balance these two effects to maximize value. In general we can say that if business performance looks good for the foreseeable future, and the firm doesn't have much debt, a little more will probably help. On the other hand, a heavily leveraged firm will probably do well to reduce its debt, especially if business looks shaky ahead. In our case we can't optimize any better than to estimate that a debt level of about 30% or 35% is appropriate if times are good. That should be reduced to less than 20% if the outlook is poor. 4. The Revere Company currently has good earnings and a capital structure that's 20% debt. Its EPS is in the upper quarter of firms in its industry. Top management's compensation is in large part based on the year-end price of the company's stock. It's now October and the president, Harry Upscale, is looking for ways to pump that price before December 31. Harry invests in stocks himself, and pays a great deal of attention to EPS when buying and selling. He also understands that leverage can magnify EPS. However, he knows little more than that about finance. Harry has strongly suggested to the treasurer that Revere restructure its capital to 65% debt in order to enhance EPS and increase stock price. You're an analyst in the firm's treasury department. The treasurer has asked you to prepare an analysis of Harry's proposal to help him talk the boss out of the idea. You've calculated the company's current DFL at 2.2, and projected that it would be 5.8 at the proposed leverage level. Draft a memo from the treasurer to Harry tactfully explaining why his idea may not work and might actually have a result opposite to what he wants to achieve. ANSWER: Harry: Our operating results are currently very good, so an increase in leverage will favorably impact EPS which will tend to have a favorable impact on stock price. However, that's only part of the picture. Because leverage magnifies EPS, it makes the measure more volatile when operating results change. In stock market terms, that makes the company more risky, which tends to negatively influence stock price. Unfortunately, the market's response to increased risk is a little vague. If there isn't much leverage in the first place, a little extra is more or less ignored. However, if the absolute level of leverage is high, adding more can have a dramatically negative effect. This is true even when operating results are good. The perennial question with respect to leverage is which effect will dominate. In other words, on balance will price go up or down if a certain amount more leverage is added? That question can rarely be answered with certainty, but a certain financial ratio may be able to give us some insights into what's likely to happen. The Degree of Financial Leverage (DFL) measures the risk associated with leverage. It relates percentage changes in EPS to percentage changes in EBIT as a function of debt. In other words it tells how big a change in EPS will occur as a result of any change in EBIT given our debt level. In this way it measures the financial risk associated with leverage. Currently our DFL is 2.2. That means a 1% change in EBIT will bring about a 2.2% change in EPS. If we increase our debt level to 65%, the DFL will be 5.8. That means the change will increase financial risk by 2.6 times. That's very significant, and it's likely that the market will not respond favorably. In summary, we advise reconsidering the proposed restructuring since the increase in risk may cause it to have an effect opposite to that which is hoped for. 5. The Appleridge Company is a large manufacturer of capital goods. (The demand for capital goods typically swings up and down a great deal between good and bad economic times.) Business has been good lately and is expected to remain so in the foreseeable future. The firm is currently relatively labor intensive in its processes. The chief engineer, Mike Quickwrench, has suggested a major project to modernize and automate the plant. At the output level planned for next year, the project will reduce total cost by 10%. Mike has presented the idea to the management team in a totally positive light. The other executives are caught up in Mike's enthusiasm and are ready to proceed. You're Apple ridge’s CFO, and feel that all sides of an issue should be discussed before it is approved. What concerns do you have? How would you present them in a way that keeps you from appearing to be overly negative? ANSWER: The problem is the additional risk that the project adds to the company's performance. In the capital goods industries it's virtually assured that significant downturns will be experienced in the future as the economy goes through booms and recessions. In some businesses, the downturns are manageable, say 20% to 30% reductions in volume. In others they're worse, and business almost disappears for awhile. Therefore, it's particularly important that management evaluate the project at production levels lower than the one planned for next year. Those levels should be consistent with previous experience in bad times. It's possible that the automation could put the firm in a position such that it would fail in a recession. The CFO should avoid appearing negative about the project, and should present his or her concerns in terms of exploring all possibilities. Show the results of both good and bad scenarios with some subjective probabilities attached. Let the team evaluate which way to go. It's possible that a modified plan can achieve most of the benefits of the automation, but avoid some of the risk. 6. The Wycombe Company is doing well and is interested in diversifying, so it's been looking around for an acquisition target. The Albe Company has been found with the help of an investment banker. Albe is quite profitable, and about half the size of Wycombe. This size relationship is reflected in their market values. Both firms are financed entirely by equity. The investment banker has advised that it will be necessary to pay a premium of about 30% over market price to acquire Albe. Wycombe's president is having a hard time with this news and has asked you for advice. Construct and explain an approach to the acquisition that might make the premium easier to rationalize. Would it affect your argument if neither Albe nor Wycombe were particularly profitable? If so, how? ANSWER: The president is struggling with the following problem: If Albe's market value truly represents the firm's worth, the premium represents a payment of extra value from Wycombe's shareholders to Albe's at the time of the acquisition. Unless there are remarkable benefits to operating the two firms together, that money is lost to Wycombe's shareholders forever. Leverage may provide some relief. First notice that neither firm has any debt at present and that they are both enjoying good profitability. That means an increase in leverage might increase value. Assume the size relationships of the market values of the two firms are roughly as follows ($100 is an arbitrary figure for Wycombe, it's the relationships that are important): Wycombe Market Value $100 Value of Albe Market Value $50 Premium (30%) 15 65 $165 If Wycombe acquires Albe by borrowing $50, the market value of the capital structure of the resulting firm may be approximately as follows. Debt $ 50 30% Equity 115 70% Total $165 100% This is a reasonable level of leverage that may cause an increase in the value of the equity. To the extent that such an increase occurs, it will mitigate the loss to Wycombe's stockholders from the premium payment. If the firms weren't profitable, increasing leverage would be likely to make their financial results worse rather than better. That means an increase in stock price and value is unlikely to come from the idea. PROBLEMS Basic Concepts and Calculations: Tables 14-1, 14-2, and Equation 14.1 (pages 585, 587, and 586) 1. The Connecticut Computer Company has the following selected financial results. 10% Debt 40% Debt 75% Debt Debt $ 10,000 Equity 90,000 Total Capital $100,000 Shares @ $5 18,000 EBIT $18,000 Interest ( 15%) 1,500 EBT $16,500 Tax (40%) 6,600 Net Income $ 9,900 ROE EPS The company is considering a capital restructuring to increase leverage from its present level of 10% of capital. a. Calculate Connecticut’s ROE and EPS under its current capital structure. b. Restate the financial statement line items shown, the number of shares outstanding, ROE, and EPS if Connecticut borrows money and uses it to retire stock until its capital structure is 40% debt assuming EBIT remains unchanged and the stock continues to sell at its book value. (Develop the second column of the chart shown.) c. Recalculate same figures assuming Connecticut continues to restructure until its capital structure is 75% debt. (Develop the third column of the chart.) d. How is increasing leverage affecting financial performance? What overall effect might the changes have on the market price of Connecticut’s stock? Why? (Words only. Hint: consider the move from 10% to 40% and that from 40% to 75% separately.) SOLUTION: a., b., c. 10% Debt 40% Debt 75% Debt Debt $ 10,000 $ 40,000 $ 75,000 Equity 90,000 60,000 25,000 Total Capital $100,000 $100,000 $100,000 Shares @ $5 18,000 12,000 5,000 EBIT $18,000 $18,000 $18,000 Interest ( 15%) 1,500 6,000 11,250 EBT $16,500 $12,000 $ 6,750 Tax (40%) 6,600 4,800 2,700 Net Income $ 9,900 $ 7,200 $ 4,050 ROE 11.0% 12.0% 16.2% EPS $.55 $.60 $.81 d. Increasing leverage is improving financial performance as measured by ROE and EPS. As debt increases, earnings, equity, and the number of shares outstanding all decrease. However, since equity decreases fastest the ratios ROE (EAT/Equity) and EPS (EAT/Shares) get larger. The increase in debt from 10% to 40% of capital is likely to increase stock price, because investors will react favorably to the improvement in ratios. In this leverage range debt is not excessively high, so the positive effect of the improving ratios will probably overcome the negative effect of increasing risk. The move from 40% to 75% debt, on the other hand, is likely to be perceived by investors as making the company uncomfortably risky. At higher leverage levels the negative effect on investors of increased risk usually overwhelms the positive effect of improving performance ratios, and the net result is a decline in stock price. 2. Reconsider the Connecticut Computer Company of the previous problem assuming the firm has experienced some difficulties, and its EBIT has fallen to $8,000. a. Reconstruct the three-column chart developed in problem 1 assuming Connecticut’s EBIT remains at $8,000. b. Interpret the result in terms of stock price and the advisability of restructuring capital under these conditions. c. Could these results have been predicted more easily? Use the ROCE concept to come to the same conclusion. SOLUTION: a. 10% Debt 40% Debt 75% Debt Debt $ 10,000 $ 40,000 $ 75,000 Equity 90,000 60,000 25,000 Total Capital $100,000 $100,000 $100,000 Shares @ $5 18,000 12,000 5,000 EBIT $8,000 $8,000 $ 8,000 Interest ( 15%) 1,500 6,000 11,250 EBT $6,500 $2,000 ($ 3,250) Tax (40%) 2,600 800 - Net Income $ 3,900 $1,200 ($ 3,250) ROE 4.3% 2.0% (13.0%) EPS $.22 $.10 ($.65) b. Stock price would almost certainly decline as a result of restructuring. Increased debt is causing a deterioration of financial performance measured by ROE and EPS as well as increasing risk. Both of these have negative effects on investors’ attitudes. Under these conditions (a low EBIT) it would virtually never be advisable to exchange equity for debt. c. Leverage is not advisable if the return on capital employed, ROCE, is less than the after tax cost of debt. Currently Connecticut’s ROCE is ROCE = EBIT(1  T) / (Debt + Equity) = $8,000(1  .4) / $100,000 = $4,800 / $100,000 = 4.8% Its after tax cost of debt is 15%(1 – T) = 15%(1  .4) = 9% Hence at an EBIT of $8,000, Connecticut’s ROCE is less than its after tax cost of debt and we would not expect adding leverage to do the firm any good. 3. Assume Connecticut Computer Company of the last two problems is earning an EBIT of $15,000. Once again, calculate the chart showing the implication of adding more leverage. Verbally rationalize the result. SOLUTION: 10% Debt 40% Debt 75% Debt Debt $ 10,000 $ 40,000 $ 75,000 Equity 90,000 60,000 25,000 Total Capital $100,000 $100,000 $100,000 Shares @ $5 18,000 12,000 5,000 EBIT $15,000 $15,000 $15,000 Interest ( 15%) 1,500 6,000 11,250 EBT $13,500 $9,000 $ 3,750 Tax (40%) 5,400 3,600 1,500 Net Income $ 8,100 $ 5,400 $ 2,250 ROE 9.0% 9.0% 9.0% EPS $.45 $.45 $.45 Leverage has no effect on financial performance, but it still adds risk hence the effect on stock price would probably be negative. At an EBIT of $15,000 the ROCE and the after tax cost of debt are both 9%. Trading equity for debt or vice versa makes no difference in performance, because the firm is earning on capital exactly what it pays for the use of additional debt funds. I.e., there’s no “leverage.” The risk effect, however, is still there because as the firm adds more debt it must pay more interest making its profit margin narrower. This will probably drive the stock’s price down in the absence of a counteracting favorable change in ratios. 4. Watson Waterbed Works Inc. has an EBIT of $2.75 million, can borrow at 15% interest, and pays combined state and federal income taxes of 40%. It currently has no debt and is capitalized by equity of $12 million. The firm has 1.5 million shares of common stock outstanding that trade at book value. a. Calculate Watson's Net Income, ROE, and EPS currently and at capital structures that have 20%, 40%, 60%, and 80% debt. b. Compare the EPS at the different leverage levels, and the amount of change between levels as leverage increases. What happens to the effect of more debt as leverage increases from a little to a lot? SOLUTION: a. INCOME STATEMENT All 20% 40% 60% 80% Equity Debt Debt Debt Debt EBIT $ 2,750 $ 2,750 $ 2,750 $ 2,750 $ 2,750 Interest -__ 360 720 1,080 1,440 EBT $ 2,750 $ 2,390 $ 2,030 $ 1,670 $ 1,310 Tax 1,100 956 812 668 524 Net Income $ 1,650 $ 1,434 $ 1,218 $ 1,002 $ 786 BALANCE SHEET Debt - $ 2,400 $ 4,800 $7,200 $ 9,600 Equity $12,000 9,600 7,200 4,800 2,400 Capital $12,000 $12,000 $12,000 $12,000 $12,000 Shrs @ $8 1.5M 1.2M .9M .6M .3M ROE 13.8% 14.9% 16.9% 20.9% 32.8% EPS $1.10 $1.20 $1.35 $1.67 $2.62 b. The effect of leverage accelerates as more leverage is added. That is, the same increment of debt brings larger changes in ROE and EPS as leverage increases. Managing EPS Through Leverage: Concept Connection Example 14-1 (page 587) 5. The Tanenbaum Tea Company wants to show the stock market an EPS of $3 per share, but doesn't expect to be able to improve profitability over what is reflected in the financial plan for next year. The plan is partially reproduced as follows. Tanenbaum Tea Company Financial Projection 20X1 ($000) EBIT $18,750 Debt $ 13,000 Interest (@12%) 1,560 Equity 97,000 EBT $17,190 Capital $110,000 Tax (38%) 6,532 Net Income $10,658 #shares = 3,700,000 Tanenbaum's stock sells at book value. Will trading equity for debt help the firm achieve its EPS goal, and if so what debt level will produce the desired EPS? SOLUTION: In ($000) After-tax cost of debt = kd(1T) = 12%(.62) = 7.4% Hence, ROCE > kd(1T) => more leverage will help performance. Book value per share = $97M/3.7M shares = $26.2162. Trial and error leads to the correct debt level of $24M, from which: EBIT $18,750 Debt $ 24,000 Interest (@12%) 2,880 Equity 86,000 EBT $15,870 Capital $110,000 Tax (38%) 6,031 Net Income $ 9,839 Change in equity = $97M $86M Shares retired at book value = $11,000,000 / $26.2162 = $419,588 New number of shares outstanding = 3,700,000  419,588 = 3,280,412 New EPS = Net Income / # shares = $9,839,000 / 3,280,412 = $3.00 Basics Plus DFL: Apply Equation 14.3 (page 595) 6. The Canterbury Coach Corporation has EBIT of $3.62 million, and total capital of $20 million, which is 15% debt. There are 425,000 shares of stock outstanding which sell at book value. The firm pays 12% interest on its debt and is subject to a combined state and federal tax rate of 40%. Canterbury is contemplating a capital restructuring to either 30%, 45%, 60%, or 75% debt. a. At the current level of profitability, will more debt enhance results? Why? b. Calculate the net income, ROE, EPS, and the DFL at the current and proposed structures, and display your results in a systematic table. c. In a short paragraph referring to your table, discuss the trade-off between performance and increased risk (reflected in the DFL) as leverage increases. Do some levels seem to make more sense than others? What business characteristics would make the higher leverage levels less of a problem? SOLUTION: In ($000) After-tax cost of debt = kd(1T) = 12%(.6) = 7.2% Hence, ROCE > kd(1T) which implies that more leverage will improve performance. b. INCOME STATEMENT Current Proposals 15% 30% 45% 60% 75% Debt Debt Debt Debt Debt EBIT $ 3,620 $ 3,620 $ 3,620 $ 3,620 $ 3,620 Interest 360 720 1,080 1,440 1,800 EBT $ 3,260 $ 2,900 $ 2,540 $ 2,180 $ 1,820 Tax 1,304 1,160 1,016 872 728 Net Income $ 1,956 $ 1,740 $ 1,524 $ 1,308 $ 1,092 BALANCE SHEET Debt $ 3,000 $ 6,000 $ 9,000 $12,000 $15,000 Equity $17,000 14,000 11,000 8,000 5,000 Capital $20,000 $20,000 $20,000 $20,000 $20,000 Shares 425,000 350,000 275,000 200,000 125,000 Book Value $40 $40 $40 $40 $40 ROE 11.5% 12.4% 13.9% 16.4% 21.8% EPS $4.60 $4.97 $5.54 $6.54 $8.74 DFL = EBIT /(EBITI) DFL 1.11 1.25 1.43 1.66 1.99 c. As ROE and EPS performance improves, so does the risk implied by the increasing DFL. The highest level of leverage yields financial risk that almost doubles business risk. That intuitively seems unacceptable. The 45% level seems reasonable. If EBIT is stable, however, there is less reason to be concerned about more leverage. Forecasting Results Through the DFL: Concept Connection Example 14-2 (page 595) 7. Balfour Corp has the following operating results and capital structure ($000). Revenue $6,000 Debt $ 1,200 Cost/Expense 4,500 Equity 8,800 EBIT $1,500 Total $10,000 The firm is contemplating a capital restructuring to 60% debt. Its stock is currently selling for book value at $25 per share. The interest rate is 9%, and combined state and federal taxes are 42%. a. Calculate EPS under the current and proposed capital structures. b. Calculate the DFL under both structures. c. Use the DFLs to forecast the resulting EPS under each structure if operating profit falls off by 5%, 10%, or 25%. d. Comment on the desirability of the proposed structure versus the current one as a function of the volatility of the business. e. Is stock price likely to be increased by a change to the proposed capital structure? Discuss briefly. SOLUTION: ($000) INCOME STATEMENT Current Proposed EBIT $1,500 $1,500 Interest (9%) 108 540 EBT $1,392 $ 960 Tax (42%) 585 403 Net Income $ 807 $ 557 BALANCE SHEET Debt $ 1,200 $ 6,000 Equity 8,800 4,000 Capital $10,000 $10,000 #Shares = Eq/BV per share $8,800,000/$25 = 352,000 $4,000,000/$25 = 160,000 a. EPS = Net Income / # Shrs Current: $807/352 = $2.29 Proposed: $557/160 = $3.48 b. DFL = EBIT / EBT Current: $1,500/$1,392 = 1.08 Proposed: $1,500/$960 = 1.56 c. % EPS = DFL (% EBIT) Fcst EPS = EPS (1  % EBIT) Current Proposed %  EBIT % EPS Fcst EPS % EPS Fcst EPS 5% 5.4% $2.17 7.8% $3.21 10% 10.8% $2.04 15.6% $2.94 25% 27.0% $1.67 39.0% $2.12 d. EPS is higher but more variable under the proposed structure. However, at a 25% reduction in EBIT, EPS is still better under the proposal than under the old structure. Hence if operating profitability isn't expected to vary much, the proposal may be a good idea. e. We can't say for sure because the ultimate impact on stock price depends on investors' subjective feelings about risk and return trade-off. However, it looks likely that the impact would be favorable if EBIT isn't expected to vary more than 25%. 8. Algebraically derive EPS = ROE  [Book value per share]. (Hint: Write the definitions of ROE, EPS, and book value, and then start substituting.) SOLUTION: Write the definition of EPS and solve for Net Income EPS = Net Income / # Shrs Net Income = EPS (# Shrs) Write the definition of ROE and substitute for Net Income ROE = Net Income / Equity = EPS (# Shrs) / Equity Solve for EPS EPS = ROE [Equity/# Shrs]. But since [Equity/# Shrs] is Book value per share, EPS = ROE (Book Value per Share). EBIT-EPS Analysis: Concept Connection Example 14.3 (page 598) 9. You're a financial analyst at Pinkerton Interactive Graphic Systems (PIGS), a successful entrant in a new and rapidly growing field. As in most new fields, however, rapid growth is anything but assured, and PIGS's future performance is uncertain. The firm expects to earn operating profits of $4 million next year, up from $1 million last year. To support this enormous growth the firm plans to raise $15 million in new capital. It already has capital of $5 million, which is 40% debt. PIGS can raise the new money in any proportion of debt and equity management chooses. The CFO is considering three possibilities: all equity, $8 million debt and $7 million equity, and all debt. Interest on the current debt as well as on new borrowing is expected to be 10%, and the company pays state and federal income taxes at a combined rate of 40%. Equity will be raised by selling stock at the current market price of $10 which is equal to its book value. The CFO has asked you to prepare an analysis to aid management in making the debt/equity decision. You are also to provide a recommendation of your own. a. Prepare an EBIT-EPS analysis of the situation showing a line for the capital structure that results from each of the three options. Calculate EPS under each new capital structure at EBIT levels of $1 million, $2 million, and $4 million. Then graph EBIT versus EPS for each option. Refer to Figure 14-3. Show last year's EPS on the graph. b. Discuss the effect the options might have on stock price. c. Make a subjective recommendation under each of the following assumptions about the $4 million forecast. Support your position with words and references to your EBIT-EPS analysis. 1. The $4 million Operating Profit projection is a best-case scenario. Anything from ($2 million) to $4 million has an equal probability of occurring. 2. The $4 million is a fair estimate with about a 60% probability. However, performance better than $4 million is unlikely. EBIT results could range anywhere from zero to $4 million. 3. $4 million is an easy target. There's an even chance of anything between $4 million and $8 million. SOLUTION: a. CAPITAL Options for New Current Capital Additions Possible New Structures Structure 1 2 3 1 2 3 Debt $2,000 - $8,000 $15,000 $ 2,000 $10,000 $17,000 Equity 3,000 $15,000 $7,000 - 18,000 10,000 3,000 Total $5,000 $20,000 $20,000 $20,000 # Shrs 300 1,500 700 - 1,800 1,000 300 Note that the number of shares comes from dividing equity by $10 per share, which is market price as well as book value. INCOME STATEMENTS AT EBIT = $4,000 Capital Structure Options 1 2 3 EBIT $4,000 $4,000 $4,000 Interest 200 1,000 1,700 EBT $3,800 $3,000 $2,300 Tax 1,520 1,200 920 Net Income $2,280 $1,800 $1,380 EPS $ 1.27 $ 1.80 $ 4.60 INCOME STATEMENTS AT EBIT = $2,000 Capital Structure Options 1 2 3 EBIT $2,000 $2,000 $2,000 Interest 200 1,000 1,700 EBT $1,800 $1,000 $ 300 Tax 720 400 120 Net Income $1,080 $ 600 $ 180 EPS $0.60 $0.60 $0.60 INCOME STATEMENTS AT EBIT = $1,000 Capital Structure Options 1 2 3 EBIT $1,000 $1,000 $1,000 Interest 200 1,000 1,700 EBT $ 800 $ 0 ($ 700) Tax 320 0 ( 280)* Net Income $ 480 $ 0 ($ 420) EPS $ 0.27 $ 0.00 ($ 1.40) For illustrative purposes assume a tax credit on losses. Note that last year's income Statement is identical to Column 1 in the last table except that there are 300,000 shares of stock outstanding, which yields an EPS of $1.60. EPS $5.00 -3- $4.00 $3.00 -2- $2.00 -1- $1.00 EBIT $1,000 $2,000 $3,000 $4,000 b. The three options display a wide range of choices with respect to the trade-off between risk and performance. Option one is relatively conservative in that there's almost no loss at EPS until a loss is experienced at EBIT. Option three, on the other hand, is very risky getting into negative EPSs while operating profits are still good. Intuitively, option three seems risky enough to decrease stock price. The choice between options one and two is subjective. An important point, however, is a comparison with last year's EPS, which can be calculated at $1.60. Option one will result in a decline in EPS at the expected level of EBIT. That fact is likely to make it unacceptable. c. 1) This is a high risk scenario in which most people would probably choose option one. Even that gives only about a 2/3 probability of a positive EPS. The others are worse. Option three looks like it could bankrupt the firm toward the bottom of the EBIT range. 2)This is a common business situation: A likely outcome has more downside risk than upside potential. Either of the first two options is supportable. 3) Option three is clearly the best choice if the outlook is really this good. Contribution and Breakeven: Concept Connection Examples 14-4 and 14-5 (pages 603 and 604) 10. Cranberry Wood Products Inc. spends an average of $9.50 in labor and $12.40 in materials on every unit it sells. Sales commissions and shipping amount to another $3.10. All other costs are fixed and add up to $140,000 per month. The average unit sells for $32.00. a. What are Cranberry's contribution and contribution margin? b. What is the firm's breakeven point in units? c. Calculate the dollar breakeven point in two ways. d. Sketch the Breakeven Diagram. SOLUTION: Variable cost per unit = V = Labor + Material + C&S V = $9.50 + $12.40 + $3.10 = $25.00 a. Ct = P  V =$32  $25 = $7.00 CM = (P  V)/P = $7/$32 = .21879 = 21.9% b. QB/E = FC/Ct = $140,000/$7 = 20,000 c. SB/E = P(FC)/Ct = ($32)$140,000/$7 = $640,000 SB/E = FC/CM = $140,000/.21875 = $640,000 d. 20,000 Units Fixed/Variable Cost Tradeoff and DOL: Concept Connection Examples 14.6 and 14.7 (pages 606 and 607) 11. Referring to the Cranberry Company of the previous problem: a. Calculate the DOL when sales are 20%, 30% and 40% above breakeven. b. Suppose automated equipment is added which increases fixed costs by $20,000 per month. How much will total variable cost have to decrease to keep the breakeven point the same? c. Calculate the DOL at the same output levels used in part a. d. Comment on the differences in DOL with and without the additional equipment. SOLUTION: a. B/E+ Q DOL 20% 24,000 6.0 30% 26,000 4.3 40% 28,000 3.5 b. QB/E = FC/(PV) After automated Equipment installed, FC = $160,000, QB/E = 20,000, and P = $32 So, 20,000 = $160,000 / ($32V), from which V = $24. Previously, V = $25, so the required decrease is $1 per unit. c. B/E+ Q DOL 20% 24,000 6.0 30% 26,000 4.3 40% 28,000 3.5 d. The DOL around a fixed breakeven point is a function of quantity only as the mix of fixed and variable costs shifts. Problems 12 – 15 refer to Burl Wood Products (BWP), a manufacturer of high quality furniture. 12. BWP projects sales of 100,000 units next year at an average price of $50 per unit. Variable costs are estimated at 40% of revenue, and fixed costs will be $2.4 million. BWP has $1 million in bonds outstanding on which it pays 8%, and its marginal tax rate is 40%. There are 100,000 shares of stock outstanding which trade at their book value of $30. Compute BWP’s contribution, contribution margin, Net Income, DOL and EPS. SOLUTION:($ Millions) Revenue 100,000 x $50 $5.00 Variable Cost @ 40% 2.00 Contribution Margin 3.00 Fixed Costs 2.40 EBIT .60 Interest Expense $1.0 x .08 .08 EBT .52 Tax @ 40% .208 Net Income .312 Contribution 50 – (50 x .4) $30 Contribution Margin 30/50 60% Net Income $312,000 DOL {100,00(50-20)/[100,000(50-20)-2400000]} 5 EPS $312,000/100,000 $3.12 13. BWP intends to purchase a machine that will result in a major improvement in product quality along with a small increase in manufacturing efficiency. The machine will cost $1 million, which will be borrowed at 9%. The quality improvement is expected to have a significant impact on BWP’s competitive position. Indeed, management expects sales to increase by 5% in spite of a planned 10% price increase. The efficiency improvement combined with the price increase will result in variable costs of 36% of revenue. Fixed cost, however, will rise by 19%. a. Compute BWP’s, new contribution, contribution margin, Net Income, DOL, and EPS if it purchases the new machine. b. If all of BWP’s projections come to pass, how will stock price be influenced? What factors should be considered in estimating a stock price change? SOLUTION: ($ Millions) a. Revenue (100,000 x $50 x 1.1 x 1.05) $5.775 Variable Cost @ 36% 2.079 Contribution Margin 3.696 Fixed Costs ($2.4 x 1.19) 2.856 EBIT .840 Interest Expense ($1.0 x .08 + $1.0 x .09) .170 EBT .670 Tax @ 40% .268 Net Income .402 Contribution ($55 - .36x $55) $35.20 Contribution Margin ($35.20/$55) 64% Net Income $402,000 DOL {105,00(35.20)/[105,000(35.20)-2856000]} 4.4 EPS ($402,000/100,000) $4.02 b. An increase in EPS will have a positive effect on stock price. A doubling of debt, however, might have a negative effect, especially if debt was already a significant percentage of capital. The decrease in DOL means results will be less volatile which should have a positive effect. It isn’t possible to say with certainty which effect will dominate. 14. Calculate BWP’s DFL and DTL before and after the acquisition of the new machine. SOLUTION: W/O machine W/machine DFL = EBIT/(EBIT – I) = .6/.52 = 1.15 .84/.67 = 1.25 DTL = DOL x DFL = 5.0 x 1.15 = 5.75 4.4 x 1.25 = 5.5 15. Use the information from the previous two problems. Calculate BWP’s breakeven point in units and dollars, with and without the purchase of the new machine. SOLUTION: Without machine: $2.4 million/$30 = 80,000 units 80,000 units x $50 = $4000,000 With machine: $2.856 million/$35.20 = 81,137 units 81,137 units x $55 = $4,462,535 Degree of Total Leverage (DTL): Concept Connection Example 14.8 (page 610) 16. The Spitfire Model Airplane Company has the following modified income statement ($000) at 100,000 units of production. Revenue $10,000 Variable Cost 6,500 Fixed Cost 2,200 EBIT $ 1,300 Interest (@ 10%) 500 EBT $ 800 Tax (@ 40%) 320 Net Income $ 480 # shares 20,000 a. What are Spitfire's contribution margin and dollar breakeven point? b. Calculate Spitfire's current DFL, DOL, and DTL. c. Calculate the current EPS and estimate what it would become if sales declined by 25%. Use the DTL first and then recalculate the modified income statement. (Assume a negative EBT generates a negative tax.) SOLUTION: a. P = $10M/100,000 = $100 V = $6.5M/100,000 = $65 CM = (PV)/P = ($100  $65)/$100 = .35 SB/E = FC/CM = $2,200,000/.35 = $6,285,714 b. DTL = DOL  DFL = 2.692  1.625 = 4.375 c. A 25% decline in sales implies EPS will decline by 25%  DTL = 25%  4.375 = 109.4% 109.4% of $24 = $26.26 $24  $26.26 = $2.26 Recalculating the income statement: Revenue $7,000 Variable Cost 4,875 Fixed Cost 2,200 EBIT $ 425 Interest (@ 10%) 500 EBT $ ( 75) Tax (@ 40%) ( 30) Net Income $ ( 45) # shares 20,000 EPS = $45,000/20,000 = $2.25 17. The Singleton Metal Stamping Company is planning to buy a new computer controlled stamping machine for $10 million. The purchase will be financed entirely with borrowed money that will change Singleton's capital structure substantially. It will also change operations by adding $1.5 million in fixed cost and eliminating $2 million in variable cost at the current level of sales. The firm's current financial position is reflected in the following statement ($000). Revenue $18,000 Variable Cost 10,000 Debt $ 5,000 Fixed Cost 5,000 Equity 15,000 EBIT $ 3,000 Total $20,000 Interest (@ 10%) 500 #shares 750,000 EBT $ 2,500 Tax (@ 40%) 1,000 EPS = $2.00 Net Income $ 1,500 a. Restate the financial statements with the new machine, and calculate the dollar breakeven points with and without it. b. Calculate the DFL with and without the new machine. c. Calculate the DOL with and without the new machine. (Hint: You don't need Q to use equation (14-11), because PQ is revenue and VQ is total variable cost.) d. Calculate the DTL with and without the new machine. e. Comment on the variability of EPS with sales and the sources of that variability. f. Is it a good idea to buy the new machine if sales are expected to remain near current levels? Give two reasons why or why not. What has to be anticipated for the project to make sense? SOLUTION: a. Financial Statements With New Machine Revenue $18,000 Variable Cost 8,000 Debt $15,000 Fixed Cost 6,500 Equity 15,000 EBIT $ 3,500 Total $30,000 Interest (@ 10%) 1,500 #shares 750,000 EBT $ 2,000 Tax (@ 40%) 800 EPS $1.60 Net Income $ 1,200 (Notice that performance is worse with the new machine.) Current New Breakeven CM = B/E = b. DFL = c. DOL = d. DTL = 1.20(2.67) = 3.2 1.75(2.86) = 5.0 e. EPS will vary substantially more (5.0/3.2 1 = 56%) under the new plan. Most of the variation will come from the increase in financial risk reflected in the increased DFL. f. The new machine doesn't seem to be a good idea for two reasons: 1. At current production levels, financial performance gets worse, and 2. Financial performance is considerably more variable (risky) with the machine. The project would make sense if a big increase in volume was expected. Capital Structure Theory – Background – The Value of the Firm (pages 611-613) 18. Schoen Industries pays interest of $3 million each year on bonds with an average coupon rate of 7.5%. The firm has 4.5 million shares of stock outstanding and pays out 100% of earnings in dividends. Earnings per share (EPS) is $3.50. Schoen’s cost of equity is 12%. Calculate the firm’s total value (the value of its debt plus that of its equity) under the assumptions of Modigliani and Miller’s simplest model. I.e., that there are no taxes and no transactions costs in financial markets. (Hint: Use Equations 14.15 - 14.17.) SOLUTION: VF = Vd + Ve VF = $3.0M/.075 + $3.50 x 4.5M shares/.12 =$40 M+ $131.25M = $171.25M 19. Assume Schoen Industries of the last problem is subject to income tax at a rate of 40%. a. Recalculate the value of the firm assuming there is no tax shield associated with debt and compare it to the value calculated in the last problem. That is, assume interest is subtracted in calculating earnings, but is not deductible in calculating taxes. How much value has theoretically been lost to investors as a result of taxes? Which investors suffer the loss, stockholders or bondholders? b. What is the value of the tax shield associated with the firm’s debt. What is the benefit of debt? Calculate the theoretical value of the firm including the benefit of debt and compare it with the value calculated in the last problem? Who gets the incremental value resulting from the tax shield? c. Under what conditions, assuming bankruptcy costs are introduced, are investors likely to receive the full benefit of debt calculated in part b? Words only. SOLUTION: a. Earnings without tax were $3.50 x 4.5M shares = $15.75M Add interest payments 3.00M Taxable income $18.75M Less tax at 40% 7.50M Less interest 3.00M Earnings available for dividends $ 8.25M Vf = Vd + Ve = I / kd + D / ke = $3M / .075 + $8.25 / .12 = $40M + $68.75M = $108.75M Loss in value due to taxes Previous value $ 171.25M Value with tax but no tax shield (108.75M) Loss in value to investors $ 62.50M Stockholders suffer the entire loss, because interest payments are fixed by Schoen’s bond contracts. b. The (annual) tax shield associated with debt is the tax saved by making deductible interest payments, which is simply the payment times the tax rate. In Schoen’s case that’s $3M x .4 = $1.2M The benefit of debt is the present value of the annual tax shield in perpetuity capitalized at the return on debt. $1.2M / .075 = $16M The benefit of debt is an addition to the value calculated earlier in this problem. Hence the value with deductible taxes is Value with tax but no tax shield $108.75M Benefit of debt 16.00M $124.75M The benefit of debt accrues entirely to stockholders for the same reason they suffered the entire value loss from the imposition of taxes, because interest payments are fixed by Schoen’s bond contracts. c. The introduction of bankruptcy costs causes the value of the firm to decline below the theoretical value with taxes because investors become concerned about risk as debt increases. See Figure 14.13a. Further, investor concern about risk is heightened if the company is facing difficult business conditions. Hence the full benefit of debt is likely to be achieved only at low debt levels and when business is reasonably good. Estimating the Optimal Capital Structure: Concept Connection Example 14-9 (page 624) 20. Griffin Ross Construction Inc. (GRC) builds upscale homes in several New England cities. The firm is subject to the ups and downs of the construction industry and has a historical beta of 2.1. GRC has traditionally operated with a capital structure of approximately 20% debt and 80% equity. The owner Griffin Ross, is interested in selling the business, and has hired you to look at approaches to enhancing its market value. You think overall value might increase if the firm operated at its optimal capital structure, but you don’t know what that optimal level is. A commercial banker has given you the following estimate of the rates that GRC could borrow depending on its level of leverage % Debt 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% kd 7% 7% 7.5% 8% 9% 11% 13% 18% N/A N/A GRC is subject to a total effective tax rate of 35%, the risk free rate is 5% and the market is returning 11%, i.e. the market risk premium is 6%. Calculate GRC’s cost of equity, ke, as well as its average cost of capital, ka (WACC), as functions of leverage where leverage, measured by debt as a percent of total capital, varies from 0% to 70% in 10% increments. Use the result to estimate GRC’s optimal capital structure. (Hint: The GRC’s beta is levered at a 20/80 debt/equity level. Begin by calculating the unlevered beta. Write equation (14.22) substitute for bL and B/E and solve for bU. Then proceed as in example 14-9. See note at the end of example 14-9.) SOLUTION: First find GRC’s unlevered beta bL = bU [ 1+(1 – T) (B/E) ]
2.1 = bU[1 + (1 - .35)(20/80)]
2.1 = bU[1 + (.65)(.25)] = bU[1.23]
bU = 1.7 Then calculate ke and ka at each leverage level. If there is no debt, B in the Hamada Equation is zero, so bL = bU = 1.7, and ka = ke and the SML yields ke = kRF + [kM - kRF] bU = 5 + [6](1.7) = 15.20% I.e., ka is simply the cost of equity. If debt is 10% of capital, B/E = 10/90 = .11. Write the Hamada equation and substitute bL = bU [ 1+(1 – T) (B/E) ]
bL = 1.7 [ 1+(1 – .35) (.11) ] = 1.7 [ 1+.65(.11)] = 1.82
Next use the SML with the levered beta, bL, to get ke.
ke = kRF + [kM - kRF] bL = 5 + [6](1.82) = 15.92%
Then calculate ka using a 10% weight for debt and a 90% weight for equity along with the investment banker’s estimate of 7% for kd.
ka = (% debt)(1-T)kd +(% equity)ke
= (.10)(.65)(7%) + (.90)(15.92%)
= .46% + 14.33% = 14.79% Use the same procedure for the remaining leverage levels. If debt is 20% of capital, B/E = 20/80 = .25, and
bL = bU [ 1+(1 – T) (B/E) ] = 1.7 [ 1+.65(.25)] = 1.98
ke = kRF + [kM - kRF] bL = 5 + [6](1.98) = 16.88%
and ka is
ka = (% debt)(1-T)kd +(% equity)ke
= (.20)(.65)(7.5%) + (.80)(16.88%)
= .98% + 13.50% = 14.48% If debt is 30% of capital, B/E = 30/70 = .43, and
bL = bU [ 1+(1 – T) (B/E) ] = 1.7 [ 1+.65(.43)] = 2.18
ke = kRF + [kM - kRF] bL = 5 + [6](2.18) = 18.08%
and ka is
ka = (% debt)(1-T)kd +(% equity)ke
= (.30)(.65)(8%) + (.70)(18.08%)
= 1.56% + 12.66% = 14.22% If debt is 40% of capital and B/E is (40/60=) .67, and we have bL = bU [ 1+(1 – T) (B/E) ] = 1.7 [ 1+.65(.67)] = 2.44
and
ke = kRF + [kM - kRF] bL = 5 + [6](2.44) = 19.64%
and ka is
ka = (% debt)(1-T)kd + (% equity)ke
= (.40)(.65)(9%) + (.60)(19.64%)
= 2.34% + 11.78% = 14.12% If debt is 50% of capital and B/E is (50/50=) 1.00, and we have bL = bU [ 1+(1 – T) (B/E) ] = 1.7 [ 1+.65(1.00)] = 2.81
and
ke = kRF + [kM - kRF] bL = 5 + [6](2.81) = 21.86%
and ka is
ka = (% debt)(1-T)kd +(% equity)ke
= (.50)(.65)(11%) + (.50)(21.86%)
= 3.58% + 10.93% = 14.51% If debt is 60% of capital and B/E is (60/40=) 1.50, and we have bL = bU [ 1+(1 – T) (B/E) ] = 1.7 [ 1+.65(1.50)] = 3.36
and
ke = kRF + [kM - kRF] bL = 5 + [6](3.36) = 25.16%
and ka is
ka = (% debt)(1-T)kd +(% equity)ke
= (.60)(.65)(13%) + (.40)(25.16%)
= 5.07% + 10.06% = 15.13% If debt is 70% of capital and B/E is (70/30=) 2.33, and we have bL = bU [ 1+(1 – T) (B/E) ] = 1.7 [ 1+.65(2.33)] = 4.27
and
ke = kRF + [kM - kRF] bL = 5 + [6](4.27) = 30.62%
and ka is
ka = (% debt)(1-T)kd +(% equity)ke
= (.70)(.65)(18%) + (.30)(30.62%)
= 8.19% + 9.19% = 17.38% Summarizing these results we have: Griffin Ross Inc.
Returns on Capital as a Function of Leverage
(%) % Debt 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% kd 7% 7% 7.5% 8% 9% 11% 13% 18% N/A N/A
ke 15.2 15.9 16.9 18.1 19.6 21.9 25.2 30.6
ka 15.2 14.8 14.5 14.2 14.1 14.5 15.1 17.4 Scanning the ka line we see that the lowest value appears at 40% debt which indicates that the optimum capital structure is in the neighborhood of 40% debt and 60% equity. Solution Manual for Practical Financial Management William R. Lasher 9781305637542