Chapter 16 Capital Structure

Chapter 16 Capital Structure LEARNING OBJECTIVES 1. Explain why borrowing rates are different based on ability to repay loans. 2. Demonstrate the benefits of borrowing. 3. Calculate the break-even EBIT for different capital structures. 551 (Slide 16-2) 4. Explain the appropriate borrowing strategy under the pecking order hypothesis. 5. Develop the arguments for the optimal capital structure in a world of no taxes and no bankruptcy and in a world of corporate taxes with no bankruptcy costs. 6. Understand the static theory of capital structure and the trade-off between the benefits of the tax shield and the cost of bankruptcy. IN A NUTSHELL Firms in developed countries have different levels of debt and equity leading to variations in their risk levels and cost of capital. In this chapter, the author starts out by explaining why borrowing rates are dependent on a firm s ability to pay. Next, the benefits of borrowing are identified and the method of calculating break-even EBIT for different capital structures is illustrated. The rationale behind the pecking order hypothesis is covered next followed by a detailed explanation of the various theories of capital structure. The chapter ends with a discussion of the static theory of capital structure and the trade-off between bankruptcy costs and tax shield benefits. LECTURE OUTLINE 16.1 Capital Markets: A Quick Review (Slides 16-3 to 16-5) Companies raise funds for growth in debt and equity markets. Investors have different risk preferences and companies have varying risk profiles. The cost that a firm pays for its debt or the rate of return that investors demand to purchase equity in a firm depends largely on the firm s debt rating and its beta or systematic risk measure. Riskier firms end up paying higher yields on debt securities and are expected to pay a higher rate of return on their equity, thereby raising their average cost of capital. Example 1: Effect of risk on borrowing rates Mike and Agnes are two venture capitalists with fairly different risk profiles. On average, both investors are willing to commit $1,000,000 per project to cutting-edge ideas and products that they think will fly. However, Mike is more conservative in that he tends to select low risk projects that he thinks have at least a 50% chance of being successful, while Agnes selects high risk projects that have at least 20% chance of doing well. Their

552 Brooks n Financial Management: Core Concepts, 2e success rates have tended to be right in line with their expectations. Based on their track records, what is the minimum rate that each investor is willing to lend $1,000,000 at? Mike s success rate = 5/10 projects; Agnes s success rate = 2/10 projects So, if they each lend $1,000,000 i.e 10 projects @ $100,000 each For Mike, each successful project must return $1,000,000/5 = $200,000 For Agnes, each successful project must return $1,000,000/2= $500,000 Mike s loan rate è ($200,000 $100,000)/$100,000 = 100% Agnes s loan rateè ($500,000-$100,000)/$100,000 = 400% So Agnes (being more of a risk-taker) has a loan rate that is 4 times higher than that of Mike. 16.2 Benefits of Debt (Slides 16-6 to 16-10) Financial leverage is the ability that owners have to use other people s i.e. creditors money at fixed rates to make higher rates of return than would have been possible by using all of one s own money. It represents one of the main benefits of taking on debt. Firms that take on debt as part of their capital structure are therefore known as leveraged firms while those that do not are known as unlevered firms. 16.2 (A) Earnings per Share as a Measure of the Benefits of Borrowing One way to measure the benefits of leverage is by comparing the EPS of firms with different capital structures under good and bad economic conditions. Table 16.1 presents 3 equal-sized firms, one with no debt, one with 50% debt, and the last one with 99.75% debt. Assuming a cost of debt of 10% for all firms and identical EBIT ($2000), EPS is calculated and shown in Table 16.2. If the firm s EBIT covers its interest cost, higher leverage benefits the stockholders with a higher EPS.

Chapter 16 n Capital Structure 553 However, if the firm s EBIT does not cover its interest cost, the reverse is true, as shown in Table 16.3 So leverage is a two-edged sword; benefiting firms in good times and hurting them in bad times. 16.3 Break- Even Earnings for Different Capital Structures (Slides 16-11 to 16-13) At a certain level of EBIT, known as the break-even EBIT, all three firms will have the same EPS as shown in Table 16.4 To calculate the break-even EBIT we use the following method: 1) We first calculate the EPS of two firms, e.g. Company 1 and Company 2; set them equal; and solve for the EBIT: EPS = (EBIT I)/# of shares EPS 1 = ( EBIT 0)/400 = (EBIT -$500)/200

554 Brooks n Financial Management: Core Concepts, 2e è 400(EBIT-$500) = 200(EBIT-0) è 2EBIT-$1000 = EBIT è EBIT = $1000 2) Next, we calculate each firm s EPS at the break-even EBIT i.e $1000: Company 1 seps = 1000/400 = $2.50; Company 2 EPS = (1000-500)/200 = $2.5 Company 3 s EPS = (1000-997.5)/1= $2.5 3) Below an EBIT of $1000, e.g. $800; leverage hurts and vice-versa as shown in Figure 16.1 16.4 Pecking Order (Slides 16-14 to 16-17) The pecking order hypothesis is based on the notion that firms have a preferred order of raising capital. Accordingly, it states that: 1. Firms prefer internal financing (retained earnings) first. 2. If external financing is required, firms will choose to issue the safest or cheapest security first, starting with debt financing and using equity as a last resort. 16.4 (A) Firms Prefer Internal Financing First: because it typically requires less effort, transactions cost, and loss of secrecy. 16.4 (B) Firms Choose to Issue Cheapest Security First and Use Equity as a Last Resort: Retained earnings being limited, firms have to use other external sources such as debt and equity.

Chapter 16 n Capital Structure 555 When they do tap the capital markets, firms tend to issue debt first, since it is less costly, and leads to less loss of control, and equity last, since too much debt can put the firm into a risk of bankruptcy. In summary, there are three implications of the pecking order hypothesis: 1. Profitable companies will borrow less (because they have more internal funds available) and may have lower debt to equity ratios, because they have more debt capacity. 2. Less profitable companies will need more external funding and will first seek debt financing in an asymmetric world, avoiding the equity market. 3. As a last resort, firms will sell equity to fund investment opportunities. 16.5 Modigliani and Miller on Optimal Capital Structure (Slides 16-18 to 16-32) Franco Modigliani and Merton Miller, two Nobel laureates, have developed a series of propositions around the question of whether or not there exists an optimal capital structure that firms can strive for. The basic assumption underlying the various propositions is that investment decision of a firm is separate from its financing decision, i.e. firms first decide which products and services to invest in and only then figure out what mix of financing sources they will use to finance the investment. 16.5 (A) Capital Structure in a World of No Taxes and No Bankruptcy: In 1956, M&M introduced their first theory which stated that in a world with no taxes and no bankruptcy risk, a firm s debt-equity mix would be irrelevant. M&M proposition I: states that in a world with no taxes and bankruptcy risk, the value of a leveraged firm (V L ) would equal that of an otherwise identical all-equity firm (V E ), i.e. the value of a firm does not depend on its capital structure. M&M proposition II: states that the value of a firm depends on three things: 1. The required rate of return on the firm s assets (which is the same for firms with identical assets or investment choices) 2. The cost of debt to the firm 3. The debt to equity ratio of the firm. In a world with no bankruptcy risk and taxes, the value of a firm would simply be the present value of its cash flow assumed to be received in perpetuity, i.e. V F = Cash Flow r where, r is the weighted average cost of capital of the firm (WACC) and can be calculated by using Equation 16.2

556 Brooks n Financial Management: Core Concepts, 2e Where E = the equity value; D =the debt value; V =the value of the firm = E+D Re = the cost of equity; Rd = the cost of debt; and Tc = the corporate tax rate Since the WACC of the firm would also be the required rate of return of the investor, R a, and the corporate tax rate is 0; the equation becomes: Since V=D+E, we can manipulate equation 16.3 to solve for the cost of equity (R e ) as shown in Equation 16.4: è R a = [(E/V)* R e ] + [(D/V)R d ] è [(E/V* R e ] = R a [(D/V*R d ] è R e = R a *V/E D/E*R d Since V=D+E, we have è R e = R a *(D+E)/E D/E*R d è R e = R a *(1+D/E) D/E*R d è R e = R a + D/E*Ra D/E*R d è R e = R a + D/E(R a R d ) Figure 16.3 illustrates the trade-off between higher levels of debt and higher cost of equity, as implied in Equation 16.4

Chapter 16 n Capital Structure 557 Example 2: Applying M&M s Propositions I and II in a world with no taxes Firm A is an all-equity firm with a required return on its assets of 9%. Firm B is a levered firm and can borrow in the debt market at 7%. Both companies operate in an utopian world of no taxes and no bankruptcy (no risk). If M&M proposition II holds, what is the cost of equity as firm B goes from (a)having 10% debt, to (b) 40% debt and finally to (c) 90% debt. Which capital structure would be the best for this levered firm? To solve this problem we need to calculate the cost of equity, and the WACC, of Firm B under the 3 different capital structures given. With 10% debtè Firm B s debt-equity ratio is 10/90; Ra=9%; Rd=7% Re = 9% + (9%-7%)*1/9 è 9.22% è WACC = Ra = (.9*9.222%) + (.1*7%) è 9% With 40% debtè D/E = 40/60 Re = 9% + (9%-7%)*.667è 10.334% WACC =.6*10.334%+.4*7% è 9% With 90% debtè D/E = 90/10 Re = 9% + (9%-7%)*9 è 27% WACC =.1*27% +.9*7% è 9% Since the WACC of the levered firm is the same as that of the all-equity firm (9%) in all three scenarios, we can say that debt does not matter. 16.5 (B) Capital Structure in a World of Corporate Taxes and No Bankruptcy Once M&M injected some reality into their capital structure discussion, i.e. that taxes are a way of life, their Propositions I and II got turned around. With interest being tax-deductible, the levered firm pays less tax on its income than an all-equity firm, and the equity holders enjoy more in residual profits as portrayed in Figure 16.4.

558 Brooks n Financial Management: Core Concepts, 2e As the firm issues more debt, its tax shield increases, and the government s share of the pie decreases, increasing the value of the equity-holders. The new Propositions I and II are as follows: Proposition I, with taxes: All debt financing is optimal. Proposition II, with taxes: The WACC of the firm falls as more debt is added. 16.5 (C) Debt and the Tax Shield: Table 16.5 shows the effect of increasing debt levels on the distribution of a firm s EBIT. Note that as the firm s debt level goes from 0% to 90%, with EBIT staying constant at $100,000, government s share of EBIT (taxes) dwindles from $25,000 to $2,500, thereby increasing the share of debt and equity holders from $75,000 to $97,500 Equation 16.5 sums up M&Ms Proposition I in a world with corporate taxes as follows: It shows that the value of a levered firm is greater than the value of an unlevered firm by the amount of the tax shield from selling debt, i.e. D*Tc The WACC equation (with Tc>0) shows that the cost of capital is reduced as the firm gets more levered.

Chapter 16 n Capital Structure 559 Example 3: An all-equity firm has a value of $8 million dollars and is currently being taxed 34% on its EBIT. The WACC for the company is currently at 16%. The current CEO who has just learned about M&Ms capital structure theory wants to sell $4 million worth of debt to take advantage of the tax shield on interest and accordingly increase the value of the firm for the equity holders. Is he justified in doing so? Please explain. All-Equity Firm 50/50 Firm Firm Value $8,000,000 $8,000,000 Debt holders share 0 $4,000,000 Government share (34%) $2,720,000 $1,360,000 Equity holders share $5,280,000 $8,640,000 Yes, the equity holder s wealth has increased from $5,280,000 to 8,640,000 16.6 The Static Theory of Capital Structure (Slides 16-33 to 16-36) So if increasing debt levels leads to increasing firm values, why do firms not attempt to go for maximum debt? The answer is bankruptcy risk. 16.6 (A) Bankruptcy: is the risk of losing the firm due to inability of a firm to pay its debt and other obligations. At bankruptcy, the value of equity is equal to zero, and the value of the firm s assets is equal to or probably less than its liabilities. Bankruptcy entails both direct and indirect costs. Direct costs include the legal and administrative fees necessary to settle the claims of creditors etc. Indirect costs of bankruptcy, called financial distress costs include lost sales, loss of valuable employees, loss of consumer confidence, and loss of profitable opportunities while facing bankruptcy. The greater the amount of debt carried by a firm, the greater the chance of bankruptcy and therefore the higher the potential financial distress costs.

560 Brooks n Financial Management: Core Concepts, 2e 16.6 (B) Static Theory of Capital Structure: The optimal capital structure (i.e. D/E)* comes at the point where the additional taxshield benefit of adding one more dollar of debt financing is equal to the direct and indirect cost of bankruptcy from that extra dollar of debt as shown in Figure 16.6 The 3 scenarios discussed in this Chapter lead to the following conclusions: 1. No taxes, no bankruptcy. Debt is irrelevant, since the values of leveraged firms and otherwise identical unleveraged firm are equal across all potential debt-equity ratios and the cost of capital is constant. 2. Taxes, no bankruptcy. The value of a firm increases by the amount of the tax shield due to debt. The value of the firm is greatest with 100% debt financing and its cost of capital is the lowest. 3. Taxes, bankruptcy. The value of a firm is maximized and its cost of capital is minimized at the point where the marginal benefit of financial leverage (the tax shield) equals the marginal cost of bankruptcy (financial distress costs). Questions 1. What is the difference between the return to an investor or lender and the cost to the borrower? Answer: The return to an investor is the cost to the seller of a financial asset. This is the same concept as the price of an asset in a transaction. The price is the same for the seller and buyer. 2. Why would one lender charge more for a loan to different borrowers? Why would two different lenders charge different rates to the same borrower? Answer: The difference in lending rates from the same lender to two different borrowers is based on perceived ability for the borrower to repay the loan, i.e. the risk to the lender. Two lenders may assess the risk of a borrower differently. A lender with a belief that the borrower has a higher potential default rate than the perception of the

Chapter 16 n Capital Structure 561 other lender will have to charge a higher rate to recoup the perceived higher potential loss for the loan. 3. What is the advantage of financial leverage, the degree to which a firm or individual utilizes borrowed money to make money? Answer: If successful, you are able to borrow the funds at a low rate and invest it into a project that earns you a greater return. In the investment world, this process is commonly known as using other people s money borrowing funds at one rate and investing at a higher rate to benefit the owner of a new idea. The more debt used, the greater the leverage a company employs on behalf of its owners. 4. How do we measure the advantage of financial leverage to the company s owners? Answer: One way to see the impact is to examine the earnings per share (EPS) of a company before and after borrowing from debt lenders. Another method is to examine the WACC of a levered firm versus that of an unlevered firm. 5. In what way is the decision on capital structure related to the company s expected earnings? Answer: There is a direct relationship between the debt a company can take on and earnings expectations. If a company is performing well it can handle more debt to benefit the owners. However, when a company does not perform well, debt amplifies the losses. 6. What is asymmetric information? How does it affect the prioritization of financing sources under the pecking order hypothesis? Answer: Information is asymmetric when one party in a transaction has a different set of information from the other party in the transaction. In our context here, asymmetric information means that managers or owners of a company know more about the future performance of the company than do potential outside lenders. Management not wishing to divulge this information to sources of capital will seek internal financing sources first. If external financing is required, firms will choose to issue the safest or cheapest security first, starting with debt financing and using equity as a last resort. 7. What does it mean when one states that the operating and financing decisions are separate from each other? How do we view the financing decision in terms of the magnitude of effect? Answer: Firms first select what products or services they will produce (operating/investing), and then will select how to best finance these products or services (the financing decision). Leverage magnifies both gains and losses. If a firm uses debt to finance an investment and it goes south, the loss is greater for the firm and the shareholders than it otherwise might be because of the interest expense. So leverage depends on how well the company is performing. When a company performs well, it can handle more debt and benefit the owners by earning a return which is greater than the cost to acquire capital. 8. Explain why M&M Proposition I in a world of no taxes and no bankruptcy states that the firm's value does not depend on its capital structure.

562 Brooks n Financial Management: Core Concepts, 2e Answer: In a world of no taxes and bankruptcy the value of a firm is based solely by the cash flow generated from the selection of products and services. The marginal advantage (tax shield) and costs of leveraging a firm (increased risk of financial distress) are ignored. Therefore, the value of a firm which is unlevered will be equal to the same firm which is levered. 9. Who loses out on a company s cash flow when it adds more and more debt is added to the financing structure? Who gains as a company when more and more debt is added? Answer: When we add debt to a firm the government share of earnings is reduced from its original value because the interest paid to the debt holders is tax-deductible. It is this tax shield that is distributed to the equity holders of a firm. Therefore, reducing the government s share of the firm increases the value of the firm to the equity holders. The more debt sold, the greater the tax shield and the smaller the government s share of the firm. 10. In a world of taxes and no bankruptcy, why is a company's optimal capital structure all debt? What happens when a company adds bankruptcy to the world of taxes with regard to the optimal capital structure? Answer: As more and more debt is added to the firm the value of the firm from the owner s perspective, increases by the size of the tax shield. This is because there is no marginal cost of borrowing to offset the marginal advantage of the tax shield so firms should finance with all debt to realize the full tax shield. When bankruptcy is taken into consideration there is a cost to adding more and more debt through both indirect and direct bankruptcy costs. This limits the amount of debt a firm should take on to well below 100%. 11. In the static theory of capital structure, what is static? Answer: The operations and assets of the company are fixed first (static) and then the firm determines the optimal balance of equity and debt to finance the operations. 12. In the static theory of capital structure, how do you find a firm's optimal capital structure? In other words, what benefit are you receiving as you add debt, and what cost are you incurring when you add debt? Answer: The benefit received by levering a firm is the tax shield (D T C ) spread across the equity holders. Direct costs incurred from debt financing are a firm s inability to meet debt payments and costs arising from bankruptcy. Indirect costs are a result of management s attention to bankruptcy concerns over the running of the firm. The optimal capital structure comes at the point where the additional tax-shield benefit of adding one more dollar of debt financing is equal to the direct and indirect cost of bankruptcy from that extra dollar of debt. Prepping for Exams 1. b 2. c 3. d 4. d 5. a

Chapter 16 n Capital Structure 563 6. d 7. c 8. c 9. d 10. d Problems 1. Different loan rates. Winthrop Enterprises is a holding company (a firm that owns all or most of some other companies outstanding stock). Winthrop has four subsidiaries. Each subsidiary borrows capital from the parent company for projects. Ervin Company is successful with its projects 85% of the time, Morten Company 92% of the time, Richmond Company 78% of the time, and Garfield Company 83% of the time. What loan rates should Winthrop Enterprises charge each subsidiary for loans? Ervin Company: To breakeven with an 85% success rate Ervin will need to recoup, $1/.85= $1.1764706. He should charge a return greater then ($1.1764706/$1.00)-1 =17.64706% Morten Company: To breakeven with a 92% success rate Morten will need to recoup, $1/.92= $1.0869565. He should charge a return greater then ($1.0869565/$1.00)-1 =8.69565% Richmond Company: To breakeven with a 78% success rate Richmond will need to recoup, $1/.78= $1.2820513. He should charge a return greater then ($1.2820513/$1.00)- 1 =28.20513% Garfield Company: To breakeven with an 83% success rate Ervin will need to recoup, $1/.83= $1.2048193. He should charge a return greater then ($1.2048193/$1.00)-1 =20.48193%. 2. Different loan rates. Keith Peterson is the CFO of Springfield Soups and Sauces. The company s typical success rate for new products is 88%. Keith wants to improve this success rate to 94%. What loan improvement (in terms of rates) would do that for Springfield Soups and Sauces? Old rate of success $1/.88 = $1.1363636-1= 13.63636% New rate of success $1/.94 = $1.0638298-1= <6.38298%> Loan rate improvement: 7.253385% 3. Benefits of borrowing. Wilson Motors is looking at expanding its operations by adding a second manufacturing location. If successful, the company will make $450,000. If it

564 Brooks n Financial Management: Core Concepts, 2e fails, the company will lose $250,000. Wilson Motors is trying to decide if it should borrow the $250,000, given the current bank loan rate of 15%. Should Wilson Motors borrow the money if a. the probability of success is 90%? b. the probability of success is 80%? c. the probability of success is 70%? Accept when expected payout exceeds cost of loan a. Expected return =.90($450,000) +.10(-$250,000) = $380,000 Cost= $250,000(1+.15) <$287,500> Expected Profit $92,500 Accept b. Expected return =.80($450,000) +.20(-$250,000) = $310,000 Cost= $250,000(1+.15) <$287,500> Expected Profit $22,500 Accept c. Expected return =.70($450,000) +.30(-$250,000) = $240,000 Cost= $250,000(1+.15) <$287,500> Expected Loss <$47,500> DECLINE! 4. Benefits of borrowing. What is the breakeven probability of success at the 15% borrowing rate in Problem 3? What is the breakeven probability of success if the loan rate is 20%? BE w/ 15% = ($450,000) + (1-X)-$250,000 = $287,500è ($250,000 1.15) $450,000X + $250,000X- $250,000 = $287,500 X = 76.785714% BE w/ 20% = ($450,000) + (1-X)-$250,000 = $300,000è ($250,000 1.20) $450,000X + $250,000X- $250,000 = $300,000 X = 78.571429% 5. EBIT breakeven (with and without taxes). Alpha Company is looking at two different capital structures, one an all-equity firm, and the other a leveraged firm with $2,000,000 of debt financing at 8% interest. The all-equity firm will have $4,000,000 value and 400,000 shares outstanding. The leveraged firm will have 200,000 shares outstanding. a. Find the break-even EBIT for Alpha Company using EPS if there are no corporate taxes.

Chapter 16 n Capital Structure 565 b. Find the break-even EBIT for Alpha Company using EPS if the corporate tax rate is 30%. c. What do you notice about these two break-even EBITS for Alpha Company? a. Interest expense = $2,000,000(.08) = $160,000 BE = (EBIT/400,000) = (EBIT- $160,000)/200,000 200,000 EBIT = 400,000 EBIT- $64,000,000,000 EBIT = $320,000 b. Interest expense = $2,000,000 (.08) (1-.3) = $112,000 BE = (EBIT/400,000) = (EBIT- $112,000)/200,000 200,000EBIT = 400,000EBIT $44,800,000,000 EBIT = $224,000 c. The addition of a tax rate introduces a tax shield lowering interest expense and decreasing tax expense. The lower breakeven point suggests that for a greater range of EBITs debt should be utilized. 6. Break-even EBIT (with taxes). Beta, Gamma, and Delta companies are similar in every way except for their capital structures. Beta is an all-equity firm with $3,600,000 of value and 100,000 shares outstanding. Gamma is a leveraged firm with the same value as Beta but $1,080,000 in debt at 9% and 70,000 shares outstanding. Delta is a leveraged firm with $2,160,000 in debt at 12% and 40,000 shares outstanding. What are the break-even EBITs for Beta and Gamma, Beta and Delta, and Gamma and Delta companies if the corporate tax rate is 40% for all three companies? Beta and Gamma, Interest expense = $1,080,000 (.09) (1-.4) = $58,320 BE = (EBIT/100,000) = (EBIT- $58,320)/70,000 70,000EBIT = 100,000EBIT $5,832,000,000 EBIT = $194,400 Beta and Delta, Interest expense = $2,160,000(.12)(1-.4) = $155,520 BE = (EBIT/100,000) = (EBIT- $155,520)/40,000 40,000EBIT = 100,000EBIT $15,552,000,000 EBIT = $259,200 Delta and Gamma, Interest expense (Delta) = $155,520; Interest expense (Gamma) = $58,320 BE = (EBIT- $58,320)/70,000 = (EBIT- $155,520)/40,000 40,000EBIT- $2,332,800,000 = 70,000EBIT $10,886,400,000 EBIT = $285,120

566 Brooks n Financial Management: Core Concepts, 2e 7. Pecking order hypothesis. Rachel can raise capital from the following sources: Source of Funds Interest Rate Borrowing Limit Parents 0% $10,000 Friends 5% $2,000 Bank Loan 9% $15,000 Credit Card 14.5% $5,000 What is Rachel s weighted average cost of capital if she needs to raise a. $10,000? b. $20,000? c. $30,000? a. WACC= [($10,000/$10,000) ] 0% = 0% b. WACC= [($10,000/$20,000) 0%] + [($2,000/$20,000) 5%] + [($8,000/$20,000) 9%] = 4.1% c. WACC = [($10,000/$30,000) 0%] + [($2,000/$30,000) 5%] + [($15,000/$30,000) 9%] + [($3,000/$30,000) 14.5%] = 6.2833% 8. Pecking order hypothesis. Ross Enterprises can raise capital from the following sources: Source of Funds Interest Rate Borrowing Limit Small Business Bureau 6% $50,000 Bank Loan 8% $40,000 Bond Market 11% $60,000 Owners Equity (Stock) 16% $80,000 Ross has a new project that has an estimated IRR of 12% but will require an investment of $200,000. Should Ross borrow the money and invest in the new project? Accept if, WACC<IRR WACC = [($50,000/$200,000) 6%] + [($40,000/$200,000) 8%] + [($60,000/$200,000) 11%] + [($50,000/$200,000)16%] = 10.4% Borrow funds

Chapter 16 n Capital Structure 567 9. Finding the WACC. Monica is the CFO of Cooking for Friends (CFF) and uses the pecking order hypothesis (POH) philosophy when she raises capital for company projects. Currently, she can borrow up to $600,000 from her bank at a rate of 8.5%, float a bond for $1,100,000 at a rate of 9.25%, or issue additional stock for $1,300,000 at a cost of 17%. What is the WACC for CFF if Monica chooses to invest: a. $1,000,000 in new projects? b. $2,000,000 in new projects? c. $3,000,000 in new projects? a. WACC = [($600,000/$1,000,000) 8.5%] + [($400,000/$1,000,000) 9.25%] = 8.8% b. WACC = [($600,000/$2,000,000) 8.5%] + [($1,100,000/$2,000,000) 9.25%] + [($300,000/$2,000,000)17%] = 10.1875% c. WACC = [($600,000/$3,000,000) 8.5%] + [($1,100,000/$3,000,000) 9.25%] + [($1,300,000/$3,000,000) 17%] = 12.46% 10. Finding the WACC. Chandler has been hired by Cooking for Friends to raise capital for the company. Chandler increases the funding available from the bank to $900,000, but with a new rate of 8.75%. Using the data in Problem 9, determine what the new weighted average cost of capital is for borrowing $1,000,000, $2,000,000, or $3,000,000. a. WACC = [($900,000/$1,000,000) 8.75%] + [($100,000/$1,000,000) 9.25%] = 8.8% b. WACC = [($900,000/$2,000,000) 8.75%] + [($1,100,000/$2,000,000) 9.25%] = 9.025% c. WACC = [($900,000/$3,000,000) 8.75%] + [($1,100,000/$3,000,000) 9.25%] + [($1,000,000/$3,000,000) 17%] = 11.68% 11. Modigliani and Miller's world of no taxes. Air Seattle is looking at changing its capital structure from an all-equity firm to a leveraged firm with 50% debt and 50% equity. Air Seattle is a not-for-profit company and therefore pays no taxes. If the required rate on the assets of Air Seattle is 20% (R A ), what is the current required cost of equity and what is the new required cost of equity if the cost of debt is 10%?

568 Brooks n Financial Management: Core Concepts, 2e R E = R A + (R A- R D ) (D/E) Current required cost of equity:.20 + (.20-.10) (0) =.20 or 20% New required cost of equity:.20 + (.20-.10) (.5/.5) =.30 or 30% 12. M&M: World of no taxes Roxy Broadcasting, Incorporated is currently a low leveraged firm with a debt-to-equity ratio of 1/ 3. The company wants to increase its leverage to 3/1 for debt-to-equity. If the current return on assets is 14% and the cost of debt is 11%, what is the current and new cost of equity if Roxy operates in a world of no taxes? R E = R A + (R A R D ) (D/E) Current cost of equity:.14 + (.14-.11) (1/3) =.15 or 15% New cost of equity:.14 + (.14-.11) (3/1) =.23 or 23% 13. Modigliani and Miller's world of taxes. Air Seattle from Problem 11 has lost its notfor-profit status, and the corporate tax rate is now 35%. If the value of Air Seattle was $5,000,000 as an all-equity firm, what is the value of Air Seattle under a 50/50 debtequity ratio? Assume that the $5,000,000 is the after-tax value of the unlevered firm. $5,000,000 after tax value, $5,000,000/.65= $7,692,307.70 implied before tax value At 50% debt amount of new bond issues = $7,692,307.70 (.5) = $3,846,153.8 Equity value after tax with new structure = $3,846,153.8 (1-.35) = $2,500,000 New equity wealth after tax = $2,500,000 + $3,846,153.8 = $6,346,153.8 Or this problem can be solved by adding the current equity wealth unlevered to the tax shield V L = V E + (D T C ) $5,000,000 + ($3,846,153.80.35) = $6,346,153.8 14. Modigliani and Miller's world of taxes. Roxy Broadcasting in Problem 12 was originally an all-equity firm with a value of $25,000,000. Roxy now pays taxes at a 40% rate. What is the value of Roxy under the 1/3 debt to equity capital structure? Under the 3/1 capital structure?

Chapter 16 n Capital Structure 569 All Equity 25/75 75/25 TOTAL Company $25,000,000 $25,000,000 $25,000,000, Debt Sold (a) $0 $6,250,000 $18,750,000 Gov t Slice $10,000,000 $7,500,000 $2,500,000 Equity Slice (b) $15,000,000 $11,250,000 $3,750,000 Equity Wealth (a+b) $15,000,000 $17,500,000 $22,500,000 Equity Increase $2,500,000 $7,500,000 Tax Shield $0 $2,500,000 $7,500,000 Once again this problem can be solved by adding the tax shield to the current after tax equity value without debt. V E = $25,000,000 (1-.4) = $15,000,000 V L = V E + (D T C ) a. $15,000,000 + ($6,250,000.4) = $17,500,000 b. $15,000,000 + ($18,750,000.4) = $22,500,000 15. Size of tax shield. Using the information from Problems 11 and 13 on Air Seattle, determine the size of the tax shield with a corporate tax rate of 15%, 25%, 35%, and 45% if Air America s capital structure is 50/50 debt-to-equity. Before tax firm value all equity = $7,692,307.70 after-tax value = $5m Tax rate = 35% (This is assumed to be the value of the firm) New debt issues with 50% debt = $7,692,307.70 (.5) = $3,846,153.8 Tax shield = (D T C ) a. T C @15% ($3,846,153.8.15) = $576,923.08 b. T C @25% ($3,846,153.8.25) = $961,538.46 c. T C @35% ($3,846,153.8.35) = $1,346,153.80 d. T C @45% ($3,846,153.8.45) = $1,730,769.20 16. Size of tax shield. Using the information from Problems 12 and 14 on Roxy Broadcasting, determine the size of the tax shield with a corporate tax rate of 15%,

570 Brooks n Financial Management: Core Concepts, 2e 25%, 35%, and 45% if Roxy s capital structure is 1/3 debt-to-equity. Determine the same if the capital structure is 3/1. Before tax firm value with all equity = $25,000,000 New debt issues with 25% debt = $25,000,000 (.25) = $6,250,000 Tax shield = (D T C ) a. T C @15% ($6,250,000.15) = $937,500 b. T C @25% ($6,250,000.25) = $1,562,500 c. T C @35% ($6,250,000.35) = $2,187,500 d. T C @45% ($6,250,000.45) = $2,812,500 New debt issues with 75% debt = $25,000,000 (.75) = $18,750,000 Tax shield = (D T C ) a. T C @15% ($18,750,000.15) = $2,812,500 b. T C @25% ($18,750,000.25) = $4,687,500 c. T C @35% ($18,750,000.35) = $6,562,500 d. T C @45% ($18,750,000.45) = $8,437,500 17. Equity value in a levered firm. Air Seattle has an annual EBIT of $1,000,000, and the WACC in the unlevered firm is 20%. The current tax rate is 35%. Air Seattle will have the same EBIT forever. If the company sells debt for $2,500,000 with a cost of debt of 20%, what is the value of equity in the unlevered and levered firm? What is the value of debt in the levered firm? What is the government s value in the unlevered and levered firm? Present Value of Cash Flow = EBIT/WACC= ($1,000,000/.20) = $5,000,000 V E = $5,000,000(1-.35) = $3,250,000 V L = V E + (D T C ) $3,250,000 + ($2,500,000.35) = $4,125,000 i.e. (E+D)è : $1,625,000+$2,500,000) Government s value: Unlevered: $5,000,000.35 = $1,750,000 Levered: ($5,000,000 $2,500,000) 0.35 = $2,500,000.35 = $875,000 18. Equity value in a levered firm. Roxy Broadcasting has an annual EBIT of $3,500,000 and a WACC of 14%. The current tax rate is 40%. Roxy will have the same EBIT

Chapter 16 n Capital Structure 571 forever. The company currently has debt of $6,250,000 with a cost of debt of 14%. Roxy will sell $12,500,000 more of debt and retire stock with the proceeds. What is the value of equity in the higher levered firm? What is the government s value in the higher levered firm? Present Value of Cash Flow = ($3,500,000/.14) = $25,000,000 V E = $25,000,000 (1-.40) = $15,000,000 V L = V E + (D T C ) $15,000,000 + ($18,750,000.40) = $22,500,000 Equity only slice: $25,000,000- $18,750,000= $6,250,000 (1-.40) = $3,750,000 Government s value: $25,000,000- $18,750,000= $6,250,000(.40) = $2,500,000 Solutions to Advanced Problems for Spreadsheet Application 1. Break-even EBIT for different capital structures in a world of no taxes. Jordan Enterprises EBIT Capital Structure $ 25,000,000.00 $ 27,500,000.00 $ 30,000,000.00 $ 32,500,000.00 $ 35,000,000.00 All - Equity EBIT $ 25,000,000.00 $ 27,500,000.00 $ 30,000,000.00 $ 32,500,000.00 $ 35,000,000.00 Interest Expense $ - $ 5.00 $ 10.00 $ 15.00 $ 20.00 Net Income $ 25,000,000.00 $ 27,499,995.00 $ 29,999,990.00 $ 32,499,985.00 $ 34,999,980.00 Shares 10,000,000 10,000,005 10,000,010 10,000,015 10,000,020 EPS $ 2.50 $ 2.75 $ 3.00 $ 3.25 $ 3.50 25.0 % Debt EBIT $ 25,000,000.00 $ 27,500,000.00 $ 30,000,000.00 $ 32,500,000.00 $ 35,000,000.00 Interest Expense $ 7,500,000.00 $ 7,500,000.00 $ 7,500,000.00 $ 7,500,000.00 $ 7,500,000.00 Net Income $ 17,500,000.00 $ 20,000,000.00 $ 22,500,000.00 $ 25,000,000.00 $ 27,500,000.00 Shares 7,500,000 7,500,000 7,500,000 7,500,000 7,500,000 EPS $ 2.33 $ 2.67 $ 3.00 $ 3.33 $ 3.67 50.0 % Debt EBIT $ 25,000,000.00 $ 27,500,000.00 $ 30,000,000.00 $ 32,500,000.00 $ 35,000,000.00 Interest Expense $ 15,000,000.00 $ 15,000,000.00 $ 15,000,000.00 $ 15,000,000.00 $ 15,000,000.00 Net Income $ 10,000,000.00 $ 12,500,000.00 $ 15,000,000.00 $ 17,500,000.00 $ 20,000,000.00 Shares 5,000,000 5,000,000 5,000,000 5,000,000 5,000,000 EPS $ 2.00 $ 2.50 $ 3.00 $ 3.50 $ 4.00

572 Brooks n Financial Management: Core Concepts, 2e $4.00 $3.80 $3.60 $3.40 $3.20 $3.00 $2.80 $2.60 $2.40 $2.20 $2.00 Earnings Per Share for Different Capital Structures All Equity 12.5% Debt 25% Debt 37.5% Debt 50% debt 2. Break-even EBIT for different capital structures in a world of taxes. Jordan Enterprises EBIT Capital Structure $ 25,000,000.00 $ 27,500,000.00 $ 30,000,000.00 $ 32,500,000.00 $ 35,000,000.00 All - Equity EBIT $ 25,000,000.00 $ 27,500,000.00 $ 30,000,000.00 $ 32,500,000.00 $ 35,000,000.00 Interest Expense $ - $ - $ - $ - $ - Taxable Income $ 25,000,000.00 $ 27,500,000.00 $ 30,000,000.00 $ 32,500,000.00 $ 35,000,000.00 Taxes $ 8,750,000.00 $ 9,625,000.00 $ 10,500,000.00 $ 11,375,000.00 $ 12,250,000.00 Net Income $ 16,250,000.00 $ 17,875,000.00 $ 19,500,000.00 $ 21,125,000.00 $ 22,750,000.00 Shares 10,000,000 10,000,005 10,000,010 10,000,015 10,000,020 EPS $ 1.63 $ 1.79 $ 1.95 $ 2.11 $ 2.27 25.0 % Debt EBIT $ 25,000,000.00 $ 27,500,000.00 $ 30,000,000.00 $ 32,500,000.00 $ 35,000,000.00 Interest Expense $ 7,500,000.00 $ 7,500,000.00 $ 7,500,000.00 $ 7,500,000.00 $ 7,500,000.00 Taxable Income $ 17,500,000.00 $ 20,000,000.00 $ 22,500,000.00 $ 25,000,000.00 $ 27,500,000.00 Taxes $ 6,125,000.00 $ 7,000,000.00 $ 7,875,000.00 $ 8,750,000.00 $ 9,625,000.00 Net Income $ 11,375,000.00 $ 13,000,000.00 $ 14,625,000.00 $ 16,250,000.00 $ 17,875,000.00 Shares 7,500,000 7,500,000 7,500,000 7,500,000 7,500,000 EPS $ 1.52 $ 1.73 $ 1.95 $ 2.17 $ 2.38 50.0 % Debt EBIT $ 25,000,000.00 $ 27,500,000.00 $ 30,000,000.00 $ 32,500,000.00 $ 35,000,000.00 Interest Expense $ 15,000,000.00 $ 15,000,000.00 $ 15,000,000.00 $ 15,000,000.00 $ 15,000,000.00 Taxable Income $ 10,000,000.00 $ 12,500,000.00 $ 15,000,000.00 $ 17,500,000.00 $ 20,000,000.00 Taxes $ 3,500,000.00 $ 4,375,000.00 $ 5,250,000.00 $ 6,125,000.00 $ 7,000,000.00 Net Income $ 6,500,000.00 $ 8,125,000.00 $ 9,750,000.00 $ 11,375,000.00 $ 13,000,000.00 Shares 5,000,000 5,000,000 5,000,000 5,000,000 5,000,000 EPS $ 1.30 $ 1.63 $ 1.95 $ 2.28 $ 2.60

Chapter 16 n Capital Structure 573 $3.00 $2.80 $2.60 $2.40 $2.20 $2.00 $1.80 $1.60 $1.40 $1.20 $1.00 Earnings Per Share for Different Capital Structures All Equity 12.5% Debt 25% Debt 37.5% Debt 50% debt Solutions to Mini- Case General Energy Storage Systems: How Much Debt and How Much Equity? This mini case requires students to focus on the impact of capital structure alternatives on earnings per share at various levels of EBIT, but also directs them to consider the implications of the various formulations of the Modigliani and Miller propositions. 1. Why should GESS expect to pay a higher rate of interest if it borrows $4,000,000 rather than $2,000,000? Prospective lenders will have estimated the probability of default under either plan and adjusted the interest rate to compensate for the risk. The higher rate with the more leveraged plan is an example of what is meant by bankruptcy costs in the Modigliani and Miller propositions. 2. Estimate earnings per share for Plan A and Plan B at EBIT levels of $800,000, $1,000,000 and $1,200,000. Plan A EBIT $ 800,000.00 $1,000,000.00 $1,200,000.00 Interest 9% 360,000.00 360,000.00 360,000.00 EBT 440,000.00 640,000.00 840,000.00 Tax 40% 176,000.00 256,000.00 336,000.00 Net Inc. $264,000.00 $384,000.00 $504,000.00 Shares outstanding 300,000.00 300,000.00 300,000.00 E.P.S. $0.88 $1.28 $1.68 Plan B

574 Brooks n Financial Management: Core Concepts, 2e EBIT $ 800,000.00 $1,000,000.00 $1,200,000.00 Interest 8% 160,000.00 160,000.00 160,000.00 EBT 640,000.00 840,000.00 1,040,000.00 Tax 40% 256,000.00 336,000.00 416,000.00 Net Inc. $384,000.00 $504,000.00 $624,000.00 Shares outstanding 400,000.00 400,000.00 400,000.00 E.P.S. $0.96 $1.26 $1.56 3. How do taxes impact your findings in Question 2? By how much would the value of GESS increase or decrease as a result of choosing Plan A or Plan B? EPS is higher at higher levels of EBIT primarily because the use of debt reduces the number of shares outstanding, but the deductibility of interest expense for tax purposes amplifies the effect of leverage. According to M&M Proposition 2, with taxes, the value of the firm is increased by the total value of the debt times the corporate tax level. The tax shelter under Plan A would be $4,000,000.40 = $1,600,000. Under Plan B it would be $2,000,000.40 = $800,000. So the choice of Plan A will add $800,000 more value than Plan B. 4. At what level of EBIT would EPS be the same under either plan? Inserting the interest under either plan calculated in Question 2, we can use the following equation to calculate the break-even level of EBIT (EBIT-$360,000)(1-.40)/300,000 shares = (EBIT-$160,000)(1-.40)/400,000 shares By rearranging and simplifying the equation, we get 400,000(EBIT-$360,000).6 = 300,000(EBIT-$160,000).6 60,000 EBIT = $57,600,000 EBIT = $960,000 When EBIT is $960,000, EPS will be $1.20 under either plan. 5. Suppose GESS s management is fairly confident that EBIT will be at least $1,000,000. Which plan would the firm be most likely to choose? GESS s management should choose the plan that results in the highest level of EPS. If they believe that EBIT will remain at or above $1,000,000 they should choose Plan A. 6. Assume that GESS has no internal sources of financing and does not pay dividends. Under these conditions, would pecking order theory influence the decision to use Plan A or Plan B? Pecking order theory will still influence GESS s management to choose Plan A because debt, of necessity, has a lower cost than equity. This would be true even without taxes because the owners of the debt are less exposed to risk than the owners

Chapter 16 n Capital Structure 575 of the equity. The after-tax cost of debt under Plan A is.6 9% or 5.4%. Under Plan B, the cost of equity must be higher than 8%. 7. We assumed that the decision to use more or less debt did not change the price of the stock. Under real-life conditions, how would the decision be likely to affect the stock price at first, and later, if management s optimism turned out to be justified? Bankruptcy costs would cause the price to fall, but the value added because of the tax shelter would cause it to rise. There is not enough information in the case to determine which effect would dominate. Once the firm reaches its target EBIT, the level of EBIT where EPS is higher than it was before, the price of the stock should rise. 8. Challenge question. What if 40% of GESS s stock was owned by a large pharmaceutical company, and this company also purchased 40% of the privately placed debt? Would this situation influence the decision to use Plan A or Plan B? By owning GESS s equity and debt in equal proportions, the investor effectively eliminates the company s leverage. Debt creates risk for stockholders because it has a prior claim on the company s earnings. However, in this case, the investor with the prior claim to payments of interest and principal would also be the owner of the equity. One implication of the M&M propositions is that an investor can approximate the results of any capital structure decision by either buying stock with borrowed money (creating leverage) or buying both the debt and the equity (undoing leverage.) Additional Problems with Solutions 1. Different loan rates. Diversified Holdings has three subsidiaries, each of which borrows funds from the parent company and has a different success rate with the projects it undertakes. Subsidiary A is successful with its projects 80% of the time, Subsidiary B gets it right 93% of the time, Subsidiary C 75% of the time, and Subsidiary D 85% of the time. What loan rates should Diversified Holdings charge each subsidiary for loans? (Slides 16-37 to 16-38) Subsidiary A: To breakeven with an 80% success rate the firm will need to recoup, $1/.80= $1.25. It should charge a return greater then ($1.25)-1 =25% Subsidiary B: To breakeven with a 93% success rate Sub. B will need to recoup, $1/.93= $1.075268. He should charge a return greater then ($1.075268/$1.00)-1 =7.526% Subsidiary C: To breakeven with a 75% success rate Sub. B will need to recoup, $1/.75 = $1.333. He should charge a return greater then ($1.3333/$1.00)-1 = 33.33% Subsidiary D: To breakeven with an 85% success rate Sub. D will need to recoup, $1/.85= $1.17647. He should charge a return greater then ($1.17647/$1.00)-1 =17.747%.

576 Brooks n Financial Management: Core Concepts, 2e 2. Benefits of borrowing. Loyola Turbo Engines is looking at expanding its operations by adding another manufacturing location. If successful, the company will make $750,000, but if it fails, the company will lose $300,000. Loyola can borrow the required capital of 300,000 at 16%. (a) If all their projections point to an 85% probability of success, should they borrow the money and go ahead with the expansion? (b) Above what minimum probability of success will the project be acceptable with a discount rate of 16%? (Slides 16-39 to 16-40) (a) Accept when expected payout exceeds cost of loan Expected return =.85($750,000) +.15(-$300,000) = $592,500 Cost = $300,000(1+.16) <$348,000> Expected Profit $244,500 Accept (b) X%($750,000) + (1-X%)(-300,000) = 348,000 1,050,000X% = 648,000è = 648000/1050000è 61.71% With a discount rate of 16%, the project would be acceptable as long as its probability of success was at least 61.71%. 3. Break-even EBIT. The Fast-Track Co. has thus far only used equity to finance its operations and currently has 1,000,000 shares outstanding with an EBIT of $1,500,000. The newly-hired CFO firmly believes that the firm would benefit its shareholders a great deal by issuing $10,000,000 of debt at the rate of 10% per year and buying back 400,000 shares. If interest is tax-deductible, the firm is being charged a rate of 10% interest on borrowed funds, and the firm is in a 35% tax bracket, is the new CEO correct? Assume that the firm s operating income will remain the same irrespective of its capital structure. Interest on $10,000,000 of debt would beè.1*$10,000,000 = $1,000,000 (Slides 16-41 to 16-42) Indifference EBIT = [EBIT*(1-.35)]/1,000,000 = (EBIT-1,000,000) *(1-.35)/600,000 è 600,000*(.65EBIT) =1000000*(.65EBIT-650,000) è 390,000EBIT = 650,000EBIT-650000*1000000 è EBIT = $1,666,666.66 So, since the firm is currently earning an operating income that is below 1,666,666.66 it would be better off not issuing debt. Check:.65*1,500,000/1,000,000 = $0.975 è EPS (no debt)

Chapter 16 n Capital Structure 577 ($1,500,000-$1,000,000*.65)/600,000 = $0.54167è EPS (with debt) 4. M&M: With and without taxes. McRonald s, which is currently valued at $10,000,000, is looking at changing its capital structure from an all-equity firm to a leveraged firm with 50% debt and 50% equity. Since McRonald s is a not-for-profit company it pays no taxes. (a) If the required rate on the assets of McRonald s is 16% (R A ), what is the current required cost of equity and what is the new required cost of equity if the cost of debt is 11%? (b) If McRonald s loses its tax-exempt status and will be taxed at 35%, how will its value change under the new leveraged capital structure? Assume that its after-tax value is $10,000,000 as an unleveraged firm. (Slides 16-43 to 16-46) (A) Under tax-exempt status: R E = R A + (R A- R D ) (D/E) Current required cost of equity:.16 + (.16-.11) (0) =.16 or 16% New required cost of equity:.16 + (.16-.11) (.5/.5) =.21 or 21% (B) If McRonald s loses its tax-exempt status: $10,000,000 after tax value, $10,000,000/.65 = $15,384,615.38 implied before tax value At 50% debt amount of new bond issues = $15,384,615.38 (.5) = $7,692,307.70 Equity value after tax with new structure = $7,692,307.70x (1-.35) = $5,000,000 New equity wealth after tax = $5,000,000 + $7,692,307.7 = $12,692,307.7 Or this problem can be solved by adding the current equity wealth unlevered to the tax shield V L = V E + (D T C ) $10,000,000 + ($7,692,307.70.35) = $12,692,307.7 5. Equity value in a levered firm. Sea Crest Corporation, which is an all-equity firm has an annual EBIT of $2,540,000, and a WACC of 15%. The current tax rate is 35%. Sea Crest Corp. will have the same EBIT forever. If the company sells debt worth $3,250,000 with a cost of debt of 10%, what is the value of equity in the unlevered and levered firm? What is the value of debt in the levered firm? What is the government s value in the unlevered and levered firm? (Slides 16-47 to 16-48) Present Value of Cash Flow = ($2,540,000/.15) = $16,933,333.33 V E = $16,933,333.33(1-.35) = $11,006,666.67 V L = V E + (D T C ) $11,006,666.67 + ($3,250,000.35) = $12,144,166.67 Government s value:

578 Brooks n Financial Management: Core Concepts, 2e Unlevered: $16,933,333.33.35 = $5,926,666.67 Levered: ($16,933,333.33 $3,250,000) 0.35 = $4,789,166.67