1 Capital Structure and Leverage Business vs. financial risk Operating leverage Financial leverage Optimal capital structure Capital structure theory

2 Uncertainty about future operating income (EBIT), i.e., how well can we predict operating income? Note that business risk does not include financing effects. What is business risk? Probability EBITE(EBIT)0 Low risk High risk

3 Business risk is affected primarily by: Uncertainty about demand (sales). Uncertainty about output prices. Uncertainty about costs. Product, other types of liability. Operating leverage.

4 What is operating leverage, and how does it affect a firm’s business risk? Operating leverage is the use of fixed costs rather than variable costs. If most costs are fixed, hence do not decline when demand falls, then the firm has high operating leverage.

5 More operating leverage leads to more business risk, for then a small sales decline causes a big profit decline. Sales $ Rev. TC FC Q BE Sales $ Rev. TC FC Q BE } Profit

6 Operating Leverage Operating Breakeven : Amount of sales that leads to zero EBIT EBIT = P*Q-V*Q-F=0 Q BE =F/(P-V) Degree of Operating Leverage (DOL) DOL= % change in EBIT/%change in SALES

7 Operating Leverage EBIT =(P-V)Q-F dEBIT/dQ=P-V DOL= dEBIT/dQ * Q/EBIT = Q*(P-V) /[Q*(P-V) –F]

8 Probability EBIT L Low operating leverage High operating leverage Typical situation: Can use operating leverage to get higher E(EBIT), but risk increases. EBIT H

9 What is financial leverage? Financial risk? Financial leverage is the use of debt and preferred stock. Financial risk is the additional risk concentrated on common stockholders as a result of financial leverage.

10 Financial Leverage DFL= % change in EPS/%change in EBIT EPS=NI /N=(EBIT-I)(1-T) /N N:number of common stock outstanding dEPS /dEBIT=(1-T) /N EBIT /EPS=EBIT /[(EBIT-I)(1-T) /N] DFL=EBIT /(EBIT-I)

11 Financial Breakeven Amount of EBIT that leads to zero EPS EPS =(EBIT-I)(1-T) /N=0 EBIT BE =I

12 Business Risk vs. Financial Risk Business risk depends on business factors such as competition, product liability, and operating leverage. Financial risk depends only on the types of securities issued: More debt, more financial risk. Concentrates business risk on stockholders.

13 Firm UFirm L No debt$10,000 of 12% debt$20,000 in assets40% tax rate Consider 2 Hypothetical Firms Both firms have same operating leverage, business risk, and probability distribution of EBIT. Differ only with respect to the use of debt (capital structure).

14 Capial Structures of the Two Firms A=$20,000=D+E for both firms E U =$20,000 D U =$0 E L =$10,000 D L =$10,000

15 Firm U: Unleveraged Prob EBIT$2,000$3,000$4,000 Interest EBT$2,000$3,000$4,000 Taxes (40%) 800 1,200 1,600 NI$1,200$1,800$2,400 Economy Bad Avg. Good

16 Firm L: Leveraged Prob.* EBIT*$2,000$3,000$4,000 Interest 1,200 1,200 1,200 EBT$ 800$1,800$2,800 Taxes (40%) ,120 NI$ 480$1,080$1,680 *Same as for Firm U. Economy Bad Avg. Good

17 Firm UBadAvg.Good BEP*10.0%15.0%20.0% ROE6.0%9.0%12.0% TIE Firm LBadAvg.Good BEP*10.0%15.0%20.0% ROE4.8%10.8%16.8% TIE1.67x2.5x3.3x *BEP same for Firms U and L. 888

18 Expected Values: E(BEP)15.0%15.0% E(ROE)9.0%10.8% E(TIE)2.5x Risk Measures:  ROE 2.12%4.24% CV ROE U L 8

19 For leverage to raise ROE, must have BEP > k d (avg. and good states). Why? If k d > BEP, then the interest expense will be higher than the operating income produced by debt-financed assets, so leverage will depress income.

20 NI=[EBIT-Dk d ](1-T) A=D+E ROE=NI /(A-D)=[EBIT-Dk d ](1-T) /(A-D) =[EBIT/A-(D/A)k d ](1-T) /(1-D/A) =[BEP-DR k d ](1-T) /(1-DR) where DR=D/A

21 dROE/dDR=[(1-T)(BEP-k d )] / (1-DR) 2 (1-T)(BEP-k d )>0 implies BEP-k d >0 or BEP>k d q.e.d.

22 Conclusions Basic earning power = BEP = EBIT/Total assets is unaffected by financial leverage. L has higher expected ROE because BEP > k d with probability of L has much wider ROE (and EPS) swings because of fixed interest charges. Its higher expected return is accompanied by higher risk.

23 If debt increases, TIE falls. EBIT is constant (unaffected by use of debt), and since I = k d D, as D increases, TIE must fall. TIE = EBIT I

24 Optimal Capital Structure That capital structure (mix of debt, preferred, and common equity) at which P 0 is maximized. Trades off higher E(ROE) and EPS against higher risk. The tax-related benefits of leverage are exactly offset by the debt’s risk-related costs. The target capital structure is the mix of debt, preferred stock, and common equity with which the firm intends to raise capital.

25 Describe the sequence of events in a recapitalization. Consider another firm, Hannibal Inc., which announces a recapitalization. New debt is issued. Proceeds are used to repurchase stock. Debt issued Price per share Shares bought =.

26 Amount D/A D/E Bond borrowed ratio ratio rating k d Cost of debt at different debt levels after recapitalization K$ AA 8% A 9% BBB 11.5% 1, BB 14%

27 Why does the bond rating and cost of debt depend upon the amount borrowed? As the firm borrows more money, the firm increases its risk causing the firm’s bond rating to decrease, and its cost of debt to increase.

28 What would the earnings per share be if Hannibal recapitalized and used these amounts of debt: $0, $250,000, $500,000, $750,000? Assume EBIT = $400,000, T = 40%, and shares can be repurchased at P 0 = $25.Nu=80,000 D = 0: EPS 0 = = = $3.00. (EBIT – k d D)(1 – T) Shares outstanding ($400,000)(0.6) 80,000

29 D = $250K, k d = 8%. = = 10,000. Shares repurchased $250,000 $25 TIE = = = 20×. $400 $20 EBIT I EPS 1 = = $3.26. [$400 – 0.08($250)](0.6) 80 – 10

30 D = $500K, k d = 9%. = = 20. Shares repurchased $500 $25 TIE = = = 8.9×. $400 $45 EBIT I EPS 2 = = $3.55. [$400 – 0.09($500)](0.6) 80 – 20

31 D = $750K, k d = 11.5%. = = 30. Shares repurchased $750 $25 TIE = = = 4.6×. $400 $86.25 EBIT I EPS 3 = = $3.77. [$400 – 0.115($750)](0.6) 80 – 30

32 D = $1,000K, k d = 14%. = = 40. Shares repurchased $1,000 $25 TIE = = = 2.9×. $400 $140 EBIT I EPS 4 = = $3.90. [$400 – 0.14($1,000)](0.6) 80 – 40

33 Stock Price (Zero Growth) If payout = 100%, then EPS = DPS and E(g) = 0. We just calculated EPS = DPS. To find the expected stock price (P 0 ), we must find the appropriate k s at each of the debt levels discussed. P 0 = = =. D 1 k s – g EPS k s DPS k s

34 What effect would increasing debt have on the cost of equity for the firm? If the level of debt increases, the riskiness of the firm increases. We have already observed the increase in the cost of debt. However, the riskiness of the firm’s equity also increases, resulting in a higher k s.

35 The Hamada Equation Because the increased use of debt causes both the costs of debt and equity to increase, we need to estimate the new cost of equity. The Hamada equation attempts to quantify the increased cost of equity due to financial leverage. Uses the unlevered beta of a firm, which represents the business risk of a firm as if it had no debt.

36 The Hamada Equation (cont’d) b L = b U [1 + (1 – T)(D/E)]. The risk-free rate is 6%, as is the market risk premium. The unlevered beta of the firm is 1.0. We were previously told that total assets were $2,000,000(80K*$25).

37 Calculating Levered Betas D = $250K b L = b U [1 + (1 – T)(D/E)] b L = 1.0[1 + (1 – 0.4)($250/$1,750)] b L = 1.0[1 + (0.6)(0.1429)] b L = k s = k RF + (k M – k RF )b L k s = 6.0% + (6.0%) = 12.51%. k s = k RF + (k M – k RF )b L

38 Table for Calculating Levered Betas Amount borrowed K$ ,000 D/A ratio 0.00% Levered Beta D/E ratio 0.00% k s 12.00%

39 Minimizing the WACC Amount borrowed K$ ,000 D/A ratio 0.00% WACC 12.00% E/A ratio % k s 12.00% k d (1 – T) 0.00%

40 P 0 = DPS/k s Amount Borrowed DPSk s P 0 $ 0$ % $ , , * 750, ,000, *Maximum: Since D = $500,000 and assets = $2,000,000, optimal D/A = 25%.

41 See preceding slide. Maximum EPS = $3.90 at D = $1,000,000, and D/A = 50%. Risk is too high at D/A = 50%. What debt ratio maximizes EPS?

42 What is Hannibal’s optimal capital structure? P 0 is maximized ($26.89) at D/A = $500,000/$2,000,000 = 25%, so optimal D/A = 25%. EPS is maximized at 50%, but primary interest is stock price, not E(EPS).

43 The example shows that we can push up E(EPS) by using more debt, but the risk resulting from increased leverage more than offsets the benefit of higher E(EPS).

44 % D/A ksks WACC k d (1 – T) $ D/A P0P0 EPS

45 If it were discovered that the firm had more/less business risk than originally estimated, how would the analysis be affected? If there were higher business risk, then the probability of financial distress would be greater at any debt level, and the optimal capital structure would be one that had less debt. On the other hand, lower business risk would lead to an optimal capital structure of more debt.

46 Total risk Total risk is the combination of business risk and financial risk. Degree of total leverage: DTL= DOL* DFL =% change in EPS/%change in SALES If DOL  then DFL should  to keep DTL constant

47 Total Breakeven The amount of sales that leads to zero EPS [(P-V)Q-F-I](1-T) /N=0 Q BE =(F-I)/(P-V)

48 Other factors to consider when establishing the firm’s target capital structure? 1.Industry average debt ratio 2. TIE ratios under different scenarios 3. Lender/rating agency attitudes 4. Reserve borrowing capacity 5. Effects of financing on control 6. Asset structure 7. Expected tax rate

49 How would the following factors affect the Target Capital Structure? 1.Sales stability? 2.High operating leverage? 3.Increase in the corporate tax rate? 4.Increase in the personal tax rate? 5.Increase in bankruptcy costs? 6.Management spending lots of money on lavish perks?

50 Long-term Debt Ratios for Selected Industries Industry Long-Term Debt Ratio Pharmaceuticals20.00% Computers25.93 Steel39.76 Aerospace43.18 Airlines56.33 Utilities56.52 Source: Dow Jones News Retrieval. Data collected through December 17, 1999.

51 Capital Structure Theory Modigliani and Miller Theory of Capital Structure Proposition I – firm value Proposition II – WACC The value of the firm is determined by the cash flows to the firm and the risk of the assets Changing firm value Change the risk of the cash flows Change the cash flows

52 Capital Structure Theory Under Three Special Cases Case I – Assumptions No corporate or personal taxes No bankruptcy costs Case II – Assumptions Corporate taxes, but no personal taxes No bankruptcy costs Case III – Assumptions Corporate taxes, but no personal taxes Bankruptcy costs

53 Case I – Propositions I and II Proposition I The value of the firm is NOT affected by changes in the capital structure The cash flows of the firm do not change; therefore, value doesn’t change Proposition II The WACC of the firm is NOT affected by capital structure

54 Case I - Equations WACC = R A = (E/V)R E + (D/V)R D R E = R A + (R A – R D )(D/E) R A is the “cost” of the firm’s business risk, i.e., the risk of the firm’s assets (R A – R D )(D/E) is the “cost” of the firm’s financial risk, i.e., the additional return required by stockholders to compensate for the risk of leverage

55 Case 1

56 Case I - Example Data Required return on assets = 16%, cost of debt = 10%; percent of debt = 45% What is the cost of equity? R E = 16 + ( )(.45/.55) = 20.91% Suppose instead that the cost of equity is 25%, what is the debt-to-equity ratio? 25 = 16 + ( )(D/E) D/E = ( ) / ( ) = 1.5 Based on this information, what is the percent of equity in the firm? E/V = 1 / 2.5 = 40%

57 The CAPM, the SML and Proposition II How does financial leverage affect systematic risk? CAPM: R A = R f +  A (R M – R f ) Where  A is the firm’s asset beta and measures the systematic risk of the firm’s assets Proposition II Replace R A with the CAPM and assume that the debt is riskless (R D = R f ) R E = R f +  A (1+D/E)(R M – R f )

58 Business Risk and Financial Risk R E = R f +  A (1+D/E)(R M – R f ) CAPM: R E = R f +  E (R M – R f )  E =  A (1 + D/E) Therefore, the systematic risk of the stock depends on: Systematic risk of the assets,  A, (Business risk) Level of leverage, D/E, (Financial risk)

59 Case II – Cash Flow Interest is tax deductible Therefore, when a firm adds debt, it reduces taxes, all else equal The reduction in taxes increases the cash flow of the firm How should an increase in cash flows affect the value of the firm?

60 Case II - Example Unlevered Firm Levered Firm EBIT5,000 Interest0500 Taxable Income5,0004,500 Taxes (34%)1,7001,530 Net Income3,3002,970 CFFA3,3003,470 Cash flow from assets (CFFA) =Free cash flow

61 Interest Tax Shield Annual interest tax shield Tax rate times interest payment 6,250 in 8% debt = 500 in interest expense Annual tax shield =.34(500) = 170 Present value of annual interest tax shield Assume perpetual debt for simplicity PV = 170 /.08 = 2,125 PV = D(R D )(T C ) / R D = DT C = 6,250(.34) = 2,125

62 Case II – Proposition I The value of the firm increases by the present value of the annual interest tax shield Value of a levered firm = value of an unlevered firm + PV of interest tax shield Value of equity = Value of the firm – Value of debt Assuming perpetual cash flows V U = EBIT(1-T C ) / R A V L = V U + DT C

63 Example: Case II – Proposition I Data EBIT = 25 million; Tax rate = 35%; Debt = $75 million; Cost of debt = 9%; Unlevered cost of capital = 12%=WACC(D=0)=R A =R E V U = 25(1-.35) /.12 = $ million V L = (.35) = $ million E = – 75 = $86.67 million

64 Case 2- Proposition I

65 Case II – Proposition II The WACC decreases as D/E increases because of the government subsidy on interest payments From these two equations we obtain This is the Hamada formula Example R E = 12 + (12-9)(75/86.67)(1-.35) = 13.69% WACC = (86.67/161.67)(13.69) + (75/161.67)(9)(1-.35)= 10.05%

66 Example: Case II – Proposition II Suppose that the firm changes its capital structure so that the debt-to-equity ratio becomes 1. What will happen to the cost of equity under the new capital structure? R E = 12 + (12 - 9)(1)(1-.35) = 13.95% What will happen to the weighted average cost of capital? WACC =.5(13.95) +.5(9)(1-.35) = 9.9%

67 Case 2- Proposition II

68 Case III Now we add bankruptcy costs As the D/E ratio increases, the probability of bankruptcy increases This increased probability will increase the expected bankruptcy costs At some point, the additional value of the interest tax shield will be offset by the increase in expected bankruptcy cost At this point, the value of the firm will start to decrease and the WACC will start to increase as more debt is added

69 Bankruptcy Costs Direct costs Legal and administrative costs Ultimately cause bondholders to incur additional losses Disincentive to debt financing Financial distress Significant problems in meeting debt obligations Most firms that experience financial distress do not ultimately file for bankruptcy

70 More Bankruptcy Costs Indirect bankruptcy costs Larger than direct costs, but more difficult to measure and estimate Stockholders want to avoid a formal bankruptcy filing Bondholders want to keep existing assets intact so they can at least receive that money Assets lose value as management spends time worrying about avoiding bankruptcy instead of running the business The firm may also lose sales, experience interrupted operations and lose valuable employees

71 Case 3- Proposition I

72 Case 3- Proposition II

73 Conclusions Case I – no taxes or bankruptcy costs No optimal capital structure Case II – corporate taxes but no bankruptcy costs Optimal capital structure is almost 100% debt Each additional dollar of debt increases the cash flow of the firm Case III – corporate taxes and bankruptcy costs Optimal capital structure is part debt and part equity Occurs where the benefit from an additional dollar of debt is just offset by the increase in expected bankruptcy costs

74 MM’s tax benefit vs. bankruptcy cost theory is logical, but doesn’t tell whole capital structure story. Main problem--assumes investors have same information as managers. Signaling theory suggests firms should use less debt than MM suggest. This unused debt capacity helps avoid stock sales, which depress P 0 because of signaling effects. Signaling theory

75 What are “signaling” effects in capital structure? Managers have better information about a firm’s long-run value than outside investors. Managers act in the best interests of current stockholders. Assumptions:

76 Therefore, managers can be expected to: issue stock if they think stock is overvalued. issue debt if they think stock is undervalued. As a result, investors view a common stock offering as a negative signal-- managers think stock is overvalued.

77 Conclusions on Capital Structure 1.Need to make calculations as we did, but should also recognize inputs are “guesstimates.” 2.As a result of imprecise numbers, capital structure decisions have a large judgmental content. 3.We end up with capital structures varying widely among firms, even similar ones in same industry.