• Determining the optimal capital structureThe tradeoff in using debt raises two related

questions1) is the higher expected rate of return

associated with debt sufficient to compensate for the increased risk?

2) what is the optimal amount of debt?

Optimal Capital StructureThat capital structure (mix of debt, preferred, and common equity) at which P0 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.

Describe the sequence of events in a recapitalization.

• Campus Deli announces the recapitalization.

• New debt is issued.• Proceeds are used to repurchase stock.

Debt issued Price per shareShares bought =

Amount D/A D/E BondBorrowed(000) ratio ratio rating kd

Cost of debt at different debt levels after recapitalization

$ 0 0 0 -- -- 250 0.125 0.1429 AA 8% 500 0.250 0.3333 A 9% 750 0.375 0.6000 BBB 11.5% 1,000 0.500 1.0000 BB 14%

Notice that with the increased use of debt the cost of debt increases. This is because lenders recognize that other things held constant, firms with higher debt levels are more likely to experience financial distress, so they require higher rates of return.

What would the earnings per share be if Campus Deli 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 P0 = $25.

D = 0:EPS0 =

= = $3.00.

(EBIT – kdD)(1 – T)Shares outstanding

($400,000)(0.6)80,000

D = $250, kd = 8%.

= = 10,000.Sharesrepurchased

$250,000$25

TIE = = = 20×.$400$20

EBITI

EPS1 =

= $3.26.

[$400 – 0.08($250)](0.6)80 – 10

D = $500, kd = 9%.

= = 20.Sharesrepurchased

$500$25

TIE = = = 8.9×.$400$45

EBITI

EPS2 =

= $3.55.

[$400 – 0.09($500)](0.6) 80 – 20

D = $750, kd = 11.5%.

= = 30.Sharesrepurchased

$750$25

TIE = = = 4.6×.$400$86.25

EBITI

EPS3 =

= $3.77.

[$400 – 0.115($750)](0.6) 80 – 30

D = $1,000, kd = 14%.

= = 40.Sharesrepurchased

$1,000$25

TIE = = = 2.9×.$400$140

EBITI

EPS4 =

= $3.90.

[$400 – 0.14($1,000)](0.6) 80 – 40

• In this example, EPS is maximized at 50% debt ($1M). Should the firm then issue 50% debt? The answer is NO.

• The optimal capital structure is the one that maximizes the firm’s stock price and not the one that maximizes the firm’s EPS.

• Now we are going to investigate what the stockholders want. A stock’s beta coefficient measures its relative volatility or risk compared to the stock market portfolio. It has been shown both theoretically and empirically that a stock’s beta increases as financial leverage increases.

Stock Price (Zero Growth)

If payout = 100%, then EPS = DPS andE(g) = 0.

We just calculated EPS = DPS. To find the expected stock price (P0), we must find the appropriate ks at each of the debt levels discussed.

P0 = = = .D1

ks – gEPS

ks

DPSks

The Hamada EquationBecause 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.

The Hamada Equation (cont’d)

bL = bU [1 + (1 – T)(D/E)].

bu : the unlevered beta of a firm, which represents the business risk of a firm as if it had no debt.

D/E: debt to equity ratio

EX) 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.

Calculating Levered BetasD = $250

bL = bU[1 + (1 – T)(D/E)]bL = 1.0[1 + (1 – 0.4)($250/$1,750)]bL = 1.0[1 + (0.6)(0.1429)]bL = 1.0857.

ks = kRF + (kM – kRF)bL

ks = 6.0% + (6.0%)1.0857 = 12.51%.

ks = kRF + (kM – kRF)bL

Table for Calculating Levered Betas

Amount borrowed

$ 0

250

500

750

1,000

D/A ratio

0.00%

12.50

25.00

37.50

50.00

Levered Beta

1.00

1.09

1.20

1.36

1.60

D/E ratio

0.00%

14.29

33.33

60.00

100.00

ks

12.00%

12.51

13.20

14.16

15.60

• If we change the capital structure by adding debt, this would increase the risk stockholders bear. That, in turn, would result in an additional risk premium.

• Ks = Krf + Premium for business risk + Premium for financial risk

Minimizing the WACC

Amount borrowed

$ 0

250

500

750

1,000

D/A ratio

0.00%

12.50

25.00

37.50

50.00

WACC

12.00%

11.55

11.25

11.44

12.00

E/A ratio

100.00%

87.50

75.00

62.50

50.00

ks

12.00%

12.51

13.20

14.16

15.60

kd (1 – T)

0.00%

4.80

5.40

6.90

8.40

• When the firm has no debt, so its capital structure is 100% equity, WACC is the cost of equity (12%).

• As the firm begins to use lower cost of debt, the WACC declines. However, as the debt ratio increases, the costs of both debt and equity rise, at first slowly but then at a faster and faster rate.

• Eventually, the increasing costs of the two components offset the fact that more low-cost debt is being used. At 25 percent debt, the WACC hits a minimum of 11.25%.

P0 = DPS/ks

AmountBorrowed DPS ks P0

$ 0 $3.00 12.00% $25.00

250,000 3.26 12.51500,000 3.55 13.20

26.03

26.89*

750,000 3.77 14.16 26.59

1,000,000 3.90 15.60 25.00

*Maximum: Since D = $500,000 and assets = $2,000,000, optimal D/A = 25%.

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?

What is Campus Deli’s optimal capital structure?

P0 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).

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).

%

15

0 .25 .75.50 D/A

ks

WACCkd(1 – T)

$

D/A.25 .50

P0

EPS

If we 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.

Long-term Debt Ratios for Selected Industries

Industry Long-Term Debt RatioPharmaceuticals 20.00%Computers 25.93Steel 39.76Aerospace 43.18Airlines 56.33Utilities 56.52Source: Dow Jones News Retrieval. Data collected through December 17, 1999.

• Capital structure theoryUnder a very restrictive set of assumptions

Modigliani and Miller (M&M) proved that the value of a firm is unaffected by its capital structure. Thus, capital structure is irrelevant.

This means that in a no tax world, the firm’s WACC is constant and the firm’s capital structure does not influence the firm’s stock price.

Assumptions: No brokerage costs, no taxes, no bankruptcy costs, investors can borrow at the same rate as corporations, symmetric information.

• The effect of taxesM&M relaxed the assumption of no corporate

taxes. The tax code allows firms to deduct interest payments as an expense but dividend payments to stockholders are not deductible.

This differential tax treatment encourages firms to use more debt in their capital structures. The more the firm borrows the greater the tax benefits that will accrue to the remaining stockholders. M&M demonstrate that if their other assumptions hold, the optimal capital structure in a tax world will be 100% debt.

• The effect of bankruptcy costsRelaxing M&M’s assumptions even more by

introducing bankruptcy costs change the analysis dramatically. M&M assumed a constant cost of borrowing.

In the real world, however, as the debt ratio increases lenders get nervous. The more nervous the lenders get the higher the rate of return they expect to get. So in an M&M world with taxes and bankruptcy, the WACC will fall at first as small amounts of debt are added to the capital structure.

As the firm continues to add debt to the capital structure the lender’s threshold level of risk is hit and they start to raise interest rates slowly at first and then more rapidly.

So, in a world with taxes and bankruptcy costs there is an optimal structure where the WACC is minimized and the stock price is maximized.

Value of Stock

0 D1 D2D/A

MM with taxes

MM with taxes and bank-ruptcy costs

MM without taxes

• Below D1 the probability of bankruptcy is so low as to be immaterial. Beyond D1, however, bankruptcy-related costs become increasingly important, and they reduce the tax benefits of debt at an increasing rate

• In the range from D1 to D2, bankruptcy-related costs reduce but do not completely offset the tax benefits of debt, so the firm’s stock price rises (but at a decreasing rate) as its debt ratio increases.

• Beyond D2, bankruptcy related costs exceed the tax benefits, so from D2 increasing the debt ratio lowers the value of the stock.

• So D2 is the optimal capital structure.

• Theoretically, the debt rate where the marginal benefits of the tax shelter equal the marginal cost of increased bankruptcy risk dictates the optimal capital structure.

• Empirically, many corporations are found to have less debt than the trade-off theory of leverage would suggest.

• The graph shows MM’s tax benefit vs. bankruptcy cost theory.

• Logical, but doesn’t tell whole capital structure story. Main problem--assumes investors have same information as managers.

Signaling theory, discussed earlier, suggests firms should use less debt than MM suggest.This unused debt capacity helps avoid stock sales, which depress P0 because of signaling effects.

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:

• If managers are supposed to behave as if they are maximizing current shareholders’ wealth by maximizing stock prices, then the announcement of a stock offering will generally be taken as a signal that the firm’s prospects (as seen by its management) are not good.

• Assume a firm that has a new product that will increase its profitability but to go into production the firm needs to raise capital.

• If the firm sells new stock, then as the profits from the new product start flowing into the firm, the price of the stock will rise.

• The current shareholders will do well but not as well as they would have done if the company would not have had to share the benefits of the new product with the new shareholders.

• Therefore, one would expect a firm with very favorable prospects to try to avoid selling new stock and, rather, to raise any required new capital by other means, including new debt.

Therefore, managers can be expected to:• issue stock if they think stock is overvalued.• issue debt if they think stock is undervalued.• Investors view a common stock offering as a negative

signal--managers think stock is overvalued. • As a result, firms try to avoid having to issue stock by

maintaining a reserve borrowing capacity, and this means using less debt in normal times than the MM theory would suggest.

Conclusions on Capital Structure1. 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.