0. Capital Structure I
RWJ: Ch 16
BMA: Ch 17

1. Outline 1. An overview of capital structure
2. Modigliani and Miller Theorem
Proposition I
Proposition II

2. An overview of capital structure
In general, there are two basic ways in which a business can obtain money
Debt: The essence of debt is that you promise to make fixed payments in the future (interest payments and repaying principal). If you fail to make those payments, you lose control of your business.
Equity: With equity, you do get whatever cash flows are left over after you have made debt payments.
Capital structure: the firm’s mix of debt and equity financing.

3. Broad categories of financial claims
Equity: common stock, preferred stock
Debt: long-term vs short-term bonds, secured vs unsecured, senior vs subordinated, convertible vs non convertible debt…
Hybrid:
Convertible bonds: can be changed to a specified number of shares of common stock.
Warrant: a long-term call option that give the investor the right to buy the firm’s common stock. Eg. Option to buy a share of stock for $50 at any time during 5 years.
Compared to convertible bonds, Warrant are usually issued privately, while CB is issued publicly.
Warrants can be divided. Normally, CB and Warrant are packaged with bonds. When selling these securities, bonds in warrants can be separated from the options, while bonds in CB is bounded with option.
Taxes are different.
Warrant can be echanged with cash. While CB is exchanged to common stock.
Hybrid securities: Convertible bonds, claims with warrants, convertible preferred stocks…

4. Graphically
The firm is operative only if its CF reaches the threshold of default level (D).
Above the level D, the cash flow is used to pay constant amount of debt, the rest contributes to the equity return.
Below the level D, equility holders gains nothing, while bondholders can claim the residual return.

5. Back to the objective of CF
Objective of CF: maximize the shareholders’ wealth.
The value of a firm is defined to be the sum of the value of the firm’s debt and the firm’s equity.
V = B + S
Max S <=> Max V
Why? S B S S B B
Value of the Firm

6. Max firm V vs max S
Debt: Fixed payment=> Market value of debt is usually given and constant
Equity: residual claim => Any change in the value of the firm results in an identical change in the value of the equity
Max S<=> Max V
As it turns out, changes in capital structure benefit the stockholders if and only if the value of the firm increases.
Eg: Assume a firm’s capital structure is
B: $25,000
S: $ 50X 1,000=$ 50,000
V: $ 75,000
The stock of the firm is called levered equity. Using debt to finance the firm is called “financial leverage” or “gearing”.
Now, the firm wants to further “lever up”, say issuing an additional $10,000 of debt and pay the proceeds out to shareholders as a special dividend of $10/share. B: $ =$ What would be the market response on the firm’s equity, value?
If V=$ unchanged, so that S= $ The stockholders’ wealth is just $ $10000 dividend = $50000 unchanged.
If V= $ 80000, increased by $5000, so that S= $ The stock holders’ wealth is $45000+$10000 dividend =$ increased by $5000.
Therefore, increasing V is equivalent to increasing S.
Whether V increases or decreases will depend on
Payout policy (in 5th or 6th weeks)
Debt risk (in next week)

7. Max firm V vs max S Market value balance sheet Levered firm
Further Levered up
Market value balance sheet
Assets | Equity 50000
| Debt
Total | B+S 75000
Using debt to finance the firm is called “financial leverage” or “gearing”.
The stock of the firm is called levered equity.
Issuing an additional $10,000 of debt and use the proceed to repurchase shares. What would be the effect on the firm’s value and equity value?
The change depends on
Firm’s payout policy
Debt risk

8. The choice between debt and equity
The goal of managing capital structure is to maximize the value of firm.
What is the optimal mix of debt and equity to achieve this goal?
The leverage affects earning and returns, but does it impact the value of firm?
Modigliani and Miller proposition I:
In perfect capital market, the capital structure is irrelevant: i.e. the firm value does not depend on its capital structure

9. In a perfect capital market
No taxes
No bankruptcy cost or other transaction costs
Firms and investors can borrow/lend at the same rate
Equal access to all relevant information (no effect on management incentives)
Perfect competition: no arbitrage opportunity

10. MM Proposition I (No Taxes)
Firm value is determined on the left-hand side of the balance sheet by real assets—not by the proportions of debt and equity securities issued to the assets. VL = VU
The nature of financing claims is irrelevant
Stocks: Common stocks vs preferred
Debt: Long-term vs short-term; Senior vs subordinate;
Hybrid: convertible vs non convertible bonds
An investor can “undo” the effect of any changes in the firm’s capital structure by borrowing or lending on their own account
homemade leverage : There exists an investment strategy to duplicate the return by the strategy.

11. Financial Leverage, EPS, and ROE
Consider an all-equity firm that is contemplating going into debt. (Maybe some of the original shareholders want to cash out.)
Proposed
$5,000, 000
$2,500,000 1
10%
250,000
$10
Current Assets $5,000,000 Debt $0 Equity $5,000,000 Debt/Equity ratio 0 Interest rate N/A Shares outstanding 500,000 Share price $10
The firm borrows $8,000 and buys back 160 shares at $50 per share.

12. All equity firm: no debt
Current Shares Outstanding = 500,000 shares Recession Expected Expansion EBIT $300,000 $650,000 $1,000,000 Interest Net income $300,000 $650,000 $1,000,000 EPS $0.60 $1.30 $2.00 ROE 6% 13% 20%

13. Levered firm: B/S=1; interest rate 10%
Current Shares Outstanding = 250,000 shares Recession Expected Expansion EBIT $300,000 $650,000 $1,000,000 Interest 250, , ,000 Net income $50,000 $400,000 $750,000 EPS $0.20 $1.60 $3.00 ROE 2% 16% 30%

14. Homemade unLeverage
An investor can “unlever” the firm by purchasing both firm’s stock and bonds: investing $500 =$250 in the stock + $250 in the bonds paying 10%.
Recession Expected Expansion
EPS –levered Firm $0.20 $1.60 $3.00
Earnings for 25 shares $5 $40 $75
plus interest on $250 (10%) $25 $25 $25
Net Profits $30 $65 $100
ROE (Net Profits / $500) 6% 13% 20%
The investor is able to earn the same return as she would have earned from an all equity firm.
Note, 40 shares at $50 per share represents a $2,000 investment, but we match the leverage ratio by borrowing $800 of the purchase price. Thus, we actually invest $1,200 of our own funds.

15. Homemade Leverage Recession Expected Expansion
Suppose an investor purchases 100 shares with homemade leverage: buying 50 shares with her own money ($500) and 50 shares by borrowing 500 at 10% interest. (B/S=1)
Recession Expected Expansion
EPS –Unlevered Firm $0.60 $1.30 $2.00
Earnings for 100 shares $60 $130 $200
Less interest on $500 (10%) $50 $50 $50
Net Profits $10 $80 $150
ROE (Net Profits / $500) 2% 16% 30%
The investor got the same return as what she would have gotten with the levered company.

16. Financial Leverage and EPS
3.00
Debt
2.50
No Debt
Advantage to debt
2.00
1.50
Break-even point
EPS
1.00
Disadvantage to debt
0.50
0.00
300,000
650,000
1,000,000
(2.00)
EBIT in dollars, no taxes

17. Some remarks The effect of financial leverage depends on EBIT.
EPS rises with EBIT.
The rise of EPS is greater for the levered firm than the unlevered firm.
However, the firm’s value (stock price) does not rise.
Financial leverage increases ROE and EPS when EBIT is greater than the break-even point.
But with additional debt, the firm will have additional financial risk that would increase the required return on its common stock.
A higher required return offsets the increase in EPS, resulting a lower firm value despite the higher EPS

18. Some remarks The effect of financial leverage depends on EBIT.
EPS rises with EBIT.
The rise of EPS is greater for the levered firm than the unlevered firm.
Financial leverage increases ROE and EPS when EBIT is greater than the break-even point.
But with additional debt, the firm will have additional financial risk that would increase the required return on its common stock.
A higher required return offsets the increase in EPS, resulting a lower firm value despite the higher EPS

19. Some remarks Measures like EPS, PE, ROE are affected by leverage.
=> Cannot reliably compare these measures across firms with different capital structures.
Most analysts prefer to use performance measures that are invariant to firms’ capital structures,
EBIT or EBITDA
True or false:
In a perfect market, if a change in leverage raises a firm’s earnings per share, the share price rise.

20. MM Proposition II (No Taxes)
The expected rate of return on the common stock of a levered firm increases in proportion to the debt-equity ration (B/S), expressed in market values.
Leverage increases the risk and return to stockholders
Rs = R0 + (B / SL) (R0 - RB)
RB is the interest rate (cost of debt)
Rs is the return on (levered) equity (cost of equity)
R0 is the return on unlevered equity (cost of capital)
B is the value of debt
SL is the value of levered equity

21. MM Proposition II (No Taxes)
The derivation is straightforward:

22. With risky debt
When debt increases, it increases both the risk of both the equity and the debt.
The required return on B and S increases also if debt becomes risky.
Capital structure is irrelevant because RWACC is constant. RE
RWACC R0 RB RF
Risk-free debt
Risky debt
Debt-to-equity Ratio

23. Remarks on MM II
Leverage increases the return to stockholders
Rs = R0 + (B / SL) (R0 - RB)
How can shareholders be indifferent to increasing leverage when it increases the expected return?
Any increase in the expected return is exactly offset by an increase in the risk and therefore in shareholders’ required rate of return.
The required return simply rises (B / SL) (R0 - RB) to match the risk increase.

24. How leverage affects Beta?
bAsset =
Debt + Equity
Debt
× bDebt +
Equity
× bEquity
Debt
bEquity =
bAsset +
(bAsset – bdebt)
Equity
The total risk of the firm (bAsset ) is unaffected by leverage
The risk of equity bEquity increases with the leverage (MM II)
When debt increases, bDebt may increase also.
But bEquity will be lower as bond holders share some of the firms’ market risk.
Debt betas of large firms are typically in the range of 0.1 to 0.3
Debt holders usually bear less risk than the stockholders.
CAPM: Ri=Rf + betai (Rm - Rf) The required return increases with beta.
Beta asset depends on the combined risk of the investment portfolio.

25. Cash and the cost of capital
Cash or risk-free securities are risk-free
=> reduce the risk of the firms’ asset.
=> can be seen as negative debt, reducing the cost of capital.
In July 2012, Cisco Systems had a market capitalization of $ billion. It had debt of $16.2 billion as well as cash and short-term investments of $48.6 billion. Its equity beta was 1.23 and debt beta was approximately zero. What was Cisco’s asset value at that time? Given that the risk-free rate of 2% and a market risk premium of 5%, estimate the unlevered cost of capital of Cisco’s business.

26. Exercise 1
Consider a firm with 1000 shares outstanding. The share price is $100.The firm has riskless debt of $10000 due next year, with a (riskless) interest rate rD. You own 10% of the firm’s equity. The firm board decides to issue $50000 of (riskless) bonds to repurchase half of its shares. Denote X the (risky) firm’s cash-flow next year. Show that you can set an investment strategy to be indifferent to the share repurchase decision.

27. Before the repurchase, you gain
10% × (X-(1+ rD ) ×10000)
After repurchase, you own 100/500=20% of the firm’s equity. The total debt value is = If you do nothing, you gain 20% × (X- (1+ rD ) ×60000).
You have larger shareholding but riskier portforlio.
If you sell half of your shares, you own 50/500 =10% of the equity and gains 50 × 100 × (1+ rD) in the next period. So your total cash flow is
10% × (X-(1+ rD ) ×60000) × (1+ rD)
= 10% × (X- (1+ rD ) ×10000)
You are thus indifferent to the firm’s capital structure decision.