1. Capital Structure (1)

2. The Capital-Structure Question and The Pie Theory
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
If the goal of the management of the firm is to make the firm as valuable as possible, the the firm should pick the debt-equity ratio that makes the pie as big as possible. S B
Value of the Firm

3. Financial Leverage, EPS, and ROE
Consider an all-equity firm that is considering going into debt. (Maybe some of the original shareholders want to cash out.)
40% ownership
Proposed
$20,000
$8,000
$12,000
2/3 8%
240
$50
Current
Assets $20,000
Debt $0
Equity $20,000
Debt/Equity ratio 0.00
Interest rate n/a
Shares outstanding 400
Share price $50
The firm borrows $8,000 and buys back 160 shares at $50 per share.

4. EPS and ROE Under Current Capital Structure
No Debt
Recession Expected Expansion
EBIT $1,000 $2,000 $3,000
Interest 0 0 0
Net income $1,000 $2,000 $3,000
EPS $2.50 $5.00 $7.50
ROA 5% 10% 15%
ROE 5% 10% 15%
Current Shares Outstanding = 400 shares

5. EPS and ROE Under Proposed Capital Structure
40% ownership
Recession Expected Expansion
EBIT $1,000 $2,000 $3,000
Interest
Net income $360 $1,360 $2,360
EPS $1.50 $5.67 $9.83
ROA 5% 10% 15%
ROE 3% 11% 20%
Proposed Shares Outstanding = 240 shares

6. EPS and ROE Under Both Capital Structures
All-Equity Recession Expected Expansion
EBIT $1,000 $2,000 $3,000
Interest 0 0 0
Net income $1,000 $2,000 $3,000
EPS $2.50 $5.00 $7.50
ROA 5% 10% 15%
ROE 5% 10% 15%
Current Shares Outstanding = 400 shares
40% ownership
Levered Recession Expected Expansion
EBIT $1,000 $2,000 $3,000
Interest
Net income $360 $1,360 $2,360
EPS $1.50 $5.67 $9.83
ROA 5% 10% 15%
ROE 3% 11% 20%
Proposed Shares Outstanding = 240 shares

7. Financial Leverage and EPS
12.00
Does leverage increase Shareholders’ Value?
Debt
10.00
8.00
No Debt
6.00
Advantage to debt
Break-even point
EPS
4.00
2.00
0.00
1,000
2,000
3,000
Disadvantage to debt
(2.00)
EBI in dollars, no taxes

8. Cost of Capital and Leverage Ratio
This is impossible!
Cost of Capital rE
WACC rD
Debt ratio

9. Assumptions of the Modigliani-Miller Model
Homogeneous Expectations
Homogeneous Business Risk Classes
Perpetual Cash Flows
Perfect Capital Markets:
Perfect competition
Firms and investors can borrow/lend at the same rate
Equal access to all relevant information
No transaction costs
No taxes

10. No Magic in Financial Leverage
MM'S PROPOSITION I
If capital markets are doing their job,
firms cannot increase value by tinkering
with capital structure.
V is independent of the debt ratio.
AN EVERYDAY ANALOGY
It should cost no more to assemble a
chicken than to buy one whole.

11. Homemade Leverage: An Example
Recession Expected Expansion
EPS of Unlevered Firm $2.50 $5.00 $7.50
ROE 3% 11% 20%
Earnings for 40 shares $100 $200 $300
Less interest on $800 (8%) $64 $64 $64
Net Profits $36 $136 $236
ROE (Net Profits / $1,200) 3% 11% 20%
We are buying 40 shares of a $50 stock on margin. We get the same ROE as if we bought into a levered firm.
Our personal debt equity ratio is:

12. Homemade (Un)Leverage: An Example
Recession Expected Expansion
EPS of Levered Firm $1.50 $5.67 $9.83
Earnings for 24 shares $36 $136 $236
Plus interest on $800 (8%) $64 $64 $64
Net Profits $100 $200 $300
ROE (Net Profits / $2,000) 5% 10% 15%
Buying 24 shares of an other-wise identical levered firm along with the some of the firm’s debt gets us to the ROE of the unlevered firm.
This is the fundamental insight of M&M

13. The MM Propositions I & II (No Taxes)
Proposition I
Firm value is not affected by leverage
VL = VU
Proposition II
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

14. The MM Proposition I (No Taxes)
The derivation is straightforward:
The present value of this stream of cash flows is VL
The present value of this stream of cash flows is VU

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

16. MM Proposition II with No Corporate Taxes
Cost of capital: r (%) r0 rB rB
Debt-to-equity Ratio

17. The Effect of Tax on WACC
Firm value: shareholders plus bondholders
a. Unlevered
After-tax earnings = Pre-tax Earnings * (1-Tc)
b. Levered
After-tax Earnings =
(Pre-Tax Earnings – Interest Paid to bondholders) * (1-Tc) + Interest Paid to bondholders)
= Pre-tax Earnings * (1-Tc)
+ Tc * Interest Paid to Bondholders

18. Tax Shield Tax Shield: Tc * Interest Paid to Bondholders
If this is a permanent steady flow:
PV( Tax Shield) = Tc * Interest / Cost of debt
= Tc * (D*rD) / rD = Tc * D
Firm value increases with leverage
VL = VU + TC B

19. rS = r0 + (B/S) × (r0 - rB) × (1-TC)
M&M Proposition II
Proposition II (with Corporate Taxes)
Some of the increase in equity risk and return is offset by interest tax shield
rS = r0 + (B/S) × (r0 - rB) × (1-TC)
Compared with no-tax case
rs = r0 + (B / SL) (r0 - rB)
rB is the interest rate (cost of debt)
rS is the return on equity (cost of equity)
r0 is the return on unlevered equity (cost of capital)
B is the value of debt
S is the value of levered equity

20. Total Cash Flow to Investors Under Each Capital Structure with Corp
Total Cash Flow to Investors Under Each Capital Structure with Corp. Taxes
All-Equity Recession Expected Expansion
EBIT $1,000 $2,000 $3,000
Interest 0 0 0
EBT $1,000 $2,000 $3,000
Taxes (Tc = 35% $350 $700 $1,050
Total Cash Flow to S/H $650 $1,300 $1,950
Levered Recession Expected Expansion
EBIT $1,000 $2,000 $3,000
Interest 8% )
EBT $360 $1,360 $2,360
Taxes (Tc = 35%) $126 $476 $826
Total Cash Flow $ $468+$640 $1,534+$640
(to both S/H & B/H): $874 $1,524 $2,174
EBIT(1-Tc)+TCrBB $650+$224 $1,300+$224 $1,950+$224
$874 $1,524 $2,174

21. Total Cash Flow to Investors Under Each Capital Structure with Corp
Total Cash Flow to Investors Under Each Capital Structure with Corp. Taxes
All-equity firm Levered firm S G S G B
The levered firm pays less in taxes than does the all-equity firm.
Thus, the sum of the debt plus the equity of the levered firm is greater than the equity of the unlevered firm.

22. Summary: No Taxes
In a world of no taxes, the value of the firm is unaffected by capital structure.
This is M&M Proposition I:
VL = VU
Prop I holds because shareholders can achieve any pattern of payouts they desire with homemade leverage.
In a world of no taxes, M&M Proposition II states that leverage increases the risk and return to stockholders

23. Summary: Taxes
In a world of taxes, but no bankruptcy costs, the value of the firm increases with leverage.
This is M&M Proposition I:
VL = VU + TC B
Prop I holds because shareholders can achieve any pattern of payouts they desire with homemade leverage.
In a world of taxes, M&M Proposition II states that leverage increases the risk and return to stockholders.

24. Tax Shield
The more we borrow, the higher the PV of tax shield we obtain!
Is it good for firm to borrow more?
Bottom line:
Higher personal tax reduce the effect of tax shield
Tax shield requires a positive taxable profits.
Borrowing is not the only way for tax shield: depreciation, R&D expense and contribution to pension funds.

25. Prospectus: Bankruptcy Costs
So far, we have seen M&M suggest that financial leverage does not matter, or imply that taxes cause the optimal financial structure to be 100% debt.
In the real world, most executives do not like a capital structure of 100% debt because that is a state known as “bankruptcy”.
In the next chapter we will introduce the notion of a limit on the use of debt: financial distress.