1. Chapter Outline15.1 The Capital-Structure Question and The Pie Theory
15.2 Maximizing Firm Value versus Maximizing Stockholder Interests
15.3 Financial Leverage and Firm Value: An Example
15.4 Modigliani and Miller: Proposition II (No Taxes)
15.5 Taxes
15.6 Summary and Conclusions
2. The Capital-Structure Question and The Pie TheoryThe 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
Value of the FirmSB 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.
3. The Capital-Structure QuestionThere are really two important questions:
Why should the stockholders care about maximizing firm value? Perhaps they should be interested in strategies that maximize shareholder value.
What is the ratio of debt-to-equity that maximizes the shareholder’s value?
As it turns out, changes in capital structure benefit the stockholders if and only if the value of the firm increases.
4. Financial Leverage, EPS, and ROE Current
Assets $20,000
Debt $0
Equity $20,000
Debt/Equity ratio 0.00
Interest rate n/a
Shares outstanding 400
Share price $50 Proposed
$20,000
$8,000
$12,000
2/3
8%
240
$50Consider an all-equity firm that is considering going into debt. (Maybe some of the original shareholders want to cash out.)
5. EPS and ROE Under Current Capital Structure 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
6. EPS and ROE Under Proposed Capital Structure Recession Expected Expansion
EBIT $1,000 $2,000 $3,000
Interest 640 640 640
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. EPS and ROE Under Both Capital Structures Levered Recession Expected Expansion
EBIT $1,000 $2,000 $3,000
Interest 640 640 640
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 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
8. Financial Leverage and EPS(2.00)0.002.004.006.008.0010.0012.001,0002,0003,000EPSDebtNo DebtBreak-even point EBI in dollars, no taxesAdvantage to debtDisadvantage to debtEBIT
9. Assumptions of the Modigliani-Miller ModelHomogeneous 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. Homemade Leverage: An Example Recession Expected Expansion
EPS of Unlevered Firm $2.50 $5.00 $7.50
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:
11. 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
12. 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
13. 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
14. The MM Proposition II (No Taxes)The derivation is straightforward:
15. The Cost of Equity, the Cost of Debt, and the Weighted Average Cost of Capital: MM Proposition II with No Corporate TaxesDebt-to-equity RatioCost of capital: r (%)r0rBrB
16. The MM Propositions I & II (with Corporate Taxes)Proposition I (with Corporate Taxes)
Firm value increases with leverage
VL = VU + TC B
Proposition II (with Corporate Taxes)
Some of the increase in equity risk and return is offset by interest tax shield
rS = r0 + (B/S)×(1-TC)×(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
17. The MM Proposition I (Corp. Taxes)The present value of this stream of cash flows is VL The present value of the first term is VU
The present value of the second term is TCB
18. The MM Proposition II (Corp. Taxes)Start with M&M Proposition I with taxes:Since The cash flows from each side of the balance sheet must equal:Divide both sides by SWhich quickly reduces to
19. The Effect of Financial Leverage on the Cost of Debt and Equity CapitalDebt-to-equityratio (B/S)Cost of capital: r(%)r0rB
20. 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 ($800 @ 8% ) 640 640 640
EBT $360 $1,360 $2,360
Taxes (Tc = 35%) $126 $476 $826
Total Cash Flow $234+640 $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. TaxesThe 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.SGSGB All-equity firm Levered firm
22. Summary: No TaxesIn 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: TaxesIn 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. Prospectus: Bankruptcy CostsSo 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.
The important use of this chapter is to get comfortable with “M&M algebra”.