- 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”.