1. Capital Structure: Part 1
For 9.220, Term 1, 2002/03
02_Lecture19.ppt
Student Version

2. Outline Introduction Theories of Capital Structure
Modigliani and Miller – No tax
M&M with Corporate Tax
Summary and Conclusions (so far)

3. Introduction
Definition: Capital Structure is the mix of financial securities used to finance the firm.
Our goal is to see if there is an optimal way for firms to finance.
Should a firm have a higher or lower D/E ratio.
What factors affect the optimal D/E choice?
In order to optimize the D/E ratio, our overall goal is to maximize the total value of the firm and thus maximize expected shareholder wealth.

4. Modigliani and Miller – No Tax Case
M&M began looking at capital structure in a very simplified world so that we would know what does or does not matter.
Assume no taxes
No transaction costs
Including no bankruptcy costs
Investors can borrow/lend at the same rate (the same as the firm).
No information asymmetries
A fixed investment policy by the firm

5. M&M No Tax: Result
A change in capital structure does not matter to the overall value of the firm. The total cash flows produced are the same, thus the total value of the cash flows is the same.
It doesn’t matter if the cash flows from the firm to its security holders are called debt or equity cash flows.

6. M&M – No Tax Case Equity, $1,000, 100% Debt, $300, 30% Equity,
$700, 70%
Equity,
$1,000,
100%
Debt,
$600, 60%
Equity,
$400, 40%

7. The M&M 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

8. M&M 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

9. M&M Proposition II (No Taxes)
The derivation is straightforward:

10. Exercise
Suppose the firm is currently all equity financed and the total value of the firm is $90 million. E[Requity] is 18%. Also, suppose Rf = 4% and E[RM] = 14%.
What is the value of the equity and the total value of the firm if the capital structure is changed to include $30 million of debt? If E[Rdebt] is 6%, then what is the new E[Requity]? What is the WACC? Compare the beta of the levered equity to the unlevered equity. What is the weighted beta of the firms securities?
Redo 1 with $60 million of debt.

11. The Cost of Equity & Debt, and the WACC: M&M Proposition II with No Corporate Taxes
Cost of capital: r (%) r0 rB rB
Debt-to-equity Ratio

12. M&M with Corporate Taxes
When corporate taxes are introduced, then debt financing causes a positive benefit to the value of the firm.
The reason for this is that debt interest payments reduce taxable income and thus reduce taxes.
Thus with debt, there is more after-tax cash flow available to security holders (equity and debt) than there is without debt.
Thus the value of the equity and debt securities combined is greater.

13. M&M with Corporate Taxes
TC = 40% in this example
Tax, $400,
40%
Equity,
$600, 60%
Tax, $280,
28%
Debt,
$300, 30%
Equity,
$420, 42%
Debt,
$600, 60%
Tax, $160,
16%
Equity,
$240, 24%

14. M&M Proposition I (with Corporate Taxes)
Firm value increases with leverage
VL = VU + TC B

15. M&M Proposition I (with 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

16. M&M Proposition II (with Corp. Taxes)
Proposition II (with Corporate Taxes)
This proposition is similar to Prop. II in the no tax case, however, now the risk and return of equity does not rise as quickly as the debt/equity ratio is increased because low-risk tax cash flows are saved.
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. Exercise
Suppose the firm is currently all equity financed and the total value of the firm is $90 million. E[Requity] is 18%. Also, suppose that TC = 40%, Rf = 4% and E[RM] = 14%.
What is the value of the equity and the total value of the firm if the capital structure is changed to include $30 million of debt? If E[Rdebt] is 6%, then what is the new E[Requity]? What is the new WACC?
Redo 1 with $60 million of debt.

18. The Effect of Financial Leverage on the Cost of Debt and Equity Capital
Cost of capital: r (%) r0 rB
Debt-to-equity ratio (B/S)

19. Summary and Conclusions
At this point, it appears clear that an increase in the debt/equity ratio increases the risk of the equity.
With corporate taxes, it also appears that the value of the firm increases as the amount of debt used increases (due to taxes being saved).
However, in reality, we don’t see 100% debt financing, so there must be other factors that affect the firm’s optimal capital structure.
The next lecture addresses these other factors and extends the theory.