1. Capital Structure Theory (1)

2. Outline Modigliani–Miller Theory Without Taxes
Modigliani–Miller Theory with Taxes
Modifications of Modigliani–Miller theory
Taking into Account Market Risk: Hamada
Model
The Cost of Capital Under Risky Debt
The Account of Corporate and Individual
Taxes (Miller Model)

3. Modigliani–Miller Theory
Choice of an optimal capital structure, i.e., a capital structure which minimizes the weighted average cost of capital, WACC, and maximizes the value of the company, V, is one of the most important tasks solved by financial manager and by the management of a company.
The first serious study (and first quantitative study) of influence of capital structure of the company on its indicators of activities was the work by Modigliani and Miller (1958).

4. Modigliani–Miller Theory
Before MM(1958) the traditional approach told that an increase in the proportion of lower-cost debt capital in the overall capital structure up to the limit which does not cause violation of financial sustainability and growth of risk of bankruptcy leads to lower weighted average cost of capital, WACC (Fig. 2.1).

5. Modigliani–Miller Theory
1. Modigliani–Miller Theory Without Taxes (1958)
Under assumptions that there are no taxes, no transaction costs, no bankruptcy costs, perfect financial markets exist with symmetry information, equivalence in borrowing costs for both companies and investors, etc., Modigliani and Miller (1958) have showed that choosing of the ratio between the debt and equity capital does not affect company value as well as capital costs (Fig. 2.2).

6. Modigliani–Miller Theory
Without taxes, the total cost (value) of any company is determined by the value of its EBIT—Earnings Before Interest and Taxes, discounted with fixed rate , corresponding to group of business risk of this company:
In other words, in the absence of taxes, value of the company is independent of the method of its funding.

7. Modigliani–Miller Theory
Equity cost of leverage company could be found as equity cost of financially independent company of the same group of risk, plus premium for risk, the value which is equal to production of difference on leverage level L:
This formula shows that equity cost of the company increases linearly with leverage level.

8. Modigliani–Miller Theory
The combination of these two Modigliani–Miller statements implies that the increasing of level of debt in the capital structure of the company does not lead to increased value of firms, because the benefits gained from the use of more low-cost debt capital will be exactly offset by an increase in risk (the financial risk, the risk of bankruptcy) and, therefore, by an increase in cost of equity capital of firms.

9. Modigliani–Miller Theory
2. Modigliani–Miller Theory with Taxes (1963)
The value of financially dependent company is equal to the value of the company of the same risk group used no leverage, increased by the value of tax shield arising from financial leverage, and equal to the product of rate of corporate income tax T and the value of debt D (Fig.2.3)

10. Modigliani–Miller Theory
The interest paid on debt are excluded from the tax base and this leads to the so-called effect of “tax shield”. The value of the “tax shield” for 1 year is equal to The value of the “tax shield” for perpetuity company is equal to
Equity cost of leverage company paying tax on profit could be found as equity cost of financially independent company of the same group of risk, plus premium for risk, which is equal to production of difference on leverage level L and on tax shield (1–T).

11. Modigliani–Miller Theory
When leverage grows:
(1) Value of company increases.
(2) Weighted average cost of capital WACC decreases from (at ) up to (at
when the company is funded solely by borrowed funds).
(3) Equity cost increases linearly from (at ) up to (at ).

12. Modifications: Hamada Model
Modifications of Modigliani–Miller theory
1. Taking into Account Market Risk: Hamada Model Robert Hаmаdа (1969) unites Capital Asset Pricing Model (CAPM) with Modigliani–Miller taxation model.

13. Modifications: Hamada Model
: the coefficient of the company of the same group of business risk, but with zero financial leverage.
: risk-free rate
: premium for business risk
: premium for financial risk
The equation shows that market risk of the company depends on the business risk and the financial risk.

14. Modifications: Risky Debt
2. The Cost of Capital Under Risky Debt One hypothesis of Modigliani and Miller was the suggestion about free of risk debt (in their theory, there are two types of assets: risky equity and free of risk debt).
Stiglitz (1969) and Rubinstein (1973) have shown that the conclusions concerning the total value of company do not change as compared to the findings derived by Modigliani and Miller under assumptions about free of risk debt.

15. Modifications: Risky Debt
However, the debt cost is changed ( ). Hsia (1981), based on the models of pricing options, Modigliani–Miller and CAPM, showed that

16. Modifications: Individual Taxes
3. The Account of Corporate and Individual Taxes (Miller Model)
: tax rate on corporate profits
: tax rate on income of an individual investor from his ownership by stock of corporation
: tax rate on interest income

17. Modifications: Individual Taxes
The Miller model allows you to obtain an estimate of the value of financially dependent company, taking into account the corporate tax, as well as tax on individuals. The Miller formula has several important consequences:
Second term of sum represents the gains from use of debt capital.
If we ignore taxes, the formula is transformed into the original version of the Modigliani– Miller model without taxes.

18. Modifications: Individual Taxes
If we neglect taxes on individuals, the formula becomes a Modigliani–Miller model with corporate taxes.
If the shareholder receives profit only in the form of dividend, and if effective tax rates on income from shares and bonds are equal, the factor for D in the formula again is equal to .
If the shareholder receives dividends, and income from capital, the situation is changed. In the case
the factor is smaller than .

19. Modifications: Individual Taxes
As a result, the effect of using of debt financing is less than in the absence of individual taxes.
In the case , is bigger than
the effect of use of debt financing is increased compared with the case of the absence of individual taxes.
If , the effect of using debt financing will also be zero. In this case, the capital structure will not affect the company value and its capital cost-in other words, you can apply Modigliani–Miller theory without tax.

20. Modifications: Individual Taxes
In the United States, an effective tax rate on the income of shareholders is lower than the one on the income of creditors, but, nevertheless, the product less than Consequently, the companies may receive the benefit from use of debt financing. However the tax benefits of debt are less than anticipated at a more earlier Modigliani–Miller model, where only corporate taxes have been taken into account.