1. FIRM VALUATION

2. Firm Valuation Assumptions: Corporate taxes - individual taxe rate is zero Corporate taxes - individual taxe rate is zero n Capital markets are frictionless n Individuals can borrow and lend at the risk-free rate n There are no costs to bankruptcy

3. n Firms issue only two types of claims: risk-free debt & (risky) equity n All firms are in the same risk class n No other taxes than corporate taxes n All cash flow streams are perpetuities n Everybody has the same information n No agency costs

4. n The value of an unlevered firm is,where  Expected future cash flow  Discount rate for an all - equity firm of equivalent risk = Corporate tax rate

5. If the firm issues debt, then,where = The amount paid to the lenders, kd = interest rate, D = amount of debt D = amount of debt =interest on debt. If the debt is risk-free then. =interest on debt. If the debt is risk-free then.

6. Ifthen In other words = Value of an unlevered firm + the PV of the tax shield provided by debt. Notice that if then (The famous Modigliani-Miller hypothesis) (The famous Modigliani-Miller hypothesis)

7. This implies that “The market value of any firm is independent of its capital structure and is given by capitalizing its expected return at the rate  appropriate to its risk class” (Modigliani-Miller, American Economic Review, 1958 june)

8. When the firm makes an investment  I, its value will change according to (source) When the firm makes an investment  I, its value will change according to (source)

9. n The above investment will affect the value of the levered firm: Note that Equity = old + ds0+dsn n Because the project has the same risk as those already outstanding, the value of the outstanding debt stays the same.

10. n Because new project is financed with new debt, equity or both Inserting  I into the above formula (), Inserting  I into the above formula (),

11. n This means that the project has to increase the shareholders’ wealth, so that and and

12. The Weighted Average Cost of Capital n Recall the formula as shown it should be greater than 1, so

13. n This results in what is called “the Weighted Average Cost of Capital”, WACC, source. n If there are no taxes the cost of capital is independent of capital structure.

14. What does mean ? n “If denotes the firm’s long run target debt ratio...then the firm can assume, that for any particular investment “.

15. An alternative definition of the weighted average cost of capital n Definition by Haley and Shall [1973] n Target leverage ratio Reproduction value Reproduction value Reproduction value = PV of the stream of goods and services expected from the project. Reproduction value = PV of the stream of goods and services expected from the project.

16. How to calculate the cost of the two components in WACC (debt & equity) n Assumptions: n The cost of debt = n The cost of equity capital is the return on

17. This can be written as (C-W, p. 449): Since the total change in equity is, the cost of equity can be written as

18. n If the firm has no debt in its capital structure, then It can be shown that (C-W, 451) WACC can be written as: tax shield Percentage of equity in the capital structure cost of equity Percentage of debt in the capital structure cost of debt

19. n This formula is the same as the Modigliani-Miller definition The M-M and the traditional definition are identical !