FIRM VALUATION Firm Valuation Assumptions n Corporate taxes

FIRM VALUATION

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

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 n

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

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

If then 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)

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 r appropriate to its risk class” (Modigliani-Miller, American Economic Review, 1958 june)

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

n The above investment will affect the value of the levered firm: Note that Equity = old + ds 0+dsn n Because the project has the same risk as those already outstanding, the value of the outstanding debt stays the same.

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

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

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

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.

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

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

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

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

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

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