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Slide 2 - Firm Valuation Assumptions: Corporate taxes - individual taxe rate is zero Capital markets are frictionless Individuals can borrow and lend at the risk-free rate There are no costs to bankruptcy
Slide 3 - Firms issue only two types of claims: risk-free debt & (risky) equity All firms are in the same risk class No other taxes than corporate taxes All cash flow streams are perpetuities Everybody has the same information No agency costs
Slide 4 - 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
Slide 5 - 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 .
Slide 6 - 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)
Slide 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 r appropriate to its risk class” (Modigliani-Miller, American Economic Review, 1958 june)
Slide 8 - When the firm makes an investment I, its value will change according to (source)
Slide 9 - The above investment will affect the value of the levered firm: Note that Equity = old + ds0+dsn Because the project has the same risk as those already outstanding, the value of the outstanding debt stays the same .
Slide 10 - Because new project is financed with new debt, equity or both Inserting D I into the above formula (),
Slide 11 - This means that the project has to increase the shareholders’ wealth, so that and
Slide 12 - The Weighted Average Cost of Capital Recall the formula as shown it should be greater than 1, so
Slide 13 - This results in what is called “the Weighted Average Cost of Capital”, WACC, source. If there are no taxes the cost of capital is independent of capital structure.
Slide 14 - What does mean ? “If denotes the firm’s long run target debt ratio ...then the firm can assume, that for any particular investment “ .
Slide 15 - An alternative definition of the weighted average cost of capital Definition by Haley and Shall [1973] Target leverage ratio Reproduction value Reproduction value = PV of the stream of goods and services expected from the project.
Slide 16 - How to calculate the cost of the two components in WACC (debt & equity) Assumptions: The cost of debt = The cost of equity capital is the return on
Slide 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
Slide 18 - 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
Slide 19 - This formula is the same as the Modigliani-Miller definition The M-M and the traditional definition are identical !