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
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
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)
When the firm makes an investment I, its value will change according to (source)
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 .
Because new project is financed with new debt, equity or both
Inserting D I into the above formula (),
This means that the project has to increase the shareholders’ wealth, so that
and
The Weighted Average Cost of Capital
Recall the formula
as shown it should be greater than 1, so
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.
What does 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
Reproduction value Reproduction value = PV of the stream of goods and services expected from the project. Definition by Haley and Shall [1973]
Target leverage ratio
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
This can be written as (C-W, p. 449):
Since the total change in equity is
, the cost of equity
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 If the firm has no debt in its capital structure, then
It can be shown that (C-W, 451) WACC can be written as:
This formula is the same as the Modigliani-Miller definition
The M-M and the traditional definition are identical !
Comments