Modigliani-Miller first studied capital markets in a world with no taxes. They found that the value of a firm is unaffected by capital structure. In other words the value of a levered firm is equal to the value of an unlevered firm. They argued that the value of the firm is dependent on the value of the firm’s assets. In an environment with no taxes, capital structure should have no affect on the assets of the firm. Therefore it should not affect the value of the firm. However it does affect the expected return of the firm:
Let’s pretend we have a company with the following capital structure:
Let’s pretend the firm intends to raise $40,000 and use it to purchase 4,000 shares of equity at $10 each. New capital structure would be:
Interest on debt is 12% and the firm has three forecasted earnings in the next year (all with equal opportunity)
- If the company experiences a “recession” year it will achieve EBIT of $10,000.
- If the company experiences a “normal” year it will achieve EBIT of $15,000
- If the company experiences an “expansion” year it will achieve EBIT of $20,000
The expected earnings of the unlevered firm are:
The expected earnings of a levered firm are:
If we were to graph these earnings we would observe the following:
Figure 1: EPS (vertical axis) verse EBIT (horizontal axis) for a levered and unlevered firm
As you can see here by increasing financial leverage we both increase the expected return of the firm ($3.33 per share versus $3.00 per share) but we also increase the financial risk. As we can see in recession times the levered firm earns less ($1.67 per share versus $2.00 per share) and in boom times the levered firm earns more ($5.00 per share versus $4.00 per share).
We can conclude the following two propositions in a world without taxes:
Proposition one:
VL = VU
VL = value of the assets of a levered firm, Vu = value of the assets of an unlevered firm
Proposition Two:
RS = Ro + D/E (Ro - Rd)
Rs = expected shareholders return, Ro = expected bondholders return, RD = debt holders expected return D = Debt value, E = Equity value
However, the weighted average cost of capital of the firm remains the same regardless of capital structure. As the financial leverage and the expected shareholder return increases the proportion of the lower cost of debt increases – which in effect balances out the two variables: