CH 16 Intermediate Corporate Finance

M&M Propositions

Case 1 M&M Propositions

Assumptions

Formulas

Implications

Optimal Capital Structure

Assumptions:

• No corporate or personal taxes

• No bankruptcy costs

Implications:

Prop 1: value of firm does not depend on capital structure

Prop 2: WACC stays constant. Re increases with debt

Optimal Capital Structure: No optimal structure

Case 1 Formulas

Proposition 1:

Vu=VL

V=D+E

V=EBIT/WACC

Proposition 2:

WACC=Ra= (E/V)Re+(D/V)Rd

Re= Ra+(Ra-Rd)(D/E)

where:

Ra = business (systematic) risk (beta-ish)

(Ra-Rd)(D/E) = Financial risk

Case II

Assumptions

Implications

Optimal Capital Structure

Assumptions:

Corporate taxes

No bankruptcy costs

Implications:

Proposition I:

The value of a firm increases with more debt. Specifically by the PV of the annual interest tax shield

Proposition II:

The WACC decreases as D/E increases because of gov subsidy on interest tax. Cost of equity increases with increase in D/E

Optimal Capital Structure: All Debt

Case II Formulas

Proposition 1:

Vu=EBIT(1-t)/WACC

VL=Vu+ DTc

PV Annual interest Tax Shield = Dtc= Debt x Tax rate

Proposition 2:

WACC=(E/V)Re+(D/E)(Rd)(1-t)

Re= Ra+(Ra-Rd)(D/E)(1-t)

Case III Assumptions, Implications, Optimal Capital Structure

Assumptions:

Corporate taxes

Bankruptcy

Implications:

As the D/E ratio increases, the probability of bankruptcy increases. (and increases bankruptcy costs)

•At some point, the additional value of the interest tax shield will be offset by the increase in expected bankruptcy cost.

•At this point, the value of the firm will start to decrease, and the WACC will start to increase as more debt is added.

Optimal Capital Structure: Part debt and part equity

How do we determine the optimal capital structure?

Occurs where the benefit from an additional dollar of debt is just offset by the increase in expected bankruptcy costs