101 Concepts for the Level I Exam

Essential Concept 36: Modigliani–Miller Propositions

MM Proposition I (without taxes): The market value of the company is not affected by the capital structure of the company.

V_L= V_U

MM Proposition II (without taxes): The cost of equity is a linear function of the company’s debt/equity ratio.

$\mathrm{r}}_{\mathrm{e}}\mathrm{=}{\mathrm{r}}_0\mathrm{+}\left({\mathrm{r}}_0\mathrm{-}{\mathrm{r}}_{\mathrm{d}}\right)\frac{\mathrm{D}}{\mathrm{E}}$

Where, r₀ is the cost of capital for a company financed only by equity and has zero debt.

MM Proposition I (with taxes): The value of the company with debt is greater than that of the all equity company by an amount equal to the tax rate multiplied by the value of the debt.

$\mathrm{V}}_{\mathrm{L}}\mathrm{=}{\mathrm{V}}_{\mathrm{U}}\mathrm{+tD}$

Where t is the marginal tax rate. The term tD is often referred to as the debt tax shield.

MM Proposition II (with taxes): The cost of equity increases as the company increases the amount of debt in its capital structure, but the cost of equity does not rise as fast as it does in the no tax case.

$\mathrm{r}}_{\mathrm{e}}\mathrm{=}{\mathrm{r}}_0\mathrm{+}\left({\mathrm{r}}_0\mathrm{-}{\mathrm{r}}_{\mathrm{d}}\right)\mathrm{(1-t)}\frac{\mathrm{D}}{\mathrm{E}}$
Where, r₀ is the cost of capital for a company financed only by equity and has zero debt.