Modigliani-Miller theorem

The Modigliani-Miller theorem states that in perfect markets without taxes, a firm's value is independent of its capital structure. Relaxing the assumptions generates the trade-off theory of optimal gearing.

ByHoang TruongUpdated June 30, 2026

FrameworkModigliani-Miller

See it move

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In a perfect market with no taxes, Modigliani-Miller shows a levered firm's value equals an otherwise identical unlevered firm's value — capital structure does not matter. Once corporate tax enters, the equation shifts: levered value equals unlevered value plus a tax shield worth the tax rate times the amount of debt, T × D, so debt now adds measurable value.

Where it fits

SubjectCorporate FinanceAdvancedTopicCapital Structure & LeverageAdvanced

The formula

LaTeX

V_L = V_U

Variables

$V_{L}$: Total value of the levered (debt-financed) firm (€)
$V_{U}$: Total value of the unlevered (all-equity) firm (€)

In a perfect market without taxes, capital structure is irrelevant — firm value depends only on operating cash flows.

LaTeX

V_L = V_U + T \cdot D

Variables

$V_{L}$: Value of the levered firm (€)
$V_{U}$: Value of the equivalent unlevered firm (€)
$T$: Corporate tax rate (decimal)
$D$: Market value of debt (€)
$T \times D$: Present value of the debt tax shield (€)

Relaxing the no-tax assumption, debt adds value equal to the present value of the interest tax shield.