Financial Subject: Modigliani Miller
Modigliani and Miller received the Nobel Prize in Economics for their work on the capital
structure of the firm. The capital structure may simply be defined as the relative proportions
of debt, equity, and other securities that a firm has outstanding.
The first result, also known as the first proposition of Modigliani & Miller simply states that
in a frictionless environment, the value of the firm does not depends on its capital structure.
The assumption of frictionless environment is a strong assumption which describes a situation
where investors face no corporate taxes, no transaction costs when they issuing securities or
debts. Moreover there is no information asymmetry and stakeholders are able to resolve
conflicts for free.
The value of the firms comes from its asset side only and its capacity to produce future cash
flows. The capital structure neither creates nor destroys value.
As a consequence, with R U being the return on unlevered equity, R E the returns of levered
equity and R D the returns of debt, we have
E
D
RE +
RD =
RU
E + D
E + D
With a few manipulations we have:
𝑅𝑅𝐸𝐸 = 𝑅𝑅𝑈𝑈 +
𝐷𝐷
(𝑅𝑅 − 𝑅𝑅𝐷𝐷 )
𝐸𝐸 𝑈𝑈
We thus reach the second proposition of Modigliani Miller which states that the cost of capital
of levered equity is equal to the cost of capital of unlevered equity plus a premium that is
proportional to the market value debt-equity ratio.
Thanks to these propositions, we can prove that the cost of capital of the firm does not depend
on its capital structure under the frictionless environment assumptions.
When the previous assumption is not meet, then the Modigliani Miller propositions do not
hold anymore. With taxes indeed the value of the levered firm is higher than the value of the
unlevered firm as it rises with the present value of the tax savings provided by the payment of
interests. We thus have
V L =V U +PV (Interest Tax shields)
Where
V L is the value of the levered firm
V U is the value of the unlevered firm
PV means Present Value
With τ being the tax rate we have
𝑅𝑅𝐸𝐸 = 𝑅𝑅𝑈𝑈 +
𝐷𝐷
(𝑅𝑅 − 𝑅𝑅𝐸𝐸 )(1 − 𝜏𝜏)
𝐸𝐸 𝑈𝑈
And as a conclusion, the WACC of the firm is affected by its capital structure.
This could lead to the conclusion that the firm should opt for debt financing only. However,
the real link between the cost of capital and the capital structure is not linear. At some point
indeed, when the firm is too indebted, the risk of bankruptcy rises. The firm has indeed a
contractual obligation to pay interests and principal to the debt holders. The levered firm faces
a financial pressure which is not known to the unlevered firm. When the levered firm has
problems in meeting its financial obligation to service its debt, it faces a situation that is
referred to as financial distress. Ultimately the firm may go bankrupt.
These costs are sometime difficult to fully measure as they include costs in terms of
reputation and legal cost to go for bankruptcy.