Modigliani-Miller theorem

The Modigliani-Miller theorems were presented by Franco Modigliani and Merton Miller in their articles The Cost of Capital, Corporation Finance and the Theory of Investment and Dividend Policy, Growth and the Valuation of Shares , published in 1958 and 1961 . They deal with the influence of a company's level of indebtedness on its cost of capital and show that neither the capital structure nor the dividend policy of a company have any influence on the company's value under certain conditions.

First theorem

In a frictionless market, that is, there is

the capital structure of a company is irrelevant to its value.

The value of a company with non- leveraged financing is equal to the value of the equity, while for a leveraged company it is composed of the value of the equity and borrowed capital:

without external financing: ${\ displaystyle W_ {U} = EK_ {U}}$
with external financing: ${\ displaystyle W_ {L} = EK_ {L} + FK_ {L}}$

Assuming two companies generate the same operating result and only differ in their capital structure, the following investment alternatives can be outlined:

Acquisition of 1% of the non-leveraged company. The yield is then 1% of the operating profit generated:

	investment	Yield
Equity	1 % ${\ displaystyle EK_ {U}}$	1% profit

Acquisition of 1% each of the equity and debt of the leveraged company. The income is then made up of the share in the interest on borrowed capital and the share in the operating result minus the proportional interest on borrowed capital:

	investment	Yield
Borrowed capital	1 % ${\ displaystyle FK_ {L}}$	1% interest
Equity	1 % ${\ displaystyle EK_ {L}}$	1% (operating profit - interest)
total	1 % ${\ displaystyle FK_ {L} + EK_ {L}}$	1% profit
	= 1% ${\ displaystyle W_ {L}}$

Both alternatives have the same gain. In well-functioning markets, two investments with identical cash flows are priced the same , so the value of the leveraged company must be equal to the value of the unlevered one.

Suppose an investor is willing to take a slightly higher risk:

Acquisition of 1% of the leveraged company:

	investment	Yield
Equity	1 % ${\ displaystyle EK_ {L}}$	1% (operating profit - interest)
total	1 % ${\ displaystyle W_ {L} -FK_ {L}}$	1% profit

Acquisition of 1% of the non-leveraged company with a private loan (corresponds to the leverage of the leveraged company):

	investment	Yield
Personal loan	- 1 % ${\ displaystyle FK_ {L}}$	- 1% interest
Equity	1 % ${\ displaystyle EK_ {U}}$	1 %
total	1 % ${\ displaystyle W_ {U} -FK_ {L}}$	1% (profit - interest)

The return from both alternatives is again identical: 1% profit after interest. The value of the two companies must therefore be the same and it does not matter at which point the debt financing (the lever) is carried out, whether by the company or the investor.

Although the prerequisites for this theorem never apply in practice, the following can be deduced from it: If the capital structure is important for a company, it is because at least one of the above assumptions does not apply. That means: If one wants to optimize the capital structure, the influence of the determinants on the capital structure must be examined.

Second theorem

The cost of equity increases with the leverage:

Relationship between equity and debt capital costs (k _e = equity capital costs; k _d = debt capital costs; k _o = average costs )

If

the first Modigliani-Miller theorem for a company holds, ${\ displaystyle U}$
${\ displaystyle U}$ is a company whose liabilities consist only of senior debt and subordinated equity,

then

which is cost of equity of the company from the spread between cost of capital and cost of debt and the leverage of this company linearly dependent : ${\ displaystyle r _ {\ mathit {EK}} = {\ overline {r_ {G}}} + ({\ overline {r_ {G}}} - r _ {\ mathit {FK}}) \ cdot {\ frac { \ mathit {FK}} {\ mathit {EK}}}}$
which is the total cost of capital of the company from the leverage of this company independently,

provided that the market values of equity and debt are considered.

This relationship can easily be represented by a corresponding cost of capital curve. This means that there is no optimal leverage for a company (or that the optimal leverage is a corner solution, i.e. 1).

Third theorem

The constancy of the weighted average cost of capital :

"The method of financing an investment is irrelevant with regard to the question of whether the investment is worthwhile." (Original: The type of instrument used to finance on investment is irrelevant to the question of whether or not the investment is worthwhile. ) The The irrelevance of the capital structure to the market value of a company presented in the first theorem can be extended to the irrelevance of the capital structure of an individual project. Although the expected return on equity rises as the level of indebtedness increases, the risk also rises at the same time. The average cost of capital therefore remains constant, which means that even a single project will not become more profitable due to increased debt financing.

literature

Franco Modigliani, Merton H. Miller: The Cost of Capital, Corporation Finance and the Theory of Investment. In: The American Economic Review. 48, 3, June 1958, pp. 261-297.
Franco Modigliani, Merton H. Miller: Dividend Policy, Growth and the Valuation of Shares In: Journal of Business , 34 (October 1961), pp. 411-433

Individual evidence

^ Richard A. Brealey, Stewart Clay Myers: Principles of Corporate Finance . 7th edition, McGraw-Hill, London 2002/2003, ISBN 978-0-07-294043-5 , p. 467 ff.
^ Louis Perridon , Manfred Steiner : Finanzwirtschaft der Unternehmens. 2004, Vahlen, ISBN 978-3800631124 , p. 494 ff.

[Brealy-Myers-1] Richard A. Brealey, Stewart Clay Myers: Principles of Corporate Finance . 7th edition, McGraw-Hill, London 2002/2003, ISBN 978-0-07-294043-5 , p. 467 ff.

[2] Louis Perridon , Manfred Steiner : Finanzwirtschaft der Unternehmens. 2004, Vahlen, ISBN 978-3800631124 , p. 494 ff.