RedGage

In a well-known work of 1977, Merton Miller tries to redeem the original intuition of the result obtained by him with Modigliani in 1958, namely the irrelevance of capital structure.

Based on an argument of general equilibrium , shows that, given the balance of the market risk capital or equity , the debt market reaches an equilibrium level of the interest rate such that the gain in value resulting in undertaking from any level of debt is null.

It would be legitimate to ask why at this point , since there would be , based on the argument of Miller, no benefit from debt, in practice companies have capital structures that are very different.

The explanation proposed by Miller is known as the argument of the neutral mutation : the adoption of a given capital structure, not harming nor benefiting a company, can be compared to what would be a mutation having similar properties in the context of the theory of evolution in biology.

In other words , since there is a capital structure " favorite , " or in some sense optimal , in practice it is reasonable to expect a variety of capital structures .

Miller gets his result as follows . In the first place , it is observed that , if the presence of a debt brings some benefit to the value of the company , the value thus created must be , according to an argument no arbitrage , such that:

    V_\mathrm{L}=V_\mathrm{U}+rB\left[1-\frac{(1-\tau_\mathrm{C})(1-\tau_{\mathrm{PS}})}{1-\tau_{\mathrm{PB}}}\right]

where , following the notation of Miller, V_ \ mathrm { L} denotes the value of the debt with the Modigliani -Miller theorem , V_ \ mathrm { U} that of its counterpart free of debt , B denotes the nominal value of the debt enterprise, and \ tau_ \ mathrm {C }, \ tau_ \ mathrm { PS } and \ tau_ \ mathrm { PB } denote the rates of taxation on business income and personal income ( the marginal investor ) arising from capital gains and income from the receipt of interest payments on corporate debt , respectively.

The expression above can be obtained by a classical no-arbitrage argument , the cash flow of the company with debt that the shareholder receives will be given a level of profit X of the company itself :

    \ ( X - rB ) ( 1 - \ tau_ \ mathrm {C } ) ( 1 - \ tau_ \ mathrm { PS } )

To replicate this cash flow, you simply buy the same share of the company debt-free ( thus obtaining X (1 - \ tau_ \ mathrm {C }) (1 - \ tau_ \ mathrm { PS }) ) and borrow an amount equal to :

    B \ frac { (1 - \ tau_ \ mathrm { PB } ) - (1 - \ tau_ \ mathrm {C }) (1 - \ tau_ \ mathrm { PS }) } {1 - \ tau_ \ mathrm { PB }}

(not just the face value of debt B , since interest payments are deductible). Combining the two values ​​, we get the expression above .

Illustration of the market balance of the debt securities in the model of Miller ( 1977). The demand curve of debt is rising curve , such that the rate of return demanded , at each amount of debt on the market , is equal to r_0 / (1 - \ tau_ \ mathrm { PB } ^ m) ; for any amount of debt , firms offer a return of r_0 / (1 - \ tau_ \ mathrm {C }).

Equilibrium condition is therefore that : \ tau_ \ mathrm { PB } ^ m = \ tau_ \ mathrm {C }, that is the question of debt equals the offer . Substituting this result in the expression obtained by Miller for the tax benefits of debt, as you get - under the hypothesis of Miller - the latter are effectively zero in terms of overall balance of the debt and equity markets .

Miller speculates that \ tau_ \ mathrm { PS } is negligible, since the payment of taxes on capital gains can be deferred indefinitely until their realization - so that in any event, the taxation of capital gains does not affect the demand and supply of debt.

Consider , therefore, the corporate debt market as a whole , or of debt securities issued by all firms of the economy, assuming that the market for the shares of all firms in the economy is in equilibrium (the law of Walras ago also ensure that the debt market will be in equilibrium ) .

The function of demand for debt securities is initially horizontal , ie for a constant level of rate of return equal to that demanded by investors exempt from taxation ( r_0 , which will be equal to the return on the market balance of the shares, in order to exclude arbitrage between the two markets , as it must be in equilibrium ) . Once exhausted investors exempt from taxation, the rate of return demanded will be higher , in order to compensate investors for the tax , it will be equal to:

        \ frac { r_0 } {1 - \ tau_ \ mathrm { PB } ^ m }

where \ tau_ \ mathrm { PB } ^ m is the rate of the marginal investor . The meaning of the above is obvious: the marginal investor will receive , net of taxes, a return exactly equal to r_0 (ie : [ r_0 / (1 - \ tau_ \ mathrm { PB } ^ m) ] \ times ( 1 - \ tau_ \ mathrm { PB } ^ m) = r_0 ), so you will not find cheaper not to buy debt and refer instead to the stock market . This condition of indifference between the two markets by the marginal investor is the basis of equilibrium in the model of Miller.

Similarly, there comes the offering of debt securities by companies . It will be constant for a rate of return equal to:

        \ frac { r_0 } {1 - \ tau_ \ mathrm {C }}

The justification of the above expression is that , once again , net of tax the company offers a return equal to that which prevails in equilibrium in the stock market , ie r_0 .

The condition of equilibrium of the debt market is that supply and demand are equal , based on the expressions derived above , this means :

    \ frac { r_0 } {1 - \ tau_ \ mathrm {C } } = \ frac { r_0 } {1 - \ tau_ \ mathrm { PB } ^ { m } } \ quad \ iff \ quad \ tau_ \ mathrm {C } = \ tau_ \ mathrm { PB } ^ { m }

In other words, the aggregate amount of debt on the market will be such that the rate of tax on the income of the marginal investor \ tau_ \ mathrm { PB } ^ { m } is exactly equal to the rate on business income \ tau_ \ mathrm {C } . Investors with higher tax rates will not hold any debt securities in their portfolios.

It is therefore argued that \ tau_ \ mathrm { PS } \ approx 0 and that in equilibrium \ tau_ \ mathrm {C } = \ tau_ \ mathrm { PB } ^ { m } . Substituting these results in the expression for the additional value created by debt , we get:

    V_ \ mathrm {U } = V_ \ mathrm { L}

ie , once the capital structure is irrelevant in the sense that , in equilibrium aggregate debt market , it does not create value for businesses. [6]

The result of Miller does not enjoy broad support among academic ( as well as among practitioners ) . [7] The criticism of Miller's argument is based essentially on the restrictive nature of its assumptions .

A first drawback of the model of Miller, for example, is the result of balance is less when it admits the possibility of short sales. Consider in particular the case of an investor i, for which the rate of taxation on income earned from debt securities is less than the marginal investor :

    \ \ Tau_ \ mathrm { PB } ^ i < \ tau_ \ mathrm { PB } ^ m

Suppose for a moment that the result of Miller is still valid , and that the investor sells short the euro a share , thereby financing the purchase of a euro debt securities . i will , at maturity of the investment, r_0 pay a return on the shares that he sold short; debt securities will get a return, net of tax , equal to:

    \ frac { r_0 } {1 - \ tau_ \ mathrm { PB } ^ m } \ times (1 - \ tau_ \ mathrm { PB } ^ {i} ) > r_0

So the investor follows a strictly positive profit , with an initial investment invalid: it is a perfect example of arbitrage . On the one hand , if such arbitrage opportunities really exist, an investor in the conditions of the course would take positions " infinite" number of shares and debt securities in order to make a profit "infinite . "

But this made it impossible to balance the market for debt securities, so that the result of Miller , ultimately, may not hold true .

On the other hand , a realistic model should exclude the situation where you can not get something from nothing, as in the case of the exhibited here . In conclusion, if we admit the possibility of short selling, the model of Miller leads to paradoxical conclusions .

A line of criticism alternative sets out more general than those of Miller. An example is the case of a structure of taxation more sophisticated , in which it is possible to retrieve a result of optimality of the capital structure ( DeAngelo and Masulis , 1980), also removing the assumption of perfect information.

It is possible to obtain a preference for particular forms of business financing (this is the general conclusion of the theories of the pecking order Myers and Majluf (1984) ) .