﻿ Modigliani and Miller's Proposition That the Value of a Corporation is Independent of Its Capital Structure
San José State University
Department of Economics

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Thayer Watkins
Silicon Valley
USA

 Modigliani and Miller's Proposition That, in the Absence of Differential Taxes on Interest and Dividends, the Value of a Corporation is Independent of Its Capital Structure

Assume for now there are no taxes on profits. The rate of return on equity is a function of leverage; i.e.,

#### requity = rassets + (rassets - rdebt)D/E,

where D/E is the debt-equity ratio. If rassets > rdebt then an increase in leverage raises the rate of return on equity. But risk also increases with leverage according to the formula

#### βequity = βassets + (βassets - βdebt)D/E.

If debt is risk free (βdebt=0) then this formula reduces to

#### βequity = βassets(1 + D/E).

The equity value of the corporation is the discounted value of the future dividends generated by its operation, where the discount rate is established by the market taking into account its risk. The total value of the corporation is the discounted value of its future earnings.

The higher rate of return on equity is offset, at least to some extent, by the higher discount rate due to the higher risk. It is not clear that the offset is exact. Modigliani and Miller develop another argument to demonstrate that the higher leverage leaves the value of the corporation unchanged.

Imagine two corporation identical in every respect except that one is unleveraged and the other is leveraged. Both have the same earnings. The unleveraged corporation distributes all of its earnings as dividends. The leveraged corporation pays out some of its earnings as interest on its debt and distributes the remainder as dividends.

Now imagine an investor who is considering two portfolios. One portfolio is made up of one percent of the stock of the unleveraged corporation. This portfolio pays dividends equal to one percent of its earnings. The second portfolio contains one percent of the stock of the leveraged corporation and one percent of its debt. This portfolio pays dividends equal to one percent of the earnings less the interest on the debt plus one percent of the interest on the debt. This is equal to exactly one percent of the earnings since the interest on the debt exactly recapture the interest that was deducted from the earnings. Since, by assumption the two corporation have the same earnings, the two portfolios provide the exactly the same income. But the value of the two portfolios would have to be exactly the same if they provide exactly the same income. But both portfolios contain one percent of the value of their corporations so the total value of the corporations (debt + equity) must be exactly the same.

This proof worked because it was possible to undo the leveraging of the one corporation by buying up an equal share of its debt. Clearly the same construction would work if the leveraged corporation had a more complicated capital structure involving unsecured debt (debentures) as well as secured debt (bonds). It would still work if there were preferred stock involved as well as common stock. No matter how complicated the structure; e.g. involving warrants, convertible bonds, promissory notes or whatever; the same argument works.

The proof breaks down if there is a difference in the tax rate on dividends and interest.

For more on Modigliani and Miller's propositions see M&M.