The Modigliani–Miller Theorem: Why the Share of Debt Does Not Create Value by Itself

The Modigliani–Miller theorem states that in a world with no taxes, no bankruptcy costs and equal access to borrowed money for all participants, a company's value is determined by its operating assets, not by the proportion in which those assets are financed with debt and equity. Shifting the financing from shares to loans does not make the business worth more — it merely redistributes the same cash flow among the holders of different claims on it. Hence the everyday version: however you slice the pie, the pie does not get any bigger.

What exactly is claimed, and what is not

The theorem, published by Franco Modigliani and Merton Miller in 1958, has two layers of meaning, and they are regularly confused.

The claim about firm value: the market valuation of a company with debt and of a company without debt must be the same if their operating cash flows are identical. The structure of liabilities is neutral.

The claim about the cost of capital: as the share of debt rises, the required return on equity rises too — by exactly as much as is needed to keep the weighted average cost of capital (WACC) unchanged. Cheap debt does not make financing cheaper overall, because it makes the shareholder's residual claim riskier. A shareholder in a highly leveraged company receives a cash flow from which the mandatory payments have already been deducted, and that flow is more volatile.

What the theorem does not claim: that debt is harmless, that a chief financial officer need not think about the liability side, or that leverage has no effect on risk. It claims something narrower and more useful — that under ideal conditions the source of value lies in operations, and that if you see value being added by a mere reshuffle of liabilities, you should look for which of the ideal conditions has been violated.

The mechanics of the proof: arbitrage on the investor's side

The logic rests not on accounting but on the ability of a private investor to replicate any capital structure independently. If a company with debt trades at a higher valuation than a comparable company without debt, the investor borrows on their own account, buys shares in the unlevered company and obtains the same risk and return profile for less. If it is the other way round, the investor buys shares in the heavily indebted company and holds bonds alongside them, offsetting the leverage at the level of their own portfolio. Trades of this kind drive the difference in valuations to zero.

This is where the key assumption is hidden: the investor must be able to borrow on the same terms as the corporation, and without limits. As soon as the rates available to an individual and to an issuer diverge, arbitrage is no longer free, and the neutrality of capital structure breaks down.

Taxes: the 1963 correction

In the 1963 version the authors introduced corporate tax. Interest on debt is deducted from the taxable base; dividends are not. A tax shield arises: part of the cash flow that used to go to the state now goes to investors. In this model the value of a company with debt exceeds the value of a company without debt by the present value of the shield, and the formal conclusion sounds absurd — the optimal structure consists almost entirely of debt.

{{callout:warning}}The tax shield works only when taxable profit is positive. A company with a loss or with large accumulated deductions services its debt with real cash but gets no tax saving — in that situation the shield exists on paper and does not exist in the till.{{/callout}}

Miller later added taxation at the level of the income recipient, and the gain from the shield largely dissolved. This is how the debate arrived at the trade-off theory: the optimum lies where the marginal benefit of the shield is balanced by the marginal expected costs of financial distress — more expensive borrowing, the loss of suppliers and customers, forced asset sales, and conflict between creditors and shareholders.

Dividends: the same logic, a different angle

In their 1961 paper the authors applied the same arbitrage argument to dividend policy: under ideal conditions an investor is indifferent between receiving cash as a payout and receiving it by selling part of a shareholding that has risen in price. Whatever schedule of cash receipts they need, they can create it themselves. The real-world importance of dividends rests on what the model leaves out — taxes, transaction costs and the signalling function of a payout. The practical side of the question is conveniently covered in the dividends section and in the payout calendar.

How to read the theorem when analysing a specific security

For the practitioner, the theorem's value is diagnostic. It tells you which question to ask.

Step 1. Separate the operating result from the financial result. Revenue, margins and turnover determine the size of the pie; interest expense only determines how it is divided. The source data come from issuers' financial statements.

Step 2. Remember that equity multiples already contain the effect of leverage. The 3,78 figure for {{instrument:SBER}} describes the shareholder's residual claim, not the value of the whole business. That is why companies with different debt loads are more properly compared on enterprise value multiples (EV/EBITDA), where debt and cash are accounted for explicitly. Comparable securities can be found in the list of stocks.

Step 3. Check the price of debt on the creditor's side. The yields on the issuer's own bonds in the bonds section and the OFZ curve as a benchmark for the risk-free rate show how safe the market considers this leverage to be. A widening spread is a sign that the costs of financial distress are no longer theoretical.

Step 4. Look for the violated assumption. If management explains a rise in value by refinancing, ask what specifically has changed: the tax base, the interest rate, the maturity, the currency of the liabilities, access to the capital market. The neutrality of capital structure is broken through precisely these channels, and each of them can be checked.

Definitions of the terms used in this analysis are collected in the glossary.

The limits of this article

This article sets out the logic of the theorem itself and its standard extensions. Numerical estimates of the tax shield, of threshold levels of debt load or of sector leverage norms for the Russian market are not available in the platform's source data, and quoting them from memory would be speculation. If a calculation is needed for a specific issuer, it should be built on that issuer's own financial statements and the actual cost of its liabilities.