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Finance 1958

The Cost of Capital, Corporation Finance and the Theory of Investment

Franco Modigliani & Merton H. Miller

How you finance a firm — debt or equity — doesn't change what it is worth.

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In depth · the introduction

Does a company become more valuable by borrowing some of its money instead of selling all of it as shares? Two economists proved that, in a perfect market, the answer is a flat no.

The big idea

A firm is worth whatever its assets are expected to earn. How it pays for those assets — by selling shares, by borrowing, or any blend — just slices the same pie differently among investors. Franco Modigliani and Merton Miller showed in 1958 that, in a market without taxes or other frictions, those slices can never add up to more (or less) than the whole pie. Borrowing looks cheap, but the cheapness is exactly cancelled by the extra risk it dumps on the remaining shareholders.

How it came about

In the 1950s most experts believed every firm had an ideal amount of debt — enough cheap borrowing to minimise its cost of capital and maximise its value. Modigliani, an economist, and Miller, a finance scholar, both at Carnegie Tech in Pittsburgh, attacked the problem with a tool from pure economics: arbitrage. If a levered firm were really worth more than an identical unlevered one, you could copy the levered firm's returns yourself by borrowing a little on your own account, buy the cheaper firm, and make free money. Since free money can't last, the two firms must be worth the same. The argument was so clean it was almost annoying — and it was right.

Why it mattered

It turned a fuzzy practical question into a sharp theorem, and gave finance a benchmark it had never had. Once you know that financing is irrelevant in a frictionless world, you can ask the productive question: which friction makes it relevant here? Taxes (interest is deductible, so debt earns a tax break)? The danger of bankruptcy (too much debt and a bad year sinks you)? Mistrust between managers and investors? Every real rule of thumb about how much to borrow is now understood as one of these deviations from MM.

An everyday picture

Merton Miller liked to explain it with a pizza. A whole pizza is the firm. You can cut it into two big slices or eight small ones, hand some slices to lenders and some to shareholders — but no way of cutting gives you more pizza. The size of the pie is set by the dough, not the knife. Debt and equity are just different-shaped slices of the same fixed amount of dinner.

A panel where a slider adds debt to a firm. A bar on the left, split into equity and debt, keeps the same total height however the split changes. A chart on the right shows the shareholders' required return rising in a straight line as debt grows, while the firm's average cost of capital stays perfectly flat.

Where it sits in the story

Modigliani–Miller is one of the founding stones of modern finance, laid in the same decade as Markowitz's diversified portfolio (1952) and a generation before Black–Scholes priced options (1973) — both also in this Library — all sharing one engine: in a market where free money is impossible, prices line up by no-arbitrage. Both authors later received the Nobel Memorial Prize. Every finance course still opens here, because you cannot understand why debt matters until you understand the world in which it wouldn't.

The original document
Original source text
Franco Modigliani & Merton H. Miller · The American Economic Review 48(3): 261–297 · June 1958
The question
A firm can raise the money to buy its assets by issuing shares (equity) or by borrowing (debt), in any mix it likes. The reigning view held that there was an optimal mix — some debt is cheap, so a little leverage should lower the overall cost of capital and raise the firm's value. Modigliani and Miller asked whether that is actually true in a market where investors can borrow and lend on the same terms as firms.
Proposition I
…the market value of any firm is independent of its capital structure and is given by capitalizing its expected return at the rate ρ_k appropriate to its class.
The proof is an arbitrage argument. If two firms with the same expected earnings sold for different prices merely because one was levered and the other not, an investor could replicate the levered firm's payoff by borrowing on personal account (homemade leverage), buy the cheaper firm, and pocket a riskless profit. Such trades would erase the price gap. It follows that the weighted average cost of capital is the same whatever the debt–equity mix.
Proposition II
If the average cost of capital is fixed, then loading on cheap debt cannot be a free lunch: the expected return that the remaining shareholders demand must rise just enough to offset it. Proposition II states this precisely — the cost of equity equals the pure-equity rate ρ_k plus a risk premium equal to the debt-to-equity ratio times the spread between ρ_k and the interest rate. The two movements cancel, and the average cost of capital stays flat.
What is assumed away
The result lives in a frictionless world: no taxes, no bankruptcy or distress costs, no asymmetric information, and firms and investors borrowing at the same rate. The authors knew these were idealisations; the value of the theorem is as a benchmark. In a 1963 correction the same authors added the corporate income tax, under which interest is deductible — a tax shield that does make leverage raise value, up to the point where distress costs begin to bite.
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Carnegie Institute of Technology · 1958