What it means
Franco Modigliani and Merton Miller set out to test a widely held belief that companies could raise their value simply by borrowing cheaply. Their conclusion, published in the late 1950s, was that under idealised conditions the value of a business depends on the cash its assets generate, not on the mix of debt and equity used to fund them.
Proposition one states that the value of a levered company equals the value of an identical unlevered one. Proposition two explains why: as a company adds cheaper debt, the risk borne by the remaining shareholders rises, so the return they demand rises in exact proportion and the overall cost of capital stays flat.
The intuition is easier than the algebra. Think of a business as a fixed quantity of cash flow to be divided up, where cutting that quantity into different slices for lenders and shareholders does not change how much there is in total.
Modigliani and Miller later added corporate tax to the model, and that is where the picture shifts. Interest is tax deductible while dividends are not, so borrowing creates a tax shield that genuinely does add value, which in the pure model implies companies should borrow as much as they possibly can.
Real firms obviously do not borrow to the limit, and the gap between theory and behaviour is the useful part. Bankruptcy costs, the risk of financial distress, restrictive lending covenants and the signal that heavy borrowing sends to the market all push in the other direction, and the trade-off between those forces is what modern capital structure theory is built on.
In practice
Real-world examples.
Example
A finance director argues that swapping equity for debt at 5% will lift returns because the company's cost of equity is 14%. A colleague points to proposition two and notes that the remaining shareholders will simply demand more than 14% once the borrowing raises their risk.
Example
A private equity house evaluating a stable utility uses the tax shield extension to justify a heavier debt load, since predictable cash flows make financial distress unlikely and the deductible interest is worth real money.
Example
A high-growth technology firm with volatile revenue deliberately stays close to debt free. Its board accepts that it gives up the tax shield in exchange for surviving a bad quarter without breaching a covenant, which is precisely the real-world cost the original theorem assumed away.
Think of it
“Modigliani-Miller is like saying a pizza is worth the same whether you cut it into 6 or 8 slices. The total value doesn't change.
Formula
Calculation
Proposition two: cost of equity = unlevered cost of capital + (unlevered cost of capital - cost of debt) x (debt / equity)
With corporate tax, proposition one becomes: value of levered firm = value of unlevered firm + (tax rate x debt)
Take a company whose assets generate a 12% return, which is its cost of capital with no debt at all, and which can borrow at 6%. It moves to a structure that is half debt and half equity, so the debt to equity ratio is 1.0.
Cost of equity = 12% + (12% - 6%) x 1.0 = 12% + 6% = 18%. The weighted average cost of capital is then (0.5 x 18%) + (0.5 x 6%) = 9% + 3% = 12%, exactly where it started. The cheap debt bought no advantage, because shareholders repriced their risk from 12% to 18% to compensate.
Now add tax. If the unlevered business is worth $50,000,000, the corporate tax rate is 25% and it borrows $20,000,000, the levered value becomes $50,000,000 + (25% x $20,000,000) = $50,000,000 + $5,000,000 = $55,000,000. That $5,000,000 is the present value of the interest tax shield, and it is the one genuine gain from borrowing in the model.Case study
Seen in the real world.
What follows is an illustrative and fictional example. Alderman Ceramics, an invented manufacturer, had a board split over a proposal to buy back $30,000,000 of shares funded entirely with new borrowing at 6%, on the argument that replacing 15% equity with 6% debt must raise returns.
The finance director walked the board through proposition two. Using the company's 11% unlevered cost of capital, she showed that at the proposed debt to equity ratio the cost of equity would rise to roughly 17%, leaving the weighted average cost of capital essentially unchanged before tax effects.
She then quantified the honest arguments on both sides in this fictional scenario: an interest tax shield worth around $7,500,000 in present value at a 25% tax rate, set against a much tighter covenant and a business whose sales fell 30% in the last downturn. The board approved a $15,000,000 buyback instead of $30,000,000, taking part of the tax benefit while keeping headroom for a bad year.
Watch out
Common mistakes.
- Quoting the theorem as proof that capital structure never matters, while skipping the assumptions of no tax, no bankruptcy cost and perfect information.
- Comparing the cost of debt with the cost of equity directly and concluding that debt is simply cheaper, which ignores the way borrowing raises the return shareholders require.
- Applying the tax-adjusted version to a loss-making company, which has no taxable profit to shield and therefore gains nothing from the deduction.
Questions
People also ask.
If capital structure is irrelevant, why do finance teams spend so much time on it?
Because the assumptions fail in practice, and taxes, distress costs and covenants make the mix matter a great deal.
Does the theorem apply to private companies?
The logic does, though private firms face tighter borrowing limits and less liquid equity, so the practical trade-offs bite harder.
What is the single most useful takeaway for a non-specialist?
Value comes from the operating performance of the assets, so borrowing changes who bears the risk rather than creating something out of nothing.
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