Financial Management · Capital structure theories and practical considerations

Modigliani and Miller Theory Without Tax Explained

Updated 11 October 2026 · Fact-checked

Modigliani and Miller (MM) without tax says that in a perfect market a firm's value and WACC do not change with gearing. Proposition 1: Vg = Vu. Proposition 2: cost of equity rises with gearing to exactly offset the cheaper debt. To solve questions, use Ke = Keu + (Keu − Kd) × D/E.

Understand Modigliani and Miller Without Taxes

Capital structure theory asks one question: can a company lower its cost of capital, and so raise its value, by changing the mix of debt and equity? MM gave the first clear answer. In a perfect world, no.

The idea is simple. A company's value comes from the earnings its assets produce, not from how those earnings are split between lenders and shareholders. Think of a pizza. Cutting it into different slices does not change how much pizza you have. Debt and equity are just different slices of the same operating earnings.

This works because of the assumptions:

Perfect capital markets, with no transaction costs and full information.
No taxes (this is the 'without tax' version).
No bankruptcy or financial distress costs.
Individuals and companies borrow at the same risk-free rate.
Debt is risk-free, or its risk is accounted for in the cost of debt.
Earnings are constant, with no growth and all earnings paid out as dividends.

Proposition 1: the value of a geared company equals the value of an otherwise identical ungeared company. So WACC is the same at every level of gearing. If two firms had different values, investors could make a risk-free profit by trading between them (arbitrage). That pushes prices back to equal.

Proposition 2: debt is cheaper than equity, so you might expect WACC to fall as you add debt. It does not. More debt makes shareholders' returns riskier (financial risk), so they demand a higher return. The rise in the cost of equity exactly cancels the saving from cheaper debt. WACC stays flat. The cost of equity rises in a straight line with the debt to equity ratio.

In ACCA FM this is the base case. You then relax the assumptions, first by adding tax (where debt becomes attractive) and then by adding distress costs and other practical factors.

Key rules to remember

Proposition 1 (value): Vg = Vu = Earnings before interest ÷ Keu; Valid with no tax and constant earnings. Vg is geared value, Vu is ungeared value, Keu is the cost of equity of the ungeared firm.
Proposition 2 (cost of equity): Keg = Keu + (Keu − Kd) × (Vd ÷ Ve); Vd and Ve are market values of debt and equity. Kd is the pre-tax cost of debt. No tax term appears because there is no tax.
WACC under MM without tax: WACC = Keu at every level of gearing; Check: WACC = Keg × Ve/(Ve+Vd) + Kd × Vd/(Ve+Vd) gives Keu.
Value of the geared firm: Vg = Ve + Vd; So Ve = Vu − Vd if you are asked for the equity value after debt is introduced.

How to solve Modigliani and Miller Without Taxes questions

Use this method for any MM-without-tax question. It works for calculation and for discussion requirements.

1Check the assumptions given. Confirm there is no tax and a perfect market. If tax is mentioned, you need the MM with tax version instead.
2Identify what you are given: ungeared cost of equity (Keu), cost of debt (Kd), market values of debt and equity, or earnings.
3Find the ungeared value: Vu = earnings ÷ Keu. This is also the geared value under Proposition 1.
4Find the equity value of the geared firm: Ve = Vu − Vd.
5Find the geared cost of equity using Keg = Keu + (Keu − Kd) × Vd/Ve.
6Check by calculating WACC. It must equal Keu. If it does not, you have an error.
7Interpret the result. State that WACC and value are unchanged, and that the cost of equity rises to reflect higher financial risk.
8If asked to discuss, name the assumptions and say why real markets differ, for example taxes and distress costs.

Quickest way: Shortcut using the flat WACC

When to use it: Use when the question asks for the cost of equity or the WACC of a geared firm and gives Keu, Kd and the gearing ratio.

Write down WACC = Keu. No calculation is needed for WACC.
For Keg, use Keu + (Keu − Kd) × D/E. Use the ratio D:E directly if given.
Quick check: Keg must be above Keu, and above Kd. If Kd is above Keu, you have mixed something up.
Do the WACC check only if time allows. It confirms your answer and takes one line.

Common mistakes in Modigliani and Miller Without Taxes

Saying WACC falls as debt is added because debt is cheaper.
Students remember that debt is cheaper than equity and stop there.
Fix: Add the second half: Ke rises to compensate for financial risk. Under MM without tax the two effects cancel and WACC is flat.
Using book values of debt and equity in the Ke formula.
Balance sheet figures are easier to find.
Fix: Use market values. MM works with market values of Vd and Ve.
Including a (1 − t) term when the question says no tax.
Students copy the with-tax formula from memory.
Fix: Read the requirement first. No tax means the formula is Keu + (Keu − Kd) × Vd/Ve with no tax adjustment.
Using Vd/(Vd + Ve) instead of Vd/Ve in Proposition 2.
It looks like the weights used in WACC.
Fix: Proposition 2 uses the debt to equity ratio, Vd/Ve. Weights with (Vd + Ve) are only for WACC.
Forgetting to deduct debt from firm value to get equity value.
Students keep the ungeared value as the equity value after borrowing.
Fix: Ve = Vg − Vd. Total value stays the same, but equity is only part of it.
Treating MM as a statement about the real world.
Students forget it rests on unrealistic assumptions.
Fix: In discussion, say it is a theoretical benchmark. Real firms face taxes, distress costs and imperfect markets.

Worked examples

Example 1

Company A is ungeared with annual earnings of $600,000 (constant, all paid out) and a cost of equity of 12%. It then issues $2,000,000 of debt at 6% and uses the proceeds to buy back shares. Assume MM without tax. Calculate the value of the geared company, the value of its equity, its cost of equity and its WACC.

Show the solution

Ungeared value Vu = 600,000 ÷ 0.12 = $5,000,000.
Under Proposition 1, geared value Vg = $5,000,000.
Equity value Ve = 5,000,000 − 2,000,000 = $3,000,000.
Keg = 12% + (12% − 6%) × 2,000,000/3,000,000 = 12% + 6% × 0.6667 = 12% + 4% = 16%.
WACC check: Ke × Ve/V = 16% × 3/5 = 9.6%. Kd × Vd/V = 6% × 2/5 = 2.4%. Total = 12.0%.

Answer: Geared value $5,000,000; equity value $3,000,000; cost of equity 16%; WACC 12%, unchanged from the ungeared level.

Example 2

Company B is geared with market value of equity $8m and debt $4m. Its cost of equity is 15% and its pre-tax cost of debt is 6%. Assume MM without tax. Calculate its WACC, and the cost of equity it would have if it became ungeared.

Show the solution

Total value V = 8 + 4 = $12m.
Equity weight = 8/12 = 0.6667. Debt weight = 4/12 = 0.3333.
WACC = 15% × 0.6667 + 6% × 0.3333 = 10% + 2% = 12%.
Under MM, WACC equals Keu, so the ungeared cost of equity is 12%.
Check using Proposition 2: 12% + (12% − 6%) × 4/8 = 12% + 3% = 15%. This matches the given Ke.

Answer: WACC is 12%, and the ungeared cost of equity is also 12%.

Exam tips

Look for the words 'no tax' or 'perfect market' in the scenario. They tell you to use the simple MM formulas.
In objective test questions, the common trap options are 'WACC falls' or 'WACC rises'. Under MM without tax, WACC stays constant and Ke rises.
In constructed response, show the formula, then the numbers, then one sentence of interpretation. The interpretation often earns a mark.
When asked to evaluate MM, list the assumptions and give a real-world limit for each, such as taxes, bankruptcy costs and different borrowing rates.
Do the WACC check at the end of a calculation. It is quick and catches arithmetic slips.

Practice questions from Capital structure theories and practical considerations

Modigliani and Miller Without Taxes in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Modigliani and Miller Without Taxes: frequently asked questions

What does MM without tax say about capital structure?

It says capital structure is irrelevant in a perfect market. Firm value and WACC stay the same at any level of gearing. Only the earnings from assets matter.

How does the cost of equity change with gearing under MM?

It rises in a straight line with the debt to equity ratio. Shareholders face more financial risk, so they want a higher return. This offsets the cheaper debt and keeps WACC constant.

What are the main assumptions of MM without tax?

Perfect capital markets, no taxes, no bankruptcy or distress costs, equal borrowing rates for individuals and firms, and constant earnings. Real markets break these, which is why the theory is a benchmark.

Is MM without tax the same as the traditional view?

No. The traditional view says WACC falls at moderate gearing, reaches a minimum, then rises, so an optimal structure exists. MM without tax says WACC is flat and no optimal structure exists.