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Financial Management · Capital structure theories and practical considerations

Modigliani and Miller With Corporate Tax Explained

Updated 11 October 2026 · Fact-checked

MM with tax says debt raises firm value because interest is tax deductible. The geared firm's value is Vg = Vu + Dt, where Vu is the ungeared value, D is permanent debt and t is the tax rate. WACC falls as gearing rises, so theory suggests almost 100% debt.

Understand Modigliani and Miller With Corporate Tax

Start with the no-tax version of Modigliani and Miller (MM). Without tax, the value of a firm depends on its business risk and cash flows, not on how it is financed. Gearing raises the cost of equity, but that exactly cancels the benefit of cheaper debt, so WACC does not change.

Now add corporate tax. Interest on debt is a tax-deductible expense. Dividends are not. So a geared company pays less tax than an identical ungeared company with the same operating profit. The saving each year is interest × tax rate. This is the tax shield on debt.

MM treat debt as permanent (irredeemable) and risk-free. The tax saving is then a perpetuity of D × interest rate × t each year. Discounted at the cost of debt, its present value is D × t. That is why the value of the geared firm is the ungeared value plus Dt.

The cost of equity still rises with gearing, but it rises by less than in the no-tax case. The tax benefit is not fully offset. So WACC falls steadily as gearing increases. Taken literally, the best capital structure is almost 100% debt.

Real companies do not do this. Higher debt brings bankruptcy costs, agency costs (lenders add restrictive covenants), and financial distress costs. Tax exhaustion also matters: if profits are too low to use the interest deduction, there is no shield. Lenders also charge higher rates as risk grows, and personal taxes on investors can reduce the benefit. So the model shows the direction of the tax effect, not a practical target.

Key rules to remember

Value of geared company
Vg = Vu + D × t
Assumes permanent debt D and tax rate t. Dt is the present value of the tax shield.
Value of ungeared company
Vu = Earnings before interest and tax × (1 − t) ÷ Keu
Keu is the cost of equity of the ungeared company. Assumes constant perpetual earnings.
Annual tax shield
Annual tax saving = D × Kd × t
Interest is D × Kd. Discounting this perpetuity at Kd gives D × t.
Cost of equity of geared company
Keg = Keu + (Keu − Kd) × (1 − t) × D ÷ E
E is the market value of equity of the geared company. Kd is the pre-tax cost of debt.
WACC of geared company
WACC = Keu × (1 − D × t ÷ (D + E))
Here D + E = Vg. WACC is below Keu whenever there is debt and tax.
Market value of equity
E = Vg − D
Use after finding Vg.

How to solve Modigliani and Miller With Corporate Tax questions

Use this order for any MM with tax question. Check the assumptions given: perpetual earnings, permanent debt, risk-free debt.

  1. 1Note the tax rate t, the earnings before interest and tax, the debt D, and the cost of debt Kd.
  2. 2Find the ungeared value: Vu = EBIT × (1 − t) ÷ Keu. If Vu is given, use it.
  3. 3Calculate the tax shield: D × t.
  4. 4Find the geared value: Vg = Vu + Dt.
  5. 5Find the market value of equity: E = Vg − D.
  6. 6If asked for the cost of equity, use Keg = Keu + (Keu − Kd)(1 − t) × D ÷ E, with E from step 5.
  7. 7If asked for WACC, use Keu × (1 − Dt ÷ Vg), or weight Keg and Kd(1 − t) by E and D as a check.
  8. 8Comment briefly on limits if the question asks: bankruptcy costs, agency costs, tax exhaustion, and other real-world factors.

Quickest way: Shortcut: Vu plus Dt, then WACC formula

When to use it: Use this for Section A and Section B objective questions, where you only need the geared value, the change in value or WACC.

  1. Change in value from issuing debt to buy back shares = D × t. You do not need to recompute Vu.
  2. If asked for Vg, add D × t to Vu.
  3. If asked for WACC, use Keu × (1 − Dt ÷ Vg). This avoids finding Keg.
  4. Sense check: Vg must be greater than Vu, and WACC must be lower than Keu.

Common mistakes in Modigliani and Miller With Corporate Tax

  • Using Vg = Vu + D instead of Vu + Dt.

    Students forget that only the tax saving adds value, not the debt itself.

    Fix: Always multiply the debt by the tax rate. Write t next to D before calculating.

  • Forgetting to deduct tax when finding Vu.

    The no-tax formula Vu = EBIT ÷ Keu is more familiar.

    Fix: Use EBIT × (1 − t) ÷ Keu in a tax question. The earnings must be after tax.

  • Using the geared value as the equity value when finding Keg.

    The word value is used for both Vg and E.

    Fix: Compute E = Vg − D first, then use E in the D ÷ E ratio.

  • Applying the tax rate to Kd twice or not at all in WACC.

    Students mix the MM formulas with the standard WACC formula.

    Fix: In the standard weighted method use Kd(1 − t). In the MM shortcut WACC formula the tax effect is already inside Dt ÷ Vg.

  • Concluding that firms should use 100% debt and stopping there.

    The model result looks like a recommendation.

    Fix: State that the model ignores bankruptcy costs, agency costs, tax exhaustion and rising cost of debt, so the optimum is lower.

  • Treating the model's perpetual debt assumption as irrelevant.

    Students apply Dt to debt that is redeemed soon.

    Fix: Use Dt only when debt is permanent. Otherwise the shield would be worth less than Dt.

Worked examples

Example 1

Company X is ungeared and expects annual earnings before interest and tax of $600,000 in perpetuity. Corporate tax is 30% and the ungeared cost of equity is 12%. The company issues $1,000,000 of permanent debt and uses it to buy back shares. Calculate the value of the company before and after the debt issue.

Show the solution
  1. Earnings after tax = 600,000 × (1 − 0.30) = $420,000.
  2. Vu = 420,000 ÷ 0.12 = $3,500,000.
  3. Tax shield = D × t = 1,000,000 × 0.30 = $300,000.
  4. Vg = 3,500,000 + 300,000 = $3,800,000.

Answer: The value is $3,500,000 before and $3,800,000 after the debt issue, an increase of $300,000.

Example 2

Using the data from the previous question, the cost of debt is 6%. Calculate the market value of equity after the debt issue, the cost of equity of the geared company, and the WACC.

Show the solution
  1. E = Vg − D = 3,800,000 − 1,000,000 = $2,800,000.
  2. D ÷ E = 1,000,000 ÷ 2,800,000 = 0.35714.
  3. Keg = 0.12 + (0.12 − 0.06) × (1 − 0.30) × 0.35714 = 0.12 + 0.06 × 0.70 × 0.35714.
  4. 0.06 × 0.70 = 0.042; 0.042 × 0.35714 = 0.015.
  5. Keg = 0.12 + 0.015 = 13.5%.
  6. WACC = 0.12 × (1 − 300,000 ÷ 3,800,000) = 0.12 × (1 − 0.078947) = 0.12 × 0.921053 = 11.05%.
  7. Check: E weight = 2,800,000 ÷ 3,800,000 = 0.73684; D weight = 0.26316. WACC = 0.73684 × 13.5% + 0.26316 × 6% × 0.70 = 9.947% + 1.105% = 11.05%.

Answer: Equity value is $2,800,000, the cost of equity rises to 13.5%, and WACC falls from 12% to about 11.05%.

Exam tips

  • Read for the assumptions: perpetual earnings and permanent debt. If they are missing, say so in written answers and apply the formula as an approximation.
  • In objective questions, check that your answer for Vg is larger than Vu and your WACC is lower than Keu. Wrong answers score zero, so a quick check is worth the time.
  • In constructed response questions, show Vu, Dt and Vg on separate lines. Method marks are given for clear workings.
  • Be ready to discuss why the theory fails in practice. Name at least three limits: bankruptcy costs, agency costs, tax exhaustion and the higher cost of debt at high gearing.
  • Compare with MM without tax. Without tax, WACC is constant and value is unchanged by gearing. With tax, WACC falls as gearing rises.

Practice questions from Capital structure theories and practical considerations

Modigliani and Miller With Corporate Tax 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 With Corporate Tax: frequently asked questions

What is the formula for the value of a geared company with tax?

Vg = Vu + Dt. Vu is the value of the same company if ungeared, D is the market value of permanent debt and t is the corporate tax rate. Dt is the present value of the tax shield.

Why does WACC fall as gearing rises in MM with tax?

Debt gets a tax deduction on its interest, so the after-tax cost of debt is lower. The cost of equity still rises, but by less than the benefit. The net result is a falling WACC.

Does MM with tax mean a company should use 100% debt?

The theory implies it, but it is not realistic. Bankruptcy costs, agency costs, lenders' higher rates and the risk of not having enough profit to use the shield all limit gearing. In practice firms aim for a balance.

How is MM with tax different from MM without tax?

Without tax, firm value and WACC do not change with gearing. With corporate tax, value rises by Dt and WACC falls as gearing increases.