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Financial Management and Business Data Analytics · Capital Structure and Capital Stacking

Theories of Capital Structure: NI, NOI, Traditional and MM

Updated 10 October 2026 · Fact-checked

Capital structure theories explain how the mix of debt and equity affects the cost of capital and firm value. The NI approach says debt raises value. The NOI approach says value is unaffected. The Traditional approach finds an optimal range. Modigliani-Miller says value is unaffected without taxes and rises by tax × debt with taxes.

Understand Theories of Capital Structure

Capital structure is the mix of debt and equity a firm uses. The big question is simple: if the firm borrows more, does its value go up, go down, or stay the same? Four theories answer this differently. The difference comes from what each theory assumes about the cost of equity (Ke) and the overall cost of capital (Ko).

The Net Income (NI) approach assumes Ke and the cost of debt (Kd) stay constant as debt rises. Debt is cheaper than equity, so the weighted cost Ko falls and value rises. Value = equity value + debt value, where equity value = Net Income ÷ Ke. The logical end point is 100% debt.

The Net Operating Income (NOI) approach assumes Ko is constant and Kd is constant. Cheap debt is offset because shareholders see more financial risk and demand a higher Ke. Value = EBIT ÷ Ko, so value does not depend on leverage. No capital structure is optimal.

The Traditional approach sits in between. Up to a point, debt is cheap and Ke rises only slowly, so Ko falls. After that, Ke rises faster and Kd also rises, so Ko starts to climb. Ko is lowest, and value highest, at an optimal range of leverage.

Modigliani-Miller (MM) gives a rigorous version of NOI. Without taxes, assuming perfect markets, value is the same for levered and unlevered firms (Proposition I), and Ke rises linearly with the debt-equity ratio (Proposition II). The argument rests on arbitrage: investors can create their own leverage, so the firm cannot add value by borrowing. With corporate tax, interest saves tax, so a levered firm is worth more by the present value of the tax shield, which is tax rate × debt when debt is perpetual.

Key rules to remember

Value of firm (general)
V = S + D
S = market value of equity, D = market value of debt.
NI approach: equity value
S = (EBIT − Interest) ÷ Ke; Ko = EBIT ÷ V
Ke and Kd constant. Ko falls as D rises. This is the no-tax form, so the weighted average of Ke and Kd equals Ko. With tax, use after-tax Kd: Ko = Ke × S ÷ V + Kd × (1 − t) × D ÷ V.
NOI approach: firm value
V = EBIT ÷ Ko; S = V − D
Ko and Kd constant. Value does not change with leverage.
NOI approach: cost of equity
Ke = Ko + (Ko − Kd) × (D ÷ S)
Ke rises linearly with D/S. Equivalent to Ke = (EBIT − Interest) ÷ S. This equivalence holds in the no-tax setting.
MM Proposition I (no tax)
V(levered) = V(unlevered) = EBIT ÷ Ko
Holds under perfect markets, no taxes, same risk class and riskless debt.
MM Proposition II (no tax)
Ke = Ku + (Ku − Kd) × (D ÷ E)
Ku = cost of equity of the unlevered firm. Ko stays equal to Ku.
MM Proposition I (with tax)
V(levered) = V(unlevered) + t × D
t = corporate tax rate. Assumes perpetual debt. t × D is the value of the interest tax shield.
MM Proposition II (with tax)
Ke = Ku + (Ku − Kd) × (1 − t) × (D ÷ E)
Ke rises more slowly than without tax.
WACC with tax (MM)
Ko = Ku × (1 − t × D ÷ V); also Ko = Ke × S ÷ V + Kd × (1 − t) × D ÷ V
Ko falls as leverage rises, so the optimum under MM with tax is the maximum debt. The weighted-average check must use after-tax Kd.
Unlevered value with tax
V(unlevered) = EBIT × (1 − t) ÷ Ku
Used as the base in the with-tax proposition.

How to solve Theories of Capital Structure questions

Every numerical on this topic follows the same pattern. Identify the theory, fix what is constant, then derive value and costs in the right order.

  1. 1Identify the theory named in the question: NI, NOI, Traditional or MM (with or without tax).
  2. 2Write down what is constant in that theory: Ke and Kd for NI, Ko and Kd for NOI, Ku and tax shield for MM with tax.
  3. 3Compute the interest (D × Kd) and, if needed, net income (EBIT − interest, less tax for MM with tax).
  4. 4Find the value: S = NI ÷ Ke then V = S + D for NI; V = EBIT ÷ Ko for NOI; V = V(U) + tD for MM with tax.
  5. 5Find the remaining quantity: Ko = EBIT ÷ V for NI; S = V − D and Ke for NOI; Ke by Proposition II for MM.
  6. 6Cross-check: Ke × S should equal net income. Also check the weighted average. Without tax, Ko = Ke × S ÷ V + Kd × D ÷ V. With tax, use after-tax Kd: Ko = Ke × S ÷ V + Kd × (1 − t) × D ÷ V.
  7. 7Compare options if asked, and state the conclusion: which structure gives the lowest Ko or highest value, and why.
  8. 8Write assumptions or the theory's conclusion in one line at the end.

Quickest way: Constant-and-solve shortcut

When to use it: Use for numerical questions asking Ko, Ke or value at one or more debt levels.

  1. Under NI, calculate S first, then V, then Ko = EBIT ÷ V.
  2. Under NOI, calculate V = EBIT ÷ Ko first, then S = V − D, then Ke = (EBIT − interest) ÷ S.
  3. Under MM with tax, calculate V(U) first, add t × D, then S = V − D, then Ke from NI ÷ S.
  4. Verify with the weighted average. Without tax, use Kd. With tax, use after-tax Kd, Kd × (1 − t), and the net income after tax for Ke. If it does not match Ko, you have an arithmetic or setup error.
  5. For theory questions, recall one line each: NI value rises, NOI value constant, Traditional optimal range, MM no tax irrelevance, MM with tax gain of tD.

Common mistakes in Theories of Capital Structure

  • Treating Ko as constant in the NI approach, or Ke as constant in the NOI approach.

    Students mix up which cost is fixed in which theory.

    Fix: Memorise: NI fixes Ke and Kd; NOI fixes Ko and Kd. Write this beside the solution before starting.

  • Using EBIT instead of net income to value equity in the NI approach.

    Students apply the NOI formula to every question.

    Fix: In NI, S = (EBIT − interest) ÷ Ke. EBIT ÷ Ko gives total firm value only in NOI.

  • Forgetting to subtract debt from V to get equity value in the NOI approach.

    V = EBIT ÷ Ko is the total value, but students treat it as equity.

    Fix: Always follow it with S = V − D before computing Ke.

  • Ignoring the (1 − t) factor in MM Proposition II with tax, or using t × D with non-perpetual debt.

    Students copy the no-tax formula or forget the perpetual-debt assumption.

    Fix: Use Ke = Ku + (Ku − Kd)(1 − t)(D ÷ E), and state that t × D assumes permanent debt.

  • Using pre-tax Kd in the weighted-average cross-check when tax is present.

    Students reuse the no-tax check, but interest saves tax, so the effective cost of debt is Kd × (1 − t).

    Fix: With tax, check Ko = Ke × S ÷ V + Kd × (1 − t) × D ÷ V, and take Ke from net income after tax.

  • Using book values of debt and equity in the weighted average check.

    Students carry book values from the balance sheet.

    Fix: Use market values: S from the theory's formula and D at its market value.

  • Saying the Traditional approach gives a single exact optimum with a formula.

    Students assume every theory is as precise as MM.

    Fix: Describe it as a U-shaped Ko curve with an optimal range where Ko is lowest. Questions usually give a table of Ke, Kd and ask you to compute Ko at each level.

Worked examples

Example 1

A firm has EBIT of ₹10,00,000 and ₹20,00,000 of 10% debt. (a) Under the NI approach, Ke is 15%. Find the value of the firm and Ko. (b) Under the NOI approach, Ko is 12%. Find the value of the firm and Ke.

Show the solution
  1. (a) Interest = 10% × ₹20,00,000 = ₹2,00,000.
  2. Net income = ₹10,00,000 − ₹2,00,000 = ₹8,00,000.
  3. Equity value S = ₹8,00,000 ÷ 0.15 = ₹53,33,333.
  4. V = S + D = ₹53,33,333 + ₹20,00,000 = ₹73,33,333.
  5. Ko = EBIT ÷ V = ₹10,00,000 ÷ ₹73,33,333 = 13.64%.
  6. (b) V = EBIT ÷ Ko = ₹10,00,000 ÷ 0.12 = ₹83,33,333.
  7. S = V − D = ₹83,33,333 − ₹20,00,000 = ₹63,33,333.
  8. Ke = ₹8,00,000 ÷ ₹63,33,333 = 12.63%.
  9. Check with the formula: Ke = 12% + (12% − 10%) × (20,00,000 ÷ 63,33,333) = 12% + 0.63% = 12.63%.

Answer: NI approach: V = ₹73,33,333 and Ko = 13.64%. NOI approach: V = ₹83,33,333 and Ke = 12.63%.

Example 2

An unlevered firm has EBIT of ₹12,00,000, Ku of 15% and a tax rate of 25%. Using MM with corporate tax, find the value of a levered firm with ₹20,00,000 of perpetual 10% debt, its cost of equity, and its WACC.

Show the solution
  1. Value of the unlevered firm = EBIT × (1 − t) ÷ Ku = ₹12,00,000 × 0.75 ÷ 0.15 = ₹9,00,000 ÷ 0.15 = ₹60,00,000.
  2. Tax shield = t × D = 0.25 × ₹20,00,000 = ₹5,00,000.
  3. Value of the levered firm V = ₹60,00,000 + ₹5,00,000 = ₹65,00,000.
  4. Equity E = V − D = ₹65,00,000 − ₹20,00,000 = ₹45,00,000.
  5. Ke = 15% + (15% − 10%) × (1 − 0.25) × (20,00,000 ÷ 45,00,000) = 15% + 5% × 0.75 × 0.4444 = 16.67%.
  6. Check: interest = ₹2,00,000; EBT = ₹10,00,000; tax = ₹2,50,000; net income = ₹7,50,000; ₹7,50,000 ÷ ₹45,00,000 = 16.67%.
  7. WACC = Ku × (1 − t × D ÷ V) = 15% × (1 − 5,00,000 ÷ 65,00,000) = 15% × 0.92308 = 13.85%.
  8. Check with after-tax Kd: 16.67% × (45 ÷ 65) + 10% × (1 − 0.25) × (20 ÷ 65) = 11.54% + 2.31% = 13.85%.

Answer: V(levered) = ₹65,00,000; Ke = 16.67%; WACC = 13.85%. Borrowing adds ₹5,00,000 of value through the interest tax shield.

Exam tips

  • In MCQs, identify the theory from one phrase: Ko constant means NOI or MM without tax; value rises with debt means NI or MM with tax.
  • In numericals, write the theory's assumption in the first line. Examiners give step marks for stating what is constant.
  • For comparison questions, a short table of V, Ke and Ko at each debt level makes the pattern clear and earns presentation marks.
  • In theory answers, include the assumptions of MM: perfect capital markets, no taxes (in the base case), same risk class, riskless debt, no transaction costs and full payout.
  • Always end with a conclusion such as optimal structure under each theory; a numerical answer without interpretation loses marks.

Practice questions from Capital Structure and Capital Stacking

Theories of Capital Structure in other exams

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

Theories of Capital Structure: frequently asked questions

What is the difference between the NI and NOI approach?

The NI approach keeps Ke and Kd constant, so more debt lowers Ko and raises value. The NOI approach keeps Ko constant, so Ke rises with debt and value stays unchanged. Under NI the optimal structure is nearly all debt, while under NOI there is no optimal structure.

What is MM Proposition I and II without tax?

Proposition I says firm value is independent of capital structure and equals EBIT ÷ Ko. Proposition II says Ke rises linearly with the debt-equity ratio: Ke = Ku + (Ku − Kd) × D/E. Together they show Ko stays constant.

How does corporate tax change the MM theory?

Interest is tax-deductible, so debt creates a tax shield. The levered firm's value is the unlevered value plus t × D, assuming perpetual debt. Ko falls as debt rises, so the theory favours maximum debt, which real-world costs of distress limit.

How is the Traditional approach different from MM?

The Traditional approach says Ko first falls, then flattens, then rises as leverage increases, so an optimal range exists. MM without tax says Ko is constant because arbitrage removes any gain. The Traditional approach does not rely on the perfect-market assumptions.