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

Understand Capital Structure Theories

Key rules to remember

Value of the firm

V = S + D

S = market value of equity, D = market value of debt.

NI approach: value of equity

S = (EBIT − I) ÷ Ke = Earnings available to equity ÷ Ke

I = interest = Kd × D. Ke and Kd are constant.

Overall cost of capital

Ko = EBIT ÷ V

Used in NI to find Ko once V is known; in NOI Ko is given.

NOI approach: value of the firm

V = EBIT ÷ Ko

Then S = V − D and Ke = (EBIT − I) ÷ S.

MM Proposition I (no taxes)

Vu = Vl = EBIT ÷ Ko

Value is independent of capital structure. Ko is the same at every debt level and equals the cost of equity of the all-equity firm, Ke(u).

MM Proposition II (no taxes)

Ke = Ko + (Ko − Kd) × (D ÷ S)

Cost of equity rises linearly with debt-equity ratio.

MM with corporate tax: value

Vl = Vu + (t × D)

t = tax rate; t × D is the present value of the interest tax shield (debt assumed permanent).

MM with tax: cost of equity

Ke = Ko(u) + (Ko(u) − Kd) × (1 − t) × (D ÷ S)

Ko(u) is the cost of capital of the unlevered firm (its Ke).

How to solve Capital Structure Theories questions

1. 1Write down the given data: EBIT, interest rate, debt amount, Ke, Ko, tax rate.
2. 2Identify the approach (NI, NOI, Traditional or MM) and note its key assumption: NI has constant Ke and Kd; NOI has constant Ko.
3. 3Calculate interest I = Kd × D and earnings available to equity = EBIT − I (and less tax if tax is given).
4. 4For NI: S = earnings ÷ Ke, then V = S + D. For NOI: V = EBIT ÷ Ko, then S = V − D.
5. 5Find the missing cost: Ko = EBIT ÷ V under NI, or Ke = earnings to equity ÷ S under NOI.
6. 6For MM, use Vl = Vu + tD with tax, or Vu = Vl without tax, and check by arbitrage if asked.
7. 7Compare the options in a short table of S, D, V, Ke and Ko, and state which structure is best.
8. 8Write a one-line conclusion tied to the theory, for example that V rises with debt under NI but stays unchanged under NOI.

Quickest way: Three-line shortcut for NI vs NOI numericals

Common mistakes in Capital Structure Theories

• Mixing up what is constant in NI and NOI.

  Both are Durand's approaches with similar names.

  Fix: Remember: NI keeps Ke and Kd constant; NOI keeps Ko (and Kd) constant. Write this at the top of your answer.

• Using EBIT instead of EBIT minus interest to value equity under NI.

  Students apply the NOI formula everywhere.

  Fix: Equity value always uses earnings after interest. EBIT is used only for the whole firm value V.

• Forgetting to subtract D from V to get S under NOI.

  Students stop once V is found.

  Fix: Always do S = V − D before calculating Ke.

• Saying MM without taxes says debt is useless because it is costly.

  Confusing irrelevance with cost.

  Fix: MM says cheaper debt is exactly offset by a higher Ke, so Ko and V stay unchanged. Explain the arbitrage logic.

• Using t × D under MM with tax when debt is not stated as permanent, or applying it to equity.

  The formula is memorised without its assumption.

  Fix: State that debt is assumed perpetual, and multiply tax rate by debt only.

• Describing the Traditional approach as Ko falling all the way with more debt, or staying flat throughout.

  It is mixed up with NI (Ko keeps falling) or NOI (Ko never changes).

  Fix: Say that Ko declines up to a point, remains more or less constant over a range of debt levels (the optimum, where Ko is lowest and V is highest), and then rises.

Worked examples