Capital structure theories: NI, NOI, traditional and Modigliani–Miller

Financial Management · Unit II · Topic 5 of 16 · 4 min read

Durand's net income and net operating income approaches, the traditional view of an optimum structure, Modigliani and Miller's propositions with and without tax and the arbitrage proof, empirical evaluation, and the January 2026 NOI problem (14% rising to 22%) and August 2024 NI problem (Rs. 10,50,000 and 9.52%) solved.

← All Financial Management topics Past papers

On this page

1. Symbols and assumptions
2. Net income (NI) approach Durand
3. Net operating income (NOI) approach Durand
4. Traditional approach
5. Modigliani Miller (1958 and 1963)
6. Empirical evaluation
How this is examined

Cases checked to exist. Read the judgment before quoting a holding.

Every case cited here has been checked to exist — the citation resolves and names the right parties. The propositions attributed to each case have not been verified line by line against the judgment. Case names link through to the full judgment: read it before quoting a holding in an examination answer, and never carry a proposition from notes into court on trust.

The examinable core. Does the mix of debt and equity change the value of the firm? NI says yes, NOI says no, the traditional view says yes up to a point, MM say no (without tax). Every recent paper set a NI or NOI problem: January 2026 (NOI) and August 2024 (NI). The one rule: V = S + D, and k_o = EBIT ÷ V.

1. Symbols and assumptions

EBIT = earnings before interest and tax (net operating income); I = interest; D = market value of debt; S = market value of equity; V = S + D; k_d = I/D; k_e = (EBIT − I)/S; k_o = EBIT/V. The theories assume only debt and equity, no tax (unless stated), all earnings paid out, constant EBIT and a given total investment, so only the mix changes.

2. Net income (NI) approach — Durand

k_d and k_e stay constant whatever the debt, and k_d < k_e. More cheap debt therefore lowers k_o and raises V. The optimum is (almost) all debt. Method: capitalise the equity earnings at k_e to get S, add D.

Worked problem (August 2024). Net operating income Rs. 1,00,000; 8% debentures Rs. 2,50,000; k_e 10%; no tax. Then debt raised to Rs. 4,00,000.

Particulars	Debt 2,50,000	Debt 4,00,000
EBIT	1,00,000	1,00,000
Less interest at 8%	20,000	32,000
Earnings for equity	80,000	68,000
S = earnings ÷ 0.10	8,00,000	6,80,000
D	2,50,000	4,00,000
V = S + D	10,50,000	10,80,000
k_o = EBIT ÷ V	9.52%	9.26%

More debt raises the value of the firm and lowers the overall cost, as NI predicts.

3. Net operating income (NOI) approach — Durand

The market values the firm as a whole: k_o is constant, so V = EBIT ÷ k_o whatever the mix. Cheap debt is exactly offset by a rise in k_e, because shareholders see more risk. There is no optimum structure. Method: find V first, deduct D to get S, then k_e = (EBIT − I) ÷ S.

Worked problem (January 2026). NOI Rs. 1,00,000; 6% debentures Rs. 5,00,000; k_o 10%. Then debt raised to Rs. 7,50,000.

Particulars	Debt 5,00,000	Debt 7,50,000
V = 1,00,000 ÷ 0.10	10,00,000	10,00,000
Less D	5,00,000	7,50,000
S	5,00,000	2,50,000
EBIT − interest at 6%	70,000	55,000
k_e = (EBIT − I) ÷ S	14%	22%

The value of the firm is unchanged at Rs. 10,00,000; the cost of equity rises from 14% to 22%. Check: k_o = 6% × 7.5/10 + 22% × 2.5/10 = 4.5 + 5.5 = 10%.

4. Traditional approach

The middle view (Ezra Solomon). Up to a point, debt is cheap and k_e rises only slowly, so k_o falls and V rises. Beyond that point both k_d and k_e rise sharply as risk grows, so k_o rises. The k_o curve is U-shaped (saucer-shaped); its lowest point is the optimum capital structure, where the value of the firm is highest.

5. Modigliani–Miller (1958 and 1963)

Franco Modigliani and Merton Miller, “The Cost of Capital, Corporation Finance and the Theory of Investment” (American Economic Review, 1958).

Proposition I: without tax, the value of a firm is independent of its capital structure: V_L = V_U = EBIT ÷ k_o.
Proposition II: k_e rises linearly with debt: k_e = k_o + (k_o − k_d) D/S. The cheap debt is cancelled by dearer equity.
Arbitrage proof: if a levered firm were valued higher than an identical unlevered firm, an investor would sell his shares in the levered firm, borrow on his own account in the same proportion (home-made leverage), and buy shares of the unlevered firm. He earns the same income with less investment. Such switching continues until the two values are equal.
Assumptions: perfect capital markets, rational investors, individuals can borrow at the same rate as firms, firms in the same risk class, no tax, no transaction costs, 100% payout.
With corporate tax (1963): interest is deductible, so V_L = V_U + tD. Debt adds value through the tax shield; the logical end is a structure almost all of debt.

The NOI approach and MM without tax give the same answer; MM supply the behavioural reason (arbitrage) that NOI lacks.

6. Empirical evaluation

Personal borrowing is not a perfect substitute for corporate borrowing: individuals pay more and do not enjoy limited liability, so arbitrage is imperfect.
Transaction costs and institutional limits (funds that may not borrow) restrict switching.
Firms do not choose all-debt structures, because of bankruptcy costs and agency costs; the trade-off theory sets the tax shield against these costs, giving an optimum, close to the traditional view.
Miller (1977, “Debt and Taxes”) showed that personal tax on interest income can cancel the corporate tax advantage.
Myers’ pecking-order theory (1984): firms prefer retained earnings, then debt, then new equity, because of information asymmetry.

How this is examined

The NI/NOI problem is a regular 10-mark Unit II question; always show V, S, D, k_e and k_o for both levels of debt and add a one-line conclusion naming the approach. The 6-mark “note on Modigliani and Miller approach of capital structure” (August 2024) is section 5 with two points from section 6.

Now try the real questions: Financial Management past question papers.