43  Capital Structure and Cost of Capital

43.1 What is Capital Structure?

Capital Structure is the proportion of debt, equity and other long-term sources of finance that a firm uses to fund its operations and growth. Gerstenberg defined it as “the composition of permanent capital — equity shares, preference shares, debentures, and long-term debt”. The closely related Financial Structure = entire liability side, including short-term sources.

TipWorking definitions

Author	Definition
Gerstenberg	“The composition of permanent capital — equity, preference, debentures and long-term debt.”
John J. Hampton	“The combination of debt and equity that makes the total capitalisation of the company.”
Pandey	“The mix of debt and equity that a firm uses to finance its assets.”
Weston & Brigham	“Permanent financing of the firm — represented by long-term debt, preferred stock and net worth.”

NoteCapital Structure vs Financial Structure

Capital Structure = long-term sources only (equity + preference + long-term debt). Financial Structure = entire liabilities side (capital structure + current liabilities). Frequent PYQ distinction.

43.2 Features of an Optimal Capital Structure

TipSeven features of an optimal capital structure

• Maximises shareholder wealth — minimises WACC.
• Flexibility — allows future expansion or contraction.
• Solvency — manageable debt obligations.
• Conservatism — moderate gearing for safety.
• Control — preserves management/ownership.
• Profitability — exploits trading on equity.
• Minimum cost — lowest weighted cost.

43.3 Factors Determining Capital Structure

TipMajor factors influencing capital structure

• Business risk — sales/operating volatility.
• Tax position — interest tax shield.
• Financial flexibility — debt capacity unused.
• Managerial conservatism / aggressiveness.
• Asset structure — tangible assets support more debt.
• Profitability and cash flow stability.
• Size and age of firm.
• Industry norms and benchmarks.
• Market conditions — debt vs equity windows.
• Regulations — banking, insurance limits.
• Growth rate.
• Control considerations.
• Cost of capital.
• Trading on equity / Leverage.

43.4 Theories of Capital Structure

There are four classical theories that NTA tests heavily:

flowchart TB
  CS[Capital Structure<br/>Theories]
  CS --> NI[1. Net Income<br/>Approach<br/>Durand]
  CS --> NOI[2. Net Operating Income<br/>Approach<br/>Durand]
  CS --> TR[3. Traditional<br/>Approach<br/>Solomon, Schwartz]
  CS --> MM[4. Modigliani-Miller<br/>1958, 1963]
    classDef default fill:#003366,color:#ffffff,stroke:#ffcc00,stroke-width:3px,rx:10px,ry:10px;

43.4.1 1. Net Income (NI) Approach — David Durand (1952)

TipNI Approach — key claims

• Both Kd (cost of debt) and Ke (cost of equity) are independent of leverage.
• Since Kd < Ke, increasing debt lowers WACC continuously.
• Therefore higher leverage → higher firm value.
• Optimal capital structure = 100 % debt (a theoretical extreme).
• Value of firm V = E + D, where E = NI / Ke.

43.4.2 2. Net Operating Income (NOI) Approach — David Durand (1952)

TipNOI Approach — key claims

• WACC (Ko) is constant regardless of leverage.
• Kd is constant; Ke rises with leverage to exactly offset the cheaper debt.
• Value of firm is independent of capital structure.
• No optimal capital structure.
• Value V = EBIT / Ko.

43.4.3 3. Traditional Approach — Ezra Solomon, Eli Schwartz

TipTraditional Approach — key claims

• A moderate amount of debt lowers WACC.
• Beyond a threshold, Ke and Kd both rise sharply due to financial risk.
• WACC is U-shaped — minimum at the optimal capital structure.
• A real-world middle-ground view that combines NI and NOI insights.

43.4.4 4. Modigliani-Miller (MM) Hypothesis

The most influential — Franco Modigliani and Merton Miller, American Economic Review (1958, revised 1963). Both won Nobel Prizes (1985, 1990).

MM Proposition I (No Tax, 1958)

V_L = V_U — In perfect capital markets without taxes, the value of a firm is independent of its capital structure. “It does not matter how you slice the pie.”

MM Proposition II (No Tax, 1958)

Ke = Ko + (Ko − Kd) × (D/E) — Cost of equity rises linearly with leverage. The benefit of cheap debt is exactly offset by the higher cost of equity.

MM with Taxes (1963)

TipMM with corporate tax (1963)

• Interest is tax-deductible → tax shield = Tc × D.
• V_L = V_U + Tc × D — the levered firm is worth more by the present value of the tax shield.
• Optimal structure = 100 % debt (in theory).

MM Assumptions

TipMM’s strong assumptions (the world without)

• No taxes (in 1958 version).
• No transaction costs.
• No bankruptcy or financial distress costs.
• Investors and firms can borrow at the same rate (homemade leverage).
• No asymmetric information.
• Investors are rational and markets are frictionless.
• Same expected operating earnings (same risk class).

43.4.5 Arbitrage Proof — The Crown Jewel

MM’s proof rests on arbitrage: if two firms with identical operating earnings have different market values due to capital structure alone, investors will engage in homemade leverage — borrowing or lending on personal account to replicate the cheaper position — eliminating the price difference.

43.5 Trade-Off Theory

Adds the costs of financial distress to MM. Firms trade off the tax benefit of debt against the cost of potential bankruptcy and financial distress. There exists an optimal level of debt, where marginal benefits equal marginal costs.

\[V_L = V_U + PV(\text{Tax Shield}) - PV(\text{Financial Distress Costs})\]

TipCosts of financial distress

• Direct costs — legal, administrative, restructuring fees.
• Indirect costs — lost sales, supplier defections, talent loss, management distraction.
• Agency costs of debt — risk-shifting, underinvestment (Myers).

43.6 Pecking Order Theory

Stewart Myers and Nicholas Majluf (1984) — based on asymmetric information between managers and outside investors. Firms follow a pecking order:

TipMyers-Majluf Pecking Order (1984)

1. Internal funds (Retained Earnings) first — no information asymmetry.
2. Debt next — limited adverse selection.
3. Equity last — strongest negative signal.

Implication: profitable firms use less debt (because they have retained earnings); unprofitable firms have more debt. No optimal capital structure.

43.7 Market Timing Theory

Baker and Wurgler (2002) — firms issue equity when overvalued and repurchase when undervalued. Capital structure is the cumulative outcome of past market-timing attempts.

43.8 Signalling Theory

Stephen Ross (1977) — debt issuance signals management’s confidence in future cash flows (since debt requires committed payments). Equity issuance signals overvaluation.

43.9 Cost of Capital — Concept

Cost of Capital is the minimum rate of return that a firm must earn on its investments to satisfy the providers of capital and maintain or increase the market value of equity. It is the hurdle rate for capital-budgeting decisions.

TipCost of capital — three perspectives

• Investor’s view — required rate of return.
• Firm’s view — minimum return on investments.
• Market view — opportunity cost of funds.

43.10 Components of Cost of Capital

TipComponent costs of capital

Component	Formula	Notes
Cost of Debt (Kd)	Kd = I(1−t)/NP — after-tax	Tax-deductible interest
Cost of Preference (Kp)	Kp = D / NP (irredeemable); annualised yield for redeemable	Not tax-deductible
Cost of Equity (Ke)	Dividend models or CAPM	Highest, no tax shield
Cost of Retained Earnings (Kr)	Kr = Ke × (1 − t)(1 − b) — adjusted for personal tax and brokerage	Generally < Ke

43.10.1 Cost of Equity — Three Models

TipThree approaches to cost of equity

Method	Formula
Dividend Yield (Discount) Model	Ke = D / P
Gordon Growth Model	Ke = (D₁ / P₀) + g
CAPM (Sharpe-Lintner 1964)	Ke = Rf + β × (Rm − Rf)
Earnings Yield Model	Ke = EPS / P
Bond Yield + Risk Premium	Ke = Bond Yield + Risk Premium

43.11 Weighted Average Cost of Capital (WACC)

\[\text{WACC (K}_o\text{)} = w_e K_e + w_p K_p + w_d K_d (1-t)\]

where \(w_e, w_p, w_d\) are weights of equity, preference and debt; Kd × (1−t) reflects the after-tax cost of debt.

43.11.1 Weights — Two Approaches

TipTwo weighting approaches

Approach	Description
Book Value	From balance sheet — simpler, more stable
Market Value	Current market prices — more accurate, more volatile
Target Capital Structure	Future planned mix — most theoretically correct

Modern academic preference: market-value weights based on target capital structure.

43.12 Marginal Cost of Capital (MCC)

The cost of raising one additional rupee of capital. Crucial for capital-budgeting decisions — the relevant hurdle rate is MCC, not historical WACC.

43.13 Leverage and Cost of Capital

As leverage increases, Kd rises beyond a threshold (lenders demand higher rates), and Ke rises with financial risk. WACC traces a U-shape in the traditional view — the minimum point is the optimal capital structure.

flowchart LR
  L[Low Leverage] --> M[Moderate Leverage<br/>Optimal — WACC minimum]
  M --> H[High Leverage<br/>WACC rises]
    classDef default fill:#003366,color:#ffffff,stroke:#ffcc00,stroke-width:3px,rx:10px,ry:10px;

43.14 EBIT-EPS Analysis (Bridge to Topic 44)

A practical tool for capital-structure decisions — compares EPS under alternative financing mixes (more debt vs more equity) at varying EBIT levels. The indifference point is where two structures give the same EPS. Above the indifference point, the more-levered structure is superior.

43.15 Capital Structure in India

TipIndian capital-structure observations

• Indian firms historically rely more on bank debt than capital markets.
• Family-controlled firms prefer debt to avoid dilution of control.
• Public-sector enterprises often face mandated capital structures.
• SEBI’s debt-listing reforms + Bharat Bond ETF (2019) have deepened debt markets.
• Companies Act 2013 — Sec 180 — borrowings beyond paid-up capital + reserves need special-resolution approval.
• SEBI Listing Regulations Reg 50 — material disclosures of capital-structure changes.

43.16 Modern Trends in Capital Structure

TipTwelve modern trends

• ESG-linked debt — sustainability-linked loans with rate adjustments.
• Green bonds, social bonds, blue bonds.
• Mezzanine financing — debt with equity features.
• Convertible debt and warrants rising.
• Perpetual debt / Tier-1 capital — banks.
• Special Purpose Acquisition Companies (SPACs).
• Crypto-collateralised debt.
• Tokenisation of equity.
• Buy-back-driven leverage to optimise structure.
• AT1 / CoCos in banking.
• InvITs and REITs as quasi-equity vehicles.
• Climate transition bonds (post-COP).

43.17 Practice Questions

Q 01 MM Easy

The Modigliani-Miller hypothesis in its original 1958 form (no taxes) states that:

• ACapital structure is irrelevant to firm value
• B100 % debt is optimal
• C100 % equity is optimal
• DCapital structure determines cost of capital

View solution

Correct Option: A

V_L = V_U — capital structure is irrelevant under MM (1958, no taxes).

Q 02 MM tax Medium

Under MM (1963 with corporate tax), the value of a levered firm is:

• AV_L = V_U
• BV_L = V_U + Tc × D
• CV_L = V_U − Tc × D
• DV_L = V_U × Tc

View solution

Correct Option: B

V_L = V_U + Tc × D — levered firm worth more by PV of tax shield.

Q 03 NI approach Medium

Under the Net Income (NI) approach by Durand, the optimal capital structure is:

• A100 % equity
• B100 % debt
• C50-50
• DIndeterminate

View solution

Correct Option: B

NI assumes Kd, Ke constant → more debt always lowers WACC → 100 % debt optimal (theoretical).

Q 04 NOI approach Medium

Under the NOI approach, WACC is:

• AConstant regardless of leverage
• BFalls with leverage
• CU-shaped
• DInverted U-shape

View solution

Correct Option: A

NOI: Ke rises to exactly offset cheaper Kd → WACC constant; firm value independent of mix.

Q 05 Traditional Medium

The traditional approach to capital structure says WACC is:

• AAlways decreasing with debt
• BConstant
• CU-shaped — minimum at optimum
• DIncreasing only

View solution

Correct Option: C

U-shaped WACC — minimum at the optimum (Solomon, Schwartz).

Q 06 Pecking Order Medium

The "Pecking Order Theory" (1984) was proposed by:

• AMyers & Majluf
• BModigliani & Miller
• CMarkowitz
• DStewart & Sharpe

View solution

Correct Option: A

Stewart Myers and Nicholas Majluf (1984). Order: Internal → Debt → Equity.

Q 07 Pecking sequence Medium

The Pecking Order sequence for raising finance is:

• AEquity → Debt → Internal funds
• BInternal funds → Debt → Equity
• CDebt → Equity → Internal funds
• DInternal funds → Equity → Debt

View solution

Correct Option: B

Internal funds → Debt → Equity.

Q 08 Trade-off Medium

The Trade-Off theory balances:

• ATax shield vs financial distress costs
• BProfit vs sales
• CDividend vs retention
• DRisk vs return

View solution

Correct Option: A

V_L = V_U + PV(Tax Shield) − PV(Distress Costs).

Q 09 CAPM Medium

In CAPM, cost of equity equals:

• ARf + β × (Rm − Rf)
• BD / P + g
• CEPS / P
• DBond yield + spread

View solution

Correct Option: A

Ke = Rf + β × (Rm − Rf). Sharpe-Lintner 1964.

Q 10 Kd after tax Medium

Post-tax cost of debt is:

• AKd
• BKd × (1 − t)
• CKd / (1 − t)
• DKd + t

View solution

Correct Option: B

Kd × (1 − t) — interest is tax-deductible.

Q 11 Gordon Medium

Gordon's growth model for cost of equity is:

• AKe = D₁ / P₀
• BKe = (D₁ / P₀) + g
• CKe = Rf + β(Rm − Rf)
• DKe = EPS / P

View solution

Correct Option: B

Ke = (D₁/P₀) + g. From P₀ = D₁/(Ke − g).

Q 12 Capital vs Financial Hard

Capital Structure differs from Financial Structure in that capital structure excludes:

• AEquity
• BPreference
• CCurrent liabilities
• DDebentures

View solution

Correct Option: C

Capital Structure = long-term only; excludes current liabilities.

Q 13 Hurdle rate Easy

In capital budgeting, the discount rate used is typically:

• ACost of debt
• BCost of equity
• CWACC
• DPrime lending rate

View solution

Correct Option: C

WACC is the hurdle rate; reflects blended cost of all sources.

Q 14 Arbitrage Hard

MM's proof relies on the mechanism of:

• AArbitrage / homemade leverage
• BCapital rationing
• CRisk pooling
• DHedging

View solution

Correct Option: A

Investors borrow/lend personally to replicate the cheaper position — eliminating price difference.

Q 15 Signalling Hard

The signalling theory of capital structure (1977) is by:

• AStephen Ross
• BStewart Myers
• CEugene Fama
• DMichael Spence

View solution

Correct Option: A

Stephen Ross (1977) — debt issuance signals confidence; equity signals overvaluation.

Q 16 Market timing Hard

The Market Timing theory (2002) is associated with:

• ABaker & Wurgler
• BMyers & Majluf
• CFama & French
• DModigliani & Miller

View solution

Correct Option: A

Malcolm Baker and Jeffrey Wurgler, *Journal of Finance* (2002).

Q 17 WACC weights Medium

The most theoretically correct weights for WACC are based on:

• ABook values
• BMarket values at target structure
• CHistorical values
• DPar values

View solution

Correct Option: B

Market value at target capital structure is most theoretically correct.

Q 18 MM Prop II Hard

MM Proposition II (no tax) gives Ke as:

• AConstant
• BDecreases with leverage
• CKo + (Ko − Kd) × (D/E) — rises linearly with leverage
• DEqual to Kd

View solution

Correct Option: C

Ke rises linearly with D/E to offset cheap debt; WACC unchanged.

Q 19 Optimal CS Easy

An optimal capital structure aims to:

• AMaximise WACC
• BMinimise WACC and maximise firm value
• CMaximise debt
• DMaximise EPS only

View solution

Correct Option: B

Optimal CS minimises WACC and maximises firm value.

Q 20 Match theories Hard

Match the theory with its author:

(i)	NI / NOI Approach	(a)	Myers & Majluf
(ii)	Capital Structure Irrelevance	(b)	Stephen Ross
(iii)	Pecking Order	(c)	Modigliani & Miller
(iv)	Signalling Theory	(d)	David Durand

• A(i)-(d), (ii)-(c), (iii)-(a), (iv)-(b)
• B(i)-(a), (ii)-(b), (iii)-(c), (iv)-(d)
• C(i)-(c), (ii)-(d), (iii)-(b), (iv)-(a)
• D(i)-(b), (ii)-(a), (iii)-(d), (iv)-(c)

View solution

Correct Option: A

NI/NOI — Durand; CS Irrelevance — MM; Pecking Order — Myers-Majluf; Signalling — Ross.

43.17.1 Advanced Format Questions

AR 1Assertion-ReasonHard

A: MM Proposition I (no tax) says capital structure is irrelevant.
R: With taxes, debt creates a tax shield raising firm value.

• ABoth true; R explains A
• BBoth true; R does not explain A
• CA true, R false
• DA false, R true

View solution

Correct Option: B

S 1Statement-basedMedium

Capital-structure theories: (i) Net Income (Durand). (ii) Net Operating Income. (iii) Traditional. (iv) MM.

• AAll four
• B(i) and (ii) only
• C(iii) and (iv) only
• D(iv) only

View solution

Correct Option: A

N 1NumericalMedium

Kd (post-tax) = 7%, Ke = 15%, Wd = 0.4, We = 0.6. WACC =

• A11.8 %
• B10 %
• C12 %
• D9 %

View solution

Correct Option: A

0.4 × 7 + 0.6 × 15 = 2.8 + 9.0 = 11.8%.

N 2NumericalHard

Interest 10%; Tax rate 30%. After-tax cost of debt:

• A7 %
• B10 %
• C13 %
• D3 %

View solution

Correct Option: A

Kd(after) = 10 × (1 − 0.3) = 7%.

43.18 Quick Recall

ImportantQuick recall

• Definitions: Gerstenberg · Hampton · Pandey · Weston-Brigham.
• Capital vs Financial Structure — long-term only vs entire liabilities.
• Optimal CS — maximises value, minimises WACC; key features: flexibility, solvency, control, profitability.
• Factors: business risk · tax · flexibility · asset structure · profitability · size · industry · market · growth · control.
• Four classical theories:
  • NI Approach (Durand 1952) — Kd, Ke constant → 100 % debt optimal.
  • NOI Approach (Durand 1952) — WACC constant → no optimal CS.
  • Traditional (Solomon, Schwartz) — U-shaped WACC → optimum exists.
  • MM (1958, 1963) — V_L = V_U (no tax); V_L = V_U + Tc × D (with tax); arbitrage proof; homemade leverage.
• MM Prop II: Ke = Ko + (Ko − Kd) × (D/E).
• Trade-Off Theory: V_L = V_U + PV(Tax Shield) − PV(Distress Costs).
• Pecking Order — Myers-Majluf (1984): Internal → Debt → Equity.
• Market Timing — Baker-Wurgler (2002): cumulative effect of past issuance timing.
• Signalling — Ross (1977): debt signals confidence; equity signals overvaluation.
• Cost of Capital: hurdle rate; minimum required return.
• Components: Kd = I(1−t)/NP · Kp = D/NP · Ke (3 models) · Kr ≈ Ke × (1−t)(1−b).
• Cost of Equity: Dividend Yield (D/P) · Gordon (D₁/P₀) + g · CAPM Rf + β(Rm − Rf) · Earnings Yield · Bond Yield + Risk Premium.
• WACC = wₑKₑ + wₚKₚ + wd × Kd(1−t).
• Weights: Book vs Market vs Target; Market-Target preferred.
• MCC — marginal cost of one additional rupee.
• India: Companies Act 2013 Sec 180 (borrowing > paid-up + reserves needs SR); SEBI debt-listing reforms; Bharat Bond ETF 2019.
• Modern trends: ESG-linked debt · green/social bonds · mezzanine · convertibles · perpetuals · SPACs · crypto debt · tokenisation · AT1/CoCos · climate transition bonds.