42  Capital Structure and Cost of Capital

42.1 What is Capital Structure?

Capital structure is the mix of long-term sources of finance — equity, retained earnings, preference shares, debentures and term loans — used by a firm to fund its operations and growth. It is the financing-decision output: once managers have decided how much the firm needs, capital structure decides where it comes from.

Two often-confused terms:

TipCapital Structure vs Financial Structure
Term What it includes
Capital structure Long-term sources only — equity + reserves + preference + long-term debt
Financial structure All liabilities — long-term + current liabilities (= the right-hand side of the balance sheet)

I.M. Pandey defines capital structure as “the proportion of debt and equity capital in the long-term financing of a firm” (pandey2021?). Brealey-Myers-Allen’s compact form: “Capital structure refers to the firm’s mix of debt and equity” (brealeymyers2020?).

42.1.1 Patterns of capital structure

TipCommon Capital Structure Patterns
Pattern Composition
All-equity Only equity shares + retained earnings — no debt
Equity + Debt Equity + long-term loans / debentures
Equity + Preference + Debt All three components
Highly leveraged Debt-heavy mix

42.2 Cost of Capital

The cost of capital is the minimum rate of return that a firm must earn on its investments to leave the value of equity unchanged. It is the opportunity cost of capital — the return investors could have earned on alternatives of similar risk (khanjain2020?; pandey2021?).

TipThree Working Definitions
Author Definition
Solomon Ezra “Minimum required earnings rate or the cut-off rate of capital expenditure.”
Hampton “Rate of return the firm requires from investment in order to increase the value of the firm in the marketplace.”
Khan & Jain “The discount rate used to evaluate the desirability of investment proposals.”

42.2.1 Components — cost of each source

A firm’s overall cost of capital is the weighted average of the costs of its individual sources.

TipCost of Each Source
Source Standard formula Comment
Cost of debt (\(K_d\)) \(K_d = \dfrac{I (1-t)}{NP}\) After-tax; interest is tax-deductible. I = interest, t = tax rate, NP = net proceeds
Cost of preference (\(K_p\)) \(K_p = \dfrac{D_p}{NP}\) Dividend ÷ Net Proceeds; not tax-deductible
Cost of equity (\(K_e\)) — Dividend approach \(K_e = \dfrac{D_1}{P_0} + g\) Gordon’s growth model
Cost of equity (\(K_e\)) — CAPM \(K_e = R_f + \beta (R_m - R_f)\) Risk-based
Cost of retained earnings (\(K_r\)) Slightly less than \(K_e\) No floatation cost

42.2.2 Weighted Average Cost of Capital (WACC)

\[\text{WACC} = K_e \cdot \frac{E}{V} + K_p \cdot \frac{P}{V} + K_d (1-t) \cdot \frac{D}{V}\]

where \(V = E + P + D\). Two weighting schemes:

TipTwo WACC Weighting Approaches
Approach Weights based on Use
Book-value weights Balance-sheet figures Simple; can lag market reality
Market-value weights Market capitalisation, market value of debt Theoretically correct

WACC is the firm’s hurdle rate — projects must earn at least WACC to be value-creating.

42.3 Capital Structure Theories

Four theories explain whether capital structure matters for firm value.

TipFour Theories of Capital Structure
Theory Core claim Implication
Net Income (NI) approach — Durand Capital structure matters. As debt rises, WACC falls and value rises Optimal: 100% debt
Net Operating Income (NOI) approach — Durand Capital structure does not matter. WACC is independent of mix No optimal point
Traditional approach Capital structure matters up to a point. WACC has a U-shape; optimal at moderate debt One optimal capital structure
Modigliani-Miller (MM) — without taxes Value is independent of structure (Proposition I); cost of equity rises with leverage (Proposition II) No optimal — no taxes
Modigliani-Miller (MM) — with taxes With tax-deductible interest, value rises with debt Optimal: maximum debt

42.3.1 MM Propositions (1958, 1963)

MM Proposition I (no taxes): \(V_L = V_U\) — the value of a levered firm equals the value of an unlevered firm. Capital structure is irrelevant.

MM Proposition II (no taxes): \(K_e = K_o + (K_o - K_d) \cdot \dfrac{D}{E}\) — the cost of equity rises linearly with the debt-equity ratio.

MM with taxes (1963): \(V_L = V_U + tD\) — interest tax shield raises the value of the levered firm. The implication is maximise debt — which is unrealistic.

The MM model rests on perfect-market assumptions (no taxes, no bankruptcy costs, no information asymmetry). Relaxing these gives the trade-off theory and the pecking-order theory.

TipTwo Modern Theories of Capital Structure
Theory Core claim
Trade-off theory Optimal capital structure balances tax shield (raises value) against bankruptcy and agency costs (lower value)
Pecking-order theory (Myers) Firms prefer internal funds > debt > new equity because of information asymmetry; no target debt-equity ratio

42.4 Optimal Capital Structure

The optimal capital structure is the mix that minimises the firm’s WACC and maximises the value of equity. In the trade-off view, it sits where the marginal benefit of the tax shield equals the marginal cost of financial distress.

flowchart LR
  N[NI: WACC ↓ as debt ↑] --- T[Traditional: WACC ↓ then ↑]
  T --- M[MM: WACC unchanged<br/>without taxes]
  M --- TO[Trade-off: optimum at<br/>tax shield = distress cost]
  style N fill:#FFEBEE,stroke:#C62828
  style T fill:#FFF8E1,stroke:#F9A825
  style M fill:#E3F2FD,stroke:#1565C0
  style TO fill:#E8F5E9,stroke:#2E7D32

42.5 Factors Affecting Capital Structure

TipFactors Influencing Capital Structure
Family Factors
Internal Size, profitability, asset structure, growth, risk attitude of management
External Tax environment, legal regulation, market conditions, interest rates, credit-rating
Cost considerations Cost of debt vs cost of equity; floatation cost
Risk considerations Operating leverage, cash-flow stability, financial distress
Control Equity dilution, voting control
Industry Industry norms; capital intensity

42.6 Practice Questions

Q 01 Capital Structure Easy

Capital structure refers to the mix of:

  • AAll current and long-term liabilities
  • BLong-term sources of finance — equity, preference, retained earnings, long-term debt
  • COnly debentures
  • DCash and cash equivalents
View solution
Correct Option: B
Capital structure = long-term sources only. Adding current liabilities gives financial structure.
Q 02 MM Proposition I Medium

Modigliani & Miller's Proposition I (no taxes) states that:

  • ACapital structure determines firm value
  • BFirm value is independent of capital structure
  • C100% debt is optimal
  • D100% equity is optimal
View solution
Correct Option: B
MM I (no taxes): VL = VU. The value of a levered firm equals the value of an unlevered firm; capital structure is irrelevant.
Q 03 MM with Tax Medium

When corporate taxes are introduced, MM (1963) shows that the value of a levered firm equals:

  • AVU
  • BVU + tD
  • CVU − tD
  • D2 × VU
View solution
Correct Option: B
With tax-deductible interest, the present value of the tax shield is tD. Hence VL = VU + tD.
Q 04 Cost of Debt Medium

A firm has an irredeemable debenture that pays 12% interest. If the corporate tax rate is 30%, the after-tax cost of debt is:

  • A12.0%
  • B9.0%
  • C8.4%
  • D3.6%
View solution
Correct Option: C
After-tax Kd = 12% × (1 − 0.30) = 12% × 0.70 = 8.4%. The interest tax shield reduces the effective cost of debt.
Q 05 Pecking Order Medium

According to Myers's pecking-order theory of capital structure, firms prefer financing in the order:

  • ANew equity → Debt → Internal funds
  • BInternal funds → Debt → New equity
  • CDebt → New equity → Internal funds
  • DEqual use of all three
View solution
Correct Option: B
Pecking order — driven by information asymmetry: Internal funds → Debt → New equity. There is no target debt-equity ratio.
Q 06 Cost of Equity Medium

A firm's expected dividend is ₹4 per share, the current market price is ₹50, and the constant growth rate is 5%. The cost of equity, by Gordon's model, is:

  • A8%
  • B10%
  • C13%
  • D15%
View solution
Correct Option: C
Ke = (D1 / P0) + g = (4 / 50) + 0.05 = 0.08 + 0.05 = 13%.
Q 07 WACC Medium

A firm's WACC is most usefully described as:

  • AMaximum return investors expect from the firm
  • BThe minimum return the firm must earn on its investments to maintain or increase value
  • CThe current dividend rate
  • DAverage market return on equities
View solution
Correct Option: B
WACC is the firm's hurdle rate — the minimum return new investments must earn to leave value unchanged.
Q 08 NI vs NOI Medium

In Durand's Net Operating Income (NOI) approach to capital structure:

  • ACapital structure has no effect on overall cost of capital
  • B100% debt is optimal
  • C100% equity is optimal
  • DOptimum is at moderate debt
View solution
Correct Option: A
In the NOI approach, the overall cost of capital and firm value are independent of leverage; cost of equity adjusts to keep WACC constant. Foreshadows MM (1958).
ImportantQuick recall
  • Capital structure = mix of long-term sources of finance. Financial structure adds current liabilities.
  • Cost of capital = minimum rate of return on investments to leave value unchanged. Sources: \(K_d\) after tax, \(K_p\), \(K_e\) (Gordon or CAPM), \(K_r\).
  • WACC = weighted average of component costs. Use market-value weights for theory; book-value for simplicity.
  • Theories: NI (Durand) — debt always good; NOI (Durand) — irrelevant; Traditional — U-shape with optimum; MM (1958) without taxes — irrelevant; MM (1963) with taxes — VL = VU + tD; Trade-off — tax shield vs distress; Pecking order (Myers) — internal → debt → new equity.
  • MM Proposition II: \(K_e = K_o + (K_o - K_d)(D/E)\) — cost of equity rises linearly with leverage.
  • Optimal structure: mix that minimises WACC and maximises firm value. Determined by tax, distress, agency, control, market and industry factors.