Capital Structure Theories
Prerequisites
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1. Introduction
The central question in capital structure theory: Does the debt-equity mix affect the firm's overall value?
Four major theories provide different answers:
- Net Income (NI) Approach
- Net Operating Income (NOI) Approach
- Traditional Approach
- Modigliani-Miller (MM) Approach
2. NET INCOME (NI) APPROACH
Proposed by: David Durand
2.1 Core Proposition
Capital structure MATTERS. Firm value CAN be increased by using more debt.
2.2 Assumptions
- Cost of Debt (Kd) remains constant regardless of debt level
- Cost of Equity (Ke) remains constant
- Corporate taxes exist
- No transaction costs
2.3 Logic
Since debt is cheaper than equity (due to tax shield), increasing debt:
- Reduces WACC (weighted average cost decreases)
- Lower WACC → Higher firm value (V = EBIT/WACC)
Conclusion: 100% debt = Optimal (maximize value)
2.4 Formula Relationships
WACC = (Wd × Kd) + (We × Ke)
As debt ↑, Wd ↑ (more weight on cheap Kd)
→ WACC ↓
→ Firm Value ↑
2.5 Graph Pattern
As Debt Increases →
- Kd: Constant (horizontal line)
- Ke: Constant (horizontal line)
- WACC: Decreases (downward sloping)
- Firm Value: Increases (upward sloping)
2.6 Criticism
Unrealistic Assumptions:
- Ke does NOT remain constant; it increases with debt due to higher financial risk
- Ignores bankruptcy costs
- 100% debt is impractical and risky
- Lenders will increase Kd at very high debt levels
3. NET OPERATING INCOME (NOI) APPROACH
Proposed by: David Durand (opposite view)
3.1 Core Proposition
Capital structure DOES NOT MATTER. Firm value is independent of debt-equity mix.
3.2 Assumptions
- Overall capitalization rate (Ko) remains constant
- Market capitalizes firm value based on EBIT, not on how it's financed
- Use of debt increases Ke proportionally
3.3 Logic
- As debt increases, financial risk increases
- Equity holders demand higher return (Ke increases)
- The benefit of cheap debt is exactly offset by increased Ke
- WACC (Ko) remains constant
- Firm value unchanged
Conclusion: Optimal structure doesn't exist. All structures are equivalent.
3.4 Formula Relationships
Firm Value (V) = EBIT / Ko
Ko = constant (market-determined overall capitalization rate)
As debt ↑:
- Kd stays low BUT Ke increases proportionally
- WACC (Ko) remains unchanged
- Firm Value (V) constant
3.5 Graph Pattern
As Debt Increases →
- Kd: Constant (horizontal line)
- Ke: Increases (upward sloping)
- WACC (Ko): Constant (horizontal line)
- Firm Value: Constant (horizontal line)
3.6 Criticism
- Assumes perfect capital markets
- Ignores tax benefits of debt
- In reality, Ke may not increase fast enough to offset debt benefits
- Doesn't explain real-world observed patterns
4. TRADITIONAL APPROACH (Middle Path)
Also called: Intermediate Approach
4.1 Core Proposition
Capital structure MATTERS. An OPTIMAL mix exists that maximizes value.
4.2 Logic - Three Stages
Stage 1: Initial Debt (Increasing Value)
- Using moderate debt reduces WACC
- Ke increases slightly but NOT enough to offset cheap debt benefit
- Firm value increases
Stage 2: Optimal Point
- Perfect balance achieved
- WACC is minimum
- Firm value is maximum ← OPTIMAL CAPITAL STRUCTURE
Stage 3: Excessive Debt (Decreasing Value)
- High debt significantly increases both Ke and Kd (bankruptcy risk)
- WACC increases despite more debt
- Firm value decreases
4.3 Graph Pattern
As Debt Increases →
Kd: Flat initially, then rises
Ke: Rises gradually, then sharply
WACC: Decreases, reaches minimum, then increases (U-shaped curve)
Firm Value: Increases, reaches maximum, then decreases (Inverted U)
Optimal Point = Where WACC is minimum & Value is maximum
4.4 Key Insight
There exists an optimal debt-equity ratio that balances:
- Tax benefits of debt
- Increased financial risk
4.5 Why It's Realistic
- Explains observed corporate behavior (moderate debt use)
- Consistent with financial distress costs
- Accounts for risk-return trade-off
5. MODIGLIANI-MILLER (MM) APPROACH
Proposed by: Franco Modigliani and Merton Miller (1958, 1963) Nobel Prize: 1985, 1990
5.1 MM Proposition I (Without Taxes)
Statement: "In a perfect capital market with no taxes, firm value is independent of capital structure."
Formula:
VL = VU
Where:
VL = Value of Levered Firm (with debt)
VU = Value of Unlevered Firm (no debt)
Logic: Arbitrage mechanism
- If two identical firms (same risk, same EBIT) have different values due to different capital structures, investors will engage in arbitrage
- This buying/selling restores equilibrium
- Result: Values equalize
Conclusion: Similar to NOI approach - capital structure irrelevant
5.2 MM Proposition II (Without Taxes)
Statement: "Cost of equity increases linearly with debt-equity ratio."
Formula:
Ke = Ko + (Ko - Kd) × (D/E)
Where:
Ke = Cost of Equity
Ko = Overall cost (WACC for unlevered firm)
Kd = Cost of Debt
D/E = Debt-Equity Ratio
Interpretation: As debt increases, Ke increases to compensate for financial risk, exactly offsetting WACC reduction.
5.3 MM Proposition I (With Taxes) - IMPORTANT
Statement: "With corporate taxes, firm value INCREASES with debt due to interest tax shield."
Formula:
VL = VU + (Tc × D)
Where:
VL = Value of Levered Firm
VU = Value of Unlevered Firm
Tc = Corporate Tax Rate
D = Market Value of Debt
Tax Shield Component: Tc × D = Present value of interest tax shield
Conclusion: More debt = Higher value (due to tax savings)
5.4 MM Proposition II (With Taxes)
Formula:
Ke = Ko + (Ko - Kd)(1 - Tc) × (D/E)
Ke still increases with debt, but less sharply due to tax benefit.
5.5 MM Assumptions (Criticized)
- Perfect capital markets (no transaction costs)
- No bankruptcy costs
- Homogeneous expectations
- No agency costs
- Individuals and corporations can borrow at same rate
Relaxing Assumptions: Later theories introduced bankruptcy costs, agency costs, which modified MM conclusions toward the Traditional approach.
6. Comparison of All Four Theories
| Theory | Capital Structure Matters? | Optimal Structure? | WACC Pattern | Key Assumption |
|---|---|---|---|---|
| NI Approach | Yes | 100% Debt | Decreases continuously | Ke and Kd constant |
| NOI Approach | No | None (all equal) | Constant (Ko) | Ke adjusts fully |
| Traditional | Yes | Optimal mix exists | U-shaped | Moderate adjustment |
| MM (No Tax) | No | None | Constant | Perfect markets |
| MM (With Tax) | Yes | 100% Debt | Decreases | Tax shield benefit |
7. Practical Reality
Most Accepted: Traditional Approach (with modifications)
Why?
- Explains real corporate behavior (moderate debt)
- Recognizes both tax benefits AND distress costs
- Optimal structure varies by firm/industry
Modified MM + Trade-off Theory:
- Value = VU + PV(Tax Shield) - PV(Bankruptcy Costs) - PV(Agency Costs)
- Firms balance tax benefits against costs of financial distress
Exam Pattern Questions and Answers
Question 1: "Explain the Net Income Approach of capital structure." (6 Marks)
Answer:
Proposition (1 mark): The Net Income (NI) Approach, proposed by David Durand, states that capital structure is directly relevant to firm valuation. By increasing debt proportion, a firm can increase its total value and decrease the weighted average cost of capital.
Assumptions (2 marks): The theory assumes that (i) cost of debt (Kd) remains constant irrespective of the level of debt, (ii) cost of equity (Ke) also remains constant, and (iii) corporate taxes exist providing tax shield benefits on interest.
Logic (2 marks): Since debt is cheaper than equity due to tax-deductibility of interest, replacing expensive equity with cheap debt reduces the WACC. As WACC decreases, the firm's value (calculated as EBIT/WACC) increases. Therefore, the theory logically concludes that maximum debt (approaching 100%) would maximize firm value.
Criticism (1 mark): The approach is unrealistic as it ignores the fact that cost of equity (Ke) increases with higher debt due to increased financial risk. It also ignores bankruptcy costs and practical constraints on excessive debt.
Question 2: "Distinguish between NI and NOI approaches." (6 Marks)
Answer:
| Aspect | NI Approach | NOI Approach |
|---|---|---|
| Relevance | Capital structure is relevant | Capital structure is irrelevant |
| Ke Behavior | Remains constant | Increases with debt |
| WACC | Decreases with more debt | Remains constant (Ko) |
| Firm Value | Increases with debt | Constant, independent of structure |
| Optimal Structure | 100% debt | No optimal; all structures equivalent |
| Realism | Overly optimistic about debt | Ignores tax benefits |
Question 3: "State MM Proposition I with corporate taxes." (4 Marks)
Answer:
MM Proposition I with corporate taxes states that the value of a levered firm (with debt) equals the value of an unlevered firm (without debt) plus the present value of the tax shield on debt.
Formula: VL = VU + (Tc × D)
Where VL is levered firm value, VU is unlevered firm value, Tc is tax rate, and D is debt amount.
Implication: Since interest on debt is tax-deductible, using debt creates a tax shield that increases firm value. This suggests that firms should use maximum debt to maximize value, though in practice bankruptcy costs limit this.
Summary
Four Theories:
- NI: More debt → Higher value (unrealistic)
- NOI: Structure irrelevant → Constant value
- Traditional: Optimal mix → U-shaped WACC ✓ Most Realistic
- MM: With tax → Favor debt; Without tax → Irrelevant
Key Formulas:
- MM (with tax): VL = VU + Tc×D
- MM Ke formula: Ke = Ko + (Ko-Kd)(1-Tc)×(D/E)
Practical Takeaway: Moderate debt is optimal (Traditional view confirmed by trade-off theory)
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