Cost of Capital & Capital Structure: Modigliani-Miller, WACC, Trade-off Theory

TAKEAWAYS

• Cost of capital is the minimum return a firm must earn to satisfy all investors (debt, preferred stock, equity).
• Capital structure is the mix of debt, preferred stock, and equity that minimizes WACC while balancing risk.
• Modigliani-Miller (MM) theory shows that value is unaffected by capital structure under perfect markets (no taxes, bankruptcy costs).
• The trade-off theory explains why real firms use debt: tax benefits offset bankruptcy risks.
• WACC = (Debt × After-tax Cost) + (Preferred Stock × Cost) + (Equity × Cost), used to evaluate projects.
• Optimal capital structure maximizes firm value by minimizing WACC (e.g., NEPSE-listed firms like Nepal Investment Bank).

1. Cost of Capital: The Minimum Required Return

Cost of capital is the opportunity cost of funds—the return investors demand for providing capital. It includes:

• Debt cost (Kd): Interest rate on loans/bonds, adjusted for tax shields.
• Preferred stock cost (Kps): Dividend yield (fixed).
• Equity cost (Ke): Expected return from retained earnings or new shares (calculated via CAPM or dividend discount model).

How It Works: The Weighted Average Cost of Capital (WACC)

WACC blends these costs based on their proportion in the firm’s capital structure: $$WACC=\left(\frac{D}{V}\times K_d\times (1-T)\right)+\left(\frac{PS}{V}\times K_{ps}\right)+\left(\frac{E}{V}\times K_e\right)$$ Where:

• $D$ = Debt, $PS$ = Preferred Stock, $E$ = Equity
• $V$ = Total capital ($D+PS+E$)
• $T$ = Corporate tax rate (e.g., 25% in Nepal)
• $K_d$ = Pre-tax debt cost, $K_{ps}$ = Preferred stock dividend yield, $K_e$ = Equity cost

Why WACC matters: It’s the hurdle rate for capital budgeting. Projects must earn ≥ WACC to create value.

Visual: WACC Calculation for a Nepali Firm

Let’s compute WACC for Nepal Investment Bank (NIBL), assuming:

• Debt: Rs 500M (60% of capital), $K_d=12\%$, $T=25\%$
• Preferred Stock: Rs 100M (10%), $K_{ps}=8\%$
• Equity: Rs 250M (30%), $K_e=15\%$ (from CAPM)

Key Insight: NIBL’s WACC is 11.7%. Any project with NPV > 0 at this rate is acceptable.

2. Capital Structure: Debt vs. Equity Trade-offs

Capital structure = how a firm finances assets (debt, preferred stock, equity). The trade-off theory (vs. MM’s neutrality) explains why firms use debt:

• Pros of Debt:
  • Tax shield: Interest is tax-deductible (saves $T\times K_d\times D$).
  • Cheaper than equity: Debt costs less than equity (lower $K_d$ vs $K_e$).
• Cons of Debt:
  • Bankruptcy risk: High debt increases financial distress costs.
  • Agency costs: Debt forces discipline (e.g., NEPSE-listed firms avoid excessive debt).

Modigliani-Miller (MM) Theory: No Free Lunch

MM’s Proposition II states:

In perfect markets (no taxes, bankruptcy costs), firm value is independent of capital structure.

But real-world firms do use debt because:

1. Taxes: Debt reduces taxable income (e.g., NIBL saves Rs 60M/year in taxes via debt).
2. Bankruptcy costs: High debt increases failure risk (e.g., collapsed microfinance firms in Nepal).
3. Asymmetric information: Managers may hide bad news with debt (pecking order theory).

Visual: MM vs. Trade-Off Theory

mindmap
  root((Capital Structure Theories))
    MM Theory
      - Perfect Markets
      - Value Unaffected by Debt
      - No Taxes/Bankruptcy Costs
    Trade-Off Theory
      - Real-World Adjustments
      - Tax Benefits vs. Bankruptcy Costs
      - Optimal Debt Level Exists
      - Example: NEPSE Firms Use ~30% Debt

Real-World Example: Nepal Investment Bank uses ~60% debt (high for Nepal) due to:

• Strong tax benefits (commercial banks pay 25% corporate tax).
• Low bankruptcy risk (government-backed).

3. Optimal Capital Structure: Finding the Sweet Spot

The optimal capital structure minimizes WACC and maximizes firm value. Firms use:

1. Break-even analysis: Plot EBIT vs. EPS to find debt levels where EPS is stable.
2. Industry benchmarks: Compare to peers (e.g., NEPSE’s average debt ratio is 40%).
3. Financial distress costs: Estimate bankruptcy costs (e.g., legal fees, lost customers).

Worked Example: Daraz Nepal’s Capital Structure

Scenario: Daraz (acquired by Alibaba) needs Rs 500M for expansion. Should it use debt or equity?

Assumptions:

• Current capital: Rs 1B (50% debt, 50% equity).
• $K_d=10\%$, $T=25\%$, $K_e=15\%$.
• New project: Rs 500M, expected EBIT = Rs 100M/year.

Step 1: Calculate Current WACC

Step 2: Test 60% Debt (Add Rs 300M debt, Rs 200M equity)

Result: WACC drops to 10.5% (better than 11.25%). Optimal choice.

Why? Tax shield from debt outweighs higher equity cost.

4. Real-World Applications: Where This Matters

## In the Real World

1. NEPSE-listed firms (e.g., Nepal Bank Ltd.)

   • Use ~40% debt to balance tax benefits and risk.
   • Example: Nepal Bank’s WACC is ~12% (debt: 10%, equity: 16%).
   • How: They issue bonds (debt) to fund projects, keeping equity for flexibility.

2. Microfinance institutions (e.g., Financo)

   • Avoid high debt due to bankruptcy risk (clients default).
   • How: Use 80% equity, 20% debt to stay liquid.

3. E-commerce (e.g., Daraz Nepal)

   • Leverage debt for expansion (e.g., Rs 500M loan for warehouses).
   • How: WACC drops from 11.25% to 10.5% with 60% debt (as shown above).

Worked Example: Kathmandu Traffic Management (Public Sector)

Scenario: The Kathmandu Metropolitan City needs Rs 2B for road upgrades. Should it use:

• Option 1: 100% equity (taxes, but no debt costs).
• Option 2: 60% debt, 40% equity (tax benefits).

Assumptions:

• $K_d=12\%$, $T=25\%$, $K_e=18\%$.
• Project NPV at 12% WACC = Rs 500M; at 15% WACC = Rs 100M.

Calculation:

Result: Option 2 (60% debt) maximizes NPV (Rs 500M vs Rs 100M). Tax shield wins.

Lesson: Even governments use debt for projects (e.g., Nepal’s Ring Road was partly debt-funded).

5. Key Formulas and Comparisons

6. Common Mistakes in Exams

1. Ignoring taxes: Forgetting $(1-T)$ in WACC calculations.
   • Fix: Always include tax rate $T$ for debt.
2. Assuming MM holds in reality: MM is theoretical; real firms care about bankruptcy costs.
   • Fix: Use trade-off theory for practical answers.
3. Miscounting weights: Using market values, not book values.
   • Fix: Use $V=D+PS+E$ (total capital).
4. Overlooking agency costs: High debt increases conflicts between shareholders and bondholders.
   • Fix: Mention "agency costs" in discussions of optimal capital structure.

Exam Tip: How to Score Full Marks

1. Define clearly:
   • Start with: "Cost of capital refers to the minimum rate of return a firm must earn to satisfy its investors..."
2. Show calculations:
   • Always compute WACC with after-tax debt cost and proper weights.
   • Example:

     "For NIBL, WACC = (0.6 × 9%) + (0.1 × 8%) + (0.3 × 15%) = 11.7%."

3. Compare theories:
   • "While MM assumes perfect markets, the trade-off theory explains why firms like Nepal Bank use ~60% debt to balance tax benefits and financial risk."
4. Apply to real firms:
   • "NEPSE-listed firms optimize capital structure by monitoring WACC trends and adjusting debt ratios to stay competitive."
5. Use diagrams:
   • Draw a WACC vs. Debt ratio graph to show the "optimal point."
   • Example:Label axes and explain the "U-shaped" curve.

Sample Exam Answer Structure

Question: "Explain the concept of cost of capital and discuss how Nepal Bank Ltd. can optimize its capital structure."

Answer:

1. Definition: Cost of capital is the minimum return required by investors to provide capital, calculated as the weighted average of debt, preferred stock, and equity costs.

2. Components:

   • Debt cost ($K_d$): 10% (pre-tax), adjusted to 7.5% after 25% tax.
   • Equity cost ($K_e$): 15% (from CAPM: $K_e=R_f+\beta \times (R_m-R_f)$).
   • Preferred stock cost ($K_{ps}$): 8% (dividend yield).

3. WACC Calculation:

4. Optimization:

   • Trade-off theory: Nepal Bank should increase debt to 60% (current) to leverage tax shields.
   • Break-even analysis: Plot EBIT vs. EPS to confirm stability at 60% debt.
   • Risk management: Monitor financial distress costs (e.g., loan defaults).

5. Real-World Tie:

   • "Like Nepal Bank, NEPSE firms use debt ratios of 40–60% to minimize WACC while avoiding excessive risk."

Final Checklist for Full Marks

• Define cost of capital and capital structure.
• Show WACC formula with after-tax debt.
• Compare MM theory vs. trade-off theory.
• Calculate optimal debt ratio (e.g., 60% for Nepal Bank).
• Use a real Nepali firm (NIBL, Nepal Bank, NEPSE) in examples.
• Include a WACC vs. Debt graph or table.
• Mention tax benefits and bankruptcy risks.