Cost of Capital: WACC, Sources, Trade-offs & Real-World Use

TAKEAWAYS:

• The cost of capital is the minimum return a company must earn to satisfy its investors, calculated separately for debt, equity, and preferred stock.
• WACC (Weighted Average Cost of Capital) blends these costs using their proportions in the company’s capital structure, reflecting the true cost of financing.
• MM Propositions explain how capital structure affects firm value and cost of capital, assuming perfect markets (Proposition I) or taxes (Proposition II).
• Trade-offs exist between debt (cheaper but risky) and equity (expensive but flexible), with bankruptcy costs and tax shields playing key roles.
• Real-world applications include NEPSE-listed companies optimizing WACC for projects, banks pricing loans based on cost of funds, and startups like Pathao balancing equity dilution vs. debt risk.
• Exam focus: Numerical problems (WACC calculation, MM applications), conceptual questions (trade-offs, capital structure theories), and case studies (Nepalese firms like Ncell or Daraz).

1. Definitions and Key Concepts

The cost of capital is the opportunity cost of funds used by a company. It represents the minimum return investors expect for providing capital (debt or equity). For a firm, this cost determines the hurdle rate for investment projects—any project with a return below this cost should be rejected.

Sources of Capital and Their Costs

A company raises capital from three primary sources, each with its own cost:

2. Weighted Average Cost of Capital (WACC)

WACC is the overall cost of capital for a company, weighted by the proportion of each source in its capital structure. It is used to:

• Evaluate new projects (NPV, IRR).
• Determine the minimum acceptable return on investments.
• Compare capital structures (debt vs. equity mix).

Formula

$$\text{WACC}=\left(\frac{E}{V}\times r_e\right)+\left(\frac{D}{V}\times r_d\times (1-T)\right)+\left(\frac{P}{V}\times r_p\right)$$ Where:

• $E$ = Market value of equity
• $D$ = Market value of debt
• $P$ = Market value of preferred stock
• $V=E+D+P$ = Total market value of capital
• $r_e$ = Cost of equity (from CAPM or DGM)
• $r_d$ = Cost of debt (after-tax)
• $r_p$ = Cost of preferred stock
• $T$ = Corporate tax rate (25% in Nepal)

WORKED EXAMPLE: WACC for a Kathmandu Retail Shop (e.g., "Shop Everest") Assume:

• Equity: Rs. 50 million (market value), $r_e=14\%$
• Debt: Rs. 30 million (market value), $r_d=10\%$, Tax rate $T=25\%$
• Preferred Stock: Rs. 5 million, $r_p=12\%$

Step 1: Calculate Weights $$\frac{E}{V}=\frac{50}{50+30+5}=\frac{50}{85}=0.588(58.8\%)$$ $$\frac{D}{V}=\frac{30}{85}=0.353(35.3\%)$$ $$\frac{P}{V}=\frac{5}{85}=0.059(5.9\%)$$

Step 2: Apply Costs $$\text{WACC}=(0.588\times 14\%)+(0.353\times 10\%\times 0.75)+(0.059\times 12\%)$$ $$=8.23\%+2.65\%+0.71\%=11.59\%$$

Interpretation: Shop Everest’s minimum required return on any project is 11.59%. Projects with IRR < 11.59% should be rejected.

MERMAID DIAGRAM: Capital Structure and WACC Trade-offs

flowchart TD
    A["Capital Structure"] --> B["Debt (Cheaper, Riskier)"]
    A --> C["Equity (Expensive, Flexible)"]
    A --> D["Preferred Stock (Hybrid)"]
    B --> E["Lower WACC\n(Up to Optimal Point)"]
    C --> F["Higher WACC\n(Due to Cost of Equity)"]
    E --> G["Tax Shield Benefit\n(Reduces \( r_d \))"]
    F --> H["Bankruptcy Risk\n(Increases \( r_e \))"]
    G & H --> I["Optimal Capital Structure\n(Minimizes WACC)"]
    I --> J["Maximizes Firm Value"]

3. Modigliani-Miller (MM) Propositions

Franco Modigliani and Merton Miller developed two key propositions explaining how capital structure affects firm value and cost of capital, assuming perfect capital markets (no taxes, no transaction costs, symmetric information).

Proposition I (No Taxes)

• Firm value is independent of capital structure. $$V_L=V_U\text{(Value with debt = Value without debt)}$$
• Cost of equity increases with debt (due to higher risk): $$r_e=r_0+(r_0-r_d)\times \frac{D}{E}$$ Where $r_0$ = Cost of equity with no debt.

Proposition II (With Corporate Taxes)

• Debt reduces WACC due to tax shields (interest is tax-deductible). $$V_L=V_U+T\times D$$
  • $V_L$ = Firm value with debt.
  • $V_U$ = Firm value without debt.
  • $T\times D$ = Present value of tax shields.

4. Trade-offs in Capital Structure

In real markets (imperfect), firms face trade-offs between:

1. Tax Benefits of Debt (lower WACC).
2. Bankruptcy Costs (higher debt → higher risk of default).
3. Agency Costs (conflicts between shareholders and debt holders).

Comparison: MM vs. Trade-off Theory

REAL-WORLD EXAMPLE: NEPSE-Listed Companies

• Ncell: Uses high debt (~60% of capital structure) due to tax shields, but monitors bankruptcy risk.
• NMB Bank: Balances debt (~40%) and equity to avoid high agency costs.
• Daraz Nepal: Relies more on equity (venture capital) to avoid debt risk in a volatile market.

5. Practical Applications in Nepal

Case 1: NTC’s Expansion Project

NTC wants to build a new fiber-optic network costing Rs. 2 billion. Its current WACC is 12% (based on 50% debt, 50% equity).

• Decision Rule: Only accept if project IRR > 12%.
• If WACC drops to 10% (due to more debt), the project becomes viable.

Case 2: Pathao’s Funding Mix

Pathao (ride-hailing app) raised funds via:

• Debt: Rs. 100 million loan at 12% (after-tax cost = 9%).
• Equity: Rs. 200 million from investors at 18% expected return.
• WACC Calculation: $$\text{WACC}=\left(\frac{200}{300}\times 18\%\right)+\left(\frac{100}{300}\times 9\%\right)=15\%$$
• Implication: Pathao must earn >15% on new ventures (e.g., electric scooter fleet).

Case 3: Bank Loan Pricing (NMB Bank)

Banks like NMB calculate their cost of funds (WACC) to price loans:

• Deposits (Debt): 8% cost (after tax shield).
• Equity: 15% cost (from shareholders).
• If NMB’s capital structure is 70% debt, 30% equity: $$\text{WACC}=(0.7\times 8\%)+(0.3\times 15\%)=9.9\%$$
• Loan Rate: Banks add a profit margin (e.g., 3%) → 12.9% loan rate.

MERMAID DIAGRAM: Accounting Cycle for WACC Calculation

6. Advantages and Disadvantages of Different Capital Sources

7. Common Mistakes to Avoid

1. Using Book Values Instead of Market Values

   • Wrong: $V=\text{Book Debt}+\text{Book Equity}$.
   • Right: $V=\text{Market Debt}+\text{Market Equity}$ (from balance sheet or stock price).

2. Ignoring Taxes on Debt

   • Always use after-tax cost of debt: $r_d\times (1-T)$.

3. Assuming WACC is Constant

   • WACC changes with capital structure (more debt → lower WACC, but higher risk).

4. Overlooking Flotation Costs

   • Issuing new equity/preferred stock has underwriting fees (e.g., 5-10%), increasing effective cost.

In the Real World

1. eSewa and Khalti (Digital Payments)

   • Idea Used: Cost of Capital for Expansion
   • How: eSewa raised Rs. 500 million in equity (from NMB Bank) and took Rs. 300 million in debt to expand its merchant network. Its WACC (~14%) determined the minimum return on new payment gateways (e.g., QR code payments). If the IRR of a new feature was <14%, it was rejected.

2. Ncell’s 4G Expansion

   • Idea Used: Debt vs. Equity Trade-off
   • How: Ncell used 70% debt (cheaper, tax-shielded) and 30% equity to fund its 4G rollout. The WACC of 11% was used to evaluate whether the Rs. 10 billion project would yield sufficient cash flows. The tax benefit from debt reduced its effective cost, but high debt also increased bankruptcy risk (monitored via credit ratings).

3. Daraz Nepal’s Inventory Financing

   • Idea Used: Short-term vs. Long-term Cost of Capital
   • How: Daraz uses short-term debt (trade credit) for inventory (lower cost) and equity from Alibaba for long-term growth. Its WACC of 16% (higher due to equity reliance) means it prioritizes high-margin products (e.g., electronics) over low-margin items (groceries).

Exam Tip

1. Numerical Problems (50% of marks)

   • Always show steps: Weights → Costs → WACC calculation.
   • Example Question: "A company has Rs. 200m equity ($r_e=15\%$), Rs. 100m debt ($r_d=10\%$), and 25% tax rate. Calculate WACC." Solution: $$\text{WACC}=\left(\frac{200}{300}\times 15\%\right)+\left(\frac{100}{300}\times 10\%\times 0.75\right)=12.5\%+2.5\%=15\%$$

2. Conceptual Questions (30% of marks)

   • Key Points to Remember:
     • MM Proposition I: Value is independent of capital structure (no taxes).
     • MM Proposition II: Debt increases firm value due to tax shields.
     • Trade-off Theory: Optimal capital structure balances tax benefits vs. bankruptcy costs.
   • Example Question: "Why might a Nepalese bank prefer equity over debt despite higher cost?" Answer:
     • To avoid bankruptcy risk (banks are highly leveraged).
     • To maintain regulatory capital ratios (e.g., Basel III requires 8% equity).
     • Agency costs (debt holders may impose restrictive covenants).

3. Case Studies (20% of marks)

   • Approach:
     1. Identify the capital structure of the company (e.g., Ncell’s 60% debt).
     2. Calculate WACC using given data.
     3. Discuss trade-offs (e.g., "NTC uses high debt for tax shields but faces higher bankruptcy risk").
   • Example Question: "How would an increase in corporate tax rate affect NMB Bank’s WACC?" Answer:
     • Higher $T$ → Lower after-tax cost of debt ($r_d\times (1-T)$).
     • WACC decreases, making debt more attractive.
     • But: Higher taxes may reduce profitability, offsetting benefits.

Final Summary Table

LAST VISUAL: WACC and Firm Value Graph

graph LR
    A["Debt Level"] --> B["Low Debt"]
    B --> C["High Cost of Equity\nLow Tax Shield\nHigh WACC"]
    A --> D["Optimal Debt"]
    D --> E["Balanced Costs\nLowest WACC\nMax Firm Value"]
    A --> F["High Debt"]
    F --> G["Very High Cost of Equity\nBankruptcy Risk\nHigh WACC"]
    E --> H["Optimal Capital Structure"]