Corporate Finance Fundamentals
Module 6: Cost of Capital
Module Overview
Welcome to Module 6! We're now ready to answer one of the most practical questions in corporate finance: What discount rate should we use to evaluate projects?
The answer is the cost of capital—what it costs the company to raise money. Every dollar a company invests must earn enough to pay back its investors (both debt holders and equity holders). This module shows you how to calculate that required return.
Learning Objectives:
By the end of this module, you will be able to:
- Calculate the cost of debt and understand after-tax cost
- Calculate the cost of equity using CAPM and other methods
- Calculate the cost of preferred stock
- Determine appropriate capital structure weights
- Calculate Weighted Average Cost of Capital (WACC)
- Use WACC as a discount rate for capital budgeting
- Understand the relationship between risk and cost of capital
- Apply cost of capital to real business decisions
Estimated Time: 5-6 hours
6.1 Introduction to Cost of Capital
What is Cost of Capital?
Cost of capital is the return that investors require for providing capital to the company.
Two perspectives, same concept:
From the company's view:
- Cost of raising money
- Minimum return required on investments
- Hurdle rate for projects
From investors' view:
- Required return on investment
- Compensation for risk taken
- Opportunity cost of capital
Why Cost of Capital Matters
1. Capital Budgeting
- Discount rate for NPV calculations
- Accept projects with return > cost of capital
- Reject projects with return < cost of capital
2. Performance Evaluation
- Did the company earn more than its cost of capital?
- Economic profit = Return - Cost of Capital
3. Valuation
- Discount cash flows at cost of capital
- Higher cost of capital → Lower valuation
4. Strategic Planning
- Helps decide which businesses to pursue
- Influences make vs. buy decisions
- Affects capital structure decisions
Sources of Capital
Companies raise capital from three main sources:
1. Debt
- Bonds
- Bank loans
- Notes payable
- Cost: Interest rate
2. Preferred Stock
- Hybrid security (between debt and equity)
- Fixed dividend payment
- Cost: Dividend yield
3. Common Equity
- Common stock
- Retained earnings
- Cost: Required return from shareholders (CAPM!)
Total cost of capital is a weighted average of these costs.
Key Concepts
1. Market Values, Not Book Values
- Use market values for weights
- Book values are historical and often wrong
2. After-Tax Costs
- Interest is tax-deductible
- Dividends are not
- This affects relative costs
3. Marginal Costs
- Use cost of new capital, not historical cost
- What will it cost to raise money today?
4. Risk-Adjusted
- Riskier projects require higher returns
- Cost of capital reflects project risk
6.2 Cost of Debt
What is Cost of Debt?
Cost of debt is the return that lenders require for lending to the company.
For existing debt: The yield to maturity (YTM) on company's bonds
For new debt: The interest rate the company would pay on new borrowing today
Calculating Cost of Debt
Method 1: Yield to Maturity on Existing Bonds
If company has publicly traded bonds, use their YTM.
Example:
Company's bonds:
- Face value: $1,000
- Coupon rate: 6% ($60/year)
- Years to maturity: 10
- Current price: $950
YTM is the rate that solves:
$950 = $60/(1+YTM) + $60/(1+YTM)² + ... + $60/(1+YTM)¹⁰ + $1,000/(1+YTM)¹⁰
Using Excel:
=RATE(10, 60, -950, 1000)
Result: YTM ≈ 6.7%
Cost of debt = 6.7%
Method 2: Rating-Based Approach
If no publicly traded bonds, use company's credit rating to estimate cost.
Example Credit Spreads (2024):
| Rating | Description | Spread over T-bills |
|---|---|---|
| AAA | Highest quality | +0.5% |
| AA | High quality | +0.8% |
| A | Upper medium | +1.2% |
| BBB | Medium | +2.0% |
| BB | Lower medium | +3.5% |
| B | Speculative | +5.5% |
| CCC | Highly speculative | +8.0% |
Example:
Company has BBB rating Risk-free rate: 4%
Cost of debt = 4% + 2.0% = 6.0%
Method 3: Bank Loan Rate
For companies without bonds, use the interest rate on recent bank loans.
Example:
Company recently borrowed at 7.5% from bank.
Cost of debt = 7.5%
After-Tax Cost of Debt
Critical adjustment: Interest is tax-deductible!
After-tax cost of debt:
r_d(after-tax) = r_d(before-tax) × (1 - Tax Rate)
Why? Every dollar of interest saves (Tax Rate × $1) in taxes.
Example:
Before-tax cost of debt: 8% Corporate tax rate: 25%
After-tax cost = 8% × (1 - 0.25)
After-tax cost = 8% × 0.75
After-tax cost = 6%
Intuition:
- Company pays 8% interest
- Saves 2% in taxes (25% of 8%)
- Net cost: 6%
Example with Numbers:
Company borrows $1,000,000 at 8% Annual interest: $80,000 Tax rate: 25%
Without tax deduction:
Cost = $80,000
With tax deduction:
Interest paid: $80,000
Tax savings: -$20,000 (25% × $80,000)
Net cost: $60,000
Effective rate: $60,000 / $1,000,000 = 6%
Always use after-tax cost of debt in WACC calculations!
Cost of Debt Example: Complete Calculation
XYZ Corporation:
Outstanding bonds:
- Face value: $1,000
- Coupon: 7%
- Maturity: 8 years
- Current price: $1,050
- Tax rate: 30%
Step 1: Calculate YTM (before-tax cost)
=RATE(8, 70, -1050, 1000)
YTM ≈ 6.3%
Step 2: Calculate after-tax cost
After-tax cost = 6.3% × (1 - 0.30)
After-tax cost = 6.3% × 0.70
After-tax cost = 4.41%
Cost of debt = 4.41%
6.3 Cost of Preferred Stock
What is Preferred Stock?
Preferred stock is a hybrid security:
- Like debt: Fixed payment (dividend)
- Like equity: No maturity, payment not required
Key features:
- Fixed dividend (typically)
- Paid before common dividends
- No voting rights (usually)
- No tax deduction for company
Calculating Cost of Preferred Stock
Preferred stock is like a perpetuity (infinite fixed payment).
Formula:
r_p = D_p / P_p
Where:
- r_p = Cost of preferred stock
- D_p = Annual preferred dividend
- P_p = Current market price of preferred stock
Note: No tax adjustment! Preferred dividends aren't tax-deductible.
Examples
Example 1:
Preferred stock:
- Annual dividend: $5 per share
- Current price: $50 per share
r_p = $5 / $50
r_p = 0.10 = 10%
Cost of preferred stock = 10%
Example 2:
Preferred stock:
- Annual dividend: $3.50
- Current price: $42
r_p = $3.50 / $42
r_p = 0.0833 = 8.33%
Cost of preferred stock = 8.33%
Example 3: With Flotation Costs
Sometimes we need to adjust for issuance costs (flotation costs).
Preferred stock:
- Annual dividend: $4
- Net proceeds from sale: $45 (after $5 flotation cost)
r_p = $4 / $45
r_p = 0.0889 = 8.89%
Flotation costs increase the cost of capital.
Why Preferred Stock Costs More Than Debt
1. No Tax Deduction
- Interest is tax-deductible
- Preferred dividends are not
- Debt has tax advantage
2. Subordinate to Debt
- Debt must be paid first
- Preferred stock is riskier
- Requires higher return
Example Comparison:
Company can issue:
- Debt at 8% (after-tax cost: 6% with 25% tax rate)
- Preferred stock at 9%
Preferred is more expensive despite similar pre-tax rates!
6.4 Cost of Equity
What is Cost of Equity?
Cost of equity is the return that shareholders require for investing in the company's stock.
Most difficult cost to estimate because:
- No contractual payment (unlike debt)
- Must estimate shareholders' expectations
- Several methods available
We'll cover three methods:
- CAPM (most common)
- Dividend Growth Model (DCF approach)
- Bond Yield Plus Risk Premium (quick estimate)
Method 1: CAPM (Capital Asset Pricing Model)
The CAPM formula from Module 5:
r_e = r_f + β[E(r_m) - r_f]
Where:
- r_e = Cost of equity
- r_f = Risk-free rate
- β = Company's beta
- E(r_m) - r_f = Market risk premium
Example 1:
Company data:
- Beta: 1.2
- Risk-free rate: 4%
- Market risk premium: 7%
r_e = 4% + 1.2(7%)
r_e = 4% + 8.4%
r_e = 12.4%
Cost of equity = 12.4%
Example 2:
Company data:
- Beta: 0.8
- Risk-free rate: 3.5%
- Expected market return: 11%
Market risk premium = 11% - 3.5% = 7.5%
r_e = 3.5% + 0.8(7.5%)
r_e = 3.5% + 6.0%
r_e = 9.5%
Cost of equity = 9.5%
Practical Tips:
1. Finding Beta:
- Yahoo Finance
- Bloomberg
- Company's own investor relations
- Typically calculated using 2-5 years of monthly returns
2. Risk-Free Rate:
- Use 10-year Treasury bond yield
- Current rate (not historical average)
- Should match project horizon if possible
3. Market Risk Premium:
- Historical: 7-8% in U.S.
- Many companies use 6-8% range
- Can vary by country and time period
Example 3: Real Company
Apple Inc. (Hypothetical data):
- Beta: 1.25
- 10-year T-bond yield: 4.2%
- Market risk premium: 7.5%
r_e = 4.2% + 1.25(7.5%)
r_e = 4.2% + 9.375%
r_e = 13.575%
Apple's cost of equity ≈ 13.6%
Method 2: Dividend Growth Model (Gordon Growth Model)
Also called: Dividend Discount Model (DDM)
Formula:
r_e = (D₁ / P₀) + g
Where:
- D₁ = Expected dividend next year
- P₀ = Current stock price
- g = Expected dividend growth rate
This comes from the perpetuity formula rearranged to solve for r.
Example 1:
Stock data:
- Current price: $50
- Next year's dividend: $2.50
- Growth rate: 5%
r_e = ($2.50 / $50) + 0.05
r_e = 0.05 + 0.05
r_e = 0.10 = 10%
Cost of equity = 10%
Example 2:
Stock data:
- Current price: $80
- Current dividend: $3.00
- Growth rate: 6%
Next year's dividend: D₁ = $3.00 × 1.06 = $3.18
r_e = ($3.18 / $80) + 0.06
r_e = 0.03975 + 0.06
r_e = 0.09975 ≈ 10%
Cost of equity = 10%
Estimating Growth Rate (g):
Method A: Historical Growth
- Calculate average dividend growth over past 5-10 years
Method B: Retention Ratio Method
g = ROE × Retention Ratio
g = ROE × (1 - Payout Ratio)
Example:
Company has:
- ROE = 15%
- Payout ratio = 40% (pays out 40% of earnings)
- Retention ratio = 60%
g = 15% × 0.60 = 9%
Method C: Analyst Forecasts
- Use growth rate forecasted by analysts
- Available from financial websites
Limitations of Dividend Growth Model:
1. Only works for dividend-paying stocks
- Many companies don't pay dividends
- Growth stocks often reinvest all earnings
2. Assumes constant growth
- Growth rates change over time
- Model is sensitive to growth assumption
3. May not reflect true risk
- Doesn't explicitly account for risk like CAPM does
Best for: Mature, stable, dividend-paying companies
Method 3: Bond Yield Plus Risk Premium
Quick approximation method:
r_e = Company's bond yield + Risk premium
Typical risk premium: 3-5%
Logic: Equity is riskier than debt, so requires higher return.
Example:
Company's bond yield: 7% Risk premium: 4%
r_e = 7% + 4% = 11%
Cost of equity ≈ 11%
When to use:
- Quick estimate needed
- Other methods not feasible
- Check if other methods are reasonable
Not as rigorous as CAPM or dividend model, but useful for ballpark estimates.
Comparing the Three Methods
Example: ABC Corporation
Method 1 - CAPM:
- Beta: 1.15
- Risk-free rate: 4%
- Market premium: 7%
- Result: 4% + 1.15(7%) = 12.05%
Method 2 - Dividend Growth:
- Current price: $60
- Next dividend: $2.40
- Growth rate: 8%
- Result: ($2.40/$60) + 8% = 12%
Method 3 - Bond Yield Plus:
- Bond yield: 6.5%
- Risk premium: 5%
- Result: 6.5% + 5% = 11.5%
Average: (12.05% + 12% + 11.5%) / 3 = 11.85%
Recommendation: Use CAPM as primary method, but verify with others. If results are similar (within 1-2%), that's good confirmation.
Cost of Retained Earnings
Question: What's the cost of using retained earnings vs. issuing new equity?
Answer: Same cost!
Why? Shareholders could receive dividends and invest them elsewhere. By retaining earnings, company must earn at least what shareholders could earn.
Cost of retained earnings = Cost of equity
New equity issuance: May be slightly higher due to flotation costs.
r_e(new) = r_e / (1 - flotation cost %)
Example:
Cost of equity: 12% Flotation costs: 5%
r_e(new) = 12% / (1 - 0.05)
r_e(new) = 12% / 0.95
r_e(new) = 12.63%
New equity is 0.63% more expensive due to flotation costs.
6.5 Weighted Average Cost of Capital (WACC)
What is WACC?
WACC is the overall cost of capital—the weighted average of all capital sources.
The formula:
WACC = w_d × r_d(1-T) + w_p × r_p + w_e × r_e
Where:
- w_d = Weight of debt
- w_p = Weight of preferred stock
- w_e = Weight of equity
- r_d = Cost of debt (before-tax)
- r_p = Cost of preferred stock
- r_e = Cost of equity
- T = Tax rate
Weights must sum to 1.0: w_d + w_p + w_e = 1.0
Determining Weights
Use market values, not book values!
Market Value of Debt:
- For bonds: Number of bonds × Market price
- For bank loans: Usually face value (loans trade near par)
Market Value of Preferred Stock:
- Shares outstanding × Market price per share
Market Value of Equity:
- Shares outstanding × Stock price
- Also called "market capitalization"
Calculate Weights:
Total Market Value = Market Value of Debt + Preferred + Equity
w_d = Market Value of Debt / Total Market Value
w_p = Market Value of Preferred / Total Market Value
w_e = Market Value of Equity / Total Market Value
WACC Calculation: Complete Example
DEF Corporation:
Capital Structure (Market Values):
- Debt: $400 million
- Preferred stock: $100 million
- Common equity: $500 million
- Total: $1,000 million
Component Costs:
- Cost of debt (before-tax): 7%
- Cost of preferred: 9%
- Cost of equity: 13%
- Tax rate: 25%
Step 1: Calculate weights
w_d = $400M / $1,000M = 0.40 = 40%
w_p = $100M / $1,000M = 0.10 = 10%
w_e = $500M / $1,000M = 0.50 = 50%
Step 2: Calculate WACC
WACC = 0.40 × 7%(1-0.25) + 0.10 × 9% + 0.50 × 13%
WACC = 0.40 × 7% × 0.75 + 0.10 × 9% + 0.50 × 13%
WACC = 0.40 × 5.25% + 0.90% + 6.50%
WACC = 2.10% + 0.90% + 6.50%
WACC = 9.50%
DEF Corporation's WACC = 9.5%
Interpretation: The company must earn at least 9.5% on its investments to satisfy all investors (debt holders, preferred shareholders, and common shareholders).
WACC Example 2: Step-by-Step
GHI Corporation:
Given Information:
Debt:
- 50,000 bonds outstanding
- $1,000 face value each
- Trading at $1,050
- Coupon: 6%, paid annually
- 10 years to maturity
Equity:
- 10 million shares outstanding
- Current stock price: $40
- Beta: 1.2
- Risk-free rate: 4%
- Market risk premium: 7%
Other:
- No preferred stock
- Tax rate: 30%
Step 1: Calculate market values
Market Value of Debt = 50,000 × $1,050 = $52.5 million
Market Value of Equity = 10,000,000 × $40 = $400 million
Total = $452.5 million
Step 2: Calculate weights
w_d = $52.5M / $452.5M = 0.116 = 11.6%
w_e = $400M / $452.5M = 0.884 = 88.4%
Step 3: Calculate cost of debt
YTM on bonds (using Excel):
=RATE(10, 60, -1050, 1000) ≈ 5.43%
After-tax cost:
r_d(after-tax) = 5.43% × (1 - 0.30) = 3.80%
Step 4: Calculate cost of equity
r_e = 4% + 1.2(7%)
r_e = 4% + 8.4%
r_e = 12.4%
Step 5: Calculate WACC
WACC = 0.116 × 3.80% + 0.884 × 12.4%
WACC = 0.44% + 10.96%
WACC = 11.4%
GHI Corporation's WACC = 11.4%
WACC in Practice: Real Example
Let's estimate Tesla's WACC (hypothetical numbers):
Capital Structure (approximate):
- Market cap (equity): $600 billion
- Debt: $10 billion
- Total: $610 billion
Weights:
w_e = $600B / $610B = 98.4%
w_d = $10B / $610B = 1.6%
Cost Components:
- Beta: 1.8
- Risk-free rate: 4%
- Market premium: 8%
- Cost of debt: 6%
- Tax rate: 21%
Cost of Equity:
r_e = 4% + 1.8(8%) = 18.4%
After-tax Cost of Debt:
r_d = 6% × (1 - 0.21) = 4.74%
WACC:
WACC = 0.984 × 18.4% + 0.016 × 4.74%
WACC = 18.1% + 0.08%
WACC = 18.2%
Tesla's WACC ≈ 18.2%
High WACC reflects:
- High beta (risky stock)
- Very little debt (no tax shield benefit)
- Growth company characteristics
6.6 Using WACC in Capital Budgeting
WACC as Discount Rate
Basic Rule: Use WACC as discount rate for projects with average risk.
NPV using WACC:
NPV = Σ [CF_t / (1 + WACC)^t] - Initial Investment
Example: Project Evaluation with WACC
Company WACC: 10%
Project Details:
- Initial investment: $500,000
- Year 1 cash flow: $150,000
- Year 2 cash flow: $175,000
- Year 3 cash flow: $200,000
- Year 4 cash flow: $150,000
Calculate NPV:
NPV = -$500,000 + $150,000/1.10 + $175,000/1.10² + $200,000/1.10³ + $150,000/1.10⁴
NPV = -$500,000 + $136,364 + $144,628 + $150,263 + $102,452
NPV = $33,707
Decision: Accept (NPV > 0)
The project earns more than the 10% WACC, creating value.
When NOT to Use Overall WACC
WACC is appropriate for projects with:
- Same risk as company's average
- Same capital structure
Adjust WACC for:
1. Different Risk Level
Low-risk project:
- Use lower discount rate
- Example: Cost savings project with certain cash flows
High-risk project:
- Use higher discount rate
- Example: New product in uncertain market
2. Different Financing
Heavily debt-financed project:
- Use project-specific WACC
- Higher debt weight in calculation
All-equity financed project:
- Use cost of equity only
- No debt component
Risk-Adjusted WACC
Approach: Adjust beta for project risk, recalculate cost of equity and WACC.
Example:
Company's overall:
- Beta: 1.0
- WACC: 11%
- Capital structure: 30% debt, 70% equity
High-risk project:
- Estimated beta: 1.5
- Risk-free rate: 4%
- Market premium: 8%
Calculate project WACC:
r_e(project) = 4% + 1.5(8%) = 16%
Cost of debt (after-tax) = 6% (unchanged)
WACC(project) = 0.30 × 6% + 0.70 × 16%
WACC(project) = 1.8% + 11.2%
WACC(project) = 13%
Use 13% instead of 11% for this riskier project.
Divisional Cost of Capital
Large companies with multiple divisions should use divisional WACC.
Example: Conglomerate Corp
Overall WACC: 10%
Division A (Utilities - Low Risk):
- Beta: 0.6
- Divisional WACC: 8%
Division B (Technology - High Risk):
- Beta: 1.4
- Divisional WACC: 13%
Problem with using overall 10% for all projects:
- Reject good low-risk projects (they can't clear 10% hurdle)
- Accept bad high-risk projects (they clear 10% but shouldn't)
Solution: Use divisional WACC.
Division A Project: NPV with 8% discount rate Division B Project: NPV with 13% discount rate
6.7 Factors Affecting Cost of Capital
Factor 1: Market Conditions
Interest Rate Environment:
- Rising rates → Higher cost of debt → Higher WACC
- Falling rates → Lower cost of debt → Lower WACC
Stock Market Performance:
- Bull market → Lower cost of equity → Lower WACC
- Bear market → Higher cost of equity → Higher WACC
Example:
2021: Low rates
- Risk-free rate: 2%
- Company WACC: 8%
2023: Higher rates
- Risk-free rate: 5%
- Company WACC: 11%
Same company, different cost of capital due to market conditions.
Factor 2: Company Risk
Business Risk:
- Volatile industry → Higher beta → Higher cost of equity
- Stable industry → Lower beta → Lower cost of equity
Financial Risk (Leverage):
- More debt → Riskier → Higher cost of debt and equity
- Less debt → Less risky → Lower cost of debt and equity
Example:
Utility Company (Low Business Risk):
- Beta: 0.6
- Cost of equity: 9%
- Cost of debt: 5%
- WACC: 7%
Tech Startup (High Business Risk):
- Beta: 2.0
- Cost of equity: 20%
- Cost of debt: 12%
- WACC: 17%
Factor 3: Capital Structure
More Debt:
- ✓ Debt is cheaper (tax deduction)
- ✗ More debt increases risk
- ✗ Cost of debt and equity increase
Optimal Capital Structure:
- Balances tax benefits of debt
- Against increased risk
- Minimizes WACC
- We'll explore this more in Module 7
Example: Impact of Leverage
Company considering different capital structures:
All Equity:
- Cost of equity: 12%
- WACC: 12%
30% Debt:
- Cost of debt: 6% (after-tax: 4.5%)
- Cost of equity: 13% (slightly higher due to risk)
- WACC: 0.30(4.5%) + 0.70(13%) = 10.45%
50% Debt:
- Cost of debt: 7% (after-tax: 5.25%)
- Cost of equity: 15% (much higher due to risk)
- WACC: 0.50(5.25%) + 0.50(15%) = 10.125%
70% Debt:
- Cost of debt: 10% (after-tax: 7.5%)
- Cost of equity: 20% (very high due to risk)
- WACC: 0.70(7.5%) + 0.30(20%) = 11.25%
Optimal: Around 50% debt (lowest WACC)
Factor 4: Firm Size
Large Companies:
- Better access to capital markets
- Lower cost of debt
- More diversified
- Lower cost of equity
- Lower WACC overall
Small Companies:
- Limited access to capital
- Higher cost of debt
- More concentrated risk
- Higher cost of equity
- Higher WACC overall
Example:
Large Cap (S&P 500):
- Average WACC: 7-9%
Small Cap:
- Average WACC: 12-15%
Startup:
- Cost of capital: 20-30%+
Factor 5: Country and Currency Risk
Developed Markets:
- Stable
- Lower risk
- Lower cost of capital
Emerging Markets:
- Higher political/economic risk
- Currency risk
- Higher cost of capital
Example:
Same business in different countries:
United States:
- Risk-free rate: 4%
- WACC: 10%
Brazil:
- Risk-free rate: 12%
- Country risk premium: +3%
- WACC: 18%
Nigeria:
- Risk-free rate: 18%
- Country risk premium: +5%
- WACC: 25%
6.8 Common Mistakes and Best Practices
Common Mistakes
Mistake 1: Using Book Values
- ✗ Book values are historical
- ✓ Always use market values
Mistake 2: Forgetting Tax Shield
- ✗ Using before-tax cost of debt
- ✓ Always use after-tax cost: r_d(1-T)
Mistake 3: Using Wrong Risk-Free Rate
- ✗ Using 3-month T-bill for long-term projects
- ✓ Match maturity to project horizon
Mistake 4: Inconsistent Assumptions
- ✗ Using nominal cash flows with real discount rate
- ✓ Nominal with nominal, real with real
Mistake 5: Using Historical Market Return
- ✗ "Market returned 15% last year, so..."
- ✓ Use long-term average (10-11%) or forward-looking estimate
Mistake 6: One WACC for Everything
- ✗ Using company WACC for all projects
- ✓ Adjust for project risk
Mistake 7: Ignoring Flotation Costs
- For new issuances, flotation costs matter
- Adjust cost upward
Mistake 8: Wrong Beta
- ✗ Using beta from different time period or frequency
- ✓ Use recent beta (2-5 years, monthly data)
Best Practices
1. Triangulate
- Calculate cost of equity using multiple methods
- If CAPM gives 12%, dividend model gives 11.5%, and bond-plus gives 12.5%, you're probably around 12%
2. Use Industry Comparables
- Compare your WACC to similar companies
- If you're way off, investigate why
3. Sensitivity Analysis
- WACC is an estimate
- Test NPV at WACC ± 2%
- See if decision changes
Example:
Base WACC: 10% Project NPV: $50,000
Test:
- At 8%: NPV = $85,000 (still positive)
- At 12%: NPV = $18,000 (still positive)
Conclusion: Decision is robust to WACC uncertainty.
4. Update Regularly
- Market conditions change
- Beta changes
- Update WACC at least annually
5. Document Assumptions
- Show how you calculated WACC
- State all assumptions clearly
- Makes it easy to update later
6. Use Company's Target Capital Structure
- Not necessarily current structure
- What structure does management target?
- Especially important for growing companies
6.9 WACC and Company Valuation
Enterprise Value and WACC
Enterprise Value (EV) represents the value of the entire firm:
EV = PV(Free Cash Flows to Firm) discounted at WACC
Free Cash Flow to Firm (FCFF):
FCFF = EBIT(1-T) + Depreciation - Capex - Change in NWC
Then:
Equity Value = EV - Debt
Example:
Company has:
- Free cash flows: $100M/year (constant)
- WACC: 10%
- Debt: $200M
Calculate EV:
EV = $100M / 0.10 = $1,000M
Calculate Equity Value:
Equity Value = $1,000M - $200M = $800M
Impact of WACC on Valuation
Lower WACC → Higher valuation Higher WACC → Lower valuation
Example:
Company with $50M perpetual cash flow:
At 8% WACC:
Value = $50M / 0.08 = $625M
At 10% WACC:
Value = $50M / 0.10 = $500M
At 12% WACC:
Value = $50M / 0.12 = $417M
2% change in WACC creates $208M value difference!
This is why WACC matters so much.
Module 6 Practice Problems
Problem Set 1: Cost of Debt
-
After-Tax Cost: Company issues bonds at 8% interest. Tax rate: 30%
Calculate after-tax cost of debt.
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YTM Calculation: Bond details:
- Face value: $1,000
- Coupon: 7% annual
- Years to maturity: 12
- Current price: $1,080
- Tax rate: 25%
a. Calculate YTM (use Excel) b. Calculate after-tax cost of debt
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Rating Approach: Company has A rating. Risk-free rate: 3.5% Spread for A rating: 1.5% Tax rate: 28%
Calculate after-tax cost of debt.
Problem Set 2: Cost of Equity
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CAPM:
- Beta: 1.35
- Risk-free rate: 4%
- Market return: 11%
Calculate cost of equity.
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Dividend Growth Model:
- Current stock price: $75
- Next year's dividend: $3.50
- Expected growth: 6%
Calculate cost of equity.
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Compare Methods: Calculate cost of equity using all three methods:
CAPM:
- Beta: 1.15
- Risk-free rate: 3.5%
- Market premium: 7%
Dividend Model:
- Price: $60
- Current dividend: $2.50
- Growth rate: 5%
Bond Plus:
- Company's bond yield: 6%
- Risk premium: 4.5%
Which estimate would you use?
Problem Set 3: WACC Calculation
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Basic WACC: Capital structure (market values):
- Debt: $300M
- Equity: $700M
Costs:
- Cost of debt (before-tax): 7%
- Cost of equity: 12%
- Tax rate: 25%
Calculate WACC.
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Three-Component WACC: Capital structure:
- Debt: $200M
- Preferred stock: $50M
- Equity: $450M
Costs:
- Cost of debt: 6.5%
- Cost of preferred: 8%
- Cost of equity: 13.5%
- Tax rate: 30%
Calculate WACC.
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Complete WACC Calculation:
Debt:
- 100,000 bonds outstanding
- $1,000 face value
- Trading at $950
- Coupon: 6%
- 8 years to maturity
Equity:
- 50 million shares
- Stock price: $25
- Beta: 1.2
- Risk-free rate: 4%
- Market return: 11%
Tax rate: 28%
Calculate WACC from scratch.
Problem Set 4: Applications
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Project Evaluation: Company WACC: 11%
Project:
- Initial investment: $800,000
- Annual cash flows: $200,000 for 6 years
a. Calculate NPV b. Should project be accepted?
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Risk-Adjusted Rate: Company overall:
- WACC: 10%
- Beta: 1.0
High-risk project:
- Estimated beta: 1.6
- Risk-free rate: 4%
- Market premium: 8%
Capital structure: 40% debt, 60% equity After-tax cost of debt: 5%
a. Calculate project's cost of equity b. Calculate project's WACC c. Should you use this or company's 10%?
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Sensitivity Analysis: Project NPV at different discount rates:
Base WACC: 12% Base NPV: $150,000
Calculate NPV if WACC is: a. 10% b. 14%
Project cash flows:
- Year 0: -$1,000,000
- Years 1-5: $280,000 each
Problem Set 5: Comprehensive Problem
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Full WACC and Project Evaluation:
XYZ Corporation:
Current capital structure:
- 200,000 bonds, $1,000 face, trading at $1,050
- Coupon: 7%, 10 years to maturity
- 30 million shares at $40/share
- Beta: 1.25
Market data:
- Risk-free rate: 3.8%
- Market risk premium: 7.5%
- Tax rate: 25%
Projects under consideration:
Project A (Average risk):
- Investment: $50M
- Cash flows: $12M/year for 6 years
Project B (Low risk, β = 0.8):
- Investment: $40M
- Cash flows: $9M/year for 7 years
a. Calculate company WACC b. Evaluate Project A using WACC c. Calculate appropriate rate for Project B d. Evaluate Project B using risk-adjusted rate e. Which projects should be accepted?
Additional Resources
Excel Templates
Download calculation templates for:
- WACC calculator
- Cost of equity (multiple methods)
- Sensitivity analysis tool
- Project evaluation with risk adjustment
Further Reading
Books:
- "Valuation" by McKinsey & Company
- "Investment Valuation" by Aswath Damodaran
Online Resources:
- Damodaran Online (data on cost of capital by industry)
- Company investor relations pages
- Bloomberg/Yahoo Finance (for betas and market data)
Looking Ahead to Module 7
You now understand how to calculate a company's cost of capital—the discount rate that reflects what investors require. This is one of the most practical applications of everything you've learned so far.
In Module 7, we'll explore Capital Structure—how companies decide their mix of debt and equity:
- The trade-off between debt and equity
- How capital structure affects firm value
- Modigliani-Miller theorems
- Optimal capital structure
- Real-world capital structure decisions
This builds directly on WACC—you'll see how changing the debt/equity mix affects the cost of capital and firm value.
Prepare for Module 7 by:
- Understanding the tax advantage of debt
- Recognizing that debt increases risk
- Reviewing WACC calculations thoroughly
Summary
Congratulations on completing Module 6! You now understand:
✓ What cost of capital represents ✓ How to calculate cost of debt (after-tax) ✓ How to calculate cost of preferred stock ✓ Three methods for calculating cost of equity ✓ How to determine market value weights ✓ How to calculate WACC ✓ When and how to adjust WACC for project risk ✓ How WACC affects valuation ✓ Common mistakes and best practices
Cost of capital bridges theory and practice. It takes the abstract concepts of risk and return and turns them into a concrete number you can use to make decisions. Every major capital budgeting decision requires an appropriate discount rate—now you know how to find it.
This is one of the most valuable skills in corporate finance. Master WACC calculation, and you'll have a tool you'll use throughout your career.
Ready for the next topic? Proceed to Module 7: Capital Structure to learn how companies optimize their financing mix.
"It's far better to buy a wonderful company at a fair price than a fair company at a wonderful price." — Warren Buffett
"The cost of capital is the single most important input in valuation." — Aswath Damodaran
You now know how to calculate that critical input. Use it wisely!
See you in Module 7!