🔢 WACC — Weighted Average Cost of Capital

Definition: WACC is the average rate a company is expected to pay to finance its assets — a blended cost of debt and equity, weighted by their proportions.

The discount rate in almost every DCF Valuation model.

Key course: Wharton FNCE 611, HBS Finance I, Booth BUSF 33001

📐 The Formula

$W A CC = \frac{E}{V} \cdot r_{e} + \frac{D}{V} \cdot r_{d} \cdot (1 - T)$

Variable	Meaning
`E`	Market value of equity
`D`	Market value of debt
`V`	E + D (total firm value)
`re`	Cost of equity
`rd`	Cost of debt (pre-tax)
`T`	Corporate tax rate
`(1-T)`	Tax shield on debt

🔑 Why the Tax Shield?

Interest payments are tax deductible — which means the government subsidizes part of debt financing. If the tax rate is 25% and interest cost is 6%, the after-tax cost of debt is only 4.5%.

This is why companies prefer some debt in their capital structure (up to a point) → see Capital Structure.

📊 Computing Each Component

1. Cost of Equity (re) — via CAPM

$r_{e} = r_{f} + β \cdot (r_{m} - r_{f})$

rf = risk-free rate (10-year US Treasury, e.g. 4.5%)
β = company’s beta (sensitivity to market)
(rm − rf) = equity risk premium (historical ~5-6%)

Example: β = 1.2, rf = 4.5%, ERP = 5.5% → re = 4.5% + 1.2 × 5.5% = 11.1%

2. Cost of Debt (rd)

Use the company’s current borrowing rate or yield-to-maturity on outstanding bonds.

Often estimated from credit rating + spread tables
Typical range: 4–8% for investment-grade companies

3. Weights

Always use market values, not book values:

E = share price × shares outstanding
D = current market value of all debt

🧮 Full WACC Example

Company: 60% equity / 40% debt, T = 25%, re = 11%, rd = 6%

$W A CC = 0.60 \times 11% + 0.40 \times 6% \times (1 - 0.25)$ $W A CC = 6.6% + 1.8% = 8.4%$

💻 Practitioner Python Implementation

def calculate_wacc(equity_val, debt_val, cost_equity, cost_debt, tax_rate):
    """Calculates the Weighted Average Cost of Capital"""
    total_val = equity_val + debt_val
    
    # Weights
    w_e = equity_val / total_val
    w_d = debt_val / total_val
    
    # After-tax cost of debt
    after_tax_debt = cost_debt * (1 - tax_rate)
    
    # WACC Calculation
    wacc = (w_e * cost_equity) + (w_d * after_tax_debt)
    
    return wacc
 
# Example inputs (in millions)
e_val = 600   # 60% weight
d_val = 400   # 40% weight
r_e = 0.11    # Cost of equity via CAPM
r_d = 0.06    # YTM on debt
t = 0.25      # Corporate tax rate
 
wacc_result = calculate_wacc(e_val, d_val, r_e, r_d, t)
print(f"Proprietary WACC: {wacc_result:.2%}")
# Output: Proprietary WACC: 8.40%

🎯 What WACC Tells Us

WACC = minimum required return for a project to create value
Projects earning > WACC create shareholder value
Projects earning < WACC destroy value
IRR > WACC → accept the project

⚠️ Common WACC Mistakes

Mistake	Correct Approach
Using book value weights	Use market value weights
Using coupon rate for debt cost	Use yield-to-maturity
Using historical beta without thought	Adjust for leverage (Hamada equation)
Wrong tax rate	Use marginal tax rate, not effective
Circular reference in model	Use iterative calculation or break the circle

🔄 WACC Sensitivity

Even small changes in WACC drastically affect valuations:

WACC	DCF Value
8%	$180M
10%	$140M
12%	$112M

This is why analysts always present WACC sensitivity tables alongside DCF models.

🎯 When Would I Use This?

Capital Allocation Decisions: “The corporate WACC is 8%. Any internal project proposing an IRR of 6% must be immediately rejected.”
CFO Debt Issuance: “If we issue $1B in junk bonds, it will raise our cost of debt, fundamentally altering our WACC and destroying our equity valuation.”
Divisional Performance Evaluation: “We cannot judge the Software division and the Real Estate division using the same hurdle rate; we must calculate a specific WACC for each.”

🔗 Connected Concepts

DCF Valuation — WACC is the discount rate
CAPM — how re is calculated
Capital Structure — how D/E ratio is chosen
Beta and Systematic Risk — the β input
Efficient Market Hypothesis — context for risk-free rate choice

🏫 School Context

Wharton: Derives WACC rigorously from Modigliani-Miller propositions
HBS: Emphasis on judgment — which beta to use, whether to lever/unlever
Columbia: Heavy use in value investing context; Graham disciples very suspicious of high WACCs on growth stocks

← 📊 Finance MOC | Related: DCF Valuation · CAPM · Capital Structure

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