Understand WACC and discount rate calculation

Core Concept: What is WACC?

WHY these specific components?

1. Weights ($E/V$ and $D/V$): Reflect the actual capital mix. A company that's 70% equity-financed weights equity cost more heavily.

2. Cost of equity ($r_e$): Shareholders take the MOST risk (last to get paid in bankruptcy), so they demand the HIGHEST return. No tax benefit.

3. Cost of debt $(1 - T_c) \cdot r_d$: Interest is tax-deductible, so the government effectively subsidizes debt. If you pay8% interest but save 25% in taxes, your after-tax cost is $8\% \times (1 - 0.25) = 6\%$.

Deriving WACC from First Principles

THE FUNDAMENTAL QUESTION: If I give this company $1, what return must it generate to satisfy both debt-holders AND equity-holders?

Step 1: Understanding Capital Structure Weights

A company's total value comes from two sources:

$V = E + D$

If you invest the company, you're implicitly buying a portfolio of its debt and equity. The fraction of each determines your expected return:

$\text{Expected return} = \text{(weight of equity)} \times \text{(equity return)} + \text{(weight of debt)} \times \text{(debt return)}$

$r_{\text{portfolio}} = \frac{E}{E+D} \cdot r_e + \frac{D}{E+D} \cdot r_d$

Step 2: The Tax Shield on Debt

WHY do we adjust debt cost by $(1 - T_c)$?

When a company pays interest, it reduces taxable income. This is called the tax shield.

• Interest payment: $I = r_d \cdot D$
• Tax saved: $T_c \cdot I = T_c \cdot r_d \cdot D$
• Net cost: $I - \text{tax saved} = r_d \cdot D - T_c \cdot r_d \cdot D = \cdot (1 - T_c)$

The effective cost per dollar of debt is:

$\text{After-tax cost of debt} = r_d \cdot (1 - T_c)$

Equity has NO tax benefit—dividends aren't tax-deductible.

Step 3: Final WACC Formula

Combining both:

Calculating Each Component

1. Cost of Equity ($r_e$)

THE PROBLEM: Equity has no explicit "interest rate" like debt. We must infer what return shareholders expect.

Method: Capital Asset Pricing Model (CAPM)

WHY this formula?

Investors split required return into two parts:

1. Time value of money ($r_f$): Compensation for waiting (even risk-free bonds pay this).
2. Risk premium ($\beta \cdot (r_m - r_f)$): Extra return for bearing market risk.

Beta measures systematic risk:

• $\beta = 1$: Stock moves with market (average risk).
• $\beta > 1$: Stock is MORE volatile than market (tech stocks, $\beta \approx 1.3$).
• $\beta < 1$: Stock is LESS volatile (utilities, $\beta \approx 0.7$).

HOW to find Beta? Regression of stock returns against market returns over2-5 years. Sources: Bloomberg, Yahoo Finance, company investor relations.

2. Cost of Debt ($r_d$)

THE QUESTION: What interest rate does the company pay TODAY?

Method 1: Yield to Maturity (YTM) on Existing Bonds

If the company has traded bonds, the YTM reflects the market's current assessment of credit risk.

$\text{Bond Price} = \sum_{t=1}^{n} \frac{C}{(1 + r_d)^t} + \frac{F}{(1 + r_d)^n}$

Solve for $r_d$ (the YTM). Financial calculators or Excel RATE() function handle this.

Method 2: Interest Rate on Recent Loans

Check the latest debt isuance or credit facility. Average if multiple debt instruments exist.

3. Market Values ($E$ and $D$)

CRITICAL: Use market values, NOT book values from the balance sheet.

• Equity: $E = \text{Shares outstanding} \times \text{Current stock price}$
• Debt: For traded bonds, use market price. For bank loans, book value ≈ market value (if recent).

WHY market values? Investors care about current market rates, not historical accounting costs.

Complete WACC Example

Using WACC as a Discount Rate

###ounted Cash Flow (DCF) Valuation

$\text{Enterprise Value} = \sum_{t=1}^{n} \frac{\text{FCF}_t}{(1 + \text{WACC})^t}$

where $\text{FCF}_t$ Free Cash Flow in year $t$ (cash available to ALL investors).

WHY WACC here? FCF belongs to both debt and equity holders, so we discount at the BLENDED cost.

Net Present Value (NPV) of Projects

$\text{NPV} = \sum_{t=0}^{n} \frac{\text{Cash Flow}_t}{(1 + \text{WACC})^t}$

• NPV > 0: Project earns MORE than WACC → Accept (creates value).
• NPV < 0: Project earns LESS than WACC → Reject (destroys value).

Common Mistakes and Confusions

Practical Adjustments

1. Adjusting for Changing Capital Structure

If you're valuing a leveraged buyout (LBO) or recapitalization, debt/equity mix will change. Use the target capital structure, not current weights.

2. Different Discount Rates for Different Divisions

A conglomerate's WACC averages ALL businesses. For project-level NPV, use a division-specific beta (reflecting that unit's risk) to compute a custom WACC.

3. Country Risk Premium (for Emerging Markets)

For non-US companies, add a country risk premium to $r_f$ or $(r_m - r_f)$:

$r_e = r_f + \beta \cdot [(r_m - r_f) + \text{CRP}]$

WHY? Emerging markets have political risk, currency risk, less liquidity. Investors demand extra return.

Connections

• Cost of Equity and CAPM – Deep dive into beta calculation and alternatives (DDM, APT)
• Capital Structure and MM Theorem – How debt/equity mix affects firm value (spoiler: WACC minimization under trade-off theory)
• Discounted Cash Flow (DCF) Valuation – WACC is the denominator in DCF; understand free cash flow numerators
• Net Present Value (NPV) and IR – WACC as the hurdle rate for capital budgeting
• Tax Shield and Interest Deductibility – Why debt is cheaper and how tax policy affects optimal leverage
• Beta Estimation and Unlevering/Relevering – Adjust beta for changing leverage when computing divisional WACCs
• Enterprise Value vs Equity Value – WACC discounts to EV; subtract net debt to get equity value

Flashcards

#flashcards/stock-market

What is WACC and why is it used? :: WACC (Weighted Average Cost of Capital) is the blended cost of a company's debt and equity financing. It represents the minimum return a company must earn on its investments to satisfy all investors. Used as the discount rate in DCF valuation and NPV calculations.

Concept Map

Hinglish (regional understanding)