Selecting Discount Rates with CAPM and WACC

Why It Matters

Your DCF model is only as good as your discount rate. Use 8% instead of 10%, and a stock worth $50 suddenly looks like $70. Use a stale risk-free rate from six months ago, and your entire valuation drifts by 10-15%.

The point is: discount rate selection isn't a minor input. It's the single most sensitive driver of your valuation, compounding through every forecast year and into terminal value.

Two tools dominate professional practice: CAPM (Capital Asset Pricing Model) for cost of equity, and WACC (Weighted Average Cost of Capital) for blending equity and debt into a single discount rate.

CAPM: Building the Cost of Equity

The Capital Asset Pricing Model gives you a required return for equity investors:

The formula: Cost of Equity = Rf + Beta x (MRP)

Where:

• Rf = Risk-free rate (what you'd earn with zero risk)
• Beta = Stock's sensitivity to market movements
• MRP = Market Risk Premium (extra return for bearing equity risk)

Risk-Free Rate Selection

For DCF models with 5-10 year projections, use the 10-year Treasury yield. As of late 2024, that's running 4.0-4.5% (compared to near-zero in 2021).

Why this matters: A stale rate from when Treasuries yielded 3% understates your discount rate by 100+ basis points. That's an 8-12% swing in your valuation (more than most margin-of-safety buffers).

Decision rule: Check the current 10-year Treasury yield on the day you finalize your model. Don't recycle old numbers.

Beta: Measuring Systematic Risk

Beta of 1.0 means the stock moves in line with the market. Beta of 1.3 means 30% more volatile (in both directions).

Interpretation guide:

• < 0.8: Low volatility (utilities, consumer staples)
• 0.8-1.2: Market-like volatility (diversified industrials, banks)
• > 1.2: High volatility (tech, small-caps, cyclicals)

The durable lesson: Beta is backward-looking (typically calculated from 2-5 years of monthly returns). It tells you what happened, not what will happen. Use it as a starting point, but adjust for structural changes in the business (spin-offs, major acquisitions, leverage changes).

Where to find it: Yahoo Finance Key Statistics, Bloomberg, or FactSet.

Levered vs. Unlevered Beta

The beta from Yahoo Finance is levered beta—it includes the risk from the company's debt. To compare companies with different capital structures, you need to unlever:

Unlevered Beta = Levered Beta / [1 + (1-Tax Rate) x (Debt/Equity)]

Example: Levered beta 1.4, tax rate 25%, D/E ratio 0.5:

Unlevered = 1.4 / [1 + (0.75)(0.5)] = 1.4 / 1.375 = 1.02

The practical takeaway: This 1.02 reflects pure business risk (stripped of financial leverage). Use unlevered betas when building comparables or re-levering to a target capital structure.

Market Risk Premium

Historical average: The S&P 500 has outperformed long-term Treasuries by roughly 5-6% annually over the past 50-90 years. This is stable and widely used.

Implied ERP (Damodaran method): Uses current stock prices to back into what premium investors are pricing today—around 4.5-5.0% in late 2024, somewhat below historical averages.

Decision rule: Use 5.5% as a reasonable middle ground for US equities. Add 1-2% for emerging markets or small-caps.

CAPM Worked Example

You're valuing a mid-cap industrial with levered beta of 1.15:

Inputs:

• Risk-free rate (10Y Treasury): 4.25%
• Beta: 1.15
• Market risk premium: 5.5%

Cost of Equity = 4.25% + 1.15 x 5.5% = 4.25% + 6.33% = 10.58%

Interpretation: Equity investors require roughly 10.6% annual return to hold this stock, reflecting its above-market volatility.

WACC: Blending Equity and Debt

When valuing the entire firm (using Free Cash Flow to Firm), blend both capital sources:

The formula: WACC = [E/(D+E)] x Re + [D/(D+E)] x Rd x (1-t)

Where:

• E = Market value of equity
• D = Market value of debt
• Re = Cost of equity (from CAPM)
• Rd = Cost of debt (pre-tax)
• t = Corporate tax rate

Why multiply debt by (1-t)? Interest payments are tax-deductible. A company paying 6% interest in the 25% tax bracket effectively pays 4.5% after the tax shield. This makes debt cheaper than it appears.

Cost of Debt Estimation

Look at the yield-to-maturity (YTM) on existing bonds. Check FINRA TRACE or Bloomberg. If no traded debt exists, use credit spreads:

Capital Structure Weights

Use market values, not book values. Book debt approximates market debt (unless rates have moved dramatically), but equity book value is often far below market cap.

Example: $5B market cap, $2B debt

• Equity weight: 5/7 = 71.4%
• Debt weight: 2/7 = 28.6%

WACC Worked Example

Continuing with the mid-cap industrial:

Given:

• Cost of equity: 10.58% (from CAPM)
• Pre-tax cost of debt: 5.75% (BBB-rated)
• Tax rate: 25%
• Capital: $5B equity, $2B debt

Step 1: After-tax cost of debt 5.75% x (1 - 0.25) = 4.31%

Step 2: Calculate WACC WACC = (5/7)(10.58%) + (2/7)(4.31%) = 7.56% + 1.23% = 8.79%

The practical takeaway: This blended 8.8% is your discount rate for FCFF-based DCF models.

Common Errors (and How to Avoid Them)

Error 1: Using the Wrong Beta

A beta of 0.9 vs 1.3 changes cost of equity by 2+ percentage points—a 15-25% valuation swing. Use the company's own 5-year monthly beta, or unlever comparables and re-lever to the target capital structure.

Error 2: Stale Risk-Free Rates

Using 1.5% from 2021 instead of current 4%+ creates 250 basis points of error. Check Treasury.gov on the day you finalize assumptions.

Error 3: Mixing WACC with FCFE Models

Decision rule: FCFF (cash flows to all capital providers) -> discount at WACC. FCFE (cash flows to equity only) -> discount at cost of equity. Mixing double-counts leverage.

Error 4: Using Book Value Weights

If equity book is $2B but market cap is $10B, you're drastically overstating debt weight. Always use market cap for equity.

Error 5: Ignoring the Tax Shield

Using pre-tax cost of debt without the (1-t) adjustment inflates WACC by 150 basis points for a 25% tax rate company.

Quick Reference

Next Steps

1. Calculate WACC for your largest holding this week. Pull the 10-year Treasury yield, find the company's beta, and look up any outstanding bonds on FINRA TRACE. Blend using market value weights.

2. Run a sensitivity table. Vary WACC +/- 100 basis points in your DCF. Note how much fair value moves (you'll find it's substantial).

3. Document your assumptions. Record the date, Rf source, beta source, and MRP choice. You'll need this when updating the model.

4. Compare to industry. Check Damodaran's WACC tables (pages.stern.nyu.edu/~adamodar/) for sector ranges.

5. Sanity check. If WACC is below 5% or above 15% for a normal operating company, something is wrong. Review your inputs.

References

Damodaran, A. (2012). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset, 3rd Edition. Wiley Finance. http://pages.stern.nyu.edu/~adamodar/

Koller, T., Goedhart, M., & Wessels, D. (2020). Valuation: Measuring and Managing the Value of Companies, 7th Edition. McKinsey & Company.

Sharpe, W. F. (1964). Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. Journal of Finance, 19(3), 425-442.