From thinking-frameworks-skills
Computes CAPM cost of equity, synthetic cost of debt, and WACC for companies in any currency. Handles emerging market premiums, bottom-up beta, multi-country operations. Useful for discount rates, betas, ERPs.
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- [Example](#example)
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Company: Ambev (Brazilian beverage company)
Step 1 -- Riskfree rate (BRL analysis)
US 10-year Treasury yield: 4.0%. Brazil government bond: 11.0%. Brazil sovereign default spread (Baa2 rating): 2.5%.
Option A -- Subtract default spread: 11.0% - 2.5% = 8.5% (riskfree rate in BRL, captures inflation differential).
Option B -- Build from US rate + inflation differential: (1.04) x (1.06)/(1.02) - 1 = 8.1% (using expected inflation: Brazil 6%, US 2%).
Use 8.5% for this analysis (Option A, simpler and directly observable).
Step 2 -- Equity risk premium buildup
Mature market ERP (implied, S&P 500): 5.0%.
Country risk premiums (CRP):
Operation-weighted CRP = 0.60 x 3.75% + 0.30 x 3.0% + 0.10 x 0% = 3.15%.
Total ERP = 5.0% + 3.15% = 8.15%.
Step 3 -- Bottom-up beta
Comparable beverage firms (global, n=20): Median unlevered beta = 0.80.
Relever at Ambev's capital structure: Levered Beta = 0.80 x (1 + (1 - 0.34) x 0.25) = 0.80 x 1.165 = 0.93.
Step 4 -- Cost of equity
Cost of Equity = 8.5% + 0.93 x 8.15% = 8.5% + 7.58% = 16.08%.
Step 5 -- Cost of debt (synthetic rating)
EBIT: R$20B, Interest expense: R$2.5B. Interest coverage = 8.0x.
Lookup: Coverage of 8.0x maps to A rating for large firms, default spread = 1.00%.
Pre-tax cost of debt = 8.5% + 1.00% = 9.50%.
After-tax cost of debt = 9.50% x (1 - 0.34) = 6.27%.
Step 6 -- WACC
Capital structure weights (market values): E/(D+E) = 80%, D/(D+E) = 20%.
WACC = 16.08% x 0.80 + 6.27% x 0.20 = 12.86% + 1.25% = 14.12%.
Interpretation: This is a BRL-denominated WACC. Use it to discount BRL-denominated cash flows. For USD-denominated analysis, rebuild using USD riskfree rate and adjust the ERP accordingly.
Copy this checklist and track your progress:
Cost of Capital Estimation Progress:
- [ ] Step 1: Determine riskfree rate for analysis currency
- [ ] Step 2: Estimate equity risk premium (mature market + country risk)
- [ ] Step 3: Estimate beta (regression or bottom-up)
- [ ] Step 4: Compute cost of equity
- [ ] Step 5: Compute cost of debt via synthetic rating
- [ ] Step 6: Compute WACC and validate
Step 1: Determine riskfree rate for analysis currency
The riskfree rate anchors the entire computation. It should be denominated in the same currency as projected cash flows.
See resources/methodology.md for the inflation-differential approach and when each method is appropriate.
Step 2: Estimate equity risk premium (mature market + country risk)
Build the ERP in two layers:
See resources/methodology.md for the four-step ERP estimation and resources/methodology.md for the three approaches to corporate country risk exposure.
Step 3: Estimate beta (regression or bottom-up)
Bottom-up beta is preferred over regression beta because it uses a larger sample, reflects the current business mix, and allows you to set the capital structure to the target rather than historical average.
See resources/methodology.md for the complete procedure and the relevering formula.
Step 4: Compute cost of equity
Apply the CAPM formula. For emerging market companies, incorporate the country risk premium into the expected return calculation. See resources/template.md for the calculation worksheet.
Step 5: Compute cost of debt via synthetic rating
Estimate what rating the company would receive based on its interest coverage ratio, then look up the corresponding default spread.
See resources/methodology.md for the complete interest-coverage-to-rating-to-spread lookup table.
Step 6: Compute WACC and validate
Combine cost of equity and after-tax cost of debt using market value weights.
See resources/template.md for the complete worksheet. Validate using resources/evaluators/rubric_cost_of_capital_estimator.json. Minimum standard: Average score of 3.5 or higher.
Pattern 1: US / Developed Market Company
Pattern 2: Emerging Market Company
Pattern 3: Private Company
Pattern 4: Multi-Division Conglomerate
Currency consistency: The riskfree rate, cash flows, and WACC should all be denominated in the same currency. Mixing a USD riskfree rate with BRL cash flows produces meaningless results.
Implied ERP over historical: Use the implied equity risk premium derived from current market levels rather than long-run historical averages. The implied ERP reflects what investors are demanding today; historical averages are backward-looking and vary widely depending on the time period chosen.
Bottom-up beta preferred: Regression betas have high standard errors (often 0.20+), reflect historical business mix, and use historical capital structure. Bottom-up betas from 15-20 comparable firms produce a more stable and forward-looking estimate.
Relevering formula: Levered Beta = Unlevered Beta x (1 + (1 - Tax Rate) x (Debt/Equity)). Use market values for debt and equity, not book values. The tax rate should be the marginal rate.
Synthetic rating from interest coverage: Map current interest coverage (EBIT / Interest Expense) to a credit rating using the appropriate table (large firm vs. small firm). Do not rely on assigned ratings for companies that may not be rated.
Market value weights: WACC uses market value of equity (not book) and market value of debt (approximate with book if trading data unavailable). Book value weights systematically underweight equity for profitable firms.
WACC matches cash flow currency: If cash flows are in BRL, the WACC should be in BRL. If cash flows are in USD, the WACC should be in USD. Converting a WACC across currencies requires adjusting for the inflation differential between the two currencies.
Key formulas:
Cost of Equity (CAPM) = Riskfree Rate + Beta x Equity Risk Premium
For emerging markets:
Cost of Equity = Riskfree Rate + Beta x Mature ERP + lambda x CRP
(Simplified: lambda = 1, so CRP is added directly)
Riskfree Rate (local currency) = Local Govt Bond Yield - Sovereign Default Spread
OR = (1 + US Rf) x (1 + Inflation_local) / (1 + Inflation_US) - 1
Country ERP = Sovereign Default Spread x (Equity Volatility / Bond Volatility)
Typical ratio: 1.5x
Operation-weighted CRP = Sum of (Revenue_i% x CRP_i) for each country i
Levered Beta = Unlevered Beta x (1 + (1 - Tax Rate) x (D/E))
Unlevered Beta = Levered Beta / (1 + (1 - Tax Rate) x (D/E))
Total Beta (private, undiversified) = Market Beta / Correlation with Market
Cost of Debt (pre-tax) = Riskfree Rate + Default Spread (from synthetic rating)
Cost of Debt (after-tax) = Pre-tax Cost of Debt x (1 - Marginal Tax Rate)
WACC = ke x (E / (D+E)) + kd(1-t) x (D / (D+E))
Current estimates (update periodically):
| Parameter | Typical Range | Source |
|---|---|---|
| US 10-year Treasury | 3.5% - 5.0% | Federal Reserve |
| Implied ERP (S&P 500) | 4.5% - 6.0% | Damodaran annual update |
| Equity/Bond volatility ratio | 1.3x - 1.7x | Use 1.5x as default |
| Unlevered beta (typical ranges) | 0.5 - 1.5 | By industry sector |
Key resources:
Inputs required:
Outputs produced:
cost-of-capital.md: Complete WACC computation with riskfree rate derivation, ERP buildup, beta estimation, synthetic rating, cost of equity, cost of debt, and final WACC with sensitivity analysis