Capital Structure Formulas Cheat Sheet
Core Capital Structure Formulas
WACC Components Reference
| Variable | Definition | How to Find It |
|---|---|---|
| E | Market value of equity (market cap) | Share price × diluted shares outstanding |
| D | Market value of debt | Book value of debt (approximation) or traded debt prices |
| Ke | Cost of equity | CAPM: Risk-free rate + Beta × Equity Risk Premium |
| Kd | Cost of debt | Yield to maturity on existing debt or new issue spread |
| T | Marginal tax rate | Statutory corporate rate (21% federal in US) |
| Rf | Risk-free rate | 10-year Treasury yield |
| β | Beta | Regression of stock vs. market returns (2–5 years weekly) |
| Rm – Rf | Equity risk premium (ERP) | Historical average ~5–7%, or implied from market data |
Leverage Ratios
| Ratio | Formula | What It Tells You |
|---|---|---|
| Debt-to-Equity | Total Debt ÷ Total Equity | How much debt per dollar of equity |
| Debt-to-Capital | Total Debt ÷ (Total Debt + Equity) | Debt as % of total capitalization |
| Net Debt / EBITDA | (Total Debt – Cash) ÷ EBITDA | Years to repay debt from cash flow (most used by lenders) |
| Interest Coverage | EBITDA ÷ Interest Expense | Ability to service debt obligations |
| Fixed Charge Coverage | (EBITDA – Capex) ÷ (Interest + Mandatory Amort.) | Cash flow after capex vs. required payments |
| Debt / Total Assets | Total Debt ÷ Total Assets | Asset-based leverage measure |
Modigliani-Miller Theorems
| Theorem | Assumption | Implication |
|---|---|---|
| MM I (No Taxes) | Perfect markets, no taxes | Capital structure is irrelevant — firm value unchanged by leverage |
| MM II (No Taxes) | Perfect markets, no taxes | Cost of equity increases linearly with leverage (offsets cheap debt) |
| MM I (With Taxes) | Corporate taxes exist | Firm value increases with debt due to interest tax shield |
| MM II (With Taxes) | Corporate taxes exist | WACC decreases with leverage (up to a point) |
Optimal Capital Structure Framework
In theory, the optimal capital structure minimizes WACC by balancing the tax benefit of debt against the costs of financial distress. As a company adds debt, WACC initially falls (due to the tax shield) but eventually rises as bankruptcy risk increases and cost of equity spikes. The practical approach is to look at peer company leverage, credit rating targets, and debt covenant requirements.
Key Takeaways
- WACC = blended cost of debt and equity, weighted by market values — it’s the discount rate in DCF models.
- CAPM is the standard model for cost of equity: Ke = Rf + β × ERP.
- Always unlever and re-lever betas when using peer comparisons for beta.
- Net Debt / EBITDA is the most widely used leverage ratio by lenders and rating agencies.
- The tax shield makes debt cheaper, but beyond a point, financial distress costs outweigh the benefit.
FAQ
What is the optimal debt-to-equity ratio?
There is no universal answer — it depends on industry, cash flow stability, and growth profile. Capital-light tech companies may have 0–0.5x D/E, while utilities can sustain 1.5–2.5x. The goal is to minimize WACC while maintaining investment-grade credit metrics.
Why does debt reduce WACC?
Interest expense is tax-deductible, creating a “tax shield” that effectively subsidizes the cost of debt. The after-tax cost of debt is always lower than the pre-tax cost. This makes the blended WACC lower as you add debt — up to the point where distress costs rise.
What equity risk premium should I use?
The historical US equity risk premium is approximately 5–7% depending on the measurement period. Many practitioners use the Duff & Phelps (Kroll) recommended ERP, which is updated quarterly. As of recent estimates, it’s around 5.5–6.0%.
How do you calculate beta for a private company?
Since private companies don’t have publicly traded stock, you use “comparable company beta.” Find publicly traded peers, unlever their betas to remove their capital structures, take the median, then re-lever using the private company’s target debt-to-equity ratio.
What is the difference between levered and unlevered beta?
Levered (equity) beta reflects both business risk and financial risk from debt. Unlevered (asset) beta strips out the effect of leverage, isolating pure business risk. You unlever to compare across companies with different capital structures.