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Capital Structure Formulas Cheat Sheet

Capital structure is the mix of debt and equity a company uses to finance its operations. Getting it right minimizes the weighted average cost of capital (WACC) and maximizes firm value. These formulas are the building blocks of corporate finance and valuation.

Core Capital Structure Formulas

Weighted Average Cost of Capital (WACC) WACC = (E / (E+D)) × Ke + (D / (E+D)) × Kd × (1 – T)
Cost of Equity (CAPM) Ke = Rf + β × (Rm – Rf)
Cost of Debt (After-Tax) Kd (after-tax) = Interest Rate × (1 – Tax Rate)
Unlevered Beta (Hamada Equation) βu = βL / [1 + (1 – T) × (D/E)]
Re-Levered Beta βL = βu × [1 + (1 – T) × (D/E)]

WACC Components Reference

VariableDefinitionHow to Find It
EMarket value of equity (market cap)Share price × diluted shares outstanding
DMarket value of debtBook value of debt (approximation) or traded debt prices
KeCost of equityCAPM: Risk-free rate + Beta × Equity Risk Premium
KdCost of debtYield to maturity on existing debt or new issue spread
TMarginal tax rateStatutory corporate rate (21% federal in US)
RfRisk-free rate10-year Treasury yield
βBetaRegression of stock vs. market returns (2–5 years weekly)
Rm – RfEquity risk premium (ERP)Historical average ~5–7%, or implied from market data

Leverage Ratios

RatioFormulaWhat It Tells You
Debt-to-EquityTotal Debt ÷ Total EquityHow much debt per dollar of equity
Debt-to-CapitalTotal Debt ÷ (Total Debt + Equity)Debt as % of total capitalization
Net Debt / EBITDA(Total Debt – Cash) ÷ EBITDAYears to repay debt from cash flow (most used by lenders)
Interest CoverageEBITDA ÷ Interest ExpenseAbility to service debt obligations
Fixed Charge Coverage(EBITDA – Capex) ÷ (Interest + Mandatory Amort.)Cash flow after capex vs. required payments
Debt / Total AssetsTotal Debt ÷ Total AssetsAsset-based leverage measure

Modigliani-Miller Theorems

TheoremAssumptionImplication
MM I (No Taxes)Perfect markets, no taxesCapital structure is irrelevant — firm value unchanged by leverage
MM II (No Taxes)Perfect markets, no taxesCost of equity increases linearly with leverage (offsets cheap debt)
MM I (With Taxes)Corporate taxes existFirm value increases with debt due to interest tax shield
MM II (With Taxes)Corporate taxes existWACC 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.

Analyst Tip
When calculating WACC, always use market values (not book values) for the debt and equity weights. For beta, unlever peer betas, take the median, then re-lever to your target capital structure. Never use a single company’s raw beta — it’s too noisy.

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.