Corporate Finance & Valuation Lab

Levered & Unlevered Beta Calculator

Model pure-play peer comp sets, Hamada equation beta unlevering/relevering, financial leverage risk premiums, and CAPM cost of equity.

Industry Presets:

1. Target Capital Structure & Market

10-Year or 20-Year Benchmark Treasury Yield.
Expected market return over risk-free rate ($E[R_m] - R_f$).
Marginal federal and state tax rate for interest tax shield.
$
$
Target borrowing rate / yield-to-maturity on senior debt.
Target Debt-to-Equity Ratio ($D/E$): 0.50x
Target Debt-to-Capital ($D / [D+E]$): 33.3%
Target Equity-to-Capital ($E / [D+E]$): 66.7%

2. Pure-Play Comparable Peers (Unlevering)

Industry Benchmark

Input observed regression betas and financial leverage for public peers to extract pure operating asset betas ($eta_U$).

Peer Company Observed Beta ($eta_L$) Debt/Equity ($D/E$) Tax Rate ($t$) Unlevered Beta ($eta_U$)
1.174
1.184
1.116
1.154
Peer Group Average $eta_U$
1.157
Peer Group Median $eta_U$
1.164
Industry Asset Beta ($eta_U$)
1.157
Pure business operating risk
Target Relevered Beta ($eta_L$)
1.591
Hamada relevered equity beta
Target Cost of Equity ($K_e$)
13.00%
CAPM expected equity return
Weighted Average Cost of Capital
10.17%
After-tax WACC discount rate

3. Risk & Return Attribution

Cost of Equity ($K_e$) Attribution

(1) Risk-Free Rate ($R_f$): 4.25%
(2) Fundamental Business Risk ($eta_U imes ERP$): 6.36%
(3) Financial Leverage Premium ($[eta_L - eta_U] imes ERP$): 2.39%
Total Cost of Equity ($K_e = (1)+(2)+(3)$): 13.00%

Hamada Multiplier Dynamics

After-Tax Debt Multiplier ($1 + [1-t] rac{D}{E}$): 1.375x
Beta Leverage Expansion ($Delta eta = eta_L - eta_U$): +0.434
After-Tax Cost of Debt ($K_d imes [1-t]$): 4.50%

4. Sensitivity Matrix: Target $D/E$ vs. Tax Rate

Relevered $eta_L$ & $K_e$

Shows target levered equity beta ($eta_L$) and resulting CAPM cost of equity ($K_e$) across varying leverage and tax shields.

Target D/E Corporate Tax Rate ($t$)
15% 20% 25% 30% 35%
* Blue highlighted cell indicates current target configuration.

Executive Guide: Hamada Equation & Pure-Play Beta Analysis

1. Why Unlever Beta? (Isolating Business Risk)

A company's observed regression beta ($eta_L$) reflects two independent risks: business/operating risk (industry cyclicality, operating leverage) and financial risk (debt interest obligations). Because comparable public companies maintain different capital structures and tax rates, comparing raw levered betas is misleading. Unlevering calculates the asset beta ($eta_U$) as if each peer were 100% equity financed.

$$eta_U = rac{eta_L}{1 + (1 - t) imes (D/E)}$$

2. Relevering for the Target Company

Once an industry benchmark asset beta ($eta_U$) is established from pure-play comps, analysts apply the target firm's planned debt-to-equity ratio ($D/E$) and corporate marginal tax rate ($t$) to calculate its expected equity beta ($eta_L$). This levered beta is fed directly into the Capital Asset Pricing Model (CAPM) to determine hurdle rates and discounted cash flow (DCF) discount rates.

$$eta_{L, ext{target}} = eta_U imes left[1 + (1 - t) imes rac{D_{ ext{target}}}{E_{ ext{target}}} ight]$$

3. Risk & Return Decomposition

Under the Hamada framework, the total expected return required by equity holders ($K_e$) is mathematically separated into three building blocks:

  • Risk-Free Rate ($R_f$): The time value of money without default risk.
  • Fundamental Business Risk Premium ($eta_U imes ERP$): Systematic compensation for operating in the underlying industry.
  • Financial Leverage Risk Premium ($[eta_L - eta_U] imes ERP$): Extra compensation required by equity holders for bearing default and interest coverage volatility.

4. Pure-Play Method in M&A & Private Equity

In mergers and acquisitions (M&A) and private company valuations, private targets lack stock market tickers. Investment bankers select 3 to 6 publicly traded pure-play peers with similar product mixes and geographic exposures, unlever their betas, take the harmonic or arithmetic mean $eta_U$, and relever it using the sponsor's target LBO capital structure.

Frequently Asked Questions

Levered beta (equity beta, $eta_L$) measures the systematic risk of a company's stock, reflecting both fundamental business/operating risk and financial risk from debt leverage. Unlevered beta (asset beta, $eta_U$) removes the effect of debt and corporate taxes, isolating pure operational business risk independent of capital structure.

The Hamada equation relates levered beta to unlevered beta using the corporate tax rate ($t$) and debt-to-equity ratio ($D/E$):
Relevering Formula: $eta_L = eta_U imes [1 + (1 - t) imes (D / E)]$.
Unlevering Formula: $eta_U = eta_L div [1 + (1 - t) imes (D / E)]$.

When a target company or project is private, thinly traded, or restructuring its capital structure, analysts cannot rely on historical regression beta. Instead, they identify publicly traded pure-play peers in the same industry, unlever their observed betas to find the average industry asset beta ($eta_U$), and relever that benchmark beta to match the target firm's optimal target debt-to-equity ratio.

Under CAPM ($K_e = R_f + eta_L imes ERP$), increasing debt ($D/E$) raises the financial risk borne by equity holders, which inflates the levered equity beta ($eta_L$). The total cost of equity decomposes into: (1) Baseline Business Risk = $R_f + eta_U imes ERP$, and (2) Financial Leverage Risk Premium = $(eta_L - eta_U) imes ERP$.

Yes. You can export complete peer comp sets, unlevered asset betas, target relevered betas, cost of capital breakdowns, and D/E vs tax rate sensitivity matrices as a UTF-8 CSV spreadsheet with formula injection defense or print an executive audit.

Continue Exploring Corporate Valuation & Capital Structure Tools

Calculate weighted average cost of capital in the WACC Lab, analyze financial leverage in the Debt-to-Equity & TIE Lab, bridge enterprise value in the Enterprise Value (EV) Lab, evaluate corporate return on capital in the ROIC & Capital Lab, or explore our Business Strategy & Decision-Making Hub.