Aswath Damodaran 137
Equity Betas and Leverage
! The beta of equity alone can be written as a function of the unlevered beta and
the debt-equity ratio
"L = "u ( 1 + (( 1 - t)D/E))
where
"L = Levered or Equity Beta
"u = Unlevered Beta
t = Corporate marginal tax rate
D = Market Value of Debt
E = Market Value of Equity
This is based upon two assumptions
- Debt bears no market risk (which is consistent with studies that have
found that default risk is non-systematic)
- Debt creates a tax benefit
Assets Liabilities
Assets A ("u) Debt D ("D =0)
Tax Benefits tD ("D= 0 ) Equity E ("L)
Betas are weighted averages,
#u (E + D - tD)/(D+E) = "L(E/(D+E))
Solve for "L,
"L = #u (E + D - tD)/E= #u (1 + (1-t)D/E)
If debt has a beta ("D)
#u (E + D - tD)/(D+E) + "D tD/(D+E) = "L(E/(D+E)) + "D D/(D+E)
"L = #u (1 + (1-t)D/E) - "D (1-t) [D/(D+E)]
