Why Capital Structure Alone Cannot Determine Levered Equity Beta

# How do I calculate levered equity beta without unlevered equity beta?


# How do I calculate levered equity beta without unlevered equity beta?












I'm doing an assignment where I have liabilities including market and book values of long-term debt.

I also have capital including common stock, paid in capital, and accumulated earnings.

I've been able to calculate the structural weights using the debt or equity over the enterprise value.

I'm stuck on calculating the cost of financing, or levered equity beta, in this case however.

Is there a way to calculate equity beta with the information I've been given that I'm missing?

## Answer by David Addison (score 0, accepted)

https://quant.stackexchange.com/a/33669

I'm going to have a try at this one.

The levered weighted average cost of capital, $\mathbb{r}_c$, is defined:

$\mathbb{r}_c = \frac{D+R+I(1-r_T)}{E+B} $

where financing costs are equal to dividends $D$, retained earnings $R$, and interest $I$; and:

$C$ is capital equal to equity, $E$, plus debt, $B$;

$E$ = 'common stock' + 'paid in capital' + 'accumulated earnings'; and,

$r_T$ is the tax shield.

In typical implementations of WACC, we rearrange as follows:

$r_c(E+B) = \frac{E}{E+B}(D+R) + \frac{B}{E+B}(I(1-r_T)) $

Equating:

$\frac{D+R}{E} := r_e$; and,

$\frac{I(1-r_T)}{B} := r_b$

allows us to solve by combination of terms for the cost of equity in familiar form:

$r_e \approx \frac{E+B}{E}(r_c - r_b ) + r_b$

which therefore implies that a CAPM-free equity beta can be set to:

$\beta_e = \frac{E+B}{E}$

For the risk-free rate, it is common to use a short-term treasury note. If the cost of capital is undefined, we can make it whatever we want it to be. If you believe the long-run return of the market is 7%, then that it was it is. Believe it or, no discount rate which approximates opportunity cost is the wrong one.