### How to calculate unlevered beta

I have derived a firm's cost of equity using the WACC formula (see here), which means that the cost of equity has factored in the firms' debt (i.e. levered beta) and now I need to calculate the firm's unlevered beta. Here is my solution thus far, please let me know if I am on the right track.

Formula to calculate unlevered beta:

`βL = βU + [1 + (1 - t)(d/e)] Where: βL = the firm's beta with leverage = 1.5 βU = the firm's beta with no leverage t = the corporate tax rate = 40% d/e = the firms debt/equity ratio = 35/65`

Calculations

`1.1 = βU + [1 + (1 - 0.40)(35/65)] 1.1 = βU + [1 + (0.6)(0.538461538461538)] 1.1 = βU + [1 + (0.6)(0.538461538461538)] 1.1 = βU + 1.323077 βU = 1.323077 - 1.1 βU = 0.223077`

## UPDATE

I had some errors above, which were pointed out in the answer below. Here is the updated question (which I think is now correct).

Revised Formula to calculate unlevered beta:

`βU = βL * [1 / (1 + (1 - t)(d/e))] Where: βL = the firm's beta with leverage = 1.5 βU = the firm's beta with no leverage t = the corporate tax rate = 40% d/e = the firms debt/equity ratio = 35/65`

Revised Calculations

`βU = 1.5 * [1 / (1 + (1 - 0.40)(35/65)) ] βU = 1.5 * [1 / 1.323077] βU = 1.5 * 0.755814 βU = 1.133721`

@BobJansen yes thank you, Bob. I had the formula wrong to begin with.

If and only if the Beta of debt is zero.

If you've found an answer you like, please mark it as accepted so that this question is closed.

Your formula is adding where you should be multiplying, and you plugged your inputs into the wrong places (your levered Beta notably). In any case, the process for un-levering/re-levering the beta goes like so:

Step 1: Find benchmark company/asset/project Beta.

Step 2: Un-lever the benchmark Beta: Unlevered Beta = Levered Beta * (1 / ( 1 + (1 - t)*D/E))

Step 3: Re-lever the beta with your company/projects D/E Ratio: Un-levered Beta * (1 + (1-t)*D/E)

thank you! this is great. Will make amendments to original question to incorporate your answers... cheers

Unlevered Beta (Beta asset) = Levered Beta / 1+(1-tax) Debt/Equity

Similarly , Levered Beta (Beta equity) = Unlevered Beta * 1+ (1-tax) Debt /Equity

These formulas assume debt carries a market risk of zero, which is a very simplifying (but sometimes inevitable) assumption.

It depends. If, and only if, you assume that debt carries a market risk of exactly 0, you may use Hamada's equation to easily go from levered to unlevered beta.

Let $\theta = D/E$

- $\beta^L = \beta^U \times(1+(1-\tau)\times\theta)$
- $\beta^U = \beta^L \div(1+(1-\tau)\times\theta)$

Where $\tau$ is the tax rate, and $D$ and $E$ are the firm's

value of debt and equity.*market*In practice, a lot of people use that just because it is hard to estimate debt betas.

If you dislike that simplifying assumption, and if you have a way to estimate a debt beta, then the correct equation is:

- $\beta^L = \beta^U \times(1+(1-\tau)\times\theta) \space – \space \beta_d\times(1-\tau)\times\theta$

For a quick source to this information, please see page 9 (printed page 71) of Prof. Aswath Damodaran's class slides at http://people.stern.nyu.edu/adamodar/pdfiles/eqnotes/discrate2.pdf

License under CC-BY-SA with attribution

Content dated before 7/24/2021 11:53 AM

Bob Jansen 8 years ago

Pages 53 and 54 of Volume 4 of the CFA level curriculum. I'm not sure where you're getting your formula but my book states $\beta_{\textrm{asset}} = \beta_{\textrm{equity}} \frac{1}{1+(1-t){\frac{D}{E}}}$.