# 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
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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 $\beta_{\textrm{asset}} = \beta_{\textrm{equity}} \frac{1}{1+(1-t){\frac{D}{E}}}$. –  Bob Jansen Apr 29 '13 at 20:42
@BobJansen yes thank you, Bob. I had the formula wrong to begin with. –  Ben Apr 29 '13 at 21:11