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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
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1 Answer

up vote 1 down vote accepted

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)

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thank you! this is great. Will make amendments to original question to incorporate your answers... cheers –  Ben Apr 29 '13 at 21:02
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