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The ulevered beta is not specifically attached to a company. Rather it is linked to industries. Of course to come up with an unlevered from computation you need to have a strong sample of the industry your company is in to compute their individual beta by regression and to delever them and roughly speaking compute the average which would stand as the unleverd beta of your company. Tough tough and tedious operation. Hopefully, The great Damodaran has already done the job for us. Just go straight to the relevant part of his website scroll down and pickup the right unleverd beta for the right industry and you're done! Hope it helps.
Unlevering beta for one company is not a VERY tedious operating. Assuming that you already have the company's levered beta, unlevering beta can be done with just a balance sheet and some arithmetic. To unlever beta: Levered Beta / ((1+(1-taxrate)*(Debt/Equity))
Yes but an unlevered makes sense only if you want to use the bottom-up approach to compute beta given the lack of statistical significance of individual betas obtained from regressions (standard error as high as the value of beta itself in many cases). Of course, for the mechanics of computing beta, you're right, with the implicite assumption that the beta of debt is 0...