If you can’t look at a historical Beta or you don’t have beta then to come up with your own from the Public or private Company, take about 5 comparable companies, look up the levered Beta for each one, unlevered each one to get rid of the influence from the companies’ respective capital structures and for comparability purposes, then take the median of the set ( usually).
Finally, re-lever the beta according to your specific company’s capital structure. This is your levered Beta for use in the cost of equity.
Of course: Bu = Bl/ [ ( 1+ (1-t)) x (D/E) ]