What beta would you use for a private company?

Since a private company has no stock price, I estimate beta from comparable public companies. Their observed betas reflect two things: business risk and financial risk from leverage. I want only the business risk, so I unlever each peer's beta with the formula: unlevered beta equals levered beta divided by one plus one minus the tax rate times debt-to-equity.

For example, a peer with a levered beta of 1.3, a 25% tax rate and a debt-to-equity ratio of 0.4 has an unlevered beta of 1.3 divided by 1.3, which is 1.0. I do this for each peer and take the median, which is less sensitive to outliers.

Then I relever at the capital structure I expect for the target, either its own or a typical structure for its industry. If the target's debt-to-equity ratio is 0.6, its levered beta is 1.0 times one plus 0.75 times 0.6, or 1.45. That beta goes into CAPM to get cost of equity. Because the target is private and often smaller, I may also add a size premium, and in some contexts a discount for lack of marketability is applied to the final value rather than the discount rate.