What is beta, and why would you unlever and relever it?

Beta measures how much a stock moves relative to the market. A beta of 1 means it moves in line with the market, and a beta of 1.5 means it tends to move 15% when the market moves 10%. It goes into CAPM, so a higher beta means a higher cost of equity. The beta you observe for a stock is a levered beta. It reflects two things, the risk of the business and the risk added by debt. I unlever to strip out the debt, which leaves the risk of the business alone. Unlevered beta is levered beta divided by 1 plus debt to equity times 1 minus the tax rate. Say a comparable company has a levered beta of 1.3, debt to equity of 40% and a 25% tax rate. 40% times 0.75 is 0.3, so I divide 1.3 by 1.3 and the unlevered beta is 1.0. Then I relever at the capital structure of the company I'm valuing. If its target debt to equity is 60%, I multiply 1.0 by 1 plus 60% times 0.75, which is 1.45.

Beta measures how much a stock moves relative to the market. A beta of 1 means it moves in line with the market, and a beta of 1.5 means it tends to move 15% when the market moves 10%. It goes into CAPM, so a higher beta means a higher cost of equity. The beta you observe for a stock is a levered beta. It reflects two things, the risk of the business and the risk added by debt. Debt adds risk because interest is fixed, so the same swing in operating profit becomes a bigger swing in what's left for shareholders. I unlever to strip out the debt, which leaves the risk of the business alone. Unlevered beta is levered beta divided by 1 plus debt to equity times 1 minus the tax rate. Say a comparable company has a levered beta of 1.3, debt to equity of 40% and a 25% tax rate. 40% times 0.75 is 0.3, so I divide 1.3 by 1.3 and the unlevered beta is 1.0. Then I relever at the capital structure of the company I'm valuing. If its target debt to equity is 60%, I multiply 1.0 by 1 plus 60% times 0.75, which is 1.45. That's higher than the peer's 1.3 because my company carries more debt. Taking the peer's beta as it stands would understate the risk and overvalue the company. I'd do this whenever the company's own beta isn't usable. A private company has no stock price, and for a public one a single regression is noisy, so I'd unlever several peers and take the median. Three details. Debt to equity uses market values. I relever at the target structure, not today's, because WACC is meant to hold for the whole forecast. And this formula assumes the debt itself carries no market risk. That's the usual interview convention, but it overstates the relevered beta when debt is heavy.