How do you calculate cost of equity without beta?

Use a method that skips CAPM. The dividend growth model needs only the stock price, the dividend and a growth rate. The build-up method stacks a risk-free rate and premiums. A third option adds a premium to the company's own bond yield.

With the dividend growth model, a $50 stock paying $2.00 that grows 4% a year has a next dividend of $2.08. That is a 4.16% dividend yield, plus 4% growth, for 8.16%. With the build-up method, 5% risk-free plus a 5% equity premium, a 3% size premium and a 2% company-specific premium give 15%.

The bond yield plus risk premium approach starts with the company's pre-tax cost of debt, say 6%, and adds a few points for equity risk. You can also borrow beta from similar public companies. See the dividend growth model guide and cost of equity for a private company.