Build-Up Method
The build-up method estimates cost of equity by adding premiums to the risk-free rate, one risk at a time. It needs no beta, which makes it the usual choice for small private companies. Typical layers are equity, size, industry and company-specific risk.
This site's example is 5% risk-free + 5% equity risk premium + 3% size premium + 0% industry + 2% company-specific risk premium = 15%. Each layer is a judgment call, so write down why you chose it. The cost of equity calculator has a private company tab for this.
The method is common in business appraisals, where the result feeds a discount rate or capitalization rate. The private company cost of equity guide covers each layer. It is also one answer to how to calculate cost of equity without beta.