Question

when calculating the cost of equity with Damodaran's beta method (cost of equity = risk free rate + beta (mature market premium+country risk premium), how to determine the result is post-tax or pre-tax?

Answer 1

This is definitely the tax-free cost of equity and in any case, the tax rate is not included here for any calculation done from the perspective of the corporation. If you want to take tax into account, that would be in two places
1. In adjusting the cost of debt for the tax shield offered to the corporation
2. modifying the free/operating cash flow of the project in numerator of the NPV calculations