Tax adjustment on WACC

In the formula for WACC, a tax adjustment is applied to the cost of Debt. It makes sense as the debt yield used in the formula is a pre-tax figure. However, I would like to understand why there isn’t a tax adjustment on the cost of Equity as well? The required rate of return on equity seems also to be a pre-tax figure, and there is capital gain tax / dividend tax for the shareholders. Thank you, K

There is no tax shield for corporate taxes when a company earns/spends money on equity, as opposed to interest payments which are tax deductible.

Company is not required to pay taxes on interest payments (aka tax shield) but it is required to pay taxes on earnings attributable to shareholders.

Net income (claimed by equity holders only) is a post tax figure.

EBIT (claimed by both equity and debt holders) is a pre-tax figure.