Interview Question Help: How does a decrease in tax rate affect WACC?

I understand it increases after-tax cost of debt, because the tax shield benefit is lessened.

However, I don't understand how/why it affects cost of equity.

Mechanically, when you unlever and relever the beta, aren't you using the same tax rate? Say you have a comp set of 5 companies all with a 20% tax rate. Your target company also has a 20% tax rate. If all tax rates go down to 10%, wouldn't you unlever the comp set at 10% tax rate and re lever at the 10% tax rate also? So aren't you getting the same beta even if tax rates stayed the same at 20%?

In a related example, say the tax rate only changes for your target company. You'd unlever the peer set at 20% and relever at the target company's expected tax rate of 10%?

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