Does cost of equity increase with debt?

Yes. More debt makes the remaining equity riskier, because lenders get paid first and profits swing more for shareholders. Under the Hamada equation, an unlevered beta of 0.9 becomes about 1.26 at a debt-to-equity ratio of 0.5 and a 21% tax rate.

Plug those betas into CAPM with a 5% risk-free rate and a 5% premium. With no debt, cost of equity is 9.5%. At a 0.5 debt-to-equity ratio it rises to about 11.3%. Robert Hamada published the equation in 1972, building on the Modigliani and Miller work on capital structure.

Overall cost of capital can still fall at first, because interest is tax deductible and debt costs less than equity. Past some point, rising default risk pushes both costs up. The levered vs unlevered beta guide shows the math, the unlevered beta entry explains the starting point, and what increases cost of equity lists the other drivers.