What increases cost of equity?
Anything that raises the risk shareholders carry or the return they could get elsewhere. Higher interest rates, a higher beta, a bigger equity risk premium and more debt all push cost of equity up. Small size, country risk and company-specific problems add to it for private or foreign businesses.
Each CAPM input matters. Starting from 11%, a risk-free rate of 6% instead of 5% lifts it to 12%. A beta of 1.4 instead of 1.2 also lifts it to 12%. An equity risk premium of 6% instead of 5% lifts it to 12.2%.
Debt works through beta. More borrowing makes the remaining equity riskier, which the Hamada equation for levered beta captures. See whether cost of equity increases with debt. For private firms, the build-up method adds a size premium, and foreign exposure brings a country risk premium. The FAQ on adding a country risk premium shows the math.