Blue Lagoon Ltd is an unlevered firm with a cost of equity of $4\%$ and a tax rate of $35\%.$

Required:

i$)$ Using Modigliani and Miller's theory with corporate taxes $($but no bankruptcy costs$),$ calculate the cost of equity of a levered firm in the same tax bracket that pays interest at $2\%$ and has a debt to equity ratio of $65\%.$

ii$)$ Explain $($with calculations$)$ what would happen to the cost of equity of the levered firm if the debt to equity ratio was reduced to $20\%$