You own your own firm, and you want to raise $$60$ million to fund an expansion. Currently, you own $100\%$ of the firm$$s equity, and the firm has no debt. To raise the $$60$ million solely through equity, you will need to sell three$-$fifth of the firm. However, you would prefer to maintain at least a $50\%$ equity stake in the firm to retain control.

If you borrow $$40$ million, what fraction of the equity will you need to sell to raise the remaining $$20$ million? $($Assume perfect capital markets.$).$