You own your own firm, and you want to raise \($40\) million to fund an expansion. Currently, you own 100% of the firm’s equity, and the firm has no debt. To raise the \($40\) million solely through equity, you will need to sell two-thirds of the firm. However, you would prefer to maintain at least a 50% equity stake in the firm to retain control.

a. If you borrow \($15\) million, what fraction of the equity will you need to sell to raise the remaining

\($25\) million? (Assume perfect capital markets.)

b. What is the smallest amount you can borrow to raise the \($40\) million without giving up control?

(Assume perfect capital markets.)