You own your own firm, and you want to raise $30 million to fund an expansion. Currently, you own 100% of the firm's equity, and the firm has no debt. To raise the $30 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 $15 million? (Assume perfect capital markets.)

b. What is the smallest amount you can borrow to raise the $30 million without giving up control? (Assume perfect capital markets.)