Question

34. You own a​ 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.)

Answer 1

a) Given 2/3 of the firm value to be sold to raise the required capital.

So, Market value of the firm = Required capital/ Proportion to be sold

                                                = 40000000/(2/3) = 60000000

Now, value of equity = Firm value – debt value of firm

                                    = 60000000-15000000

                                    = 45000000

Percentage of equity = Require capital remaining / value of debt for debt

                                    = 25000000/45000000

                                    = 55.56%

Required percentage of equity to be sold by the firm = 55.56%

b) Let X be the total debt amount

Total amount required = (total amount raised through equity)+Total debt

40000000=(50%*(60000000-X))+X

By solving X

Total debt amount to be raised = $20,000,000