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You own your own firm and you need to raise $50 million to fund an expansion.Following the expansion,your firm will be worth $75 million in its unlevered form.You want to go ahead with the expansion,but you are concerned that you may not be able to maintain ownership of over 50% of your firm's equity.In other words,you are concerned that if you use equity to finance the expansion,you may lose control of your firm.
-Assume that capital markets are perfect,you issue $30 million in new debt,and you issue $20 million in new equity.Your ownership stake in the firm following these new issues of debt and equity is closest to:

Question

Quizplus · Accepted Answer

The current value of the firm is $75 million, and raising $30 million in new debt and $20 million in new equity brings the total value of the firm to $125 million.

The value of the equity before the new issue is $75 million - $0 million (debt) = $75 million. After the new issue, the value of equity is $125 million - $30 million (debt) = $95 million.

Thus, the percentage ownership stake is ($95 million / $125 million) x 100% = 76%.

However, the question asks for the ownership stake after issuing the new debt and equity, so we need to adjust for the new equity issued.

Your original stake in the firm is ($75 million / 100%) x 100% = 100%.

You issue $20 million in new equity, so your ownership stake after the new issue is:

($75 million / $125 million) x 100% x (100% - 20%) = 55%.

Therefore, the closest answer choice is D) 55%.

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