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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 except for the existence of corporate taxes.Your firm pays 21% of earnings in taxes and you decide to issue $25 million in new debt and $25 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 value of the firm after the expansion will be $75 million, so issuing $25 million in new equity will mean the firm has a total equity value of $50 million. This implies that the pre-expansion value of the equity is $25 million, and thus the pre-expansion ownership stake of the owner is $25 million / $75 million = 33.33%.

The new debt will not affect ownership, so the owner's stake after the financing will depend only on the ownership stake represented by the new equity. The owner's stake in the new equity is:

New equity stake = $25 million / ($25 million + $25 million) = 50%

Therefore, the owner's total ownership stake after the financing is:

Total ownership stake = pre-expansion equity stake + new equity stake

Total ownership stake = 33.33% + 50% = 83.33%

However, the question asks for the ownership stake in the firm's unlevered equity, so we need to adjust for the tax shield on the new debt. The interest deduction on the new debt will reduce the firm's taxable income and thus its tax bill. The tax shield is:

Tax shield = interest deduction x tax rate

The interest deduction is $25 million x 0.07 = $1.75 million per year, and the tax shield is:

Tax shield = $1.75 million x 0.21 = $0.3675 million per year

The present value of the tax shield is:

PV of tax shield = $0.3675 million / 0.1 = $3.675 million

This implies that the value of the firm's unlevered equity after the financing is:

Unlevered equity value = pre-expansion unlevered equity value + PV of tax shield - value of new debt

Unlevered equity value = $25 million + $3.675 million - $25 million = $3.675 million

The owner's stake in the unlevered equity is therefore:

Unlevered equity stake = $25 million / $3.675 million = 68.03%

Rounding to the nearest percentage gives an ownership stake of 68%. However, the closest choice is B) 55%, which is the best answer.

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