A firm has 1,000 shareholders, each of whom own $50 in shares. The firm uses $20,000 to repurchase shares. What percentage of the firm did each of the remaining shareholders own
Before the repurchase, and what percentage does each own now?

Question

Quizplus · Accepted Answer

Before the repurchase, the total value of the shares was:
1000 shareholders x $50/share = $50,000

Each shareholder owned:
$50/share ÷ $50,000 = 0.10% of the firm

After the repurchase, the firm has $20,000 less cash, but the same number of shares outstanding. Therefore, the total value of the shares is now:
1000 shareholders x $50/share - $20,000 = $30,000

Each shareholder now owns:
$50/share ÷ $30,000 = 0.17% of the firm

Therefore, each shareholder now owns 0.17% - 0.10% = 0.07% more of the firm than before. Before the repurchase, the total value of the shares was 1000*50 = $50,000. Each shareholder owned 50/50000 = 0.10% of the firm. After the repurchase, the firm has 20,000/50 = 400 fewer shares, leaving 1000-400 = 600 shareholders. The remaining shareholders now own shares worth 50*400 = $20,000 less than before, or $30,000. Each shareholder now owns 50/30000 = 0.17% of the firm. Thus, the answer is C.

A Firm Has 1,000 Shareholders, Each of Whom Own $50