A firm has $300 million of assets that includes $40 million of cash and 10 million shares outstanding. If the firm uses $30 million of its cash to repurchase shares, what is the new price per share?

Question

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Initially, the firm has $300 million in assets and 10 million shares, so the price per share is $30 ($300 million / 10 million shares). After repurchasing $30 million worth of shares, the assets decrease to $270 million. The firm uses $30 million to buy back shares at $30 each, repurchasing 1 million shares, leaving 9 million shares outstanding. The new price per share is $270 million / 9 million shares = $30.

A Firm Has $300 Million of Assets That Includes $40