Question

3. consider an economy with corporate taxes only, and no other taxes. the corporate tax rate is 30%. consider a firm with total value of $100 million, 10% risk-free debt, and 1 million shares outstanding. the firm has announced that it will issue new debt so that the debt-to-value ratio is 20%. debt will still be risk-free and the proceeds from the debt issuance will be used to buy back common stock. no new asset will be purchased. what will be the share price after this announcement and how many shares will be repurchased?

Answer 1

The share price after the announcement will be $10, and 1 million shares will be repurchased.

Step-by-step explanation:

The share price after the announcement will depend on the number of shares repurchased. To determine the number of shares repurchased, we need to find the value of the debt issued and the value of the shares after the repurchase. The debt-to-value ratio is 20%, which means the value of the debt issued is 20% of the total value of the firm, i.e., $20 million. Since the risk-free debt is 10% of the total value, the remaining 10% of debt is issued, resulting in $10 million. The proceeds from the debt issuance are used to buy back common stock. Therefore, the value of the shares after the repurchase is $100 million - $10 million = $90 million.

The number of shares repurchased can be calculated by dividing the value of the debt issued ($10 million) by the share price after the repurchase. Let's assume the share price after the repurchase is denoted by P. So, we have the equation $10 million / P = 1 million shares. Rearranging this equation, we find P = $10 million / 1 million shares = $10 per share. Therefore, the share price after the announcement will be $10, and the number of shares repurchased will be 1 million shares.