$$Many companies use stock repurchases to increase earnings per share. For example, suppose

that a company is in the following position:

Net profit $$10$ million

Number of shares before repurchase $1$ million

Earnings per share $$10$

Price$$earnings ratio $20$

Share price $$200$

The company now repurchases $200,000$ shares at $$200$ a share. The number of shares

declines to $800,000$ shares and earnings per share increase to $$12\mathrm{.}50.$ Assuming the price$$

earnings ratio stays at $20,$ the share price must rise to $$250.$Discuss