DONT USE AI 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.$\backslash$