Dilution Here is recent financial data on Pisa Construction Inc. Stock price $$40$ Market value of firm $$400,000$ Number of shares $10,000$ Earnings per share $$4$ Book net worth $$500,000$ Return on investment $8\%.$Pisa has not performed spectacularly to date. However, it wishes to issue new shares to obtain $$80,000$ to finance expansion into a promising market. Pisas financial advisers think a stock issue is a poor choice because, among other reasons, sale of stock at a price below book value per share can only depress the stock price and decrease shareholders wealth. To prove the point they construct the following example: Suppose $2,000$ new shares are issued at $$40$ and the proceeds are invested. $($Neglect issue costs.$)$ Suppose return on investment does not change. Then Book net worth $=$ $$580,000$ Total earnings $=\mathrm{.}08(580,000)=$ $$46,400$ Earnings per share $=\_\_\_\_\_\_46,40012,000=$ $$3\mathrm{.}87$ Thus, EPS declines, book value per share declines, and share price will decline proportionately to $$38\mathrm{.}70.$ Evaluate this argument with particular attention to the assumptions implicit in the numerical example.