There is no effect on the numerator since the cash received from the exercise of the options is not income. The denominator increases by 12,500 based on the treasury method. The method assumes the company would repurchase as many shares as possible with the proceeds from the exercise.
Therefore, 50,000 X $30 = $1,500,000/40 = 37,500. Since they could repurchase 37,500 at the average stock price, there would be 12,500 shares still outstanding.

As implied by its name, private equity is not traded publicly. It is a vehicle for pooling funds from many investors and investing them in real estate projects in the form of equity, privately held.

That's the definition of real GDP.

The objective of a short sale is to borrow securities, sell them at the current market price and then replace them with the same securities purchased at a lower price.