Company Z's stock trades at $45 a share. The company is contemplating a 3-for-2 stock split. Currently, the company has EPS of $3.00, DPS of $0.50, and 20 million shares of stock outstanding. Assuming that the stock split will have no effect on the total market value of its equity, what will be the company's stock price following the stock split?

a. How many shares of stock will be outstanding after the split?

b. Calculate EPS after the split.

C. Calculate DPS after the split.

D. Calculate price per share after the split

e. Calculate price after the split if the PE increases by 2 points (for example, if PE was 10 prior to split, it increases to 12 after the split)

f. Why do companies split their stock? Why might a split cause the P/E to increase?