step by step of all equations used and explanations claearly

. (a) Suppose Carter Chemical Company's management conducts a study and concludes that if Carter expands its consumer products division (which is less risky than its primary business, industrial chemicals), the firm's beta will decline from 1.1 to 0.9. However, consumer products have a somewhat lower profit margin, and this will cause Carter's growth rate in earnings and dividends to fall from 7 percent to 6 percent. Should management make the change? Assume the following:

ER_M= 10% ; R_F=7.5%; D₀=$2.

(b) Assume all the facts as given in part (a), except the one about the changing beta coefficient. By how much would the beta have to decline to cause the expansion to be a good one? (Hint: set P₀under the new policy equal to P₀under the old one, and find the new beta that produces this equality.)