USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
The aggregate market currently has a retention ratio of 60 percent, a required rate of return of 12 percent, and an expected growth rate for dividends of 4 percent.
-Refer to Exhibit 9.9. If the payout ratio changes to 50 percent, but there are no other changes, what will be the new P/E?
A) 3.25
B) 4.16
C) 5.75
D) 6.25
E) 7.67

Question

Quizplus · Accepted Answer

The new payout ratio is 50%, which means the retention ratio is now 50% as well (since payout ratio + retention ratio = 100%). The expected growth rate can be recalculated using the formula g = b * ROE, where b is the retention ratio and ROE is the return on equity. However, since the growth rate and required rate of return remain unchanged, we can directly use the Gordon Growth Model (Dividend Discount Model for a perpetuity) to find the P/E ratio: P/E = (1 - b) / (r - g) = (1 - 0.5) / (0.12 - 0.04) = 0.5 / 0.08 = 6.25.