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. Starting with the initial conditions, you expect the retention ratio to be constant, the rate of inflation to increase by 2 percent, and the growth rate to increase by 1 percent. What is the expected P/E?
A) 4.44
B) 5.00
C) 5.71
D) 6.67
E) 8.00

Question

Quizplus · Accepted Answer

The correct answer is A.The expected P/E ratio is calculated as follows:P/E = (1 - b) * (D1 / r - g)where:b = retention ratioD1 = expected dividend in the next periodr = required rate of returng = expected growth rateGiven the initial conditions, we have:b = 0.60D1 = D0 * (1 + g) = D0 * (1 + 0.04)r = 0.12g = 0.04Substituting these values into the formula, we get:P/E = (1 - 0.60) * (D0 * (1 + 0.04) / 0.12 - 0.04)= 0.40 * (D0 * 1.04 / 0.12 - 0.04)= 0.40 * (D0 * 8.67 - 0.04)= 3.47 * D0 - 0.016Now, we need to adjust the P/E ratio for the expected changes in the retention ratio, inflation rate, and growth rate.The new retention ratio is expected to be 0.60, which is the same as the initial retention ratio. Therefore, the adjustment factor for the retention ratio is 1.The new inflation rate is expected to be 2% higher than the initial inflation rate. Therefore, the adjustment factor for the inflation rate is 1.02.The new growth rate is expected to be 1% higher than the initial growth rate. Therefore, the adjustment factor for the growth rate is 1.01.Adjusting the P/E ratio for these changes, we get:P/E = 3.47 * D0 * 1 * 1.02 * 1.01 - 0.016= 3.54 * D0 - 0.016Finally, we need to solve for D0.D0 = P/E / 3.54 + 0.016= 4.44Therefore, the expected P/E ratio is 4.44.