Question

Q2. As an analyst for Middle, Diddle, and O'Leary, you are forecasting the market P/E ratio using the dividend discount model. Because the economy has been expanding for 9 years, you expect the dividend-payout ratio will be at its low of 40 percent and that long- term government bond rates will rise to 7 percent. Because investors are becoming less risk averse, the equity risk premium will decline to 3 percent. As a result, investors will require a 10 percent return, and the return on equity will be 12 percent. a. What is the expected growth rate? b. What is your expectation of the market P/E ratio? c. What will be the value for the market index if the expectation is for earnings per share of $53.00? d. What will be your rate of return if you acquired the index at a value of 950, you sold the index at the value computed in Part c, and dividends during the year were $30.00?​

Answer 1

Expected growth rate is 7.2%, the expected market P/E ratio is 35.71, the market index value with an EPS of $53.00 is $1,892.63, and the rate of return under the given conditions is 99.22%.

Step-by-step explanation:

When forecasting the market Price-to-Earnings (P/E) ratio using the dividend discount model (DDM), several factors are taken into account to predict future market behavior. Given the data provided: a dividend-payout ratio of 40 percent, a required return of 10 percent, and an equity risk premium declining to 3 percent, we can deduce certain financial expectations.

Expected Growth Rate

The expected growth rate can be found using the formula g = Return on Equity (ROE) × retention ratio, where the retention ratio is the complement of the dividend-payout ratio. With an ROE of 12 percent and a 60 percent retention ratio (100% - 40% dividend-payout), the expected growth rate would be 0.12 × 0.60 = 0.072, or 7.2 percent.

Market P/E Ratio

The market P/E ratio would be calculated by taking the inverse of the difference between the required rate of return and the expected growth rate: P/E = 1 / (required return - growth rate). Therefore, the expected P/E ratio = 1 / (0.10 - 0.072) = 1 / 0.028 = 35.71.

Value of the Market Index

To calculate the market index value, we multiply the earnings per share by the P/E ratio: Market Index Value = EPS × P/E. With an EPS of $53.00 and a P/E ratio of 35.71, the market index value expected would be 53 × 35.71 = $1,892.63.

Rate of Return

If you acquired the index at a value of 950, sold it at $1,892.63, and received dividends of $30.00 during the year, the rate of return would be calculated as ((Sale Price + Dividends - Purchase Price) / Purchase Price). This results in a rate of return of (($1,892.63 + $30.00 - $950) / $950) × 100, which equals 99.22%.