Current index price
$ 80.00
Equity Risk Premium
9.0%
Estimated dividend next period
$ 1.20
Estimated earnings next period
$ 8.00
Financial Leverage
0.80
Government bond rate
6.8%
Net Profit Margin
12.0%
Total Asset Turnover
1.80
Your answer: C was incorrect. The correct answer was B) 36.6%.
Using the earnings multiplier approach, we will multiply the earnings multiplier (the justified P/E ratio) by the expected earnings to get an expected future price. Adding in the expected dividend, we can then estimate an expected rate of return. To calculate the earnings multiplier, we first need the growth rate for the market, which is the retention ratio times the return on equity (ROE). The dividend payout is $1.20 out of $8.00 in earnings so the retention ratio is $6.80/$8.00 = 85%. Using duPont analysis, the ROE is the net profit margin times the total asset turnover ratio times the financial leverage: 12% × 1.80 × 0.80 = 17.28%. The growth rate is then 85% × 17.28% = 14.69%.
We will also need the dividend payout ratio and the required return on stock. The former is just one minus the retention ratio or 1 - 0.85 = 15%. The required return on equity is the government bond rate plus the equity risk premium: 6.8% + 9% = 15.8%.
The equity multiplier is the dividend payout ratio divided by the required return on equity minus the growth rate: 0.15 / (0.158 - 0.1469) = 13.51.
The expected future price of the series is the earnings multiplier times the future earnings: 13.51 × $8.00 = 108.08. The expected return is the expected dividend plus the price change in the series divided by the original price: ($1.20 + $108.08 - $80.00) / $80.00 = 36.60%.
Your answer may differ by a few tenths of a percent depending on how many decimal places you carried intermediate calculations to. If you used your calculator’s memory throughout, the return would have been calculated as 36.39%.
$ 80.00
Equity Risk Premium
9.0%
Estimated dividend next period
$ 1.20
Estimated earnings next period
$ 8.00
Financial Leverage
0.80
Government bond rate
6.8%
Net Profit Margin
12.0%
Total Asset Turnover
1.80
Your answer: C was incorrect. The correct answer was B) 36.6%.
Using the earnings multiplier approach, we will multiply the earnings multiplier (the justified P/E ratio) by the expected earnings to get an expected future price. Adding in the expected dividend, we can then estimate an expected rate of return. To calculate the earnings multiplier, we first need the growth rate for the market, which is the retention ratio times the return on equity (ROE). The dividend payout is $1.20 out of $8.00 in earnings so the retention ratio is $6.80/$8.00 = 85%. Using duPont analysis, the ROE is the net profit margin times the total asset turnover ratio times the financial leverage: 12% × 1.80 × 0.80 = 17.28%. The growth rate is then 85% × 17.28% = 14.69%.
We will also need the dividend payout ratio and the required return on stock. The former is just one minus the retention ratio or 1 - 0.85 = 15%. The required return on equity is the government bond rate plus the equity risk premium: 6.8% + 9% = 15.8%.
The equity multiplier is the dividend payout ratio divided by the required return on equity minus the growth rate: 0.15 / (0.158 - 0.1469) = 13.51.
The expected future price of the series is the earnings multiplier times the future earnings: 13.51 × $8.00 = 108.08. The expected return is the expected dividend plus the price change in the series divided by the original price: ($1.20 + $108.08 - $80.00) / $80.00 = 36.60%.
Your answer may differ by a few tenths of a percent depending on how many decimal places you carried intermediate calculations to. If you used your calculator’s memory throughout, the return would have been calculated as 36.39%.