- What is the year-end price of the stock?
The dividend at year-end (D0) is $3.60 x 0.30 = $1.08. According to the dividend growth model, the year-end stock price is $1.08(1.075)/(0.10 – 0.075) = $46.44.
- What is the year-end price/earnings ratio?
The year-end price/earnings ratio is $46.44/$3.60 = 12.90x.
- What is the year-end price/earnings ratio for each of the following incremental changes in the above assumptions?
- The growth rate is 9 percent.
D1 = $1.08 x 1.09 = $1.1772. P0 = $1.1772/(0.10 – 0.09) = $117.72. P/E = 32.7x.
- The dividend payout rate is 40 percent.
D0 = $3.60(0.40) = $1.44. D1 = $1.44(1.075) = $1.548. P0 = $1.548/(0.10–0.075) = $61.92.
P/E = $61.92/$3.60 = 17.2x.
- The required return on equity is 9 percent.
D1 = $1.08 x 1.075 = $1.161. P0 = $1.161/(0.09 – 0.075) = $77.40. P/E = 21.5x.
- What is the year-end price/earnings ratio if all three assumptions are changed?
D1 = $1.44 x 1.09 = $1.5696. P0 = $1.5696/(0.09 – 0.09) = infinity. Clearly the price would be very high. If the required return is 10 percent, the price would be $156.96, and P/E = 43.6x. If the required return is 9.5 percent, the price would be $313.92, and P/E = 87.2x. If the required return is 9.10 percent, the price would be $1,569.60, and P/E = 436x.
