An analyst is reviewing the valuation of DuPont as of the beginning of July 2013 when DuPont is selling for $52.72. In the previous year, DuPont paid a $1.70 dividend that the analyst expects to grow at a rate of 4 percent annually for the next four years. At the end of Year 4, the analyst expects the dividend to equal 35 percent of earnings per share and the trailing P/E for DuPont to be 13. If the required return on DuPont common stock is 9.0 percent, calculate the per-share value of DuPont common stock.
Exhibit 6 summarizes the relevant calculations. When the dividends are growing at 4 percent, the expected dividends and the present value of each (discounted at 9.0 percent) are shown. The terminal stock price, V4, deserves some explanation. As shown in the table, the Year 4 dividend is 1.70(1.04)4 = 1.9888. Because dividends at that time are assumed to be 35 percent of earnings, the EPS projection for Year 4 is EPS4 = D4/0.35 = 1.9888/0.35 = 5.6822. With a trailing P/E of 13.0, the value of DuPont at the end of Year 4 should be 13.0(5.6822) = $73.8682. Discounted at 9 percent for four years, the present value of V4 is $52.3301.
Exhibit 6. Value of DuPont Common Stock Time** Value Calculation Dt or Vt Present Values Dt/(1.09)t**or Vt/(1.09)t 1 D1 $1.70(1.04)1 $1.7680 $1.6220 2 D2 1.70(1.04)2 1.8387 1.5476 3 D3 1.70(1.04)3 1.9123 1.4766 4 D4 1.70(1.04)4 1.9888 1.4089 4 V4 13 × [1.70(1.04)4/0.35] = 13 × [1.9888/0.35] = 13 × 5.6822 73.8682 52.3301 Total $58.3852
In this Question, I did not get the concept behind the calculation of V4. Can anybody explain the basic approach have used in the calculation of V4.??