The following graph shows the value of a stock\'s dividends over time. The stock
ID: 2743279 • Letter: T
Question
The following graph shows the value of a stock's dividends over time. The stock's current dividend is $1.00, and dividends are expected to grow at a constant rate of 2.70% per year. The intrinsic value of a stock should equal the sum of the present value (PV) of all of the dividends that a stock is supposed to pay In the future, but many people find it difficult to imagine adding up an Infinite number of dividends. Calculate the PV of the dividend pa d today (D_0) and the PV of the dividends expected to be paid 10 and 20 years from now (D_10 and D_20). Assume that the stock's required return (r_s) is 8.40%. Using the red curve (cross symbols), plot the present value of each of the expected future dividends for years 10, 20, and 50. The resulting curve will illustrate how the PV of a particular dividend payment will decrease depending on how far from today the dividend is expected to be received.Explanation / Answer
Current dividend paid is $ 1 and dividend growth rate is 2.70 % per year , we can calculate the future dividends for year 10, 20 and 50. (current period is year 0 so at the end of 10th year it will be 11 years for 20th year it will be 21 years and so on)
D0= $1.00
D10 = $1.00 * (1.027)^11 = $ 1.3405
D20 = $1.00 * (1.027)^21 = $1.7498
D50 = $1.00 * (1.027)^51 = $3.8913
We then calculate the present value of each dividend for period 10, 20 and 50; the stock’s required rate of return or cost of equity is 8.40%
PV of D0 = $1.00
PV of D10 =$1.3405 / (1.084)^11 = $0.5520
PV of D10 =$1.7498 / (1.084)^21 = $0.3216
PV of D10 =$3.8913 / (1.084)^51 = $0.0636
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