The following graph shows the value of a stocks dividends ov

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 3.50% 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 paid 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 10.40%. Using the orange curve (square 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.

Solution

Current dividend paid is $ 1 and dividend growth rate is 3.50 % per year, we can calculate the future dividends for year 10, 20 and 50.

D0= $1.00
D10 = $1.00 * (1.035)^10 = $ 1.41
D20 = $1.00 * (1.035)^20 = $1.99

D50 = $1.00 * (1.035)^50 = $5.59

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 10.40%

PV of D0 = $1.00
PV of D10 =$1.41 / (1.104)^10 = $0.52

PV of D10 =$1.99 / (1.104)^20 = $0.28

PV of D10 =$5.59 / (1.104)^50 = $0.04

Period

Dividend’s expected Future value

Expected Dividend’s present value

Now

$1.00

$1.00

End of year 10

$1.41

$0.52

End of year 20

$1.99

$0.28

End of year 50

$5.59

$0.04

A graph can be plotted by using above Expected Dividend’s present value along with Dividend’s expected Future value.

Period	Dividend’s expected Future value	Expected Dividend’s present value
Now	$1.00	$1.00
End of year 10	$1.41	$0.52
End of year 20	$1.99	$0.28
End of year 50	$5.59	$0.04