Question

The following graph shows the value of a stock’s dividends over time. The stock’s current dividend is $1.00 per share, 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 present value (PV) of the dividend paid today (D₀) and the discounted value of the dividends expected to be paid 10, 20, and 50 years from now (D10, D20, D50D10, D20, D50). Assume that the stock’s required return (rss) is 10.40%.

Note: Carry and round the calculations to four decimal places.

Time Period	Dividend’s Expected Future Value	Dividend’s Expected Present Value
Now
End of Year 10
End of Year 20
End of Year 50

Answer 1

Time period Now End of Year 10 Dividend's expected future value Dividend's expected present value $1.00 $1.00 $1.4106 $0.5245 [1*(1.035-10)] (1.41/(1.104-10)] $1.9898 $0.2751 [1*(1.035^20)] [1.99/(1.104^20)] $5.5849 $0.0397 [1*(1.035450) ] [5.58/(1.104450)] End of Year 20 End of Year 50