The following graph shows the value of a stock\'s dividends over time. The stock
ID: 2771396 • 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 paid today (D0) and the PV of the dividends expected to be paid 10 and 20 years from now ( 10 and 20). Assume that the stock's required return (rs) is 8.40%. Note: Carry and round the calculations to four decimal places.Explanation / Answer
Time Period Dividend's Expected Future Value PVF Expected Div Present Value Now 1.0000 1.0000 1.00 End of Year 10(1*(1.027)^10 1.3053 0.4464 0.58 End of Year 20(1*(1.027)^20 1.7038 0.1993 0.34 End of Year 50(1*(1.027)^50 3.79 0.02 0.07 Time Period PVF 1.00 0.92 2.00 0.85 3.00 0.79 4.00 0.72 5.00 0.67 6.00 0.62 7.00 0.57 8.00 0.52 9.00 0.48 10.00 0.45 11.00 0.41 12.00 0.38 13.00 0.35 14.00 0.32 15.00 0.30 16.00 0.28 17.00 0.25 18.00 0.23 19.00 0.22 20.00 0.20 21.00 0.18 22.00 0.17 23.00 0.16 24.00 0.14 25.00 0.13 26.00 0.12 27.00 0.11 28.00 0.10 29.00 0.10 30.00 0.09 31.00 0.08 32.00 0.08 33.00 0.07 34.00 0.06 35.00 0.06 36.00 0.05 37.00 0.05 38.00 0.05 39.00 0.04 40.00 0.04 41.00 0.04 42.00 0.03 43.00 0.03 44.00 0.03 45.00 0.03 46.00 0.02 47.00 0.02 48.00 0.02 49.00 0.02 50.00 0.02
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