A 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 (D0D0) and the PV of the dividends expected to be paid 10, 20, and 50 years from now (Dˆ10D^10, Dˆ20D^20, and Dˆ50D^50). Assume that the stock’s required return (rsrs) is 8.40%.

EBK CONTEMPORARY FINANCIAL MANAGEMENT
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ISBN:9781337514835
Author:MOYER
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Chapter7: Common Stock: Characteristics, Valuation, And Issuance
Section: Chapter Questions
Problem 13P
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A 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 (D0D0) and the PV of the dividends expected to be paid 10, 20, and 50 years from now (Dˆ10D^10, Dˆ20D^20, and Dˆ50D^50). Assume that the stock’s required return (rsrs) is 8.40%.
A 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 (Do) and the PV of the dividends expected to be paid 10, 20, and 50 years from now (D10, D20, and
D50). Assume that the stock's required return (r,) is 8.40%.
Expected Dividend's
Time Period
Future Value Present Value
Now
End of Year 10
End of Year 20
End of Year 50
Using the grey curve (star 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.
Note: Round each of the discounted values of the of dividends to the nearest tenth decimal place before plotting it on the graph. (Tool tip: Mouse over
the points in the graph to see their coordinates.)
Transcribed Image Text:A stock's current dividend is $1.00, and dividends are expected to grow at a constant rate of 2.70% per year. The intrinsic value of a stock should equal the sum of the present value (PV) of all of the dividends that a stock is supposed to pay in the future, but many people find it difficult to imagine adding up an infinite number of dividends. Calculate the PV of the dividend paid today (Do) and the PV of the dividends expected to be paid 10, 20, and 50 years from now (D10, D20, and D50). Assume that the stock's required return (r,) is 8.40%. Expected Dividend's Time Period Future Value Present Value Now End of Year 10 End of Year 20 End of Year 50 Using the grey curve (star symbols), plot the present value of each of the expected future dividends for years 10, 20, and 50. The resulting curve will illustrate how the PV of a particular dividend payment will decrease depending on how far from today the dividend is expected to be received. Note: Round each of the discounted values of the of dividends to the nearest tenth decimal place before plotting it on the graph. (Tool tip: Mouse over the points in the graph to see their coordinates.)
(?
5.00
Discounted Dividends
4.00
FV of Dividends
3.00
2.00
1.00
PV of Dividends
10
20
30
40
50
60
YEARS
DIVIDENDS ($)
Transcribed Image Text:(? 5.00 Discounted Dividends 4.00 FV of Dividends 3.00 2.00 1.00 PV of Dividends 10 20 30 40 50 60 YEARS DIVIDENDS ($)
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