The following graph shows the value of a stock\'s dividends over time. The stock

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 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.

Explanation / Answer

Working:

Time period Dividend Expected future value Expected dividend's present value Now      1.0000      1.0000 End of year 10      1.4106      0.5245 End of year 20      1.9898      0.2751 End of year 50      5.5849      0.0397

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