Question

4. Expected dividends as a basis for stock values

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 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 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 8.40%.

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

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.

Note: Round each of the discounted values of the dividends to the nearest tenth decimal place before plotting it on the graph. You can mouse over the points in the graph to see their coordinates.

Answer 1