Question

8. 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, 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 (Do) and the PV of the dividends expected to be paid 10 and 20 years from now (D10 and D20). Assume that the stock's required return (r) is 10.40%. (Note: Round the calculations to two decimal places.) Dividend's Expected Future Value Expected Dividend's Present Value Time Period 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.

Answer 1

Current Dividend = D0 = $ 1 and Perpetual growth rate = 3.5 %, Required Return = 10.4 %

Expected Dividends After Year 10 = D10 = 1 x (1.035)^(10) = $ 1.411 PV of D10 = 1.411 / (1.104)^(10) = $ 0.524

Expected Dividends After Year 20 = D20 = 1 x (1.035)^(20) = $ 1.989, PV of D20 = 1.989 / (1.104)^(20) = $ 0.275

Expected Dividends After Year 50 = D50 = 1 x (1.035)^(50) = 5.585, PV of D50 = 5.585 / (1.104)^(50) = $ 0.0397