5. Expected dividends as a basis for stock values The following graph shows the

Question

5. Expected dividends as a basis for stock values The following graph shows the value of a stock's dividends over time. The stock's aurrent 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 difficuilt to imagine adding up an infinite number of dividends. Calaulate the PV of the divicend paid today (Ds) and the PV of the dividends expected to be paid 10 and 20 years from now (D10 and D20), Assume that the stocks required return (r) is 10.40%. Note: Carry and round the calaulations to four decimal places Time Period Dividend's Expected Expected d's Future Value Present Value Now End of Year 10-- End of Year 20 End of Year 50 $1.1877 $1.3629 $1.4106 I $1.2723 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 ilustrate 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. You can mouse over the points in the graph to see their coordinates DIVIDENDS IS 6.00 Discounted Dividends FV of Dividends RO

Explanation / Answer

Dividend to be paid today = $1.0000

Present value of dividend paid today = $1.0000

Dividend to be paid after 10 years = $1.00 * (1 + 3.5%)10

= $1.4106

Present value of dividend to be paid after 10 years = $1.4106 / (1 + 10.4%)10

= $0.5245

Dividend to be paid after 20 years = $1.00 * (1 + 3.5%)20

= $1.9898

Present value of dividend to be paid after 20 years = $1.9898 / (1 + 10.4%)20

= $0.2751

Dividend to be paid after 50 years = $1.00 * (1 + 3.5%)50

= $5.5849

Present value of dividend to be paid after 10 years = $5.5849 / (1 + 10.4%)50

= $0.0397

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