Questions: 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 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.)

Solution Steps

The present value at time 0 is already given as $10. We need to calculate the present values for years 10, 20, and 50. The future value for year 10 is $1.41. Since the blue line depicts the FV of Dividends and passes through (0,0) and (10, 5.5), the slope can be calculated as (5.5-0)/(10-0) = 0.55. The future values at year 20 and year 50 can thus be estimated to be 20 * 0.55 = 11 and 50 * 0.55 = 27.5 respectively. We can estimate the PVs by looking at the discounted values at 0 (10), 10 (approximately 1.5), and considering that the discounted values follow an exponential decay. The PV for year 20 should be less than the PV for year 10 and greater than 0. The PV for year 50 should be close to 0. Hovering the mouse over the orange squares indicates PV for year 10 ~ 1.5, PV for year 20 ~ 0.5, and the PV for year 50 is essentially 0.

Plot the present values on the graph using the orange curve (square symbols). Year 10: (10, 1.5) Year 20: (20, 0.5) Year 50: (50, 0)

Final Answer: