Question

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 (Do) and the discounted value 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 8.40%. Note: Carry and round the calculations to four decimal places. Time Period Dividend's Expected Expected Dividend's Future Value Present Value Now End of Year 10 End of Year 207 End of Year 50 | ▼ Using the red curve (cross 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. You can mouse over the points in the graph to see their coordinates.

Answer 1

PV of Dividend Paid now = D0 = 1

Dividend after year 10 = 1*(1+2.70%)¹⁰ = 1.3078
PV of Dividend now = (1+2.70%)¹⁰/(1+8.4%)¹⁰ = 0.5827

Dividend after year 20 = 1*(1+2.70%)²⁰ = 1.7038
PV of Dividend now = (1+2.70%)²⁰/(1+8.4%)²⁰ = 0.3395

Dividend after year 30 = 1*(1+2.70%)³⁰ = 2.2239
PV of Dividend now = (1+2.70%)³⁰/(1+8.4%)³⁰ = 0.1978

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