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 4.50% per year. The intrinsic value of a stock should equal the sum of the present value (PV) of all of the dividendss 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 (Da) and the discounted value of the dividends expected to be paid 10, 20, and 50 years from now (D10, D20, Ds0). Assume that the stock's required return (r) is 5.40% 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 blue curve (circle symbols), plot the future value of each of the expected future dividends for years 10, 20, and 50. The resulting curve will illustrate how the FV of a particular dividend payment will increase 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

Time period Dividend's Expected Future Value Now Expected Dividend's Present Value $ 1.00 End of Year 10$ $ 1.5530 =1*(1+4.5%)^10 0.9178 =1.553/(1+5.4%)^10 End of Year 20 $ 2.4117 =1*(1+4.5%)^20 $ 0.8424 =2.4117/(1+5.4%)^20 End of Year 50 $ 9.0326 $ 0.6513 =1*(1+4.5%)^50 =9.0326/(1+5.4%)^50

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