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 $1.00 per share, and dividends are expected to grow at a constant rate of 4.50% per year. The intrinsic value of a stock should equal the sum of the present value (PV) of all of the dividends that a stock is supposed to pay in the future, but many people find it difficult to imagine adding up an infinite number of dividends. Calculate the present value (PV) of the dividend paid today (Do) and the discounted value of the dividends expected to be paid 10, 20, and 50 years from now (D10, D20, D50). Assume that the stock's required return (r.) is 5.40%. Note: Carry and round the calculations to four decimal places. Time Period Dividend's Expected Future Value Dividend's Expected Present Value Now End of Year 10 End of Year 20 End of Year 50 Using the blue curve (circle symbols), plot the future value of each of the expected future dividends for years 10, 20, and 50. The resulting curve will illustrate how the FV of a particular dividend payment will increase depending on how far from today the dividend is expected to be received. Note: Round each of the discounted values of the dividends to the nearest tenth decimal place before plotting it on the graph. You can mouse over the points in the graph to see their coordinates. 10.00 Expected Dividends 8.00 FV of Dividends DIVIDENDS ($) PV of Dividends 0 10 20 30 YEARS 40 50 60

Answer 1

First we will calculate Dividend's Expected Future value
Now as the dividend is growing at rate of 4.5% per year and D₀ = 1
So

D₁ = $1* (1.045) = $1.045

D₁₀ = $1 * ( 1+ 4.5/100)^10

D₁₀ = $1 *(1.045)^10

D₁₀ = $1.5530 approx

D₂₀ = $1 * (1+.045)^20

D₂₀₌ $2.4117

D₅₀ = $1 * (1+.045)^50

D₅₀= $9.0326

Now we will calculate Dividend's Expected Present  value

As the required return is 5.4% we will discount with this rate

Present value of D₀ = $1 (As the present value of the dividend is given )

Present value of D₁₀ = D₁₀ / (1.054)^10

= $1.5530 / 1.6920

= $ 0.9178

Present value of D₂₀ = D₂₀ / (1.054)^20

=$2.4117/ 2.8629

=$ 0.8424

Present value of D₅₀ = D₅₀ / (1.054)^50

= $9.0326/ 13.8685

=$ 0.6513