nent09-Stocks and Their Valuation 4. Expected dividends as a basis for stock val

Question

nent09-Stocks and Their Valuation 4. Expected dividends as a basis for stock values A Aa 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 (D1o and Do). Assume that the stock's required return () s 8.40% Note: Carry and round the calculations to four decimal places. Time Period Dividend's Expected Expected Dividend's liegt Future Value Present Value No End of Year 10 End of Year 20 End of Year 50 IMG:4516.i 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 on the graph. You can mouse over the points in the graph to see their coordinates. before plotting it

Explanation / Answer

Given Information:-

Current Dividend- $1 per share

Expected constant growth rate - 2.70%

Stocks required return-8.40%

Dividend in 10th year- $1.25 (from graph)

Dividend in 20thyear- $1.75 (from graph)

Dividend in 50th year- $3.75 (from graph)

Present Value of the dividends = Dividend per share/(required return- expected growth rate)

= 1/(.084-.027)= $17.5439.

Discounted (present) value of dividend - Dividend in that year/(1+ required rate of return)^ no.of years

Thus in 10th year- $1.25(1+0.084)^10= 0.5580

in 20th year- $1.75(1+0.084)^20= 0.3487

in 50th year- $3.75(1+0.084)^50= 0.0665

Thus you will see that as the year increase their present value is decreasing

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