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Expected dividends as a basisfor stock values

A stock's current dividend is $$1\mathrm{.}00,$ and dividends are expected to grow at a constant rate of $3\mathrm{.}50\%$ 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 PV of the dividend paid today $(D_0)$ and the $PV$ of the dividends expected to be paid $10,20,$ and $50$ years from now $($ widehat$(D{)}_{10},$widehat$(D{)}_{20},$ and

widehat$(D{)}_{50}).$ Assume that the stock's required return $(r_s)$ is $10\mathrm{.}40\%.$

Expected Dividend's

Time Period Future Value Present Value

Now

End of Year $10$

End of Year $20$

End of Year $50$