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 $)$ and the $PV$ of the dividends expected to be paid $10,20,$ and $50$ years from now $,$ and widehat$(D{)}_{50}).$ Assume that the stock's required return $)$ is $10\mathrm{.}40\%.$

$\backslash$table$[[,$Expected Dividend's$],[$Time Period,Future Value Present Value,$],[$Now$,,],[$End of Year $10,,],[$End of Year $20,,],[$End of Year $50,,],[,,]]$

Using the orange curve $($square 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. $($Tool tip: Mouse over the points in the graph to see their coordinates.$)$