In practice, the use of the dividend discount model is refined from the method presented in the textbook. Many analysts will estimate the dividend for the next $5$ years and then estimate a perpetual growth rate at some point in the future, typically $10$ years. Rather than have the dividend growth fall dramatically from the fast growth period to the perpetual growth period, linear interpolation is applied. That is$,$ the dividend growth is projected to fall by an equal amount each year. For example, if the high growth period is $15$ percent for the next $5$ years and the dividends are expected to fall to a $5$ percent perpetual growth rate $5$ years later, the dividend growth rate would decline by $2$ percent each year.

The Value Line Investment Survey provides information for investors. Below, you will find information for Boeing found in the $2017$ edition of Value Line:

$2018$ dividend: $$6\mathrm{.}5($initial dividend$)$

$5-$year dividend growth rate: $12\%($per year$)$

Although Value Line does not provide a perpetual growth rate or required return, we will assume they are:

Perpetual growth rate: $5\%$

Required return: $10\%$

Also, assume:

Payout ratio: $45\%($constant$)$

PE ratio at constant growth rate $($year $11$ and beyond$)$: $15$

a$.$ Assume that the perpetual growth rate begins in year $11$ and use linear interpolation between the high growth rate and perpetual growth rate. Construct a table that shows the dividend growth rate and dividend each year. Based on that, what is the stock price at the end of Year $11?$ What is the stock price today?

b$.$ Instead of applying the constant dividend growth model to find the stock price in the future, analysts will often combine the dividend discount method with multiples. Use the PE ratio to calculate the stock price when Boeing reaches a perpetual growth rate in dividends $($end of year $11).$ Now find the value of the stock today by finding the present value of the dividends during the supernormal growth rate and the price you calculated using the PE ratio.