Question

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: $6.5 (initial dividend)
5-year dividend growth rate: 15% (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: 11%

Also, assume:

Payout ratio: 45% (constant)
PE ratio at a constant growth rate (year 11 and beyond): 15

1. 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?

2. 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.

Answer 1

2018 dividend: $6.5 (initial dividend) we say as D0 i.e Dividend at year zero
5-year dividend growth rate: 15% (per year) = G

Perpetual growth rate: 5% Required return: 11%

Also, assume:

Payout ratio: 45% (constant) Retained earning will be : 55 %
PE ratio at a constant growth rate (year 11 and beyond): 15

Now to find out the stock price today = 6.5 / 11% = $ 59.09

Also Expected price of the Stock at the 11th Year ended will be as follows.

Year Dividend Discounting factor @ 11%

1 6.5 0.9009

2 7.475 0.8116

3 8.596 0.7312

4 9.886 0.6587

5 11.368   0.5935

6th year we can apply perpetual growth formula = D7 / Ke - G

= 11.9364 / 11-5

= 1,9894 DF 0.5346

Total value will multiple cash flows of each year with the respective discounting factors then add all of them you will reach at the total net value of the stock at the end of 11th year..