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 constant growth rate (year 11 and beyond): 15

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

First, lets calculate the dividends upto end of year 11 (after which there is a perpetual growth rate in dividends)

Next, we calculate stock price when Boeing reaches a perpetual growth rate in dividends (end of year 11)

stock price when Boeing reaches a perpetual growth rate in dividends (end of year 11) = PE ratio * EPS in Year 11

EPS in year 11 = dividend per share / payout ratio

EPS in year 11 = $7.70 / 0.45 ==> $17.11

stock price at this time = PE ratio * EPS = 15* $17.11 ==> $256.67

Next, we calculate the value of stock today as :

present values of dividends + present value of the stock price at end of year 11. The discount rate used is 11%

PV of dividend in year X = dividend / (1 + 0.11)^X

Value of stock today = sum of PVs ==> $125.24