Question

A fast-growing firm recently paid a dividend of $0 55 per share. The dividend is expected to increase at a 10 percent rate for the next three years. Aberwards a more stable percent grow that can be assumed. 

If a 6 percent discount rate is appropriate for this stock, what is its value to Do not found intermediate calculations?  

Answer 1

The value of the stock will be a sum of a growing annuity of the stream of dividends for the next three years and growing perpetuity of stream of dividends thereafter

We call the PV of the perpetual annuity as the terminal value of the dividend stream. We use the Gordon Growth Model to calculate it.

Terminal value = D₁ / (r - g)

D₁ is dividend next year (in this case dividend in 4^th year)
r is the discount rate
g is the perpetual growth rate

Note that the value we get here is PV as year 3 and needs to discount further in today's date. The following table shows the calculations

Recent dividend	$       0.55
First 3 years growth rate	10%
Perpetual growth rate	5%
Discount rate	6%
Year	0	1	2	3
Dividend		$       0.61	$       0.67	$       0.73
PV of dividends		$       0.57	$       0.59	$       0.61
Terminal value				$    76.87
PV of terminal value	$    64.54
Value of share	$    66.32

Hence the value of the share today is $66.32