Question

As an analyst, you have gathered the following information on a company you are tracking. The current dividend is $0.75. Dividends are expected to grow at a rate of 12% over the next three years, decline linearly to 4% over the next six years, and then remain at a long-term equilibrium growth rate of 4% in perpetuity. The required return is 9%. The value of the company is closest to:

            a) $20.25.

b) $23.2056

c) $78.25

d) $15.76

e) None of the options

Answer 1

Value of company = present value of dividends + present value of terminal value at end of year 9

terminal value at end of year 9 = dividend in year 10 / (required return - constant growth rate)

dividend growth declines linearly from 12% from year 3 to 4% by year 9 (over 6 years). So dividend growth rate declines by 8 / 6 each year, which is 1.33%. The dividend growth rates, and dividends over the next 9 years are below :

Year	Dividend growth rate	Dividend
0		$0.75
1	12%	$0.84
2	12%	$0.94
3	12%	$1.05
4	10.67%	$1.17
5	9.33%	$1.27
6	8.00%	$1.38
7	6.67%	$1.47
8	5.33%	$1.55
9	4%	$1.61

Terminal value at end of year 9 = ($1.61 + 4%) / (9% - 4%) ==> $33.47

Now, we calculate the present value of each dividend upto year 9, and the present value of the terminal value at end of year 9. The discount rate used is 9% which is the required return.

The total present value (of dividends and terminal value) is $22.58

This is the value of the company today