Question

Computech Corporation is expanding rapidly and currently needs to retain all of its earnings; hence, it does not pay dividends. However, investors expect Computech to begin paying dividends, beginning with a dividend of $1.00 coming 3 years from today. The dividend should grow rapidly - at a rate of 47% per year - during Years 4 and 5, but after Year 5, growth should be a constant 8% per year. If the required return on Computech is 12%, what is the value of the stock today? Do not round intermediate calculations. Round your answer to the nearest cent. $

Answer 1

As per dividend discount model, value of stock today is the present value of dividends.
Step-1:Present value of dividend upto year 5
Year	Dividend	Discount factor	Present value
a	b	c=1.12^-a	d=b*c
3	$       1.00	0.71178	$       0.71
4	$       1.47	0.635518	$       0.93
5	$       2.16	0.567427	$       1.23
Total			$       2.87
Working:
Dividend of year:
4	$       1.00	x	1.47	=	$       1.47
5	$       1.47	x	1.47	=	$       2.16
step-2:Present value of dividend after year 5
Present value	=	D5*(1+g)/(Ke-g)*DF5			Where,
	=	$    33.11			D5	Dividend of year 5	$       2.16
					g	Growth rate	8%
					Ke	Required return	12%
					DF5	Discount factor of year 5	0.567427
Step-3:Present value of all dividends
Present value of all dividends	=	$       2.87	+	$    33.11
	=	$    35.98
So, value of stock today is $ 35.98