Question

Synovec Co. is growing quickly. Dividends are expected to grow at a rate of 25 percent for the next three years, with the growth rate falling off to a constant 6 percent thereafter. If the required return is 11 percent, and the company just paid a dividend of $1.15, what is the current share price? Answer is $39.08. Can you just show all work on how to get that number?

Answer 1

As per dividend discount method, current share price is the present value of future dividends.
Step-1:Present value of dividend of next 3 years
Year	Dividend	Discount factor	Present value
a	b	c=1.11^-a	d=b*c
1	$       1.44	0.900901	$       1.30
2	$       1.80	0.811622	$       1.46
3	$       2.25	0.731191	$       1.64
Total			$       4.40
Working;
Dividend of Year :
1	=	$       1.15	*	1.25	=	$       1.44
2	=	$       1.44	*	1.25	=	$       1.80
3	=	$       1.80	*	1.25	=	$       2.25
Step-2:Calculation of terminal value of dividend at the end of year
Terminal value	=	D3*(1+g)/(Ke-g)*DF3		Where,
	=	$    34.82		D3	=	$       2.25
				g	=	6%
				Ke	=	11%
				DF3	=	0.731191
Step-3:Sum of present value of future dividends
Sum of present value of future dividends	=	$       4.40	+	$    34.82
	=	$    39.21
So, current share price is $ 39.21
Difference in decimal places is due to rounding off difference.