Question

A stock is expected to pay the following dividends: $1.2 four years from now, $1.6 five years from now, and $1.8 six years from now, followed by growth in the dividend of 5% per year forever after that point. There will be no dividends prior to year 4. The stock's required return is 13%. The stock's current price (Price at year 0) should be $____________.

Answer 1

As per dividend discount method, current stock price is the present value of dividends.
Step-1:Present value of next 6 year's dividend
	Year	Dividend	Present value of 1	Present value of dividend
	a	b	c=1.13^-a	d=b*c
	4	$       1.20	0.6133	$                  0.74
	5	$       1.60	0.5428	$                  0.87
	6	$       1.80	0.4803	$                  0.86
	Total			$                  2.47
Step-2:Terminal value of dividend at the end of year 6
	Terminal Value		=	D6*(1+g)/(Ke-g)		Where,
			=	1.80*(1+0.05)/(0.13-0.05)		D6	Year 6 dividend		$       1.80
			=	$                23.63		g	Growth rate		5%
						Ke	Required Return		13%
Step-3:Present value of terminal value
	Present value		=	Terminal value at the end of Year 6*Present value of 1
			=	$                23.63	*	0.4803
			=	$                11.35
	Working:
	Present value of 1		=	(1+i)^-n		Where,
			=	(1+0.13)^-6		i	13%
			=	0.48032		n	6
Step-4:Present value of all dividends
	Present value of all dividends			=	$       2.47	+	$    11.35
				=	$    13.82
Thus,
	The stock's current price (Price at year 0) should be				$    13.82