Question

Sparkle Jewelers expects to pay dividends (per share) of $0.75, $1.50, $2.60, $3.50 during the next four years. Beginning in the fifth year, the dividend is expected to grow at a rate of 5 percent indefinitely. If investors require a 15 percent return to purchase Sparkle’s stock, what is the current value of the company’s stock?

Answer 1

As per dividend discount model, current price of stock is the present value of future dividends.
Step-1:Present value of future dividends of next 4 years
	Year	Dividend	Discount factor		Present value of dividend
	a	b	c=1.15^-a			d=b*c
	1	$       0.75	0.8696			$       0.65
	2	$       1.50	0.7561			$       1.13
	3	$       2.60	0.6575			$       1.71
	4	$       3.50	0.5718			$       2.00
	Total					$       5.50
Step-2:Calculation of terminal value of dividend
	Terminal value of dividend			=	D4*(1+g)/(Ke-g)			Where,
				=	3.50*(1+0.05)/(0.15-0.05)			D4	$       3.50
				=	$    36.75			g	5%
								Ke	15%
Step-3:Calculation of present value of all future dividends
	Present value of next 4 years dividend					$       5.50
	Present value of terminal value					$    36.75
	Present value of all future dividends					$    42.25
	Thus, current value of company's stock is				$    42.25
	Working:
	Present value of terminal value				=	Terminal value * Present value of 1
					=	$    36.75	*(1.15^-4)
					=	$    21.01