Question

Singing Fish Fine Foods has a current annual cash dividend policy of ​$3.75 The price of the stock is set to yield a return of 10%. What is the price of this stock if the dividend will be paid

a. for 12 ​years?

b.for 17 ​years?

c.for 41 ​years?

d.for 60 ​years?

e.for 100 ​years?

f.​forever?

Answer 1

As per dividend discount model, price of stock is the present value of future dividends.
a.	$    25.55
Working:
# 1	Present value of annuity of 1			=	(1-(1+i)^-n)/i			Where,
				=	(1-(1+0.10)^-12)/0.10			i	0.10
				=	6.813692			n	12
# 2	Present value of dividend			=	Annual dividend*Present value of annuity of 1
				=	$       3.75	*	6.813692
				=	$    25.55
b.	$    30.08
Working:
# 1	Present value of annuity of 1			=	(1-(1+i)^-n)/i			Where,
				=	(1-(1+0.10)^-17)/0.10			i	0.10
				=	8.021553			n	17
# 2	Present value of dividend			=	Annual dividend*Present value of annuity of 1
				=	$       3.75	*	8.021553
				=	$    30.08
c.	$    36.75
Working:
# 1	Present value of annuity of 1			=	(1-(1+i)^-n)/i			Where,
				=	(1-(1+0.10)^-41)/0.10			i	0.10
				=	9.799137			n	41
# 2	Present value of dividend			=	Annual dividend*Present value of annuity of 1
				=	$       3.75	*	9.799137
				=	$    36.75
d.	$    37.38
Working:
# 1	Present value of annuity of 1			=	(1-(1+i)^-n)/i			Where,
				=	(1-(1+0.10)^-60)/0.10			i	0.10
				=	9.967157			n	60
# 2	Present value of dividend			=	Annual dividend*Present value of annuity of 1
				=	$       3.75	*	9.967157
				=	$    37.38
e.	$    37.50
Working:
# 1	Present value of annuity of 1			=	(1-(1+i)^-n)/i			Where,
				=	(1-(1+0.10)^-100)/0.10			i	0.10
				=	9.999274			n	100
# 2	Present value of dividend			=	Annual dividend*Present value of annuity of 1
				=	$       3.75	*	9.999274
				=	$    37.50
f.	$    37.50
Working:
	Present value of dividend			=	Annual dividend/Yield
				=	$       3.75	/	10%
				=	$    37.50