Question

Which of the following has the highest Present Value? Select one: a. $1,200/yr. for 10 years discounted at 10%. b. $1,200/yr. for 10 years discounted at 8%. c. $1,000/yr. for 10 years discounted at 10%. d. $1,000/yr. for 10 years discounted at 8%. e. $1,200/yr. for 12 years discounted at 8%.

Answer 1

e. $1,200/yr. for 12 years discounted at 8%.

Working:

a.	Present value		$ 7,373.48
Working:
	# 1
	Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
		=	(1-(1+0.10)^-10)/0.10		i	10%
		=	6.1445671		n	10
	# 2
	Present value	=	Annual cash flow	*	Present value of annuity of 1
		=	$ 1,200.00	*	6.144567
		=	$ 7,373.48
b.	Present value		$ 8,052.10
Working:
	# 1
	Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
		=	(1-(1+0.08)^-10)/0.08		i	8%
		=	6.7100814		n	10
	# 2
	Present value	=	Annual cash flow	*	Present value of annuity of 1
		=	$ 1,200.00	*	6.710081
		=	$ 8,052.10
c.	Present value		$ 6,144.57
Working:
	# 1
	Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
		=	(1-(1+0.10)^-10)/0.10		i	10%
		=	6.1445671		n	10
	# 2
	Present value	=	Annual cash flow	*	Present value of annuity of 1
		=	$ 1,000.00	*	6.144567
		=	$ 6,144.57
d.	Present value		$ 6,710.08
Working:
	# 1
	Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
		=	(1-(1+0.08)^-10)/0.08		i	8%
		=	6.7100814		n	10
	# 2
	Present value	=	Annual cash flow	*	Present value of annuity of 1
		=	$ 1,000.00	*	6.710081
		=	$ 6,710.08
e.	Present value		$ 9,043.29
Working:
	# 1
	Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
		=	(1-(1+0.08)^-12)/0.08		i	8%
		=	7.536078		n	12
	# 2
	Present value	=	Annual cash flow	*	Present value of annuity of 1
		=	$ 1,200.00	*	7.536078
		=	$ 9,043.29