Question

Your grandfather has offered you a choice of one of the three following alternatives: $11,000 now; $4,500 a year for ten years; or $66,000 at the end of ten years. Use Appendix B and Appendix D for an approximate answer, but calculate your final answer using the formula and financial calculator methods. a-1. Assuming you could earn 8 percent annually, compute the present value of each alternative: (Do not round intermediate calculations. Round your final answers to 2 decimal places.) a-2. Which alternative should you choose? $66,000 received at end of ten years $4,500 received each year for ten years $11,000 received now b-1. If you could earn 9 percent annually, compute the present value of each alternative: (Do not round intermediate calculations. Round your final answers to 2 decimal places.) b-2. Which alternative should you choose? $66,000 received each year for ten years $4,500 received at end of ten years $11,000 received now

Answer 1

a-1	Assuming you could earn 8 percent annually compute the present value of each alternative
	Present value today			$11,000
	Year	Cash flow	Discount factor @ 8%	Present Value
	1	$4,500	0.925926	$4,166.67
	2	$4,500	0.857339	$3,858.02
	3	$4,500	0.793832	$3,572.25
	4	$4,500	0.73503	$3,307.63
	5	$4,500	0.680583	$3,062.62
	6	$4,500	0.63017	$2,835.76
	7	$4,500	0.58349	$2,625.71
	8	$4,500	0.540269	$2,431.21
	9	$4,500	0.500249	$2,251.12
	10	$4,500	0.463193	$2,084.37
				$30,195.37
	Present value if $ 4500 received for 10 years					$30,195.37
	$66000*0.4632					30571.20
a-2	Alternative 3 will be chosen since the present value today is $ 30571.20
b-1	Assuming you could earn 9 percent annually compute the present value of each alternative
	Present value today			$11,000
	Year	Cash flow	Discount factor @ 9%	Present Value
	1	$4,500	0.917431	$4,128.44
	2	$4,500	0.84168	$3,787.56
	3	$4,500	0.772183	$3,474.83
	4	$4,500	0.708425	$3,187.91
	5	$4,500	0.649931	$2,924.69
	6	$4,500	0.596267	$2,683.20
	7	$4,500	0.547034	$2,461.65
	8	$4,500	0.501866	$2,258.40
	9	$4,500	0.460428	$2,071.93
	10	$4,500	0.422411	$1,900.85
				$28,879.46
	Present value if $ 4500 received for 10 years					$28,879.46
	$66000*0.4224					27878.40
b-2	Alternative 2 will be chosen since the present value today is $ 28879.46