Question

CP 14-3 Present Values

Alex Kelton recently won a jackpot in the Colorado lottery while he was visiting his parents. When he arrived at the lottery office to collect his winnings, he was offered the following three payout options:

a. Receive $100,000,000

b. Receive $25,000,000 today and $9,000,000 per year for 8 years, with the first payment being received one year from today.

c. Receive $15,000,000 per year for 10 years, with the first payment being received one year from today.

Assuming that the effective rate of interest is 7% which payout option should Alex select? Use the present value tables in Appendix A . Explain your answer and provide any necessary supporting calculations.

Answer 1

best option is the one for which present value is higher.
Option -1
present value =		100,000,000
Option -2
	i	ii	iii=i*ii
year	Cashflow	PVIF @ 7%	present value
0	25,000,000	1.00000	25,000,000
1	9,000,000	0.93458	8,411,215
2	9,000,000	0.87344	7,860,949
3	9,000,000	0.81630	7,346,681
4	9,000,000	0.76290	6,866,057
5	9,000,000	0.71299	6,416,876
6	9,000,000	0.66634	5,997,080
7	9,000,000	0.62275	5,604,748
8	9,000,000	0.58201	5,238,082
present value=			78,741,687
Option -3
	i	ii	iii=i*ii
year	Cashflow	PVIF @ 7%	present value
0	0	1.00000	-
1	15,000,000	0.93458	14,018,692
2	15,000,000	0.87344	13,101,581
3	15,000,000	0.81630	12,244,468
4	15,000,000	0.76290	11,443,428
5	15,000,000	0.71299	10,694,793
6	15,000,000	0.66634	9,995,133
7	15,000,000	0.62275	9,341,246
8	15,000,000	0.58201	8,730,137
9	15,000,000	0.54393	8,159,006
10	15,000,000	0.50835	7,625,239
present value=			105,353,723
since present value is higher for option 3. Therefore ans = option 3