Question

Gabrielle just won ​$2.75 million in the state lottery. She is given the option of receiving a total of ​$1,400,000 ​now, or she can elect to be paid ​$110,000 at the end of each of the next 25 years. If Gabrielle can earn 5​% annually on her​ investments, from a strict economic point of view which option should she​ take?

Answer 1

SOLUTION :
CALCULATION OF PRESENT VALUE OF OPTION : 1
Present value of option 1 = Total Amount received now
Present value of option 1 =		$                    14,00,000
CALCULATION OF PRESENT VALUE OF OPTION : 2
Annual interest rate = 5% it means PVF of $ 1 is also 5%
Year	Amount Recd. Per Year	PVF of $ 1 @ 5%	Cumulative Value
1	$                 1,10,000	0.9524	$             1,04,761.90
2	$                 1,10,000	0.9070	$                 99,773.24
3	$                 1,10,000	0.8638	$                 95,022.14
4	$                 1,10,000	0.8227	$                 90,497.27
5	$                 1,10,000	0.7835	$                 86,187.88
6	$                 1,10,000	0.7462	$                 82,083.69
7	$                 1,10,000	0.7107	$                 78,174.95
8	$                 1,10,000	0.6768	$                 74,452.33
9	$                 1,10,000	0.6446	$                 70,906.98
10	$                 1,10,000	0.6139	$                 67,530.46
11	$                 1,10,000	0.5847	$                 64,314.72
12	$                 1,10,000	0.5568	$                 61,252.12
13	$                 1,10,000	0.5303	$                 58,335.35
14	$                 1,10,000	0.5051	$                 55,557.47
15	$                 1,10,000	0.4810	$                 52,911.88
16	$                 1,10,000	0.4581	$                 50,392.27
17	$                 1,10,000	0.4363	$                 47,992.64
18	$                 1,10,000	0.4155	$                 45,707.27
19	$                 1,10,000	0.3957	$                 43,530.74
20	$                 1,10,000	0.3769	$                 41,457.84
21	$                 1,10,000	0.3589	$                 39,483.66
22	$                 1,10,000	0.3418	$                 37,603.49
23	$                 1,10,000	0.3256	$                 35,812.84
24	$                 1,10,000	0.3101	$                 34,107.47
25	$                 1,10,000	0.2953	$                 32,483.30
	Total Present Value =		$           15,50,333.90
Answer =
	PV of option 1 =	$                    14,00,000
	PV of option 2 =	$                    15,50,334
We can select option 2 because the present value of this option is higher than option 1
	Answer = Option 2