Question

Juan has just won a lottery. He can get $14 million now (after-tax, lumpsum or one-time option), or he can get $1 million annually for 25 years starting today (after-tax, 25 payments of $1 million each). Whichever option he chooses, he can save his money at a local bank, which is offering a 7% per year return on deposits. Juan is not sure if he should pick a lumpsum option or 25-payments option. He comes to you for help. What is the benefit (or loss) of choosing the lumpsum option in today’s dollars?

Answer 1

PV of 25 Year CFs:

PV of CF = CF * PVF(r%, n)

r is int rate per anum, nth year.

Year	CF	PVF @7%	Disc CF
0	$ 10,00,000.00	1.0000	$     10,00,000.00
1	$ 10,00,000.00	0.9346	$       9,34,579.44
2	$ 10,00,000.00	0.8734	$       8,73,438.73
3	$ 10,00,000.00	0.8163	$       8,16,297.88
4	$ 10,00,000.00	0.7629	$       7,62,895.21
5	$ 10,00,000.00	0.7130	$       7,12,986.18
6	$ 10,00,000.00	0.6663	$       6,66,342.22
7	$ 10,00,000.00	0.6227	$       6,22,749.74
8	$ 10,00,000.00	0.5820	$       5,82,009.10
9	$ 10,00,000.00	0.5439	$       5,43,933.74
10	$ 10,00,000.00	0.5083	$       5,08,349.29
11	$ 10,00,000.00	0.4751	$       4,75,092.80
12	$ 10,00,000.00	0.4440	$       4,44,011.96
13	$ 10,00,000.00	0.4150	$       4,14,964.45
14	$ 10,00,000.00	0.3878	$       3,87,817.24
15	$ 10,00,000.00	0.3624	$       3,62,446.02
16	$ 10,00,000.00	0.3387	$       3,38,734.60
17	$ 10,00,000.00	0.3166	$       3,16,574.39
18	$ 10,00,000.00	0.2959	$       2,95,863.92
19	$ 10,00,000.00	0.2765	$       2,76,508.33
20	$ 10,00,000.00	0.2584	$       2,58,419.00
21	$ 10,00,000.00	0.2415	$       2,41,513.09
22	$ 10,00,000.00	0.2257	$       2,25,713.17
23	$ 10,00,000.00	0.2109	$       2,10,946.88
24	$ 10,00,000.00	0.1971	$       1,97,146.62
PV of Annuity CF			$ 1,24,69,334.00

Receiving $ 14 M is better as PV of future CFs is $ 12,469,334.00