Question

You have just won the lottery. You will receive $2,580,000 today, and then receive 40 payments of $1,290,000 These payments will start one year from now and will be paid every six months. A representative from Greenleaf Investments has offered to purchase all the payments from you for $20 million. The interest rate is an APR of 10 percent compounded daily. Assume there are 12 months in a year, each with 30 days. What is the present value of the cash flows from your lottery winnings?

Answer 1

The interest is compounding daily and cash flow is semiannually. So we need to compute interest rate daily first and then days per period are multiplied by number of periods to get total days for each cash flow separately. Then total PV can be computed adding PV of individual cash flows as per the table below.

Semiannual Period(n)	Days in a period (d= 30x6)	Cash Flow (C)	1+r [=1+(0.1/360)	n x d	(1+r) n x d	PV [=C/(1+r)n x d]
0		$2,580,000				$2,580,000
1	180
2	180	$1,290,000	1.000277778	360	1.105155571	$1,167,256.48
3	180	$1,290,000	1.000277778	540	1.161810043	$1,110,336.42
4	180	$1,290,000	1.000277778	720	1.221368837	$1,056,192.00
5	180	$1,290,000	1.000277778	900	1.283980842	$1,004,687.89
6	180	$1,290,000	1.000277778	1080	1.349802575	$955,695.32
7	180	$1,290,000	1.000277778	1260	1.418998581	$909,091.82
8	180	$1,290,000	1.000277778	1440	1.491741836	$864,760.89
9	180	$1,290,000	1.000277778	1620	1.568214187	$822,591.72
10	180	$1,290,000	1.000277778	1800	1.648606801	$782,478.88
11	180	$1,290,000	1.000277778	1980	1.733120646	$744,322.10
12	180	$1,290,000	1.000277778	2160	1.821966992	$708,026.00
13	180	$1,290,000	1.000277778	2340	1.915367938	$673,499.84
14	180	$1,290,000	1.000277778	2520	2.013556972	$640,657.31
15	180	$1,290,000	1.000277778	2700	2.116779548	$609,416.32
16	180	$1,290,000	1.000277778	2880	2.225293706	$579,698.76
17	180	$1,290,000	1.000277778	3060	2.339370711	$551,430.35
18	180	$1,290,000	1.000277778	3240	2.459295737	$524,540.41
19	180	$1,290,000	1.000277778	3420	2.585368575	$498,961.74
20	180	$1,290,000	1.000277778	3600	2.717904385	$474,630.38
21	180	$1,290,000	1.000277778	3780	2.857234485	$451,485.52
22	180	$1,290,000	1.000277778	3960	3.003707174	$429,469.29
23	180	$1,290,000	1.000277778	4140	3.15768861	$408,526.67
24	180	$1,290,000	1.000277778	4320	3.319563718	$388,605.28
25	180	$1,290,000	1.000277778	4500	3.48973716	$369,655.35
26	180	$1,290,000	1.000277778	4680	3.668634338	$351,629.48
27	180	$1,290,000	1.000277778	4860	3.856702465	$334,482.63
28	180	$1,290,000	1.000277778	5040	4.054411678	$318,171.93
29	180	$1,290,000	1.000277778	5220	4.262256217	$302,656.61
30	180	$1,290,000	1.000277778	5400	4.480755655	$287,897.87
31	180	$1,290,000	1.000277778	5580	4.710456205	$273,858.82
32	180	$1,290,000	1.000277778	5760	4.951932077	$260,504.38
33	180	$1,290,000	1.000277778	5940	5.205786919	$247,801.15
34	180	$1,290,000	1.000277778	6120	5.472655324	$235,717.38
35	180	$1,290,000	1.000277778	6300	5.753204417	$224,222.87
36	180	$1,290,000	1.000277778	6480	6.048135522	$213,288.87
37	180	$1,290,000	1.000277778	6660	6.358185915	$202,888.06
38	180	$1,290,000	1.000277778	6840	6.684130668	$192,994.43
39	180	$1,290,000	1.000277778	7020	7.026784588	$183,583.26
40	180	$1,290,000	1.000277778	7200	7.387004248	$174,631.01
41	180	$1,290,000	1.000277778	7380	7.765690136	$166,115.31
					Total PV	$23,276,461

Present value of the lottery winnings is $ 23,276,461 which is more than offered $ 20 Million.