Question

You just won the lottery worth $70,000,000. After reading the fine print you learn that you have two options:

Option A: Take the cash value of $47.6 million today (before taxes)

Option B: You are guaranteed to receive 30 graduated payments over 29 years. The first payment is made today. These payments will increase by 5% per year until the final payment. The first payment, received today, equals $1,900,000.

Assuming a required rate of return of 6%, calculate the present value of Option B.

Answer 1

Solution :-

Option A :- Present Value of Price = $47.6 million = $47,600,000

Option B :- Present Value of Price = $49.85 million = $49,847,718

Year	Cashflow	PVF@6%	PV of Cashflow
0	$1,900,000	1.000	$1,900,000
1	$1,995,000	0.943	$1,882,075
2	$2,094,750	0.890	$1,864,320
3	$2,199,488	0.840	$1,846,732
4	$2,309,462	0.792	$1,829,310
5	$2,424,935	0.747	$1,812,052
6	$2,546,182	0.705	$1,794,958
7	$2,673,491	0.665	$1,778,024
8	$2,807,165	0.627	$1,761,250
9	$2,947,524	0.592	$1,744,635
10	$3,094,900	0.558	$1,728,176
11	$3,249,645	0.527	$1,711,872
12	$3,412,127	0.497	$1,695,723
13	$3,582,733	0.469	$1,679,725
14	$3,761,870	0.442	$1,663,879
15	$3,949,964	0.417	$1,648,182
16	$4,147,462	0.394	$1,632,633
17	$4,354,835	0.371	$1,617,231
18	$4,572,577	0.350	$1,601,974
19	$4,801,205	0.331	$1,586,861
20	$5,041,266	0.312	$1,571,890
21	$5,293,329	0.294	$1,557,061
22	$5,557,995	0.278	$1,542,372
23	$5,835,895	0.262	$1,527,821
24	$6,127,690	0.247	$1,513,408
25	$6,434,074	0.233	$1,499,131
26	$6,755,778	0.220	$1,484,988
27	$7,093,567	0.207	$1,470,978
28	$7,448,245	0.196	$1,457,101
29	$7,820,658	0.185	$1,443,355
	Total		$49,847,718

Now The Present Value of Price of Option B that is $49,847,718 is More

So choose Option B