Question

Jackie Chan has just won the state lottery, paying $50,000 a year for 20 years. He is to receive his first payment a year from now. The state advertises this as the Million Dollar Lottery because he will receive a total of $1,000,000 over the next 20 years. If the interest rate is 8 percent, what is the true value of the lottery?

Answer 1

Given

Annual amount = $ 50000

Duration = 20 Years

Interest rate = 8 %

True value of the lottery = sum of the present value of future discounted cash inflows

Calculation of True value of lottery
Year	Cash Inflow	Disc @ 8 %	Discounted Cash flows
1	$50,000	0.9259	$46,296.30
2	$50,000	0.8573	$42,866.94
3	$50,000	0.7938	$39,691.61
4	$50,000	0.7350	$36,751.49
5	$50,000	0.6806	$34,029.16
6	$50,000	0.6302	$31,508.48
7	$50,000	0.5835	$29,174.52
8	$50,000	0.5403	$27,013.44
9	$50,000	0.5002	$25,012.45
10	$50,000	0.4632	$23,159.67
11	$50,000	0.4289	$21,444.14
12	$50,000	0.3971	$19,855.69
13	$50,000	0.3677	$18,384.90
14	$50,000	0.3405	$17,023.05
15	$50,000	0.3152	$15,762.09
16	$50,000	0.2919	$14,594.52
17	$50,000	0.2703	$13,513.45
18	$50,000	0.2502	$12,512.45
19	$50,000	0.2317	$11,585.60
20	$50,000	0.2145	$10,727.41
		9.8181
	Total		$490,907.37

Therefore True value of the lottery is $ 490907.37