Question

A lottery jackpot of $220 million will be paid out in the following sequence.

Year 1: $20 million

Years 2-5:$30 milloon

After Year 6-7:$40 million

however the winner has the choice to except a lump sum payment right now. If the winner could invest a lump sum payment and earn 7%, what is the minimum lump sum payment the winner should except?

Answer 1

We need to find out the prsent value of the payments received and sum it up to calculated the NPV as shown in the below schedule:

Year	CF	Discount Factor	Discounted CF
1	$20.00	1/(1+0.07)^1=	0.934579439	0.934579439252336*20=	18.69
2	$30.00	1/(1+0.07)^2=	0.873438728	0.873438728273212*30=	26.20
3	$30.00	1/(1+0.07)^3=	0.816297877	0.816297876890852*30=	24.49
4	$30.00	1/(1+0.07)^4=	0.762895212	0.762895212047525*30=	22.89
5	$30.00	1/(1+0.07)^5=	0.712986179	0.712986179483668*30=	21.39
6	$40.00	1/(1+0.07)^6=	0.666342224	0.666342223816513*40=	26.65
7	$40.00	1/(1+0.07)^7=	0.622749742	0.622749741884591*40=	24.91
				NPV = Sum of all Discounted CF	165.22

So the winner can accept a lump sum payment of $165.22 and be indifferent between the lump sum and the stream of CF.