Question

You bought a ticket in the first ever Lottery ticket . . . and you won! You now need to decide which payout option to take: a) an immediate lump sum of $160,000; b) $1,000 per month to be received at the end of this month and every month thereafter for 50 years in total; or, c) $10,000 to be received one year from now and every year thereafter forever. Assuming an annual discount rate of 7.5%, which payout option should you take based on a comparison of the present value of each of the 3 payout options? [NOTE: You must show your work for each of the 3 options to receive points]

Answer 1

Option a:

Present Value of Option a is immediate lump sum payment = $160,000

Option b:

P = Monthly payment = $1,000

n = 50*12 = 600 months

r = monthly discount rate = 7.5%/12 = 0.625%

Present Value of the Payments = P * [1 - (1+r)^-n] / r

= $1,000 * [1 - (1+0.625%)^-600] / 0.625%

= $1,000 * 0.976206191 / 0.00625

= $156,192.991

Present Value of Option b is $156,192.99

Option c:

Annual Payment = $10,000

r = Discount rate = 7.5%

Present Value of Option c = Annual Payment / Discount rate

= $10,000 / 7.5%

= $133,333.33

Presnt Value of Option c is $133,333.33

It is better to choose Option a - Accept lumpsum payment of $160,000