4. You have just won the lottery and have a choice as to how you will receive yo

Question

4. You have just won the lottery and have a choice as to how you will receive your $45,000,000 winnings. You can either receive 20 annual payments of $2,250,000 with the first payment occurring now or 240 monthly payments of $187,500 with the first payment occurring now. Ignoring inflation and taxes, if your personal discount rate is 4%, then which payment scheme would you prefer (show your work). If the state has a discount rate of 6.5% and normally makes annual payments for 20 years, what would be the payout if you take your winnings in one payment right now?

Explanation / Answer

(a)

4% annual discount rate = (4 / 12) = 0.33% monthly discount rate.

Option - 1

Present value (PV) of the annual payments = $2,250,000 x Present value interest factor of annuity at 4%, 20 years x (1.04) [Since this is an annuity due]

= $2,250,000 x 13.5903 (From PVIFA Table) x 1.04

= $31,801,302

Option - 2

Present value (PV) of the monthly payments = $187,500 x Present value interest factor of annuity at 0.33%, 240 months x (1.0033) [Since this is an annuity due]

= $187,500 x 165.5973 (From PVIFA Table) x 1.0033

= $31,151,957

So, option 1 is preferred since its present value is higher.

(b)

Present value (PV) of the annual payments = $31,801,302 (Computed, part (a))

Up-front award amount = $45,000,000

Payoff = $(45,000,000 - 31,801,302) = $13,198,698 if you decide to take up-front payment.

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