Question

# You've won the lottery! You will be paid \$1 million per year starting now with 10...

You've won the lottery! You will be paid \$1 million per year starting now with 10 additional annual \$1 mm payments.

 If r=5%, what is the PV of your winnings?

 The lottery commission offers you an option to take \$1,000,000 now and \$500,000 per year for 36 additional annual payments. Should you accept it?

 Does your answer change if you are 70 years old with no heirs?

 How is your answer affected if you can sell the “bonds”, i.e. the contracted payments?

 1] PV of winnings = 1000000*1.05*(1.05^11-1)/(0.05*1.05^11) = \$        8,721,735 2] PV of alternative payments = 1000000+500000*(1.05^36-1)/(0.05*1.05^36) = \$        9,273,426 Yes, the alternative offer of the commission should be accepted as it has higher PV at the required return of 5%. 3] Yes. My answer would change as I would take the 1st option because I will be only 81 years by the end of the payment period, and is likely to survive that age. The alternative will end only at my age of 106 years, which I am most likely not to reach. 4] If the contracted payments can be sold, then the alternative offer of the commission of 36 years, will be preferred, as it can be sold for a higher value.