# solution

In January 2016, the record-shattering Powerball jackpot amounting to \$1.5864 billion was won by three ticket holders, John and Lisa Robinson, Maureen Smith, and Mae and Marvin Acosta. Each winner was awarded a nominal sum of \$528.8 million. The Michigan Lottery can pay Powerball and Mega Millions jackpot winnings in one of two ways: as an annuity or in one lump-sum/cash-option payment for the present cash value of the jackpot share. When a winner selects annuity payments, the jackpot is paid out in equal installments over 30 years. When a winner selects the cash option, the Lottery pays the winner the present cash value of the announced jackpot in one lump-sum payment. In effect, the Lottery takes all of the money that would have been invested to fund the 30-year annuity and turns it all over to the winner, retaining absolutely none of the prize. All three winners of the January 2016 Powerball jackpot opted to take a cash-option payment amounting to \$327.8 million per ticket. Regardless of which option the winner selects, the Michigan Lottery is required by law to withhold estimated income taxes for federal (25%) and state (4.9%) on any prize over \$5,000. These amounts are estimates only, and the winner is required to satisfy any further tax liability for the year in which the prize award is claimed. 3. What discount rate is the Powerball lottery using when decid- cing to pay a lump sum of \$327.8 million to each of the three Benido winning ticket holders? TO 4. Is the State of Michigan justified in advertising the prize amount as \$1.586 billion? Explain. BES TO 5. If the only option available was an annuity payment plan, what could the winner do to maximize the value of his/her winnings 10 assuming that the risk-free rate of interest is 5%? 6. Why do most winners select the cash option plan when given a choice? 7. If Michigan Lottery would like to give the annuity option an equal chance of being selected, how would it have to structure its payments? TO 5 Sipas 10

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