Question

Suppose you have just won a $5 million lottery today. When you win the lottery, you generally receive payments of the lottery jackpot over twenty years. Therefore, your $5 million lottery winnings consist of twenty annual payments of $250,000 each. But wait! Don’t forget about the taxes. The IRS will take 25 percent of each check, so you are left with $187,500 each year. Assume that the annual interest rate is 3%.

So, if someone offered you a lump-sum of $2 million for your lottery winnings today, would you take it? Please explain how would you answer this question?

Answer 1

We need to calculate the present value of lottery payment over the years and compare with it the offer;

present value is found using annuity formula

PV of annuity = A*[1-(1+r)^-n]/r

where A= each year payments ; r=interest rate ; n =no of years.

PV of payments of 187500 for 20 years= 187500*[1-(1+3%)^-20]/.03 =2789526.53 =2.7 million ---- use equation, pv of annuity

Since PV of cashflow of lottery is 2.7 million which is greater than 2 million, we should not take his offer.