Question

1. Assume I won 50 million dollars in a lottery that pays installments of 10 million dollars a year for five years or a lump sum of less than 50 million dollars. If I take the installments, my first installment would come the day I claimed my winnings at the state lottery office. If I take the lump sum, I would receive that payment the day I claimed my winnings at the state lottery office. Assume that the interest rate is 5% per year. Calculate what the lump sum should be so that it would exactly equal the stream future installments. You must show and explain your work to be given credit for this assignment.

2. What would your answer change be if the first installment in the question above did not come until one year after I claimed my winnings. You must show and explain your work to be given credit for this assignment.

Answer 1

1.

R = 5%

If lottery payment is taken in instalments. (It is a case of annuity due).

Then,

Present value of the lottery payment = 10 + 10/1.05 + 10/1.05^2 + 10/1.05^3 + 10/1.05^4

Present value of the lottery payment = $45.46 Million

If the lump-sum payment of the lottery is equal to the present value of the instalment of lottery payment, then the winner person will be indifferent between these two options.

Hence, the value of the Lump-sum payment should be equal to $45.46 Million as it will be equal to the present worth of the instalment payment of the lottery.

2.

If installment payment takes place at the end of year,

Then,

Present value of the lottery payment = 10*(1-1/1.05^5)/.05 = $43.29 Million approx.

Since the present value of instalment is less than the payment in Q. 1, then the winner person would prefer to have the lump-sum payment of $45.46 Million that is higher than the $43.29 Million of instalment in this case.