Question

1. Assume I won 5 million dollars in a lottery that pays installments of 1 million dollars a year for five years or a lump sum of less than 5 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 6% per year. Calculate what the lump sum should be so that it would exactly equal the present value of the stream of future payments. You must show and explain your work to be given credit for this assignment. Assume there are no taxes on my winnings.

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.

I do not need pages of explanation. Just three or four sentences for each question. However, I do need to see your work.

Answer 1

1.

The first payment is done on the same day of winning the lottery. Hence, it is a case of annuity due. The Present value of annuity (due) payments will be calculated and that will be equivalent to the lumpsum payment made today, when lottery is won.

Annual payment P = $1 Million

R = 6%

Time = 5 years

So,

Present value of annuity due = (1*(1-1/(1+6%)^5)/.06)*(1+6%)

Present value of annuity due = $4.465 Million

So, lumpsum payment of $4.465 Million is equal to the payment series of $1 million as mentioned in the question.

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2.

In this case, the first payment is done after 1 year of the  winning the lottery. Hence, it is a case of ordinary annuity . The Present value of annuity payments will be calculated and that will be equivalent to the lumpsum payment made today, when lottery is won.

Annual payment P = $1 Million

R = 6%

Time = 5 years

So,

Present value of annuity = (1*(1-1/(1+6%)^5)/.06)

Present value of annuity = $4.21 Million

So, lumpsum payment of $4.21 Million is equal to the payment series of $1 million as mentioned in this part of the question.