Question

Assignment Eight 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 4% per year. Calculate what the lump sum should be so that it would exactly equal the stream of future installments. 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. interest rate = 4%

5m total winnings

either 1m dollar paid today and 1m each after 1 year or a lumpsum today

It is asked to calculate lumpsum that will be equivalent to the yearly instalment of 1m today and 1m each in next four years

We need to find the present value of the 1m today and 1m each in next four years

Present value of annuity is found by using factor (P/A, I%, n)

where I is interest rate and n is time period

Present value = 1m + 1m *(P/A, 4%,4)

= 1000000 + 1000000 * 3.629895224

= 4,629895.22

This is the equivalent present value of instalment payment in future

Cash Flow diagram

2. When first instalment is after 1 year from today, then equivalent value would change.

Now we are receiving 1m each year for next five years

Present value now will be = 1000000 *(P/A, 4%,5)

= 1000000 * 4.45182233

= 4451822.33

Present value will decrease as all payment are in future. Any future payment is discounted, so net present value is always less than the payment received in future

Cash flow diagram