Question

4. The state lottery claims that its grand prize is $1 million. The lucky winner will receive $100,000 upon presentation of the winning ticket plus $100,000 at the end of each year for the next 9 years. Assume a 10% discount rate. a-Why isn't this really a million-dollar prize? (5 Points) b-What would it actually be worth in dollars to you? (5 Points) C-What would the 10 yearly payments need to be for the present value of the lottery to be $1 million? Hint: The first step is to determine what type of an annuity the lottery represents. (10 Points)

Answer 1

Please refer to below spreadsheet for calculation and answer. Cell reference also provided.

Annual Payment of lottery No. of Annual payment Discount rate Type of Annuity $100,000.00 10 10% Annuity Due a. 9 Because of Time value of money. The present value(discounted value) of future cash flows is always less than its Nominal value. Thus, Present worth of annual payment of lottery is less than its lumpsum amount i.e $1 million. 11 12 Present worth of Lottery $675,902.38 13 b. 14 15 $1,000,000.00 Required Present worth of lottery No. of Annual payment Discount rate Type of Annuity 17 18 19 20 10% Annuity Due 21 Annual payment $147,950.36

Cell reference -

Annual Payment of lottery No. of Annual payment Discount rate Type of Annuity 100000 10 0.1 Annuity Due 7 a. Because of Time value of money. The present value(discounted value) of future cash flows is always less than its Nominal value. Thus, Present worth of annual payment of lottery is less than its lumpsum amount i.e $1 million. 9 10 11 12 13 b. 14 15 16 c. Present worth of Lottery =PV(C4,C3,-C2,,1) 1000000 10 17 Required Present worth of lottery No. of Annual payment Discount rate Type of Annuity 18 0.1 Annuity Due Annual payment =PMT(C18,017,-C16,,1) 22

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.