Question

Suppose you have just won the first prize in a lottery. The lottery offers you two possibilities for receiving your prize. The first possibility is to receive a payment of $16,000 at the end of the year, and then, for the next 10 years this payment will be repeated, but it will grow at a rate of 4%. The interest rate is 12% during the entire period. The second possibility is to receive $100,000 right now. Which of the two possibilities would you take?

Answer 1

Option 1:

Year	Cash flow
1	16000
2	(16000*1.04)=$16640
3	(16640*1.04)=17305.60
4	(17305.60*1.04)=$17997.824
5	(17997.824*1.04)=$18717.73696
6	(18717.73696*1.04)=$19466.44644
7	(19466.44644*1.04)=$20245.1043
8	(20245.1043*1.04)=$21054.90847
9	(21054.90847*1.04)=$21897.10481
10	(21897.10481*1.04)=$22772.989
11	(22772.989*1.04)=$23683.90856(Approx)

Present value of inflows=cash inflow*Present value of discounting factor(rate%,time period)

=16000/1.12+16640/1.12^2+17305.60/1.12^3+17997.824/1.12^4+18717.73696/1.12^5+19466.44644/1.12^6+20245.1043/1.12^7+21054.90847/1.12^8+21897.10481/1.12^9+22772.989/1.12^10+23683.90856/1.12^11

which is equal to

=$111,488.75(Approx)

Hence the first possibility is better having higher present value.

answered by: anonymous