Question

Consider a lottery that pays to the winner an annuity of $350 that begins immediately (an annuity due) and then annually in year 1 through year 11 with one exception. Because of high administrative costs associated with running the lottery, the payment in year 6, and only 6, is not $350 but $0. Using an interest rate of 7%, determine the present value of this cash flow stream.

Answer 1

Annuity will pay cash flow of $350 each year from year 0(i.e., today) to year 11 with exception of $0 cashflow in year 6.

Calculating the Present value of cash flow stream:-

Year	Cash Flow of Stream ($)	PV Factor @7%	Present Value of Cash Flow stream ($)
0	350.00	1.00000	350.00
1	350.00	0.93458	327.10
2	350.00	0.87344	305.70
3	350.00	0.81630	285.70
4	350.00	0.76290	267.01
5	350.00	0.71299	249.55
6	-	0.66634	-
7	350.00	0.62275	217.96
8	350.00	0.58201	203.70
9	350.00	0.54393	190.38
10	350.00	0.50835	177.92
11	350.00	0.47509	166.28
			2,741.32

So, the present value of this cash flow stream is $2,741.32