Question

Consider a lottery that pays to the winner an annuity of $600 that begins immediately (an annuity due) and then annually in year 1 through year 13 with one exception. Because of high administrative costs associated with running the lottery, the payment in year 8, and only 8, is not $600 but $0. Using an interest rate of 5%, determine the present value of this cash flow stream.

Answer 1

Annuity will pay cash flow of $600 each year from year 0(i.e., today) to year 13 with exception of $0 cashflow in year 8.

Calculating the Present value of cash flow stream:-

Year	Cash Flow of Stream ($)	PV Factor @5%	Present Value of Cash Flow stream ($)
0	600.00	1.00000	600.00
1	600.00	0.95238	571.43
2	600.00	0.90703	544.22
3	600.00	0.86384	518.30
4	600.00	0.82270	493.62
5	600.00	0.78353	470.12
6	600.00	0.74622	447.73
7	600.00	0.71068	426.41
8	-	0.67684	-
9	600.00	0.64461	386.77
10	600.00	0.61391	368.35
11	600.00	0.58468	350.81
12	600.00	0.55684	334.10
13	600.00	0.53032	318.19
			5,830.04

So, the present value of this cash flow stream is $5830.04