Question

You have just won the lottery and will receive $500,000 in one year. You will receive payments for 22 years, which will increase 4 percent per year. The appropriate discount rate is 10 percent.

Required:

What is the present value of your winnings?

Multiple Choice

• $5,907,208

• $5,670,920

• $20,290,274

• $20,290,274

Answer 1

The total investment value at the end of each year is calculated. Each year there is 4 % increment in the cash flows. The cash flow for each year is rounded off to the nearest dollar value. The present value of cashflow for each year can be calculated with help of factor for present value of future amount table. Take the present value factor corresponding to the the rate of return (10 %) and no. of year and multiply with the annual cash flow.

The present value for each year is calculated as under-

Year	cashflow received per year (in $)	PVF(10%,n)	Present value of cashflow
1	500000	0.909	454500
2	520000	0.826	429520
3	540800	0.751	406141
4	562432	0.683	384141
5	584929	0.621	363241
6	608327	0.564	343097
7	632660	0.513	324555
8	657966	0.467	307270
9	684285	0.424	290137
10	711656	0.386	274699
11	740122	0.35	259043
12	769727	0.319	245543
13	800516	0.29	232150
14	832537	0.263	218957
15	865839	0.239	206936
16	900472	0.218	196303
17	936491	0.198	185425
18	973950	0.18	175311
19	1012908	0.164	166117
20	1053425	0.149	156960
21	1095562	0.135	147901
22	1139384	0.122	139005
		Total	5906952

Correct option is A as it is nearest to the answer derived from upon calculation. The present value of your winnings is $5,907,208. The difference is due to rounding off.

Hope it clarifies!