Sample Project Report

This is a sample report. Included are some comments relating to the reports that were submitted. Those comments are italicized.

Determining the Future Value of Twenty Annual Payments

We first evaluate the total amount a lottery winner will have if he (or she) receives twenty annual payments of $50,000. In the table below, in the first row we indicate a $50,000 payment will incur a total income tax payment of $15,000, from the Federal Tax at 25% and the State Tax of 5%, leaving an investable balance of $35,000.

In each row after the first, we calculate the the interest on the payment from a year earlier, obtained by multiplying the balance after the previous payment by the annual interest rate of 6%. We then calculate the income tax on that interest by multiplying the interest by the combined tax rate of 30%. We then take the balance after the previous payment, add the interest and subtract the tax, to get the balance available after the income tax is paid.

We then take into account the next payment of $50,000, less the tax of $15,000 on that, to get the balance available after that next payment.

In the last row, after the final payment of $50,000, we add in the interest earned a year later, less the income tax on that interest, to obtain a final balance of $1,108,822.28.

[Note: Someone reading this explanation should be able to read the table and verify the entries are correct. The fact that the calculations were done using a spreadsheet is irrelevant and need not even be mentioned.]

Payment #	Interest on Balance From One Year Earlier	Tax on Interest	Balance After Tax is Paid on Interest	Payment	Tax on Payment	Balance After Payment
1				50,000.00	15,000.00	35,000.00
2	2,100.00	630.00	36,470.00	50,000.00	15,000.00	71,470.00
3	4,288.20	1,286.46	74,471.74	50,000.00	15,000.00	109,471.74
4	6,568.30	1,970.49	114,069.55	50,000.00	15,000.00	149,069.55
5	8,944.17	2,683.25	155,330.47	50,000.00	15,000.00	190,330.47
6	11,419.82	3,425.94	198,324.35	50,000.00	15,000.00	233,324.35
7	13,999.46	4,199.83	243,123.98	50,000.00	15,000.00	278,123.98
8	16,687.43	5,006.23	289,805.18	50,000.00	15,000.00	324,805.18
9	19,488.31	5,846.49	338,447.00	50,000.00	15,000.00	373,447.00
10	22,406.82	6,722.04	389,131.78	50,000.00	15,000.00	424,131.78
11	25,447.90	7,634.37	441,945.31	50,000.00	15,000.00	476,945.31
12	28,616.71	8,585.01	496,977.01	50,000.00	15,000.00	531,977.01
13	31,918.62	9,575.58	554,320.05	50,000.00	15,000.00	589,320.05
14	35,359.20	10,607.76	614,071.49	50,000.00	15,000.00	649,071.49
15	38,944.28	11,683.28	676,332.49	50,000.00	15,000.00	711,332.49
16	42,679.94	12,803.98	741,208.46	50,000.00	15,000.00	776,208.46
17	46,572.50	13,971.75	808,809.21	50,000.00	15,000.00	843,809.21
18	50,628.55	15,188.56	879,249.20	50,000.00	15,000.00	914,249.20
19	54,854.95	16,456.48	952,647.67	50,000.00	15,000.00	987,647.67
20	59,258.85	17,777.65	1,029,128.87	50,000.00	15,000.00	1,064,128.87
	63,847.73	19,154.31	1,108,822.28

Determining the Future Value of a Single Payment of One Million Dollars

We now determine what a single payment of $1 million will grow to after twenty years.

We first recognize that after paying combined Federal and State Income Taxes totalling $300,000, based on a combined 30% tax rate, we will be left with $700,000 to invest.

In the table below, we calculate the interest earned each year, based on the balance at the end of the previous year and multiplying by the annual interest rate of 6%. In the third column, we use the 30% combined tax rate to find the income tax that must be paid on that interest. We then take the previous year's balance (from the fourth column of the previous row), add the interest (in the second column) less the tax (in the third column), to obtain the balance at the end of the year, which is entered into the fourth column.

At the end of the 20^th year, we find we have a balance of $1,593,868.25.

Payment 1,000,000

Tax 300,000

Balance After Tax 700,000

Year Interest Tax on Interest Balance at End of Year

1 42,000.00 12,600.00 729,400.00

2 43,764.00 13,129.20 760,034.80

3 45,602.09 13,680.63 791,956.26

4 47,517.38 14,255.21 825,218.42

5 49,513.11 14,853.93 859,877.60

6 51,592.66 15,477.80 895,992.46

7 53,759.55 16,127.86 933,624.14

8 56,017.45 16,805.23 972,836.35

9 58,370.18 17,511.05 1,013,695.48

10 60,821.73 18,246.52 1,056,270.69

11 63,376.24 19,012.87 1,100,634.06

12 66,038.04 19,811.41 1,146,860.69

13 68,811.64 20,643.49 1,195,028.84

14 71,701.73 21,510.52 1,245,220.05

15 74,713.20 22,413.96 1,297,519.29

16 77,851.16 23,355.35 1,352,015.10

17 81,120.91 24,336.27 1,408,799.74

18 84,527.98 25,358.40 1,467,969.33

19 88,078.16 26,423.45 1,529,624.04

20 91,777.44 27,533.23 1,593,868.25

Determining a Lump Sum Payment With the Same Future Value as the Twenty Annual Payments

The amount to which an initial balance will grow is clearly proportional to the size of that balance. Since the future value of the twenty payments of $50,000 is 1,108,822.28/1,593,868.25 of the future value of a single $1,000,000 payment, a single payment of 1,108,822.28/1,593,868.25 of $1,000,000, or $695,680.01, would grow to the same value as the twenty $50,000 payments.

[Note: Alternatively, we could have taken the spreadsheet used to find the future value of the $1,000,000 payment and adjusted the initial amount until the final balance came out to $1,108,822.28.]

Analyzing the Pros and Cons

Under the assumptions given, there isn't much to analyze. One has far more funds with the single million dollar payment than if one gets twenty $50,000 payments.

[Note: One could interpret the question more generally and discuss the advantages and disadvantages of lump sum payments and annuities with the same future values. Some groups created tables and listed some purported pros and cons of each; such a table would be an aid to an analysis, but would not itself constitute an analysis.]

Assumptions Made and Factors Omitted

It was assumed that one could obtain a fixed interest rate of 6% over a period of 20 years. It's unlikely that a constant rate of return would be available over that long a period, but that simplification is still useful and does not detract from the ability to evaluate the relative merits of the two payout methods.

It's likely that anyone with significant funds to invest would invest in a variety of vehicles, especially since equities have historically yielded more than fixed income instruments and also receive preferential tax treatment. (Of course, as demonstrated the last few weeks, equities are also highly volatile in the short term.) The benefits of a balanced portfolio would accrue relatively equally to both scenarios, so the inference about the benefit of an immediate lump sum payment remains valid.

The assumption of constant Federal and State income tax rates was an extreme simplification, for several reasons. One is that governments frequently tinker with tax rates. Another is that the marginal tax rate will be affected by other income. More important, the average tax rate on a single payment of $1 million is likely to be far higher than the average tax rate on the individual $50,000 payments, decreasing the future value of the lump sum payment. This is a very significant factor which really should be considered in a careful analysis.