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

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 |

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 |

[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.]

[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.]

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.

Totally ignored was the fact that state income taxes are deductible expenses under Federal income tax regulations.