Cost Of Living Adjustments
By:
William R. Larsen
September 19, 2002
What happens when Cost of Living Adjustments (COLA) are reduced? How does this change effect total benefits? Is there a simple mathematical way to determine the equivalent benefit reduction? Yes there is.
Let us start with a model of how COLA works. Let us assume a person's OASI benefit is $1,000. This amount is adjusted by inflation of 3% a year for twenty-five years. Table One shows in column 2 these payments. The total benefits paid are $36,459. What happens if we reduce COLA by 0.5%? Column 4 shows this cash flow and it totals $34,158 or 6.31% less than column 2.
We now calculate the present value for this cash flow. Column 3 totals $25,000 which it should. Column 5 totals $23,596 or 5.61% less than the present value of the full COLA column. Which value is correct, 5.61% or 6.31% or are both wrong?
Column 6 takes the $1,000 initial benefit and reduces it by 6.31% to $937 and then increases by the full COLA of 3%. The total value is $34,158 which is identical to column 2.
Column 7 takes the $1,000 initial benefit and reduces it by 5.61% and then increases it by the full COLA of 3%. The total value is $34,412 which does not match any of the other columns.
The correct answer is: a 0.5% reduction in COLA each year is equivalent to an initial benefit cut of 6.31%.
Table Two lists the equivalent up front benefit cut for COLA reductions versus retirement span. The average life expectancy at age 65 is about 18 to 19 years. A 3% reduction is about a 23% initial benefit cut.
| Table One
Cost of Living Adjustment and Effect of Reductions | ||||||
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Year | Value | Present Value | Reduced | Reduced Present Value | Check -6.31 % | Check -5.61 % |
| 1 | $1,000 | $1,000 | $1,000 | $1,000 | $937 | $944 |
| 2 | $1,030 | $1,000 | $1,025 | $995 | $965 | $972 |
| 3 | $1,061 | $1,000 | $1,051 | $990 | $994 | $1,001 |
| 4 | $1,093 | $1,000 | $1,077 | $986 | $1,024 | $1,031 |
| 5 | $1,126 | $1,000 | $1,104 | $981 | $1,054 | $1,062 |
| 6 | $1,159 | $1,000 | $1,131 | $976 | $1,086 | $1,094 |
| 7 | $1,194 | $1,000 | $1,160 | $971 | $1,119 | $1,127 |
| 8 | $1,230 | $1,000 | $1,189 | $967 | $1,152 | $1,161 |
| 9 | $1,267 | $1,000 | $1,218 | $962 | $1,187 | $1,196 |
| 10 | $1,305 | $1,000 | $1,249 | $957 | $1,222 | $1,232 |
| 11 | $1,344 | $1,000 | $1,280 | $953 | $1,259 | $1,268 |
| 12 | $1,384 | $1,000 | $1,312 | $948 | $1,297 | $1,307 |
| 13 | $1,426 | $1,000 | $1,345 | $943 | $1,336 | $1,346 |
| 14 | $1,469 | $1,000 | $1,379 | $939 | $1,376 | $1,386 |
| 15 | $1,513 | $1,000 | $1,413 | $934 | $1,417 | $1,428 |
| 16 | $1,558 | $1,000 | $1,448 | $930 | $1,460 | $1,471 |
| 17 | $1,605 | $1,000 | $1,485 | $925 | $1,503 | $1,515 |
| 18 | $1,653 | $1,000 | $1,522 | $921 | $1,549 | $1,560 |
| 19 | $1,702 | $1,000 | $1,560 | $916 | $1,595 | $1,607 |
| 20 | $1,754 | $1,000 | $1,599 | $912 | $1,643 | $1,655 |
| 21 | $1,806 | $1,000 | $1,639 | $907 | $1,692 | $1,705 |
| 22 | $1,860 | $1,000 | $1,680 | $903 | $1,743 | $1,756 |
| 23 | $1,916 | $1,000 | $1,722 | $898 | $1,795 | $1,809 |
| 24 | $1,974 | $1,000 | $1,765 | $894 | $1,849 | $1,863 |
| 25 | $2,033 | $1,000 | $1,809 | $890 | $1,904 | $1,919 |
| Totals | $36,459 | $25,000 | $34,158 | $23,596 | $34,158 | $34,412 |
| Equivalent benefit reduction | -6.31% | -5.61% | ||||
|
Table Two Equivalent Benefit Cut Based on COLA Reduction | |||||||||||
| Reduction from 3.00% Is Equivalent to this Benefit Cut | |||||||||||
| Term | 0.25% | 0.50% | 0.75% | 1.00% | 1.25% | 1.50% | 1.75% | 2.00% | 2.25% | 2.75% | 3.00% |
| 18 | -2.2% | -4.4% | -6.5% | -8.6% | -10.5% | -12.5% | -14.4% | -16.2% | -18.0% | -21.5% | -23.1% |
| 19 | -2.4% | -4.7% | -6.9% | -9.1% | -11.2% | -13.2% | -15.2% | -17.1% | -19.0% | -22.6% | -24.4% |
| 20 | -2.5% | -4.9% | -7.3% | -9.6% | -11.8% | -13.9% | -16.0% | -18.1% | -20.0% | -23.8% | -25.6% |
| 21 | -2.6% | -5.2% | -7.7% | -10.1% | -12.4% | -14.7% | -16.8% | -19.0% | -21.0% | -24.9% | -26.8% |
| 22 | -2.8% | -5.5% | -8.1% | -10.6% | -13.0% | -15.4% | -17.7% | -19.9% | -22.0% | -26.0% | -28.0% |
| 23 | -2.9% | -5.8% | -8.5% | -11.1% | -13.7% | -16.1% | -18.5% | -20.8% | -23.0% | -27.1% | -29.1% |
| 24 | -3.1% | -6.0% | -8.9% | -11.6% | -14.3% | -16.8% | -19.3% | -21.6% | -23.9% | -28.2% | -30.3% |
| 25 | -3.2% | -6.3% | -9.3% | -12.1% | -14.9% | -17.5% | -20.1% | -22.5% | -24.9% | -29.3% | -31.4% |
| 26 | -3.4% | -6.6% | -9.7% | -12.7% | -15.5% | -18.3% | -20.9% | -23.4% | -25.8% | -30.4% | -32.6% |
| 27 | -3.5% | -6.9% | -10.1% | -13.2% | -16.1% | -19.0% | -21.7% | -24.3% | -26.8% | -31.5% | -33.7% |
