By Mark K. Altschuler

While it is established under Hayden v. Hayden, 284 N.J. Super. 418 (1995), Risoldi v. Risoldi, 320 N.J. Super. 524 (1999) and many other appellate decisions that defined benefit pensions as marital property, there have been disputes over the marital value of past payments, if a pension already is in pay status at the time of divorce. If there is no dispute as to future payments being marital property, why would there be a dispute about past payments, assuming the past pension payments were not shared by the parties? In fact, past payments have even more value than future payments.

One argument raised about past payments is that the cases do not mention them. That is true. However, the cases do not exclude past payments either. In fact, the marital portion of each pension payment, whether past or future, is determined in these cases by the coverture fraction, automatically including both past and future payments.

If pension payments are marital property, that applies to both past and future payments. Each pension payment has a marital component, due to the pension being acquired during the marriage, or at least partially acquired during the marriage. If the pension payment is marital property, the date of retirement makes no difference. Whether that pension payment occurs in the past or future, a component of that payment, defined by coverture, is marital property.

Marital pension payments kept by the employee are the same as dissipation of a marital asset. Another way of looking at this is a 401(k) scenario. Suppose the 401(k) was acquired during the marriage but completely dissipated by the employee after the date of complaint. It would not be reasonable to say the marital value is zero, because a marital asset had been dissipated by the employee after the date of separation. By the same token, marital pension payments kept and spent by the employee spouse represent dissipation of a marital asset.

But if there were no court order to share the payments that was ignored, why would this be dissipation of a marital asset? Assuming the case is settled by reduction to present value and immediate offset, the future payments are a marital asset that has value, without court order. By the same token, the past payments also have value. There is no mathematical difference at all between past and future payments. The same equation used to calculate present value is used to calculate the accumulated value of past payments.

Mathematically, the attached graphic demonstrates there is no difference between past and future payments. Past payments are compounded due to “t” (time) being negative, and future payments are discounted due to time being positive. Today’s value of a single dollar payment, at any point in time, is(1+i)^{-t}, where i is the interest rate. If t is in the future, the exponent is negative, and the payment is discounted to today with interest. If t is in the past, the exponent is positive, and the payment is compounded to today with interest. If t=o (date of valuation), the interest term is 1, since any number to the zero power is 1, and there is no compounding or discounting.

For example, the payment one year from today has value (1+i)^{-1}, or 1/(1+1), and is discounted with one year’s interest. The payment from 1 year ago has value (1+i)^{-(-1)}, or(1+i)^{1}, and is compounded with one year’s interest. In the graph below, today’s value of a payment of one dollar at time t is shown above the dashed line, as (1+i)^{-t}. The same term is shown below the dashed line in fractional form.

The payment t years in the future has value today equal to (1+i)^{-t}, or 1/(1+i)^{t}, and is discounted with t years interest. The payment from t years ago has value today of (1+i)^{-(-t)}, or (1+i)^{t}, and is thus compounded with t years interest.

The graph does not take into account mortality. Each payment at time t is assumed to be made, with the annuitant living until time t, in the graph above. Now consider the equation below showing the present value calculation at age 65 where the date of commencement of benefits is age 65. Each payment is in the future, and is thus discounted with the appropriate years of interest. In addition, the mortality terms are included because the annuitant may not live long enough to collect the payment.

The mortality terms shown represent the probability of living from age 65 to the number of years needed to collect the pension payment, where this is one year, two years … up to 45 years, since the mortality table ends at age 110. The value today of dollar one paid one year from now is discounted with one year’s interest, 1/(1.06),and multiplied by the probability of living one more year from age 65, which is _{1}P_{65}.The value of a dollar paid at age 110, 45years from now, is discounted with 45 years interest, 1/(1.06)^{45}, and multiplied by the probability of living the additional 45 years from age 65 to age 110, which is _{45}P_{65}. All these terms are summed and result in the present value of a dollar a year annuity beginning at age 65 and payable for life. In this case, the interest rate is 6 percent, so i = .06.

Present Value = 1 + _{1}P_{65}/(1.06) +_{2}P_{65}/(1.06)^{2} + … + _{45}P_{65}/(1.06)^{45} = 9.9165

Suppose at the time of valuation the annuitant is 67 years old and payments commenced at age 65? If all payments are in the future, it means all payments are discounted to present value with interest. That is the casein the equation above, where valuation is at age 65. If we are in the middle of a stream of payments, some are discounted, and some are compounded. In the case where the annuitant is 67, the payments at 65 and 66 are compounded, instead of discounted. Looking at the equation below, where the annuitant is 67, the form of the equation is exactly the same as 65, except there are two payments, at 65 and 66, where t is negative (t = -1, t = -2). So rather than starting out at zero, t starts at -2. The algebraic form of each payment is the same, (1+i)^{-t}. However, when t is negative, such as t = -2, (1+i)^{-(-2)} = (1+i)^{2}, and the exponent is positive, the payment is compounded, instead of discounted. However, the mathematics of the equation is the same, and so there is no difference between compounding and discounting, except for t starting at -2 instead of zero.

Similarly, the probability terms have the same format. However, the future terms contain the probability of living one, two years or more up to 43 years into the future (age 110). The past terms contain the probability of having lived from 65 to 67 (_{-2}P_{67})and from 66 to 67. The probabilities, of course, are one, or 100 percent, since the annuitant is alive at 67.

The first version of the equation showing the present value at 67 is the general form, showing that the first two terms, for payments at 65 and 66, have the same algebraic format as the other terms. In fact, the payment at 67, for t = 0, also has the same format, where the general format for each payment is _{t}P_{67} (1+i)^{-t} , since the payment is discounted for both interest and mortality. For t= 0, this term is _{0}P_{67} (1+i)^{0} . The probability of living zero time into the future is one, or 100 percent, and any number to the zero power is one. Thus, the present value of the payment at time t=zero, is, of course, one.

The second version of the equation showing the present value at 67 is simplified, since the first three mortality terms are one (100 percent). Six percent is substituted for the general interest term, and (1+i)0, of course, is one.

Present Value = _{-2}P_{67}(1+i)^{2} + _{-1}P_{67}(1+i)^{1}+ _{0}P_{67}(1+i)^{0} + _{1}P_{67}(1+i)^{-1} + …_{43}P_{67}(1+i)^{-43}

Present Value = (1.06)^{2} + (1.06)^{1} + 1 +_{1}P_{67}/(1.06)^{1} + … _{43}P_{67}/(1.06)^{43}However, looking at the first version of the present value equation, it can be seen that the algebraic form for all terms, past and future, is the same. From a mathematical point of view, past payments are included in present value calculations, just the way future payments are. The only difference is the past payments have more value, since the interest terms are compounding, not discounting, and the mortality terms are one, since the annuitant lived from the date payments commenced until current date.

Legally, each payment has a marital portion as defined under case law, whether pastor future. The past payments did not disappear; indeed, they have more value than the future payments. If a marital asset is dissipated by one party, it still has value, in terms of equitable distribution. The marital value of past payments dissipated by the annuitant do indeed have value, and this value is calculated using the same methodology as future pension payments.*Actuary Mark K. Altschuler is president of Pension Analysis Consultants in Elkins Park, Pa. A member of the American Academy of Economic and Financial Experts, he has prepared more than20,000 marital pension valuations and draft QDROs for counsel and writes a national newsletter on pension issues in marital dissolution, DIVTIPS. Reach him at 800-288-3675.*

Reprinted with the permission of New Jersey Lawyer© March 10, 2008