### MATHEMATICS AND DIVORCE – MAKING THINGS ADD UP

by John T. Bird

I am reminded of the old aphorism: Give a man a hammer and every problem looks like a nail. I am a divorce lawyer so when asked how to use math in a law practice, I answer from that point of view.

The intent of this article is to assist all lawyers who read it (and perhaps their paralegal assistants and secretaries) in dealing efficiently, accurately, and economically with mathematical aspects of divorce cases.

The Child Support Guidelines have made calculation of child support much less a factor in divorce. This article does not address that issue, except to point out that it is important for private practitioners to be able to calculate interest on unpaid child support judgments.

**Income Calculation – Time is Money**

First, it’s important to understand that there are not four weeks in a month. In fact, there are four weeks only in one month, February. In every other month there are between four weeks and two days (4.2857 weeks) and four weeks and three days (4.4286 weeks). While a small looking difference, the use of only four weeks for a month can result in a mathematical error of more than $400 in a year when calculating minimum wage. To properly calculate monthly income, multiply the hourly rate by 40 and that answer by 52. Divide the result by 12. That is monthly income.

Second, twice a month is not “every two weeks”. There are 24 pay periods per year for people paid twice a month; there are 26 pay periods if paid every two weeks. Many of our clients will tell us that they or their spouse “get paid twice a month”, when in fact they get paid every two weeks. Don’t take their word for it. Look at the pay stubs. A mistake will cost nearly 8% of annual income – $1,200 for a minimum wage earner.

**Interest on Judgments**

The calculation of interest on judgments, especially child support judgments, will pay the cost of the typical stand-alone legal math calculator ($150) in one case. Allowing judgment debtors, usually payor parents, to use the sum of the unpaid judgments as the arrearage is error and probably malpractice. With the special treatment of non-dormancy of child support judgments, the use of simple spreadsheet mathematics to calculate interest, using the current judgment rates as stated in K.S.A. 16-204(3), 10%, can result in recovery for payees of interest on the judgments sufficient to pay the attorney fees incurred in collecting.

**Calculating Present Value, Future Value and Pension and Maintenance Lump Sum ****Values**

The calculation of present day values is best left to the specialized software available to all practitioners. I use a product found at legalmath.com called Legal Math. It calculates the present value of maintenance, the present value of pension plans or any other future money payment situation, will calculate the present value of a lump-sum to be received in the future, and will calculate the future value of any periodic payment or investment. It likewise calculates the future value of a lump sum invested over time. It calculates the monthly payment available over time from a known lump sum. It has a module to do calendar math, adding or subtracting days from an unknown date and calculate the number of days between dates. It also tracks interest on sporadic/irregular payments on

judgments applying the payments to accrued interest then to the oldest judgment, unless the payee directed otherwise as the payments made were received.

Recognizing situations where math and software tools can and should be used is essential. In addition, the lawyer has to understand the concepts well enough to explain them to clients.

Most people have some type of vague understanding that streams of payments may have different values from the sum of the payments, because they’ve heard about it when they read about how much the lottery pays for the “cash option". The lottery is a handy tool to help clients understand the concepts. Ask your client: “Would you rather win $1 million in a lottery that pays one dollar year for 1 million years or a lottery that pays $1 million the day you win?” No one gets that one wrong. Then I show the calculation in my Legal Math calculator, on my computer screen, by filling in the blanks. How much is the monthly payment? How long does it last? What is the number of months the payment will be made? What is the assumed investment interest rate per year? The interest rate according to most economists I have used as expert witnesses over the years has been an average of 7% over the past 65 years. It is difficult to convince most clients that they can earn 7% in any easy or safe investment, and most right now think that 3% to 5% is the most they could expect over the short-term. I use math to show them what the ranges are, which is most heavily influenced by the interest rate, of course. I then ask them a simple question: “If I ask you which you would rather have, $100 per month for 240 months assuming you could invest that money at an interest rate of 5% per annum, or $15,215.67, which would you take?” After they ponder that for a moment I tell them that the correct answer is “either”, because they are exactly equal. In other words, if I give you $15,215.67 today, you invest it at 5%, and withdraw it at the rate of $100 per month, after 240 months, you will have spent it all and you will have zero left.

Calculation of the value of pensions is dependent upon whether the pension is a defined benefits or defined contributions plan. Probably the primary error made by lawyers regarding pension plans is not understanding that some plans are defined benefits plans. Those have a defined present day value. The calculation of the value of those plans is dependent on the following factors: 1) The periodic payment to be received, assuming no further contributions to the plan; 2) the frequency of payment, usually monthly; 3) the number of months until the payments began (how far away is the pension owner from being able to receive the monthly payments); 4) the number of months over which the payments are to be received (See Kansas PIK Civil mortality tables for life expectancy); and 5) the assumed investment interest rate per year. In addition, the client should consider the probable tax rates on the monthly benefits. The result will be the present value of the future right to receive the payments. It is determined by first calculating the lump-sum amount needed as of the date of retirement to fund the periodic payments and then, to account for the delay before the benefits are received, the lump-sum is discounted back to the present date. The monthly assumed benefit is usually calculated by the employer or the plan administrator. The annual statements from most pensions have that information, although sometimes it is difficult to find it. It’s worth the effort, as a defined benefits plan can easily have a present day cash value of $18,000 per $100 of benefits. In other words, a run-of-the-mill KPERS plan of $1,000 per month can be valued at $180,000.

Present day values of maintenance/alimony are more difficult to calculate and are often worth the effort. Soon, because of the new Federal Tax Code, maintenance will no longer be tax deductible by the payor or includable by the payee, but any maintenance award ordered by any court prior to the end of 2018 will still receive that favorable treatment. Even after the end of 2018 maintenance will be a handy tool to assist in balancing distributions of assets where one party receives income generating assets and is not able to borrow enough to buy out the departing spouse. Maintenance can be terminable on events not within the control of the payor, including death of either party, remarriage, or the passage of a finite period of time. To calculate the value of the payments, and to do an apples-to- apples comparison with a lump sum, many of the same factors in making the earlier calculations are necessary. The monthly maintenance amount to be paid, the frequency of payment, the number of months until those payments begin, the number of months over which the payments are to be received, and the assumed investment interest rate per year are the crucial ones. To know how many months the payments are to be received, it is necessary to know also what contingencies might result in the payments not being received, either totally or partially. The death of the payor can be and often is eliminated as a factor by an agreement to provide life insurance to cover the remaining payments. It’s interesting to note that many people are willing to agree to an acceleration of the payments, with no discount for the present day value. If you represent the payor it will be worth the trouble of calculating present value if an accelerating event occurs. The number of months for which the payments are to be received is also potentially influenced by the death of the payee, which is usually not a large factor for recipients, as, to put it bluntly, why do they care if monthly payments are received if they aren’t here to spend them? In situations where the payments are being made in lieu of substantial payments of assets, though, it is important to know whether or not the payments will continue to be received or paid in some lump sum, as the estate of the payee is then affected. The third major contingency, remarriage, while theoretically entirely within the control of the payee, has a certain discount value to some. On the one hand, the payor who thinks that his ex-wife is only getting the divorce so that she can quickly remarry is often willing to agree to maintenance and bet on the power of new love to relieve him of the future payments. A divorcing person who is negotiating to receive maintenance almost never thinks that they intend to remarry. I use mathematics and statistics to show these people that they are betting against the odds. The majority of people who have divorced, close to 80%, go on to marry again. On average, they remarry within 48 months after divorcing, with younger adults tending to remarry more quickly than older adults. There is little data to show how influential the existence of a maintenance decree is on remarriage, but there is no question that at the very least, having cash in hand as opposed to a potentially evanescent maintenance entitlement affects decisions. The use of co-habitation as a terminating factor makes calculation of the true value of a maintenance entitlement even more complex. In all those events, in order to at least have a starting point, it is necessary to be able to use math (or a simple software program), to show the client what the present day value of a stream of payments is.

**Math Can Go Out the Door When Emotion Rules**

All of the adroit calculations in the world will not overcome the toxic effects of pathological personalities in divorce cases, and so it becomes ultra-important that clients understand the true present day value of money in hand versus the promise of payments by a person who may intend to never cooperate and may in fact be willing to forego income or even be incarcerated in order to avoid payment of monthly judgments. It’s important to remind clients as the mathematical analysis is done that there is truth in the old saying: A bird in the hand is worth two in the bush.