By Dr. John F. Sase with Gerard J. Senick
“For the rational study of the law the blackletter man may be the man of the present, but the man of the future is the man of statistics and the master of economics.”
–Oliver Wendell Holmes, Jr. “The Path of the Law” (Harvard Law Review 457,1897)
“Economics is the most advanced of the social sciences, and the legal system contains many parallels to and overlaps with the systems that economists have studied successfully.”
–Richard A. Posner, “The Economic Structure of the Law: The Collected Economic Essays of Richard A. Posner, Volume One” (Edward Elgar Publishing, 2001)
In this month’s column, we will explore the phenomenon of growth rates and discount rates as used by forensic economists entering evidence into the Michigan circuit court. As a result, we will discuss what every Michigan attorney should know about present and future values of losses. With no disrespect to those attorneys who have a flair for math and/or undergraduate degrees in Finance, Economics, Engineering, or other Math-intensive fields, we will keep this month’s topic grounded. Hopefully, every one of our readers will understand and be able to use this information effectively in their practices. We say this in all seriousness because many attorneys have told me (Dr. Sase), “I went to law school because I couldn’t handle the math for medical school.” Therefore, the challenge falls to my collaborator Mr. Senick and me to translate “Economese” into clear, concise English in order to demystify this important topic.
Then and Now
Both growth rates and discount rates represent concepts of the “time value” of money. Put simply, most goods and services cost more today than they did fifty years ago. When I was a boy, I could walk down the street to “Al’s Trading Post,” our neighborhood corner store in Northwest Detroit. My father and uncles raised their children to be self-reliant. Therefore, I would earn my money by picking up soda-pop bottles and return them for cash at Al’s. Often, I would buy a Snicker’s bar. In the mid-1950s, we still could purchase a candy bar for five cents. Today, a scaled-down version of that same Snicker’s bar costs seventy-five cents or more. At first glance, this may seem outrageous. However, when we stop and realize that most prices, and the income to pay those prices, have risen substantially over the years, it becomes less so. On average, prices and income have risen more than seven-fold since the 1950s. During this time, the prices of many goods have risen more slowly than average while some services, like a long-distance phone call, have fallen. On the other hand, prices for goods like gasoline and services like health care have risen faster than average. The amount that we paid for that sweet childhood memory of nougat, caramel, nuts, and chocolate has risen by 15-fold.
Over the years, we have learned to understand and to methodically address the phenomenon of continuously rising prices. Union contracts, as well as many that are non-union, have a built-in automatic wage increase. This ensures that employee income keeps up with the average rise in the prices of those typical goods and services that we purchase and consume. This maintains a constant standard of living. In short, this Cost of Living Allowance (COLA) helps earnings to keep pace with the increase in prices.
Here and Now
As an individual’s experience, skills, and knowledge continue to grow, the value of his/her time that is dedicated to work production grows as well. This type of inflation does not reflect changes in the normal time value of money. Rather, it represents a relative increase of value in the here and now. In order to retain an employee with increasing real value in a competitive labor market, employers must compensate him/her for this additional value that s/he adds to the job.
Therefore, an increase in a person’s earnings reflects two sources. First, the wage or salary rises over time in order to keep pace with the changing time value of money as the prices of consumer products increase. Second, an individual’s value in production increases due to additional education, training, and experience. Although economists sometimes delineate the rate of growth of future earnings in terms of time-value and merit-value, usually they do not. In many governmental and private-sector corporate jobs, the employer includes a standardized merit increase in the grade/scale pay tables. In addition, these tables may be adjusted annually or, at least, periodically to reflect the change in the time-value of the wages.
A Unified Growth Rate
Currently, the Michigan Court does not state a prescribed growth rate for future earnings as iterated in the Michigan Civil Jury (M Civ JI) instructions on Damages (MCR 2.516, Chapters 50 through 53). Specifically in M Civ JI 53.06: Effect of inflation on future damages, the instructions state, “The plaintiff is not required to introduce evidence regarding inflation, because there is no expert consensus on the rate of inflation and it would unnecessarily and unduly prolong trials.” (See Kovacs v Chesapeake & Ohio Railway Co, 426 Mich 647; 397 NW2d 169 [1986].)
As an economist, I (Dr. Sase) rely upon published growth-rate tables that are based upon large samples. These tables provide ranges of rates on a year-by-year basis. Furthermore, I use tables that contain values that can be determined independently by replication of the process through accepted scientific method. This ability to replicate the process ensures that both the process and the work product comply with the Daubert Standard and can meet any Daubert challenge. Sources such as the tables published by the OASDI Trustees of the Social Security Administration, an agency of the U.S. Federal government, fulfill these requirements.
What Is Normal?
One may ask, “What is a normal rate of inflation?” For illustrative purposes, let us look at price inflation of consumer goods as calculated and published as the Consumer Price Index by the U.S. Department of Labor, Bureau of Labor Statistics. Changes in price levels from one year to the next have varied widely over the past half-century. For example, during the Vietnam War, prices in 1968 experienced an annual increase of 4.2%. However, during a period of Stagflation (high unemployment accompanied by high inflation), prices in 1980 spiraled upward at an annual rate of 13.5%. This rate fell through the 1980s and early 1990s before returning to an era of more regular fluctuation. In 2005, the rate of inflation hovered at 3.4%.
In the forecasting of rates outward into the future, it becomes a somewhat spurious task to track the imminent fluctuations of these rates. Therefore, most forecasters of future rates rely heavily on information about historical change. From this information, forecasters have developed the belief that a greater number of data points can produce better estimates. For example, if one were to complete a child’s connect-the-dots drawing of an elephant, one may expect that a picture containing thirty to fifty dots will render a better representation of an elephant than a picture having only five to ten dots.
If one takes the average of the inflation rates of the most recent fifty years, the result will vary slightly from an average of only forty data points. Though we have experienced some wide fluctuations in annual inflation, the average rate for fifty years turns out to be 4.1%. Coincidently, if we consider the change in home prices (which have changed wildly in recent years), we would find that these prices have risen at a rate of approximately 4% per year over the same period of time. For this reason, economists consider an investment in a family home as one that keeps pace with inflation in the long run while providing a place to reside.
Time Produces Big Differences
Over the course of a few years, the difference between the value of a dollar growing at 4.5% rather than 3.5% remains relatively small. However, over longer periods of time, such as the fifty years discussed above, the difference between respective end values can be great. Using an example based upon these two growth rates, we find that $1,000 invested at 3.5% interest compounded annually for fifty years reaches a value of $5,500. On the other hand, the same amount invested at 4.5% attains a value of a whopping $9,000. In this case, this means that a one percent difference in the growth rate produces an end value that approaches a two-fold difference.
Why does this large difference in value occur? It results from the phenomenon of compounding. The concept of compound interest proves to be important for two reasons. First, it explains why a dollar amount grows exponentially into the future. Second, it helps us to understand how our puzzling Michigan statutory discount rate works.
Looking forward in time, we can see why an interest rate that economists and financiers commonly refer to as “simple interest” produces an exponential gain in value. Some experts explain interest that compounds itself once per year as interest built upon interest. Rather than get into a longwinded technical explanation, let us consider the following example to explain what we mean.
Suppose that you lend me $100 for one year. In return, I agree to repay that amount plus an additional 10% (i.e. $10) for your trouble. Three possible scenarios could play themselves out. First, at the end of the year, I may return the full $110. This includes $100 of principle plus $10 of interest. Second, I may give you $10 at the end of the year, but arrange with you to keep the $100 for another year and again pay you 10% for the use. Third, we may arrange that I keep the full $110 for the second year and pay 10% for the use of this larger total amount. In other words, at the end of year two, I would give you $121, the original $100 of principal plus $21 of interest – $10 for the first year and $11 for the second (10% of the $110). This is what economists and financiers call simple interest – an amount that indeed is compounded, though only once per year. If we continue the compounding for another year, I would owe you $133.10 at the end of the third year.
The Mysterious Michigan Discount Rate
When I first studied the calculation of Michigan’s discount rate of 5%, I had to scratch my head. I felt that all of the years that I invested in earning an MBA, a Masters in Economics, and a Doctorate in Economics had taught me nothing in this case. This is due to the fact that the Michigan Discount rate is called a “simple rate,” though it differs significantly in the way that it is calculated. This is in opposition to how simple interest is explained in most Economics and Finance courses. Therefore, I realized that my reaction was more a matter of symantics than one of mathematics.
Our Michigan simple rate originated in the case of Nation v. W.D.E. Electric. Co. The full explanation appears in Cite 563 North Western Reporter 2d Series 235 (Mich 1997) with the calculation clearly explained in footnote two per Judge Boyle. The Michigan rate used for discounting future losses to present value may best be described as a “simple, simple rate.” In other words, it is a multiplicative rather than an exponential rate. What this means is that the Michigan Discount rate is multiplied by the number of years and then added to one to arrive at the number that we call the discount factor. This discount factor is the number by which we divide some future value of loss in order to arrive at a present value.
Let us look at a comparative example. Suppose that we expect to have a loss of $115.80 three years in the future. If we were to discount this amount to present value using a standard financial simple rate of 5% (i.e. compounded once annually), we would divide our dollar amount by a factor of 1.158-a factor that equals 1.05 times 1.05 times 1.05. In performing our discounting calculation, we arrive at a present value of $100 ($115.80 divided by 1.158).
However, if we use the Michigan Discount Rate for our calculation, we will get a slightly different result. Our discount factor for three years would be 1.150 (1 plus the product of .05 times 3) instead of 1.158. Though the difference between the two numbers may seem insignificant, nevertheless a difference exists in the final result because $115.80 divided by 1.150 equals $100.70. Though small in the short run, the difference becomes more dramatic in the long run. For example, we will determine the present value of a loss that is expected thirty years in the future. Let us say that this future value equals of $4,322. The standard financial method would leave us with $1,000. However, using the Michigan 5% Discount factor will produce a present value of $1,729 – an amount that is almost double.
The Impact on Clients
What impact does the use of a compounded growth rate offset by a non-compounded discount rate have on awards to clients? The answer is quite simple – it depends! Recent years are marked by lower interest rates – the rates that would be used for discounting by a federal court judge. As a result, many practitioners argue, or at least complain, that our statutory discount rate of 5% is too large. This contention glares more brightly when we compare the discount rate of 5% to inflation rates that are low historically. However, an offset effect exists. This is due to the fact that the Michigan discount rate remains non-compounded. For a long-term comparison, let us consider an example in which we contrast the effective Michigan 5% discount rate to the fifty-year average inflation rate of 4.1%. Common sense tells us that, if we increase a dollar by 4.1% and subsequently discount that future value by 5%, we end up with an amount that is less than our starting dollar amount.
Basically, this is true. However, the rub lies in the fact that the growth rate is compounded while the discount rate is not. This means that, at some point in the future, the balance of the scale tips and the discounted future value becomes greater that our starting value. In the case of these two rates, the flip occurs between seventeen and eighteen years into the future. The non-compounding discounting “catches up” with inflation. Another way to explain this is to say that awardees suffer in the short run from the disparity between rates but benefit over longer periods of time from the same disparity.
Wrapping Up the Fish
We hope that our exploration of growth rates, the discount rate, future value, and present value as used in the Michigan Circuit Court has shed a bit of light on the subject. In addition, we hope that we have helped law students as well as practicing attorneys to gain a deeper understanding of a subject that can be confusing and often intimidating. If you would like to visit the SASE Associates YouTube channel (www.youtube.com/saseassociates), you can view a colorful animated presentation about Michigan’s Mysterious Discount Rate (http://www.youtube.com/watch?v=yDP86JV06w4).
Dr. John F. Sase has practiced Forensic Economics since 1997. He is the founder of SASE Associates, a consulting practice that focuses on Forensic Economics and Urban-Regional/Industrial Economics. Dr. Sase also teaches Economics at local universities. He earned his M.A. and MBA at the University of Detroit and his Ph.D. in Economics at Wayne State University and is a graduate of the University of Detroit Jesuit High School. Dr. Sase can be reached at (248) 569-5228 and by e-mail at drjohn@saseassociates.com.
Gerard J. Senick is a freelance writer, editor, and musician. He earned his degree in English at the University of Detroit and was a Supervisory Editor at Gale Research Company (now Cengage) for more than 20 years. Currently, he edits books for publication and gives seminars on writing. Mr. Senick can be reached at (313) 342-4048 and by e-mail at gary@senick-editing.com.
