TEA.10.0 – 2008. * The Earnings Analyst* 10: 153pp.

TEA.10.1 – **Arithmetic Means, Geometric Means, Accumulation Function, and Present Value Functions****. ***Gary R. Skoog and James E. Ciecka*. There are “well known” relations between the arithmetic mean of a random variable and the mean. Part of this paper is offered with the belief that perhaps some of these relations are not as well-known and transparent as is sometimes assumed. In addition to asserting several relations, we provide proofs of propositions with the thought that forensic economists engaged in personal injury and business valuation litigation will find it useful to have a single and convenient reference for concepts and propositions involving the arithmetic and geometric mean. This paper also deals with a proposition and an often-cited example that has been proffered to show that the arithmetic mean of returns on an investment, when compounded for multiple time periods, gives the expected value of wealth. We examine this proposition and show sufficient conditions under which it is correct. Finally, and perhaps of most interest to forensic economists, this paper examines the expected present value function when discounting with the arithmetic mean and geometric mean.

TEA.10.2 – **Correcting the Expected Value of the “Actuarial Approach” When Using the U.S. Life Tables. ***Edward T. Wolpert*. U.S. Life Tables death-rate data is commonly relied upon by forensic economists when estimating survival probabilities and life expectancy in matters of civil litigation. When measuring future expected values, the “actuarial approach” will start with a future expected payment, and then reduce this payment by the probability of survival, subsequently arriving at an expected value. Notwithstanding, usage of this approach will underestimate the expected value unless a partial year survival credit is included, and expected values are extended beyond age 100 (the terminal age category of the U.S. Life Tables). This paper provides the requisite information to correct the actuarial approach for these potential deficiencies.

TEA.10.3 – **Sample Selectivity Bias of the U.S. Chamber of Commerce Employee Benefits Study. ***Lawrence M. Spizman. *The United States Chamber of Commerce Employee Benefits Study present annual fringe benefit information the U.S. employers provide to their workers. Forensic economists use this study to estimate fringe benefit losses. This paper demonstrates that the selectivity bias from the sample of firms responding to the Chamber’s survey questionnaire raises serious issues about the reliability of the Employee Benefits Study for litigation purposes.

TEA.10.4 – **Use of the Workers’ Compensation Earning Capacity (WCEC) Formula in Determining Diminished Future Earning Capacity in California****. ***Enrique N. Vega, Eugene E. Van de Bittner, Maria I. Toyofuku, Susan K. Van de Bittner, and Arlene Mohebbi.** ** *California’s new workers’ compensation law changed the standard for determining permanent disability from diminished ability to compete for jobs in the open labor market to diminished future earning capacity. California adopted a new *Schedule for Rating Permanent Disabilities (Schedule)*, (California Division of Workers’ Compensation, 2005), which provides an adjustment factor for diminished future earning capacity. Challenges to the adequacy and validity of the *Schedule* were soon brought by injured workers and their attorneys. Courts have ruled that since the *Schedule* is *prima facie* evidence regarding permanent disability ratings, it can be rebutted through evidence brought by the injured workers. Van de Bittner (2006) developed a Workers’ Compensation Earning Capacity (WCEC) Formula, which provides an estimate of diminished future earning capacity expressed as a percentage. This article expands on the application of the formula to individual cases, the foundational and often crucial assumptions that the DFEC expert needs to make when applying the formula, the methodology relied upon to meet evidentiary rules of admissibility, as well as its potential use in other legal arenas.

TEA.10.5 – **Historical Net Discount Rates – An Update Through 2007. ***Thomas R. Ireland. *The eight tables presented in this article are updated versions of the eight tables that were presented in publications by this author that contained calculations through 1999 [Ireland, 2000] and updates through 2001 [Ireland, 2000-01], 2003 [Ireland, 2002] and 2005 [Ireland 2006]. A basic rule for all calculations provided in this series has been that the data in making the calculations must come from the *Economic Report of the President *(henceforth ERP). Tables 1-4 have been prepared on the same basis as in all three previous versions of the table except that the tables now include data for the year 2007. Tables 1-4 begin with 1956 and end with 2007, allowing 50 year comparisons to be made between various discount rates and both the CPT (Consumer Price Index) and the MCPI (Medical Consumer Price Index). Tables 5-8 begin with 1965 and end with 2007, allowing 40 year comparisons to be made between various discount rates and Average Weekly Earnings for all American workers.

TEA.10.6 – **A Technical Note: Why Rates Vary Among Different Debt Securities. ***Kevin S. Marshall and Mariam M. Margaryan. *This technical note provides a brief review of the components that make up the quoted, or nominal, market rate of interest on a given debt security and the conceptual relationship between the referenced market rate and its risk determinants. When comparing the well-being of an individual or firm before and after an intervening and causative event, it is common for an analyst to proceed by “(1) converting future utility into future dollars using standard principles of valuation, then (2) transform future dollars into present dollars by discounting at the market rate of return on capital, and finally (3) convert present dollars into present utility using standard principles of valuation.” The market rate of return on capital is often described as “the return that could have been earned on alternative investments at a specific level of risk.” Capital is generally composed of (1) debt and/or (2) equity. When discounting at a market rate of return with respect to debt, understanding the underlying risk determinants of the interest rate is of critical importance.

TEA.10.7 – **A Technical Note: A Pension is a Pension is a Pension. ***Lane Hudgins and Thomas R. Ireland. *The title of this note is taken from the legal decision in *Rotolo Chevrolet v. Superior Court *(2003). That decision provided a specific answer to a question that is important in valuing the loss of pension benefits in both personal injury and wrongful termination litigation. The implications of this decision for various types of cases is examined in this note.

TEA.10.8 – **A Technical Note: ****The Arithemetric Growth Rate and the Geometric Growth Rate: Two Measures of Change. ***J. Herbert Burkman. *In reviewing economic data it is often useful to report the average growth rate for a series of values occurring periodically (weekly, monthly, annually). Average growth, a measure of central tendency, represents a value that describes the mean growth rate for a set of data. As values accumulate and trends emerge through time, a question frequently arises: what is the average growth rate of the variable in the series for a selected period? A preliminary response to this first question is another question: what average is reported, the *arithmetic growth rate* or the *geometric growth rate*? This response, in turn, gives rise to a third question: does it matter which average growth rate is reported? Furthermore, given that there is a choice, is one preferable? Which growth rate best characterizes the changes experienced in the series if the two average growth rates are found to be different? This brief technical note suggests answers to the questions posed.