Super Sisters, Inc.

Gunther, Richard ; Efrat, Rafi

CASE DESCRIPTION

The primary subject matter of this case sequence is the integration of statistics and business law. Secondary issues examined include the use and meaning of descriptive statistics, regression analysis, statistical index numbers, the legal responsibilities for detaining a customer in a store, the liability of a merchant for compensatory damages arising out of the commission of a tort, and related strategic management issues. The case has a difficulty level of three, appropriate for junior level. The case is designed to be taught in three class hours. That time estimate includes a formal class presentation by a team and a challenge by another student team. It is expected to require ten to fifteen hours of outside preparation by students for the case.

CASE SYNOPSIS

After observing a customer engage in suspicious conduct, the Loss Prevention Manager of a store detains the shopper after grasping her by the arm and shoving her back to the store. Apparently, the shopper lost her balance and fell on her back sustaining significant physical damage. The shopper was then escorted to the loss prevention room where she was asked to wait for the store manager, who showed up more than an hour later. Following some questioning in the loss prevention room, the shopper was allowed to leave after it was determined that she did not engage in shoplifting. Due to the significant injuries the shopper sustained she was permanently unable to resume her work as a successful sales person for a pharmaceutical company. She is now suing the store for lost future income under the legal claim of false imprisonment.

The statistics portion of the case requires students to use Excel to compute descriptive statistics, perform regression analysis, and project future income. Students are also required to carefully define the statistical terms they are using and explain the meaning of their results In the legal portion of the case, students are referenced to legal opinions and asked to evaluate whether the shopper is likely to be able to recover under the claim of false imprisonment. The students are then expected to utilize their previous statistical analysis to conclude whether, and if so how much, the court is likely to award the shopper for lost future income. Students also need to determine if the shopper is likely to recover compensatory damages for injury and a punitive award. Finally, the student is asked to recommend strategic management policies that would serve to avoid reoccurrences of the problem.

This case requires students to apply materials learned in most Business School's lower division core (LDC). It is used in a course at the beginning of the junior year that has goals to integrate LDC material while developing teamwork and communication skills. Specifically, the case requires knowledge of elementary statistics and a beginning business law course. Student teams prepare the case with tutoring from faculty who provide "just-in-time" specific knowledge as requested by student teams. A team of students formally presents their case solution, another team acts as a "challenge team" and the whole class participates in an active question and answer session.

INSTRUCTORS' NOTES

Recommendations for Teaching Approaches

This case is designed for a junior level business course that integrates core material. The primary subject matter includes concepts from business law and statistics. Secondary issues include the meaning and use of descriptive statistics, regression analysis, price indices, inflation, present value, merchants' law for false imprisonment, and personal injury claims. It is assumed the student will have had a previous lower division course in statistics and business law. The completion of a previous introductory course in accounting and economics is recommended.

It is recommended that approximately 3 class hours be devoted to this case. This time includes a class of about 1.5 hours where students, after reading the case, discuss the facts and decide what coaching assistance they need in the case. The instructor then covers the background material she or he feels is appropriate for the case. Additional background reading could also be assigned. It is suggested that the second class period of 1.5 hours include either (1) a formal class presentation by a team of students, with possibly a challenge by another student team, or (2) a more traditional discussion of the case led by the instructor. In either situation, an overview of the issues in the case is given and the answers to the questions at the end of the case are discussed. It is suggested that the student teams or instructor use slides or PowerPoint presentations as appropriate.

This case is fictitious but was loosely based on several real world situations. It includes issues and analysis that have practical implications in statistics, law, accounting, and economics. It has been the experience of the authors that the many interesting issues in this case will challenge and motivate students.

ANSWERS TO SPECIFIC CASE QUESTIONS

1. Put the data from Exhibit 3 in an Excel file. Use Excel, along with this file, to determine Mrs. Kim's real income for the last fifteen years. Do this by first converting each price index from percent by dividing by 100. Then, divide gross income by your converted (adjusted) price index. Using Excel, find the mean, median, and standard deviation of her past real income. Explain the meaning of these statistics. Can you use mean income to forecast future earnings? Take into account both statistical and non-statistical considerations.

One purpose for the first part of the question is to get students to think about the difference between actual income and real income. Students are also asked to prepare their spreadsheet for further analysis. After doing the required computations on the Excel worksheet provided with the case, they should get the results shown in Exhibit 1.

Students can then use the Excel procedures for descriptive statistics to answer the rest of this question. The results are shown in Exhibit 2 below. Students must then pick out the mean, median, and standard deviation from the Excel output. They also must define them.

The mean real income (35,500.32) is the sample average, a measure of central tendency of the sample. The median (35,449.46) measures the real income in the middle position of the sample; equal numbers of observations have income both below and above the median. If the size of the sample is an odd number, the median is the middle value. If the size is even, the median is the average of the two values in the middle. The standard deviation (878.31) measures the variability or dispersion of real income and is the positive square root of the variance.

Exhibit 1 shows that mean gross income appears to increase with time. Using the mean of a time series to forecast the future would ignore the effects of time and not be appropriate. However, real income does not appear to be related to time (see Exhibit 1). A better case can be made for projecting mean real income into the future. The confidence level in Exhibit 2 indicates that one can be 95% confident the population or real mean will be between (35,500.32 + 486.39) and (35,500.32 - 486.39). Therefore, real income does not appear to vary too much and is not related to time. It is reasonable to assume then that Mrs. Kim's real income will continue to be about 35,500.32 for some time in the future, provided Mrs. Kim's work situation and the economy remain the same as they have for the last 15 years.

2. How do you interpret the price indices in Exhibit 3? How are they constructed? Use Excel regression to analyze the relationship between the adjusted price index (dependent variable, i.e. 1.136) and year (independent variable, i.e. 1987). Interpret your regression findings by discussing the coefficient of determination (R-square), the regression coefficient, the p-values, and the regression equation. Can you use the regression equation to predict the price indices? Take into account statistical, macroeconomic, and other considerations.

What is a price index? A price index shows the relationship between the price level in a given year and the price level in a base year. The base year of the index is 1982-1984. The index value for the base year is always 100. The price index value for 1987 is 113.6. This means that the general level of prices has risen by 13.6% since 1982-1984 for the bundle of goods in the index purchased in 1982-1984.

How does one use price indices? Any time series of economic data will be reported for each year at the price level that exists in that year. This is called nominal data. Nominal means at the existing level of prices. One uses the price index to adjust a nominal time series of data to eliminate the effects of inflation so as to see what is happening to the real variable over time. (Real means adjusted for inflation. Real data is sometimes reported as in constant dollars). The calculation for each year is

Real xx = Nominalxx / (Price Indexxx/100)

So

Real 87 = Nominal87 / (Price Index87/100)

By dividing the nominal gross income data by the adjusted price index for each year, one gets a real time series. In this case the real time series shows that the gross salary has remained relatively flat over the 15-year period.

How are price indices constructed? A price index is constructed by taking a basket of goods and services, purchased in the base year, and calculating what it would cost to buy the same basket with the same goods in the same quantities in some other year. By comparing the total expenditure necessary to purchase the same basket, one can isolate the price change effect. The most commonly quoted price index is the Consumer Price Index or C.P.I. The C.P.I. is calculated by taking a historic basket of consumer goods, purchased in some past base year, and estimating the current cost of buying the same basket.

Example: Suppose there are two goods, X and Y. In the base year of 2000 the average consumer purchased the following quantities at the indicated prices.

Basket 2000: [P.sub.x] = $200, [Q.sub.x] = 100; [P.sub.y] = $10, [Q.sub.y] = 300.

Suppose the prices of these two goods in 2001 are [P.sub.x] = $210; [P.sub.y] = $11 How much have prices risen?

CPI 2001 = [([P.sub.01] x [Q.sub.00]) / ([P.sub.00] x [Q.sub.00])] x 100.

The numerator is what it costs to buy the same basket today; the denominator is what it cost to buy the basket in 2000 (the base year). The ratio will then reflect the amount of change in prices.

CPI 2001 = {[($210 x [100.sub.x]) + ($11 x [300.sub.y])] / [($200 x [100.sub.x]) + ($10 x [300.sub.y])]} x 100

= {[($21,000) + ($3,300)] / [($20,000) + ($3,000)]} x 100

= ($24,300) / $23,000) x 100 = 1.057 x 100 = 105.7

The price index has risen from 100 to 105.7, thus the price level has risen by 5.7%

Excel regression is used to analyze the relationship between the adjusted price index and year. The regression results for the Super Sisters case are shown in Exhibit 3 below. The coefficient of determination measures the percent of the variation of the price indices accounted for by the variation in year. It is rather high for a regression, over 99%.

P-value is known as the observed level of significance. It is a measure of the probability of error. Exhibit 3 shows that the p-value for year is 3.98706E-15 or about 3.987 x [10.sup.-15]. This number is expressed in scientific notation. The number -15 in the exponent implies that one can move the decimal in 3.987 to the left fifteen places giving .000000000000003987. The probability of error is therefore extremely small. The relationship between year and adjusted price index is significant at any level, including .05 or .01, above .000000000000003987, the p-value. Thus, the relationship between year and price index is significant, strong, and apparently linear. (Students may want to draw a scatter diagram to reinforce these ideas).

The regression coefficient for year of 0.043725 would represent the slope of the straight trend line. On average each new year will bring an increase in the price index of 0.043725. Thus, the inflation is about 4%. The regression equation is

Y (Price Index) = Intercept + Year Coefficient (X or Year)

Y (Price Index) = -85.718117 + 0.043725 (X or Year)

The formula above could be used to predict the price index for future years. For example, you can plug the year 2002 in the equation about and get 1.819, a prediction for the price index.

As long as the economy of Green behaves in the future as it has in the past, the equation above could provide a reasonable forecast for the price index. However, if there were an increase in inflationary pressures in the future, which have not occurred for the last 15 years, then the regression equation would lose its utility. Conversely, less inflation in the future would also lessen the usefulness of the equation.

Analysis of the causes of any sustained inflation has shown that the major determinant of inflation is growth of the money supply in excess of real economic growth. If the monetary authority (in the US it is the Federal Reserve) is expected to follow the same basic policies in the coming years as it followed during the time series of data, the regression can be used to predict the future changes in the index.

3. Assume that Mrs. Kim's real income will not change over the next ten years. Use the mean real income from question 1 to determine projected real income for the future ten years of Mrs. Kim's work expectancy. Use the regression equation from question 2 to project adjusted price indices for the next ten years. Assume that Mrs. Kim pays 20% of her actual income in taxes and that Green will not provide significant state assistance. Use the projected real income and adjusted price indices to estimate Mrs. Kim's net actual income for the next ten years. What would be the likely amount of an award to Mrs. Kim based on a present value rate of 10%? Discuss the factors that could cause Mrs. Kim's future income to differ from your estimate.

Exhibit 4 below shows a ten-year projection for Mrs. Kim's income. The mean real income from question 1 becomes the projected real income shown in column 6. The regression equation from question 2 is used to calculate the adjusted price indices shown in column 5. The adjusted index (column 5) is multiplied by real income (column 6) to determine the actual gross income in column 3. A tax of 20% is subtracted from gross income in column 3 to get net income in column 7. Net income is multiplied by a present value factor with a rate of 10% to get the values in column 8, which are then totaled. (A spreadsheet that will accept alternate values could be used for grading purposes.)

Factors that could cause Mrs. Kim's future income to differ from the estimate in Exhibit 4 are numerous. They include the wage market for Mrs. Kim's position, inflation, changes in income tax rates, changes in interest rates, state assistance, etc.

4. Would the merchant's defense relieve Super Sisters, Inc. from liability under the cause of action of false imprisonment? In answering this question, please read and identify the relevant law from the following case precedent: Thomson v. LeBlanc, 336 So. 2d 344 (1976).

No, the merchant's defense is not likely to relieve Super Sisters, Inc. from liability under the cause of action of false imprisonment. A merchant has the privilege to detain a customer on the merchant's premises provided that: (a) the party making the detention had a reasonable cause to believe that the detained person had committed a theft. Reasonable cause requires that the detaining officer have articulable knowledge of particular facts sufficiently reasonable to suspect the detained person of shoplifting. To have articulable knowledge, the merchant must conduct preliminary investigation of his suspicion, if time permits; (2) the detention must not have lasted longer than for a reasonable period of time; and (3) the detention must have been conducted in a reasonable manner. In determining whether the detention was conducted in a reasonable manner, courts examine the following factors: (a) whether the merchant threatened the customer with an arrest; (b) whether the merchant coerced the customer; (c) whether the merchant attempted to intimidate the customer; (d) whether the merchant used abusive language towards the customer; (e) whether the merchant used force against the customer; (f) whether the merchant promptly informed the customer of the reasons for the detention; (g) whether the detention took place in public next others. See Thomson v. LeBlance.

Super Sisters, Inc. (the "Sisters") would argue that the merchant privilege protects it from liability for false imprisonment to Mrs. Kim. First, Mr. Lee, its Theft Prevention Manager, had a reasonable basis to believe that Mrs. Kim had committed a theft. Mr. Lee had a reasonable basis to believe that Mrs. Kim had committed a theft because, based on concrete personal observations, he had articulable knowledge of particular facts suggesting that Mrs. Kim had just engaged in shoplifting. The articulable knowledge of particular facts is based on Mr. Lee's personal observations of Mrs. Kim, who was standing next to calligraphy sets in the store, making a sudden move to her pocket. Mr. Lee then observed her proceeding at an accelerated pace toward the store's exit. He noticed that Mrs. Kim's side pocket was stuffed. Mr. Lee then conducted a preliminary investigation of what he believed to be a shoplifting incident as he proceeded directly to where Mrs. Kim had been standing and noticed that a calligraphy pen set was missing from a rack that was fully stocked up earlier that day.

While Mrs. Kim will concede that Sisters may have had a reasonable basis to believe that a theft may have taken place, she would argue that Sisters have not conducted the detention in a reasonable manner and for a reasonable time. First, the detention was not conducted in a reasonable manner. While Mr. Lee did not threaten Mrs. Kim with an arrest or use abusive language when dealing with her, he intimidated, used force and effectively coerced Mrs. Kim to follow him to the Loss Prevention Room. The intimidation, the force and the coercion was accomplished when Mr. Lee shouted at Mrs. Kim in public, grasped her by the arm and shoved her back to the store, causing her to lose her balance and severely hitting her back. Also, Mr. Lee failed to conduct the detention in a reasonable manner because he did not promptly inform Mrs. Kim of the reasons for her detention but waited for more than eighty minutes to do so.

Second, the detention lasted for an unreasonably long period of time. While a reasonable length of detention under these circumstances would have been anywhere from five to fifteen minutes, here the detention lasted for at least eighty minutes.

Therefore, since Sisters would not be able to demonstrate two of the three required elements for the merchant's privilege, Mrs. Kim would be able to prevail in her cause of action against Sisters for false imprisonment.

5. Assuming that Super Sisters, Inc. is liable for false imprisonment and assuming that Mrs. Kim is deemed unable to locate another job for life due to her present medical condition, is a court likely to award her compensation for loss of future income? What standard will a court consider in determining whether Mrs. Kim is entitled to compensation? In your opinion, is Mrs. Kim's settlement offer reasonable? Support your opinions with a discussion of the legal and practical possibilities. In answering this question, please read and identify the relevant law from the following case precedent: Caldwell v. Kehler, 643 A.2d 564 (1994).

Yes, a court is likely to award Mrs. Kim compensation for loss of future income. The principal goal of damages in personal injury actions is to compensate fairly the injured party. Fair compensatory damages resulting from tortuous infliction of injury encompass no more than the amount that will make the plaintiff whole. The injured party has the right to be compensated for diminished earning capacity. The measure of damages for tort recovery encompassing diminished earning capacity can be based on the wages lost as a result of the defendant's wrongdoing. That measure includes the value of the decrease in the plaintiff's future earning capacity. Although generally objectionable for the reason that their estimation is conjectural and speculative, loss of future income dependent upon future events are allowed where their nature and occurrence can be shown by evidence of reasonable reliability. The award of damages for loss of future income depends upon whether there is satisfactory basis for estimating what the probable earnings would have been had there been no tort. A satisfactory basis for an existing basis may include reliance on specific statistical models based on past earning records. The proper measure of damages for lost future income in personal injury cases is the present value of net income after taxes. See Caldwell v. Khler, at 2-3.

Here, statistical analysis of past earnings could be used to estimate with reasonable degree of reliability the present value of Mrs. Kim's net loss of future income. Based on the statistical analysis discussed above, the projected present value of Mrs. Kim's net loss of future income is $345,913.37.

To facilitate an amicable resolution of this dispute, Sisters should seriously consider making a counter offer to Mrs. Kim's settlement proposal. This would avoid costly and risky litigation, especially since Mrs. Kim has overestimated her loss of future income by more than $400,000 ($750,000-$345,913.37). Since Sisters would likely be held liable under false imprisonment for the injuries sustained by Mrs. Kim, the settlement counter offer should include all of Mrs. Kim's documented medical bills of $765,000. Further, based on the analysis above, the net present value of Mrs. Kim's lost income is $345,913.37. Hence, Sisters' counter settlement offer should be at least $1,110,913.37.

In determining the total amount of the counter settlement offer, Sisters may also consider increasing the amount to take into account the costs of litigation to the extent this dispute goes to trial. Further, they may consider the possibility of a jury awarding Mrs. Kim punitive damages. Lastly, Sisters may wish to consider the costs of bad publicity that may be triggered by a prolonged litigation.

6. What actions would you recommend should be taken to prevent a reoccurrence of a situation similar to that involving Mrs. Kim? What company policies need to changed or added? Discuss the relevant management issues.

This is an open-ended question. Many good answers are possible here as long as they are well thought out. Certainly the way operations are currently carried out needs to be changed. Jimmie Lee and, perhaps, other personnel need to be given training on customer relations and the customer's legal rights. Mr. Lee may also need to be disciplined. Preventative actions also need to be taken to prevent shop lifting. Objective procedures are needed to determine when a person's actions are suspicious and if they should be detained. Some policy needs to be set so that upper levels of management can be quickly accessed when they are needed.

Richard Gunther, California State University, Northridge

Rafi Efrat, California State University, Northridge

Exhibit 1: Calculation of Real Income

 Gross Price Adjusted
Number Year Income Index Price Index Real Income

1 1987 41,273 113.6 1.136 36331.87
2 1988 42,805 118.3 1.183 36183.43
3 1989 44,239 124.0 1.240 35676.61
4 1990 45,724 130.7 1.307 34983.93
5 1991 47,472 136.2 1.362 34854.63
6 1992 49,391 140.3 1.403 35203.85
7 1993 52,888 144.3 1.443 36651.42
8 1994 50,547 148.2 1.482 34107.29
9 1995 54,810 152.4 1.524 35964.57
10 1996 55,019 156.9 1.569 35066.28
11 1997 58,734 160.5 1.605 36594.39
12 1998 55,879 163.0 1.630 34281.60
13 1999 61,125 166.6 1.666 36689.68
14 2000 59,350 172.2 1.722 34465.74
15 2001 62,781 177.1 1.771 35449.46

Exhibit 2: Descriptive Statistics for Real Income

 Real Income

Mean 35500.32
Standard Error 226.78
Median 35449.46
Mode #N/A
Standard Deviation 878.31
Sample Variance 771424.78
Kurtosis -1.31
Skewness -0.08
Range 2582.39
Minimum 34107.29
Maximum 36689.68
Sum 532504.74
Count 15.00
Confidence Level (95.0%) 486.39

Exhibit 3: Regression Results

 Regression Statistics

Multiple R 0.996142035
R Square 0.992298954
Adjusted 0.991706566
R Square
Standard Error 0.01787684
Observations 15

 ANOVA

 df SS

Regression 1 0.535325175
Residual 13 0.004154558
Total 14 0.539479733

 Coefficients Standard Error

Intercept -85.71811667 2.130285995
X Variable 1 (Year) 0.043725 0.001068346

 Regression Statistics

Multiple R
R Square
Adjusted
R Square
Standard Error
Observations

 ANOVA

 MS F

Regression 0.535325175 1675.082335
Residual 0.000319581
Total

 t Stat P-value

Intercept -40.23784453 4.96517E-15
X Variable 1 (Year) 40.92776973 3.98706E-15

Exhibit 4: Projections of Mrs. Kim's Income

 Gross Price Adjusted
Number Year Income Index Price Index

16 2002 64586.91 181.93 1.819
17 2003 66139.16 186.31 1.863
18 2004 67691.41 190.68 1.907
19 2005 69243.66 195.05 1.951
20 2006 70795.91 199.42 1.994
21 2007 72348.17 203.8 2.038
22 2008 73900.42 208.17 2.082
23 2009 75452.67 212.54 2.125
24 2010 77004.92 216.91 2.169
25 2011 78557.17 221.29 2.213
Total =

 Real Net
Number Income Actual Present V.

16 35500.32 51669.53 46972.30
17 35500.32 52911.33 43728.37
18 35500.32 54153.13 40686.05
19 35500.32 55394.93 37835.48
20 35500.32 56636.73 35166.95
21 35500.32 57878.53 32670.92
22 35500.32 59120.33 30338.08
23 35500.32 60362.13 28159.38
24 35500.32 61603.94 26126.08
25 35500.32 62845.74 24229.75
Total = 345913.37