Quantitative Methods for Decision CIV1322

CIV1322 Quantitative Methods for Decision Making FinalExam/Project(dueTuesdayApril15,by11:59pm)

INTRODUCTION

In this problem, you will analyze the decision faced by a multinational corporation headquartered in the U.S. related to its Diversity, Equity and Inclusion initiatives. In brief, you will be asked to review some background information and data about the current political situation and then to take the viewpoint of the company to help it decide what to do. It is partly up to you to identify what are the relevant questions that need to be asked/answered, though I also provide a number of guiding questions near the end of the assignment directionsWhilethecontext for thisproblemisbasedon acurrentreal-world situation,theproblem

includes a mix of real data and hypothetical data/estimates. Even in cases where real datawere used, only limited attempts were madeto ensure they are fully accurate or from highly reputable sources; the priority is to create an interesting case study rather than an accurate one. You will likely find this does not provide all the data you want/need. You are welcome/encouraged to supplement with your own additional research, but this is not strictly required. Please note that youarebeinggradedonthethoughtfulnessofyourapproachandapplicationsoftechniquesfrom the class rather than the truth or accuracy of your findings. You are welcome to make (and justify) simplifying assumptions as needed so that you can instead spend your time demonstrating your ability to use the tools and concepts we discussed throughout the semester.

Similarly,youwill likelynotbeabletoanalyzeeveryrelevantdimensionofthisproblem; instead, please pick (and justify) a subset of criteria/factors you will consider.

Generaldisclaimer:Someoftheideasandbackgroundtextforthisprojectweredevelopedwith the assistance of generative AI.

StudentuseofAI:TheuseofChatGPToranyGenerativeAImodelisprohibitedforgenerating primary text or for directly solving any aspect of this assignment. AI tools may be used as a writing assistant (e.g., improving grammar, writing flow, etc.) as long as the ideas, content, and calculations are strictly yourown. You may also use AI tools like asearch engine to helpsearch for specific pieces of information (e.g., what was Targets operating revenue in 2023?), but it may NOT be used for any more substantive responses (e.g., it may NOT be used to create a decision tree, to create fundamental objectives, to ask for other ideas to improve your analysis, etc.)

Pleaseincludeanexplicitstatement onyourcoverpagedescribingif/howanyAItoolswereused.

PROBLEMCONTEXT

In recent years, many corporations have implemented Diversity, Equity and Inclusion (DEI)¹initiatives to promote a more inclusive workplace (or potentially for other reasons such as to improve their corporate image). In late 2024 and early 2025, several major U.S. companies began reassessing these programs due to legal challenges, political shifts (e.g., actions by the Trump administration^2,3) and debates over their effectiveness. Some companies like Walmart, Target,Lowes,MetaandothershavescaledbackontheirDEIcommitments.Othercompanies like Apple, Costco, Microsoft, Delta Airlines, Goldman Sachs, and others have instead reinforced their commitment to DEI.

In particular, Target andCostco have been in thenews illustrating theiropposite responsesto the current political situation (details below). For this case study, you are being asked to provide advice to a multi-national corporation headquartered in the US who is considering what to do about their DEI initiatives. While this problem was written with Costco in mind, I have since decided to leave the choice open. You are welcome to focus on Target (considering reversing its decision) or Costco (deciding whether to continue as planned), or another company of your choosingeitherrealorhypothetical.Ifyouchooseahypotheticalcompany,youareencouraged to draw from real data pertaining to companies like Target and Costco to help ground your case study. The company would like your advice regarding what it should do (e.g., cancel its DEI initiatives? Continue as planned? Modify in some way?).

DETAILS

In January, Target announced it was ending its DEI programs, including an end to its pledge to invest $2 billion in Black-owned businesses over 5 years ($400M per year).⁴At the same time, Costcoshareholdersvotedoverwhelmingly tomaintaintheir DEIinitiatives.⁵Asaresultof these moves, Target has faced backlash while Costco has seen an increase in sales. For example, on February 28, there was a national boycott where Target saw a 9% drop in web traffic while Costco saw a 22% rise.⁶Weeks later, it appears that Target has continued to face an average 6.2% drop in foot traffic and 3.1% quarterly loss in revenues (i.e., January-March 2025 compared to last year) while Costco has continued to see an average 5.2% increase in foot traffic.⁷

Itisunclearifthesechangeswillbelong-termorjusttemporary.[Youarewelcometoassumea duration or probability here, or to treat this via sensitivity analysis].

¹InCanadaandatU ofTweoftenusethetermEDI.

²https://www.usatoday.com/story/money/2025/03/04/trump-dei-backlash-explained/81170427007/

³https://www.ctvnews.ca/world/article/trump-says-corporate-diversity-efforts-are-illegal-but-are-they/

⁴https://www.reuters.com/business/retail-consumer/target-ends-its-3-year-diversity-equity-inclusion-initiatives-2025-01-24/

⁵https://www.reuters.com/business/retail-consumer/costco-shareholders-vote-against-proposal-report-diversity-programs-2025-01-23/

⁶https://www.supermarketnews.com/consumer-trends/target-hit-hardest-by-dei-boycott-costco-saw-double-digit-traffic-increase

⁷https://www.retailbrew.com/stories/2025/03/28/target-suffers-eighth-consecutive-week-of-foot-traffic-losses-since-caving-on-dei

Forreference

• Targets annual sales from February 2024 to February 2025 were approximately $107 billion,resultingin$30 billioninnet operatingrevenue(i.e., aftersubtractingdirectcosts from these sales). After subtracting out other overhead/administrative expenses, their annual profit was $5.2 billion before tax, or $4.1 billion after tax.⁸
• Costcoannualsales(September2023-September2024)wereapproximately$250billion, resulting in $27 billion in net operating revenue (i.e., after subtracting direct costs from these sales). After subtracting out other overhead/administrative expenses, their annual profit was $9.7 billion before tax, or $7.4 billion after tax⁹

In addition to the arguments around corporate image and improved sales, there may be (non- quantifiable) ethical reasons to retain DEI policies, as well as concerns about retaining good relationships with partner companies and suppliers who may value these policies. There is also some evidence that diverse workplaces have higher employee satisfaction, are more productive, andmayoutperformothercompaniesfinanciallyinthelongrun.¹⁰Employeesatisfactionmay,in turn, be helpful for retaining talent and reducing turnover/retraining, which may have its own monetary benefits. Of course, there remains some debate surrounding these issues/findings.

On the other hand, DEI initiatives also incur direct costs. While these costs are generally not publiclyavailable,IhaveusedAItogenerateanestimateforCostcoofapproximately$120-175 million in direct costs annually (see Appendix A). Costco is also facing pressure from 19 Republican controlled state governments to back off or justify its policies^11,12. There are numerous reasons why a company may not wish to face the pressure of continuing its DEI programs. This may include concerns about retaining government contracts or tax breaks, concerns around attracting additional public scrutiny (which may increase operating costs), fear of alienating certaincustomers, or the threat of regulation or lawsuits. Tohelp quantifysome of these costs, I will provide some made up numbers about potential lawsuits from the federal government, or Republican controlled state governments.

Assume there is an approximately 15% chance (per year) that a lawsuit may be filed each year for the next 4 years (i.e., as long as Trump is president). If a lawsuit is filed, assume a 50% chancethatCostcowouldlose.BelowaresomeAIgeneratednumberssurroundingthepotential impact of a DEI-related lawsuit:

• Legaldefensecosts(paidregardless):~$2-10million
• Legalsettlementandregulatorycompliancecosts(paidintheeventtheylose):~$800 million
• Branddamage:1-2%lossinannualsales forafewyears ifthey

oEven ifthey win,theexistence ofthelawsuitmaystillcause somebranddamage.

⁸https://corporate.target.com/press/release/2025/03/target-corporation-reports-fourth-quarter-and-full-year-2024-earnings

⁹https://investor.costco.com/news/news-details/2024/Costco-Wholesale-Corporation-Reports-Fourth-Quarter-and-Fiscal-Year-2024-Operating-Results/default.aspx

¹⁰https://www.mckinsey.com/featured-insights/diversity-and-inclusion/diversity-matters-even-more-the-case-for-holistic-impact

¹¹https://www.emarketer.com/content/target-costco-no-good-answers-dei-backlash

¹²https://www.reuters.com/sustainability/society-equity/republican-state-attorneys-pressure-costco-drop-diversity-policies-2025-01-28/

Thereiscurrentlya30% chancethattheDemocratswilltakecontroloftheUSSenateattheend of 2026.¹³ If that happens, you may assume that most of the political pressure is removed, and the chance of a lawsuit drops to 0% in 2027 and 2028. In that event, political pressure may switch to insisting companies ramp up their DEI initiatives again. To satisfy the public, they wouldlikelyhavetoincreasetheirDEIexpendituresby50% comparedtoasituationwherethey had never scaled back.

For afeeof$5 million,youcanhireastatistician(e.g.,NateSilver) topredicttheoutcomeof the 2026 elections; assume he has an accuracy of 80%.

In analyzing this problem, you are welcome to use some or all of the data provided above. You shouldnotfeellikeyouhavetoaddresseverythingmentioned, but thenyoushouldeitherjustify what you omit and/or else mention omissions as adiscussion in the limitations of your analysis. You are also welcome to consider other factors such as influence from shareholders,

international implications of the companys decision, long-term talent acquisition, etc. however these are NOT required. You will need to make your own decisions about things like the scope, timeframe, and framing of the analysis, selection of a discount rate (if needed), etc. You are also welcome to challenge the assumptions Ive provided or use different numbers/assumptions if you feel they would be more appropriate or lead to a more interesting analysis.

ASSIGNMENT

Prepare a report to help Costco (or another company of your choosing) decide how to proceed. Be sure to include clear final recommendations. Make (and justify) any reasonable assumptions you need to perform your analysis.¹⁴You can use any software or tools you like (with the exceptionof restrictionsongenerativeAImentionedonthefirstpage). Youmayalsowish todo some additional research, but this is primarily an exercise in demonstrating your own thinking/analysis rather than your abilitytofindthe best data. You probably wont have enough time/information to conduct all the analyses you would like. In that case, please include a discussion acknowledging the limitations of your analysis and describe clearly what additional analyses you would recommend.

Ofcourse, youareexpectedtoincludeatleastsomequantitativeanalysis, butathoughtful qualitative discussion can also provide a lot of value.

Pleaseincludesection headingsin yourreport.

If yourenotsurewheretostart, belowaresomequestionsyou could consider. YoudoNOT necessarily need to answer all of these questions, nor should you limit yourself to just these questions. It is up to you how to approach the problem.

• Canyouhelpthecompanystructureitsdecision?Whatareitsgoals, andoptions?(hint: are there some diagrams/figures you can use?)
• Whatistheexpectedmonetary cost/valueofeachoption?
• Whatdo yourcalculationssuggestthecompany should do?
• Shouldthe companypayforanelectionforecast?
• Whatotherfactorsshouldthecompanyconsider?Howcan/shouldthecompanyconsider non-monetary factors?
• How might risk aversion influence your results? (Recall that a typical coefficient of absoluteriskaversion forasingleindividualwouldcorrespondtoarisktolerance(R)in the 1000s. The value of R would likely be in the millions or maybeeven in the billions for a large corporation).
• Howsensitiveareyourresults/recommendationstotheassumptionsmade?

oNote: the providedassumptions are all veryapproximate as well. If youfinda fairly clear decision that isnt sensitive to small changes, you can/should still considerhowdifferentthenumberswouldhavehadtobecometochangeyour decision.

• Whatadditionaldatawouldyouliketohave? Howwouldyoudecidewhether itisworth the cost of commissioning a study to collect this data?
• Discussanyconcernsorlimitationsofyouranalysis,and/oryourproposedadditional

Atthebeginningof yourreport,pleaseincludeanexecutivesummary(inwordsandgraphics, recallingtheintentionandcomponentsofanexecutivesummary) summarizingyourapproach and findings.

¹⁴Forsomeaspects, youmaysimplyneedtomakeupnumberstoproceed;thatisfine. Justification is preferred, but there are times where it simply wont be possible.

FORMAT

Coverpage:Includestandardinformation(name,date,title,etc.)aswellasyourstatementon the use of AI

Executivesummary: 1-2 pages

Report: maximum 8 pages (12 pt font, 1 margins, 1.5 spacing; not including cover page, references, orappendix).Ifyoubuildamodel(e.g., inExcelor DecisionTools),pleasesubmit that as supporting information. An appendix is permitted (e.g., for additional explanations or figures) providedthatthekeyinformationisallpresentedinthe mainbodyofthereportitself.

This assignment is to be completed individually. You may use any books, webpages, class notes, etc. that you like. You may not discuss with anyone other than the course instructor.

ADVICE

Pleaseresist theurgeto spend considerablymoretimethanneeded on extraresearch orbuilding increasingly complicated models; focus on performing a reasonable first-order analysis that demonstrates your ability to organize/frame the problem and providea reasonable answer in the availabletimeframe.Youarebeinggiven awholeweek tocompletethisreport,buttheintention is for you to spendroughly 1-2 days of time(after looking at and digesting the material) doing the requested analysis.

One suggestion you might try is to create a rough draft of your entire analysis in ~3 hours, and then spend the rest of your time refining the approach; this will ensure you dont get stuck. I am also available for questions as needed.

If you are struggling with the complexity of the problem, you may choose to ignore some of the information or create your own simpler version of the question. Simplifying the analysis does not automatically result in a lower grade, but it will raise the bar for what I expect in the rest of your analysis. You can score well on the exam by having an excellent analysis of a simplified problem, or by having a very good analysis of a more complex problem. This is similar to how certain sporting events (e.g., gymnastics) have separate considerations for difficulty and execution.

ROUGHRUBRIC

I will assign a rough letter grade or yes/no associated with various categories that will be assembledtocreateaholisticfinalgrade.Draftcategories(roughlyequalweight)arebelow.

• Executive summary:
• Assumptionsandestimation:
• Writtencommunication:
• Graphicsandtables:
• Structuringobjectives:
• Structureddecision making:
• Engineeringeconandcost-benefit analysis:
• Handlingof probabilitiesand consequences:
• Value ofinformation:
• Handlingmultiple criteria:
• Sensitivity/uncertaintyanalysis:
• Discussionoflimitations/futureanalysis:
• Focusseson important/relevantquestions:
• Reportincludesinsightfulanalysisbeyondthescopeof thedataprovided:
• Calculationsappearto beaccurate:
• Conclusions:

APPENDIXA: ChatGPTestimateofCostcospending onDEI initiatives

WhileCostcodoesn'tpublishadetailedDEIbudget,wecancreateareasonedestimatebased on:

1. PubliclyknownDEIspendingbenchmarksfromsimilarcompanies,

2.Executivecompensationtiedto DEI,and

3. Programscope,includingemployeetraining,communitypartnerships,andsupplier

Q?1.PeerBenchmarking

• Targetpledged $2Bover5yearsto Black-ownedbusinesses(approx.$400M/year).
• Walmartcommitted$100Mover5 yearstoracialequity (approx.$20M/year).
• Appleallocated$100MtoitsRacialEquityandJustice

ThesecompaniesaremuchlargerthanCostcoin certain respectsbut provideuseful ranges.

2.ExecutiveBonusIndicators(Costco-specific)

• CEORon Vachrisreceiveda$93,333 DEI-relatedbonusin2024.
• Othertopexecutivesreceivedupto$24,000eachformeetingDEI
• ThissuggestsDEI isintegratedintocorporateKPIsandperformanceevaluation,not just HR.

Thisimpliesasubstantialinternalbudgetfortraining,consulting,analytics,andprogram development.

3.EmployeeTraining&Development

Costcohas~316,000employees(asof 2024).Letsestimate:

• DEItrainingcostperemployeeperyear:$100$250(modularonline+facilitated workshops)

Midpoint:$175/employee/year316,000employees=$55.3M/year

?Ju,SupplierDiversity&CommunityEngagement

LetsassumeCostco:

• Spends~$5B/yearongoodsfromdiversesuppliers(averyconservative5%ofits sourcing).
• Allocates12%ofthatspendtoDEI-specificinitiatives(support,outreach, certification, partnerships)

? Estimate:$50M$100M/year

?.9EstimatedTotalAnnualDEI Spend(EducatedEstimate)