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Marketing Math

This article explores various techniques in marketing math and economic analysis, including break-even analysis, cannibalization, pro forma income statements, and economic value calculation.

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Marketing Math

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  1. Professor Joel Huber Marketing 360 Marketing Management Fuqua School of Business Marketing Math

  2. Marketing Math • 22% of American high school seniors report that they are in the top 10% of their high school class. • WSJ; 8/30/00

  3. Overview • Objectives • Techniques • Break even analysis and cannibalization • Channel margins • Pro forma income statements • Economic value calculation • Price response • Expected value calculations • Advice

  4. Objectives • Marketing is a rigorous discipline. • Those that substantiate and analyze get more resources and make fewer mistakes. • Those that do not tend to get fired. • Qualitative analysis precedes quantitative analysis • Why is this analysis needed?

  5. Break Even Analysis • Question: how much do I need to sell to break even? • This implies profit=0. • Profit = (P-VC)Q-FC • Set profit = 0 • Q=FC/(P-VC)=FC/Contribution • There are different forms of break even • Project • Annual

  6. Break Even Analysis • IBM has a new PC. • $10,000,000 in marketing • $10,000,000 in R&D • Corporate overhead is 20% of revenue. • Retail price is $1,000 • Cost of PC is $200 • How many PCs does IBM need to sell?

  7. Cannibalization • New product sales also affect existing product sales, and this must be considered in evaluating the impact of a new offering

  8. Cannibalization • IBM has a new PC. • $10,000,000 in marketing • $10,000,000 in R&D • Cost of PC is $200 • Corporate overhead is 20% • Retail price is $1,000, 50% retail margin • For every 10 sold replaces one $1000 margin high-end IBM model • How many PCs does IBM need to sell?

  9. Pro Forma Income Statements • If your decision affects several years results, then pro forma income statements are critical • If necessary for decision, compute present value , where r is discount rate and t is period

  10. ProForma Income Statement

  11. Economic Value Calculation Slicing the Value Salami VIU Customer Surplus(Economic Driving Force) Price Margin(Profit) Cost Cost of Production(Loaded)

  12. Economic Value-in-Use Example: A chemical plant uses 200 O-rings to seal valves carrying corrosive materials. Those O-rings cost $5.00 each and must be changed during regular maintenance every two months. A new product lasts three months. What is the value of the new O-ring?

  13. Value-in-Use Tips Be sure to include all costs when doing a VIU calculation. Use costs = (Annual) • Purchase cost + Fabrication cost + Finishing cost + Inventory cost + Maintenance/Service cost Scrap adjustment + Level-of-requirement adjustment + Changeover cost + Risk premium + other Use the user’s cost of capital when making multi-year calculations.

  14. Chicago Sun-Times July 5, 2002 Little to gain from MBA classes: A business degree does not guarantee a successful career or a higher salary, a Stanford University business professor concluded in an analysis of 40 years of research on the economic value of the MBA. Little of what is taught to students in business school prepares them for the corporate workplace, said Jeffrey Pfeffer, an expert in organizational behavior who has taught at elite business schools for 30 years. Rather, students are paying for prestigious names to add to their resumes and the opportunity to network with like-minded colleagues, Pfeffer said. MBA programs can cost more than $100,000. "The simplest advice is that if you don't get into a leading business school, the economic value of the degree is really quite limited," said Pfeffer. "Obviously, if you get admitted to Harvard or Stanford or another elite school, the very fact of your admission is going to increase your worth in the job market," he said. "But there is not much evidence the actual education does very much." What is the economic value of your Fuqua MBA?

  15. Value of MBA: Assumptions

  16. Calculations

  17. Economic Value Calculation • What is the value of a flu shot?

  18. Annals of Internal Medicine • Design: Cost-benefit analysis • Net Benefit (Cost) = Benefits of Vaccination and Treatment – Costs of Vaccination and Treatment • Data Sources: Published data and patient survey • Perspective: Societal • Outcomes Measured: US dollars

  19. Decision Tree for Flue Vaccine: Vaccinate and Rimantadine if Infected Side Effect from Intervention Vaccinate and Zanamivir if Infected Infection Vaccinate and Oseltamivir if Infected Vaccinate and No Intervention if Infected No Side Effects from Intervention No vaccine and Rimantadine if Infected No vaccine and Zanamivir if Infected No vaccine and Oseltamivir if Infected No Infection No vaccine and No Intervention if Infected

  20. Costs:

  21. Benefits:

  22. Probabilities

  23. Estimated value in use for different options Vaccinate and Rimantadine if Infected $31 $30 $29 $29 $5 $2 Base $0 Vaccinate and Zanamivir if Infected Vaccinate and Oseltamivir if Infected Vaccinate and No Intervention if Infected No vaccine and Rimantadine if Infected No vaccine and Zanamivir if Infected No vaccine and Oseltamivir if Infected No vaccine and No Intervention if Infected

  24. Sensitivity Analysis Variable Base Value Threshold Alternate Favored Strategy Probability Influenza Infection 15% <6.4% No Vaccine/ Use Rimantadine if Infected Work-Days Lost Influenza without Treatment 2.8 <0.97 No Vaccine/ Use Rimantadine if Infected Prevalence Influenza B 16.33% >35% Vaccine and Zanamivir Work-Days Gained from Rimantadine 0.5 <0.36 Vaccine and Zanamivir from Zanamivir 0.5 >0.62 Vaccine and Zanamivir From Oseltamivir 0.5 >0.73 Vaccine and Oseltamivir

  25. Given influenza incidence >6.4%, influenza vaccination had higher net benefit than non-vaccination strategies in nearly all scenarios Health benefits of most anti-viral treatments equaled or exceeded their costs for most scenarios, driven primarily by the number of work days gained. Key drivers of benefits are work days lost and shift in probability of getting flu Conclusions:

  26. Price Response to Economic Value • Constant Elasticity Model • Qty = 1000*price-2 • Elasticity = dQ/dp * p/Q = -2 • Linear Demand Model • Qty = 1100-200*price • Elasticity = p/Q

  27. Constant Elasticity Model

  28. Linear Demand Model

  29. Optimizing Price • Set d(Profit/dp) = 0 • Qty = 1100-200*price • Variable Cost=0.10 • Fixed Cost = 0 • p* = 1100/400 - 0.5*0.1 = 2.70

  30. Optimizing Price

  31. Expected Value Calculation • Expected Value (x) = S (x*prob (x)) • Two market segments exist, business class and leisure class. • There are 150 business travelers and 100 leisure travelers. • Business travelers pay $1000/ticket • Leisure travelers pay $200/ticket • What is the expected price of the ticket?

  32. Expected Value Calculation • Prob (ticket holder is business) = (150/(200+150)) = 3/5 • Prob (ticket holder is leisure) = 2/5 • Expected Value (x) = S (x*prob (x)) • Expected Revenue = (3/5)*$1000 + (2/5)*$200 = $600 + $80 = $680

  33. Advice • In cases, there are many, many numbers and many, many analyses. • The foregoing are only a small set. • Without structure you will quickly get lost (sometimes even with structure). • Even harder in real world, because numbers are not so readily available. • So, how to proceed?

  34. Advice • Step 1: Define the problem that is trying to be solved • For example, if the goal is to determine, will this idea fly, then a simple back-of-the envelope (break even, payback) analysis makes sense.

  35. Advice • Step 2: Break the problem into smaller pieces • E.g., what does one need to know to do a break even? • Fixed costs, then variable costs, then prices • Solve these one by one • What are all the variable costs? Are they known, if so, great. If not: • Can they be determined? • Regress total costs against volume, constant is fixed cost

  36. Advice • Step 3 • Once all the pieces are there, and have been solved one by one, add them back up, BE=FC/(P-VC) • Do not try to do everything at once • Last, remember, the analyses must have some purpose, otherwise you will get lost. Always start with the objectives.

  37. Summary • Assessing the merits of a business opportunity invariably means working the numbers • Try it from different perspectives, customers will • Marketing combines precise numbers with rough assumptions • Vaguely right beats precisely wrong • Sensitivity analysis and research mandated if assumptions affect answers • But so does finance - what is the cost of capital?

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