Marketing Management
(Marketing 360) Professor Kurt Carlson
Marketing Math
Marketing Math
22% of American high school seniors say they are in the top 10% of their high school class.
#3 Recruiter Priority (Analytical Skills)
Ahead of leadership potential, strategic thinking, years of experience, and original thinking
(WSJ Survey of Recruiters 9/9/02)
Take Away: It ain’t easy, but it can get you a job!
Today’s Outline
Session 1: Marketing Math
Session 2: Customer Analysis (begin)
It’s Time to Test the Poll
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I’m lost I sort of I can teach
get it. this stuff.
Marketing Math Overview
Why Use Math in Marketing?
Techniques
Markup and Margins
Break Even (BE) analysis and cannibalization
Pro forma income statements
Price response
Expected Value Calculation (EVC)
Advice
Why Use Math in Marketing?
Decisions will be made. You can make them with or without the benefit of quantitative analysis.
It is hard to argue that you will make better decisions without analysis. Arguments supported by analysis are more persuasive.
Analysis is unambiguous…if you aren’t afraid of numbers.
Managing Uncertainty
Situations faced by business managers are wrought with uncertainty. There is no reason to carry more uncertainty than is necessary.
Merely attempting to quantify a problem can reveal areas of uncertainty.
Once quantified, sensitivity analyses can reveal impact of uncertainty.
Caveats of Using Math
The illusion of comprehension (overconfidence)
Entrenchment can be more extreme when one’s beliefs are based on numbers
Qualitative analysis is still required.
Math is the hammer, but all things are not nails…
And some nails ought not be driven. (., sacred values)
Many people fear and distrust numbers
Margins and Mark-ups
% Margin = *100
= % of sales price kept by seller
Mark-up =
= % the price was increased by seller
Channel Pricing and Margin
Margin: difference between the acquisition price and selling price of a good for a member of the channels of distribution.
Manufacturer
Wholesaler
Retailer
Consumer
Manufacturer cost: $
Selling price to wholesalers: $
Purchase price from manufacturer: $
Selling price to retailers: $
Purchase price from wholesaler: $
Selling price to consumer: $
Purchase from retailer at $
Selling price Purchase price to consumers - from wholesaler
Retailer’s percent margin
=
Selling price to consumer’s
=
13%
Retailer’s percent margin
=
=
Poll #1
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1 2 3 4 5 6 7
I’m lost I sort of I can teach
get it. this stuff.
Break Even Analysis (BE)
Useful for examining feasibility of an offering.
A Breakeven analysis answers the following question:
How many units must be sold to cover the costs of the undertaking?
How many units must be sold for Profit = 0?
Break Even Quantity (BEQ)
Break-Even Quantity: firm’s total revenues equal total cost; below BEQ, the firm has a loss; above BEQ, the firm shows a profit.
Total revenue
Total cost
Total revenue
Total cost
Loss
Profit
Units
$
1,000
BEV
500
2,000
Fixed Cost Unit Contribution
BEQ =
Obtaining the BE Quantity
Profit = TR – TC = pQ – (Qv + FC)
p = price
Q = quantity sold
v = per unit variable costs
FC = fixed costs relevant (not sunk) to the decision
set Profit = 0 and solve for q to get BE quantity
BEQ =
When Breaking Even is Not Enough
Assume there is a Target Profit Impact of πT, then the quantity necessary to achieve πT is given by
Q’ =
Corporate Tax
-Sometimes the corporation requires the business to return a target percentage, r, of revenue
-The target profit impact becomes πT = rpq, and
q’ =
An example of a BE Analysis
IBM PC division has plans to develop a new PC
Division will incur $10M marketing-related costs
R&D costs $10M
Unit cost is $200
Corporate takes 20% of revenue for overhead
Retail price expected to be $1,000
Retailer margin is 30%
How many PCs does IBM need to sell to break even?
Classifying Fixed Costs
Fixed costs can be relevant or sunk (irrelevant)
The volume needed to Break Even by accounting is not necessarily the relevant volume for decision making.
Suppose the PC were already developed and that new forecasts call for sales of between 40-50 thousand PCs.
Should IBM launch the new PC?
Relevant FC = $10M
BE = 27778 Yes, Launch!
Sensitivity Analysis
What if the margin was, .10, .20, .30, .40, .50, or .60?
Margin BE %Change
10% 38462 %
20% 45455 %
30% 55556 %
40% 71429 %
50% 100000 %
60% 166667 %
Margin
Cannibalization
Cannibalization occurs when the sales of a new product undermine the sales of current products.
Let d be the unit decrease in sales of a current product for each unit sold of a new product, and let u be the unit contribution of the cannibalized product.
Then Q’ =
Poll #2
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1 2 3 4 5 6 7
I’m lost I sort of I can teach
get it. this stuff.
Pro Forma Income Statements
If your decision affects several years results, then pro forma income statements are a good tool
If necessary for decision, compute present value
Year 1
Year 2
Year 3
Revenue (
pq
)
1,250
1,800
2,500
Total Variable Costs (
vq
)
563
810
1,125
Total Contribution (
pq
-
vq
)
688
990
1,375
Fixed Costs
(FC)
900
950
1,000
Profit Impact (
pq
-
vq
-
FC) =
-213
40
375
, where r is the discount rate and t is period
Economic Value Calculation
Reference
Value
Positive
Differentiation
Value
Negative
Differentiation
Value
Differentiation Value is the value to the customer (both positive and negative) of any differences between the firm’s offering and the reference offering.
Reference Value is the cost to the customer of the competing offering that the customer views as the best alternative to the firm’s offering.
EVC
EVC = Reference Value + Pos. Differentiation Value – Neg. Differentiation Value
EVC tells the economic value of the offering to the customer.
EVC Example
Several years ago DuPont introduced Alathon 25®, a resin designed for use in pipes
Most common substitute pipe sold for $ per unit
Alathon 25® failure rate was 3%/period, compared to 8%/period
Labor cost of replacing a failed pipe is $ per unit
Alathon 25® properties required inspection of pipe once per period at cost of $ per unit, compared to no inspection
What is EVC per unit of Alathon 25® pipe?
Reference
Value
Positive
Differentiation
Value
Negative
Differentiation
Value
EVC Alathon 25® Pipe
Will customers adopt Dupont’s new pipe?
Inspection
Cost = $
$
Labor Savings =
$60*.05 = $
&
Replacement
Savings =
$*.05* = $
EVC = $
P of substitute pipe = $
Tips on Doing an EVC Analysis
Make sure to include all of the customer’s costs of adoption when doing an EVC.
Purchase cost
Fabrication cost
Finishing cost
Inventory
Maintenance
Changeover cost
Risk premium
When doing multi-year calculations, use customers’ cost of capital as the discount rate.
Poll #3
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1 2 3 4 5 6 7
I’m lost I sort of I can teach
get it. this stuff.
EVC in Action
AT&T beats IBM & Lockheed for $ TMAC Award
Washington—The Treasury Department last week awarded a $ billion Treasury Multiuser Acquisition Contract (TMAC) to an AT&T led team which reportedly came in as high bidder over lower bids from IBM Corp. and Lockheed Corp.
Industry sources last week said that AT&T’s bid of $ billion for the contract was nearly $500 million more than the lowest bid of $931 million reportedly submitted by the Lockheed led team. It is believed that IBM Corp.’s bid fell in the middle of the two at approximately $ billion.
—Electronic News Monday, July 22, 1991.
IBM and Lockheed Protest
Washington—IBM Corp. and Lockheed Corp last week told the GSA Board of Contract Appeals that the government cannot justify the more than $500 million premium it will pay for awarding high-bidder AT&T the Treasury Multiuser Acquisition Contract (TMAC).
In separate protests filed last week with the GSA Board, unsuccessful bidders IBM and Lockheed asked that award of the massive Internal Revenue Service contract to AT&T be overturned. An initial hearing on the protests will likely be held early this week.
—Electronic News Monday, July 29, 1991.
General Service Administration Acts
Washington—The GSA Board of Contract Appeals last week halted a potential $ billion computer contract award to AT&T, charging the Treasury Department failed to adequately justify the selection of a far more costly proposal by AT&T over a much lower bid by IBM and Lockheed Missiles and Space.
The board upheld the protests of IBM and Lockheed, and ordered the Treasury Multiuser Acquisition Contract (TMAC) sent back to the agency for further consideration.
—Electronic News Monday, September 30, 1991.
IRS Reinstates the Deal
Washington—The Internal Revenue Service last week re-awarded a $ billion computer contract to AT&T…based on “an in-depth analysis” of the proposal offered by AT&T as well as those from competing bidders IBM Corp. and Lockheed Missiles and Space.
“While the cost of the AT&T proposal was the highest of the three, it represented the best value to the government when all factors, including technical capabilities, management and support services, the risk of future additional costs, and the impact on productivity of the IRS user workforce were considered for each of the three different proposals,” the IRS said Friday.
—Electronic News, Monday, March 23, 1992.
The Origin of Demand Curves
Aggregate Demand for an offering varies with price because the value of the offering varies across customers
Example
Motorola has a new mobile phone
Market potential is 1B customers
Value to potential customers is uniformly distributed between $0 and $50
What is the demand function for this phone?
Demand Function
Because valuations are uniformly distributed, the demand function is linear Q = mP + b
Q = 1B when p = $0 and Q = 0, when p = $50
m = slope = rise/run = (1B – 0)/(0 – $50) =
b = vertical intercept = 1B
Demand Function:
Q = -(.02B)P + 1B
The Demand Function Gives Way to Revenue and Profit Functions
Revenue Function
TR = QP = (mP + b)P
Profit Function
= TR – TC = TR – Qv - FC
= (mP + b)P – (mP + b)v – FC
= (mP + b)(P – v) – FC
What’s the optimal price?
The Revenue Maximizing Price
Differentiate d(TR)/dp = 2mP + b
Set d(TR)/dp = 0, and solve for P
P* = -b/2m
P* = -1B/2()
P* = $25
The Profit Maximizing Price
Differentiate dProfit/dp = 2mP + b – mv
Set dProfit/dp = 0, and solve for P
P* = (mv – b)/2m
= v/2 + 25
Let v = 5, then
P* = $
Poll #4
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1 2 3 4 5 6 7
I’m lost I sort of I can teach
get it. this stuff.
Advice on Using Math in This Class
The cases we will discuss have many #s.
A structured process will help you avoid getting lost in useless analyses.
What is this structured process?
Advice (continued)
Define the problem to be solved
If the issue is to determine whether or not to launch a new product, BE probably makes sense.
Break into pieces…what is needed to do BE?
Fixed costs, unit variable costs, price
Are they available? Can they be computed?
Reassemble the pieces and calculate
Apply result to the issue, if it does not help, you probably should not have done it. (The selection criterion is “need to know.”)
Summary
Assessment of a business situation invariably requires some form of quantitative analysis
Marketing math combines rough assumptions and precise numbers
Two keys here:
Avoid arbitrary assumptions. Your assumptions should be guided by and consistent with the facts
The impact of an invalid assumption can be determined via a sensitivity analysis.
Take Aways
Break Even (BE): feasibility of the offering
Sensitivity Analyses: check impact of assumptions
Cannibalization: extended impact of the offering
Economic Value Calculation (EVC): economic attractiveness to the customer
Demand Functions and Pricing: calculate Q for any P or determine optimal P
