Sample Quantitative Questions Chapter 4 Ted Mitchell

A Marketing Machine Producing Revenues From the 4P’s The Marketing Machine Inputs to The Marketing Machine Price Tags Product Quality Promotion Place Revenue Output from The Marketing Machine Revenues Revenue

Typology of Demand Producing, Quantity Sold, Q, Marketing Machines Two-Factor Model Calibrated from a Single Observation Two-Factor Meta-Model Calibrated from a minimum of two observations Input from Positive Elements of Marketing Mix, π Promotion, Place, Product Type #1 Quantity Sold, Q = r x π Conversion rate, r = Q/π Quantity Sold, Q = (Q/π) x π Type #3 ∆Quantity Sold, ∆Q = m x ∆π Conversion rate, m = ∆Q/∆π Slope-Intercept version Q = a + m(π) Input from Negative elements of the Marketing mix Price Tag, P Type #2 Quantity Sold, Q = r x P Conversion rate, r = Q/P Quantity Sold, Q = (Q/P) x P Type #4 ∆Quantity Sold, ∆Q = m x ∆P Conversion rate, m = ∆Q/∆P Slope-Intercept version Q = a - m(P) See Chapter 3 for details

Typology of Basic Revenue Machines Two-Factor Machine Single Point of Calibration Two-Factor Meta-Model Two or More Points of Calibration Positive Input From Marketing Mix, π Promotion, Place, Product Quality Type #1 Revenue, R = (R/π) x π Type #3a: demand extension Revenue, R = P x Q Revenue, R = P(a + b( π )) Revenue, R = aP + bP( π ) Type #3b: direct observation Revenue, R = a + m π Negative Input From Marketing Mix, Price Tag, P Type #2 Revenue, R = (R/P) x P Revenue, R = Q x P Type #4a: demand extension Revenue, R = P x Q Revenue, R = P (a-b P ) Revenue, R = a P – b P 2 Type #4b: direct observation Revenue, R = a + m P

1) Analysis of a Revenue Machine from Total Expenditure on Servers You own two coffee shops. You are trying to understand the role that servers play in the creation of revenues The shops sell 3 different sizes of coffees and pastries and you have aggregated information on the weekly revenues and the total amount spent on servers each week. Coffee shop #1 spends $1,333 on server wages and generates $10,000 in revenues Coffee shop #2 spends $2,000 on server wages and generates $14,000 in revenues What is the revenue returned per dollar of server wages in each coffee shop?

Calculating Sales Return on Server Expense Café #1Café #2 Weekly Server Expense, S $1,333$2,000 Return per dollar of expense, r = R/S Weekly Sales Revenue, R = r x S $10,000$14,000

Calculating Sales Return on Server Expense Café #1Café #2 Weekly Server Expense, S $1,333$2,000 Return per dollar of expense, r = R/S $10,000/$1,333 =$7.5 per dollar or 750% return $14,000/$2,000 =$7.0 per dollar or 700% return Weekly Sales Revenue, R = r x S $10,000$14,000

2) Analysis of an Average Revenue Returned You own two coffee shops. You are trying to understand the role that servers play in the creation of revenues The shops sell 3 different size coffees and pastries and you have aggregated information on the weekly revenues and the total amount spent on servers each week. Coffee shop #1 spends $1,333 on server wages and generates $10,000 in revenues Coffee shop #2 spends $2,000 on server wages and generates $14,000 in revenues What is the average rate of revenue being returned by the two stores?

Calculating Sales Return on Server Expense Café #1Café #2Average cafe Weekly Server Expense, S $1,333$2,000$3,333/2 = 1,666.5 Return per dollar of expense, r = R/S $10,000/$1,333 =$7.5 per dollar or 750% return $14,000/$2,000 =$7.0 per dollar or 700% return NOT 725% Weekly Sales Revenue, R = r x S $10,000$14,000$24,000/2 = $12,000

Calculating Average Revenue Returned on Server Expense Café #1Café #2Average cafe Weekly Server Expense, S $1,333$2,000$3,333/2 = 1,666.5 Return per dollar of expense, r = R/S $10,000/$1,333 =$7.5 per dollar or 750% return $14,000/$2,000 =$7.0 per dollar or 700% return $24,000/$3,33 3 = 7.2 dollars per dollar or 720% return Weekly Sales Revenue, R = r x S $10,000$14,000$24,000/2 = $12,000

3) Calculate the Meta-Return Rate of Meta-Revenue Machine You observed two coffee shop performances. You are trying to understand the role that servers play in the creation of revenues The shops sell 3 different size coffees and pastries and you have aggregated information on the weekly revenues and the total amount spent on servers each week. Observation #1 café spends $1,333 on server wages and generates $10,000 in revenues Observation #2 café spends $2,000 on server wages and generates $14,000 in revenues What is the Meta-Revenue Return rate, m?

Calculating Meta-Sales Return Rate Observation #1Observation #2Meta-machine Weekly Server Expense, S $1,333$2,000∆S = $777 Return per dollar of expense, r= R/S $10,000/$1,333 =$7.5 per dollar or 750% return Not Used $14,000/$2,000 =$7.0 per dollar or 700% return Not Used m = ∆R/∆S m = $4,000/$777 m = $5.15 per dollar or 515% Weekly Sales Revenue, R = r x S $10,000$14,000∆R = $4,000

4) Forecasting with the single point meta-revenue server machine The boss proposes a $200 change in the total expenditure on servers as a means to increase revenues. The calibrated meta-revenue server machine for a single point (∆R, ∆S) is ∆R = 515%(∆S) What is the forecasted change in Revenue, ∆R, given a proposed increase in server expense, ∆S = $200? Forecasted change in Revenue, ∆R = 5.15 ($200) Forecasted change in Revenue, ∆R = $1,030

Forecasting Revenue works in concert With an analysis of a breakeven revenue, BER In future classes we will calculate the breakeven revenue needed to cover the proposed change in the cost of the server expenditure, ∆S It is usually more convenient to forecast the revenue using the slope-intercept equation of the meta-revenue server machine

5) Calculate the y-intercept of the slope-intercept equation of meta-revenue server machine You have observed two coffee shop performances. You are trying to understand the role that servers play in the creation of revenues The shops sell 3 different size coffees and pastries and you have aggregated information on the weekly revenues and the total amount spent on servers each week. Observation #2 café spends $2,000 on server wages and generates $14,000 in revenues What is the y-intercept of the slope-intercept equation of the Meta-Revenue machine?

5) Calculate the y-intercept of the Meta-Revenue Server Machine Calibrated meta-revenue server machine uses 1) one of the observed performances and 2) the calculated meta-conversion rate, m ∆R = m x ∆S (R – R 2 ) = 515% x (S – S 2 ) R – $14,000 = 5.15 x (S – $2,000) Set the proposed input value to S=0 and solve for R = y-intercept, a

5) Calculate the y-intercept of the Meta-Revenue Server Machine Set the proposed input value to 0 and solve for R = y-intercept, a a – $14,000 = 5.15 x (0 – $2,000) a = $14,000 – $10,300 = $3,700 The y-intercept is a = $3,700 The slope-intercept equation of the meta- revenue server machine is Revenue, R = $3, %(Server expenditure, S)

6) Forecast the Sale Revenue from a proposed level of server expenditure Market Research has calibrated the meta-revenue server machine as Revenue, R = $3, %(Server expenditure, S) The boss is proposing an increase in server availability that will result in a total server expenditure of S = $2,200 What is the forecasted Sales Revenue that will be produced by the meta-revenue with $2,200 in server expense as an input? Forecasted Revenue, R = $3, ( $2,200) Forecasted Revenue, R = $3,700 + $11,330 Forecasted Revenue, R = $15,030

6) Forecast the Sale Revenue from a proposed level of server expenditure Market Research has calibrated the meta-revenue server machine as Revenue, R = $3, %(Server expenditure, S) The boss is proposing an increase in server availability that will result in a total server expenditure of S = $2,200 What is the forecasted Sales Revenue that will be produced by the meta-revenue with $2,200 in server expense as an input? Forecasted Revenue, R = $3, ( $2,200) Forecasted Revenue, R = $3,700 + $11,330 Forecasted Revenue, R = $15,030 Always remember to convert the percent return back into a decimal before doing any calculations

Revenue = kπ a S = server expenditure R = Revenue x x x x x x x x x x x x Linear Revenue Meta-Machine is a secant that approximates the Revenue function R = a + m(S) R =$3, %(S) R = kPπ a

7) Extend the meta-demand price equation or demand curve Into a meta-revenue price equation Market Research has estimated that the demand for a medium size coffee is explained by the size of the price tag as Quantity sold, Q = 6,000 – 900(price tag, P) What is the meta-revenue price machine equation? Multiply both sides by the price tag, P (P x Q) = 6,000P – 900(P)(P) Revenue, R = 6,000P – 900P 2

Estimated Meta-demand price machine or Demand curve Price per Cup $3.90$4.00 Quantity Sold 2,400 Demand Equation Q = 6,000 – 900(P) Revenue = 2,400 x $4.00 Revenue = $9,600 TJM

8) Forecast a revenue from the meta-revenue price machine using the expanded demand equation Market research has estimated that the meta- revenue price equation that best explains revenues from sales of medium size cups at different prices is Revenue, R = 6,000P – (900cp$ x P 2 ) Management wants to set the selling price at $4.10 a cup. What is the forecasted revenue at that price? Revenue, R = 6,000($4.10) – 900cp$ x ($4.10) 2 Revenue, R = $24,600 – (900cp$ x 16.81$ 2 ) Revenue, R = $24,600 – $15,129 = $6,471

Revenue Price per cup 0 TJM R= P(a-bP) R = aP - bP 2 R= a-mP

An Optimal Price, Pr* In Future Chapters we will learn that the optimal selling price, Pr* for maximum revenue for this demand curve is dR/dP = 6,000 – 2(900 cp$)P set = 0 Pr* = a/2(b) = (6,000 cups) /2(900 cp$) Pr* = $3.33 per cup