1. First of Two Types of Percent: Relative Percentage Conversion or Efficiency Rates, %i Ted Mitchell

2. The two types of percents 1) Those dealing with the size of the final state, F, of a variable relative to the original size of the state, I, of the variable. F = F/I x I F= %i x I Your initial weight was I=150 pounds and your current weight is %i=110% of your initial weight. You current weight is F=165 pounds. 2) Those dealing with the size of the change in the original variable relative to the original size of the variable (F-I) = (F-I)/I x I ∆I = %∆i x I Your initial weight was I =150 pounds and you had a change in weight of %∆i =10%. The change from your initial weight is ∆I =15 pounds.

3. This set of slides deals with the first type 1) Those dealing with the size of the final state, F, of a variable relative to the original size of the state, I, of the variable. F = F/I x I F= %i x I %i is the ratio of the Size of the Output to the Size of the Input and is often called the percent efficiency of the process I have 40% efficiency because 40% of my sales calls result in transactions

4. Working With Relative Percentage Conversion Rates Relative Percentage Conversion Rates are those dealing with the ratio of the size of the final state, F, of a variable relative to the initial size, I, of the variable. F = F/I x I F= %i x I My firm’s sales are 30% of the total sales in the industry

5. Working With Relative Percentage Conversion Rates Relative Percentage Conversion Rates can be considered to the percent conversion rate of a Two-Factor Model in which the Input and the Output variable are measured with the same metric F = F/I x I F= %i x I Output: Size of the Final State = (the percent conversion rate or conversion efficiency, %i) x (Input: Size of the Initial State

6. In Marketing Management There are many popular relative conversion rates that have inputs and output using the same metric: Customer Retention rate: Loyal Customers, L = % T x Total Customers Market Share rate: Firm’s Sales, R = % I x Total Industry Sales, R I Sales Revenue Returned on Advertising rate: $ of Revenue, R = % A x $ of Advertising Expense, A

7. Marketing Outputs that are Relative amounts of Inputs Output, $3 Cost = 60% x Input, $5 Revenue Cost is 60% of Revenue Output, 3 returning customers = 60% x Input, 5 total customers 60% Retention rate Output, 3 sales = 60% x Input, 5 total industry sales 60% Market Share Output, 3 satisfied customers = 60% x Input, 5 total customers 60% satisfaction rate Output, 3 aware customers = 60% x Input, 5 total customers 60% awareness level

8. Relative Percentage Conversion Rate %i = (Output, Final Value, F) / (Input, Initial Value, I) Reflects a reduction or shrinkage process when the relative percentage conversion is between 0% and 100% (0 < %i < 1) Current revenue is 80% of last year’s revenues Reflects a growth or expansion process when the relative percentage conversion is greater than 100% ( %i > 1) Sales Revenue Returned on Promotion ‘Investment’ or expenditure is 500%

9. Relative Percentage Conversion problems come in Three flavors Percentage Problems are Mathematical Identities You need to know all three components to properly forecast with a Two-Factor Percentage Machine or compare 2 Performances If you know 2 of the 3 components you can calculate the third!

10. 1) Calculate Output or Final State, F Biz-Café has a marketing discount machine. You put the current price tag into the Machine and it creates a new price tag through a reduction process that makes the new tag 90% of the current tag. Your current price tag is $4. What is the value of the Input? Current Price tag = $4 What is the conversion rate (reduction rate)? %i = 90% reduction rate What is the value of the new price tag? New Price tag, F = 0.9 x $4 = $3.60

11. 2) Calculate the Percentage Rate or Ratio of Conversion, %I You have observed the performance of a discount machine. You saw the Output, O, was a new price tag of $4 You saw the Input, I, was a price tag of $5 What is the discount machine’s conversion rate? O/I = $4/$5 = 80 cents per every dollar of price tag Or 80 cents on the dollar Or an 80% relative reduction The conversion rate as a percent is value free and has no context

12. 3) Calculate the Input or Initial state, I Biz-Café reviews last week’s decision to reduce the selling price of its coffee. The newly determined selling price is F=$3.50 a cup. The new price is 70% of the old price. What was the old price, P? Output, F = (conversion rate, %i) x Input, I New Price, F = %p x Old Price, P Old Price, P = (New Price, F) / %p Old Price, P = $3.50/0.70 = $5.00 The Old Price, P, was $5.00 a cup

13. The Three Types are That can be asked about using simple percentages described as the efficiency or the conversion or the rate factor in a two factor model Output = Conversion Factor x Input Factor Type 1) Given the Rate of the Conversion Factor, %i, and the size of the Input Factor, I, determine the size of the Output, O Type 2) Given the size of the Output, O, and the size of the Input Factor, I, determine the Rate of Conversion as a percent %i Type 3) Given the Rate of Conversion Factor, %i, and the Output, O, determine the size of the Input, I

14. The Three Types In equation form they are Type 1) find the output, O = %i x I is the classic Slope-Origin form of the percentage equation Type 2) find the rate, percent or ratio of conversion, %i = O / I is the common calculation for the percentage rate from an observation of O and I measured using the same metric ($, customers, transactions, etc.) Type 3) find the input, I = O / %i

15. We use percentage rates because They are convenient for discussion purposes because they are context free However you can maintain the original context Remember a percent is a ‘per centum’ A 60% customer retention rate can be stated as 60 loyal customers per 100 customers served A 5% interest rate can be stated as a return of $5 for every $100 invested

16. Questions? Can You 1) Define a traditional Percent in terms of the value of initial base and final output? 2) Describe the Three Elements of a Two-Factor Model of Percentage Conversion Machine? 3) Transform traditional “Math Questions” involving percent into problems in a business context? 4) Can you add context to percentage questions by maintaining the metrics for input and output?