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Amount of Change as an Output, ∆ Percent Change as a Conversion Rate, %∆

Amount of Change as an Output, ∆ Percent Change as a Conversion Rate, %∆. Ted Mitchell. Learning Objectives. 1) To create a Two-Factor Model in which the Output is the amount of the change, ∆I, and the rate of the conversion process is the percent change of the Input, %∆I

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Amount of Change as an Output, ∆ Percent Change as a Conversion Rate, %∆

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  1. Amount of Change as an Output, ∆Percent Change as a Conversion Rate, %∆ Ted Mitchell

  2. Learning Objectives • 1) To create a Two-Factor Model in which the Output is the amount of the change, ∆I, and the rate of the conversion process is the percent change of the Input, %∆I • (F-I) = (F-I)/I x I • ∆I = %∆I x I

  3. The Traditional Percent • is often presented in terms of three elements • 1) The amount of Input or Base, I • 2) The amount of the Final state or output, F • 3) The conversion rate or percent as the ratio%I = F/I • F = (F/I) x I • F = %I x I

  4. Modify the Traditional Elements • 1) The amount of Input or Base, I • 2) Modify Output to the size of the change∆I = (F-I) • ∆I means the size of the change from I • 3) Modify conversion rate or percent %∆I = (F-I)/I • The percent change model is • ∆I = %∆I x I • (F-I) = ((F-I)/I) x I

  5. Example 1: Use the letters I and F to represent Initial and Final states. • John was I = 60 inches tall last year. This year he is F = 64 inches tall. His height increased by 4 inches. The growth process is the conversion process. • John’s Initial state is I = 60 inches • John’s Finial State is F = 64 inches • ∆I = (F – I) • ∆I = 64 inches – 60 inches = 4 inches • Use ∆I to indicate that the change is from state, I to state, F, where I is treated as the initial or base point for the calculation

  6. 3 Elements in the Percent Change model • John was I = 60 inches tall last year. This year he is F = 64 inches tall. His height increased by 4 inches. The growth process is the conversion process. • ∆I = %∆I x I • (F-I) = ((F-I)/I) x I • (64 – 60) = (4/60) x 60 • 4 inches = 0.0667 x 60 inches • 4 inches = 6.67% x 60 inches

  7. Example 2: • The price last week was I = $10 and the price this week, F = $6. The amount of the change in the price was $4. • Output = Conversion rate x Input • ∆I = %∆I x I • (F – I) = ((F-I)/I) x I • $6 - $10 = -$4/$10 x $10 • -$4 = -0.40 x $10 • -$4 = -40% x $10

  8. Example 3: • The amount of profit last week was I =$8,000 and increased by ∆I = $3,000 this week to a profit of F = $11,000 • ∆I= %∆I x I • (F – I ) = ((F-I)/I) x I • $11,000 - $8,000 = ($3,000/$8,000) x $8,000 • $3,000 = 0.375 x $8,000 • $3,000 = 37.5% x $8,000

  9. Using Percent Change, %∆I, in a Two-Factor Model

  10. Percent Rate of Change is • 1) very important in many types of business analysis • 2) it very common to discussion the size of a change, in terms of a percent or as a rate of increase or decrease from an initial state • In order to discuss a percentage rate of change it is necessary to have a base or initial to measure the relative size of the change

  11. Two Similar But Different Definitions • 1) A Basic Percent, %I, is defined as a ratio of the Final state, F, to the Initial state, I • %I = F/I and is read as a percentage of the Initial state, I • 2) A Percent Change, %∆I, is defined as the ratio of the size of the change from the initial state over the size of the initial state • %∆I = ∆I/I = (F-I)/I and is read as a percentage change in size from the initial state, I

  12. The key to understanding • the relationship between a percentage change and a basic percentage rate is • To see both as versions of a Two-Factor Model • Output = Conversion Factor x Input • Final state, F = %I x I • Change from Initial state, ∆I = %∆I x I

  13. The best known examples • Of using the amount of difference, ∆I, as an output and the Percent Change, %∆I, as the conversion factor are: • 1) Calculating the dollar value of a coupon or a percent discount off the regular price. • 2) Calculating the percent Markup on Cost • 3) Calculating the percent Markup on Price • 4) Calculating the Gross (Profit) Return(ed) on Sales (Revenue), GROS

  14. Calculating the Dollar Value of a Coupon • You have received a coupon that gives you a sale price at 20% discount off the regular price. The regular price is P = $30 for the item. What is the dollar value of the coupon? • (Sale Price – Original Price) = [(Sale Price – Original Price)/Original Price] x Original Price • (Ps – Po) = [(Ps-Po)/Po] x Po • ∆Po = %∆Po x Po • ∆Po = -20% x $30 • Dollar value of the reduction = ∆Po = -0.20 x $30 = -$6

  15. For A Formal Solution Use a Two-Factor Model • You have received a coupon that gives you a sale price at 20% discount off the regular price. The regular price is P = $30 for the item. What is the dollar value of the coupon? • Output = Dollar Value of the Coupon • Output = (Sale Price – Original Price) = (Ps-Po) • Input = Regular price of the Product, Po • Conversion Rate = Percent Discount • Conversion Rate = [(Sale Price – Original Price)/Original Price] • Conversion Rate = (Ps-Po) / Po • (Ps – Po) = [(Ps-Po)/Po] x Po • Formal procedure is • ∆Po = %∆Po x Po

  16. Using the Formal Procedure looks Like Overkill • Until you are asked the following: • For competitive reasons you wish to provide your customers with a coupon that is worth $5 off the regular selling price and you want the coupon to be prints offering them a 25% discount off the regular price. What is the regular price, Po, that you must set for the product? • ∆Po = %∆Po x Po • Po = ∆Po / %∆Po • Regular Price, Po = $5 / 25% = $5/0.25 = $20

  17. Calculating the Markup on Cost Using Two-Factor Model • You have a wagon to sell that cost you V = $20. You will sell the wagon for a price of P= $50. What is your percent markup on cost, Mv = %∆V? • Converting the Cost into a profit per unit using Markup on Cost as the conversion rate • Output = conversion rate x Input • ∆V = %∆V x V • ∆V is the change from the cost, V • (P-V) = %∆V x V • %∆V = (P-V)/V • %∆V = ($50-$20)/$20 = 1.50 = 150% • Markup on Cost, Mv = 150%

  18. Calculating the Markup on Price Using a Two-Factor Model • You have a wagon to sell that cost you V = $20. You will sell the wagon for a price of P= $50. What is your percent Markup on Price, Mp = %∆P? • Converting the Price, P, into a Profit per Unit (P-V) using Markup on Price, Mp, as the conversion rate • Output = conversion rate x Input • ∆V = %∆P x P • ∆V is the change from the cost, V • (P-V) = %∆P x P • %∆P = (P-V)/P • %∆P = ($50-$20)/$50 = 0.60 = 60% • Markup on price, Mp = 60%

  19. Calculating the Gross Return on Sales Using a Two-Factor Model • You have a wagon selling business and your cost of goods sold last period was, COGS = $200. Your sales revenue was $500. What is your percent of Gross Profit returned on Sales Revenue, GROS = %∆R? • Converting the Revenue, R, into a Gross Profit (R-COGS) using the Gross Return on Sales , GROS, as the conversion rate • Output = conversion rate x Input • ∆COGS = %∆R x R • ∆COGS is the change from the costof goods sold • (R-COGS) = %∆R x R • %∆R = (R-COGS)/R • %∆R = ($500-$200)/$500 = 0.60 = 60% • Gross Return on Sales, GROS = 60%

  20. Samples of the Three Types of Problems using Percent Change %∆I Ted Mitchell

  21. Remember there were 3 Types of Problems • When dealing with Basic Percent as a Two-Factor Model • Output = Conversion Factor x Input Factor • 1) Calculate Output, O = %I x Input • 2) Calculate conversion rate, %I= Output / Input • 3) Calculate the Input, I = Output / %I

  22. There are3 Types of Problems • When dealing with a percent change as a Two-Factor Model • The Output is the change between the initial state and the final state, ∆I = (F-I) • 1) Calculate Output, ∆I = %∆I x Input • 2) Calculate Percent, %∆I = ∆I / Input%∆I = (F-I) / I • 3) Calculate the Input, I = ∆I / %∆II = (F-I) / %∆I

  23. Remember these Models are identities • If you know 2 of the 3 elements that define the Two-Factor Market, then you can calculate the third!

  24. Example of Type 1 • The Output is the change between the initial and the final state, ∆I = (F-I) • 1) Calculate Output, ∆I = %∆I x Input • You are planning to buy a house next year. You are told that the price of a house is likely to increase by12% from the current price of $150,000. • What is the dollar increase you should expect to pay if housing prices go up? • Output, ∆I = 12% x $150,000 = $18,000 increase

  25. In a Type 1 Problem You have to recognize • You are planning to buy a house next year. You are told that the price of a house is likely to increase by12% from the current price of $150,000. • What is the dollar increase you should expect to pay if housing prices go up? • 1) The Output is the change between the initial price and and the final price, ∆I = (F-I) • 2) The Input is the initial price, I = $150,000 • 3) The percentage size of the change in the initial price is the Conversion Rate,%∆I = 12% • Output, ∆I = 12% x $150,000 = $18,000 increase

  26. Type 1) Calculate Output, ∆I = %∆I x Input • The price of coffee was $4 last week. A 20% increase in last week’s price was implemented this week. What is dollar increase in the price of the coffee?Recognize • 1) The Output is the change, ∆, between the input and the output, ∆1 = (F-I) • 2) The Input is the Initial price of the coffee, I = $4 • 3) The size of the change is %∆I = 20% from the initial state • ∆I = %∆I x I • ∆I = 20% x $4 • ∆I = 0.20 x $4 = $0.80 is the amount of the price increase

  27. 2) Calculate conversion rate, %∆I = ∆I / Input%∆I = (F-I) / I • The amount of customer satisfaction increased by 15 points last week. Last week the customer satisfaction was recorded as 60 points. What is the percentage change from last week? • Recognize • 1) The Output as the size of the change, ∆I = 15 • 2) The Input is the initial size of the awareness, I = 60 • 3) The conversion rate, %∆I is a percentage change • ∆I = %∆I x I • %∆I = ∆I/I = 15 points / 60 points • %∆I = 15/60 = 0.25 = 25%

  28. 3) Calculate the Input, I = ∆I / %∆II = (O-I) / %∆I • This week there was 20 point increase in the customer awareness level from last week and the increase represented a 50% increase in last week’s awareness level. What was last week’s awareness level? • Recognize • 1) The Output is the size of the change, ∆I, between the initial state, I, and the final state, F, with ∆I = (F-I) • 2) The size of the change as a percentage of the initial state is the conversion rate, %∆I = 50% • 3) The size of the initial state is the input and must be calculated • ∆I = %∆I x I • I = ∆I/%∆I = 20 points/50% = 40 points • The awareness level last week 40 points

  29. Any questions on • Using a Two-Factor model with the percent change being the conversion factor, and the size of the change from the initial state to final state being the output of the model • ∆I = %∆I x I • Output, O = ∆I = (F-I) • Conversion factor , %∆I = ∆I / I = (F-I)/I • Input is the Initial state, I

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