1. Profit Dynamics This module reviews breakeven and covers the concepts of target profit and volume and price-volume interaction. Author: Paul Farris Marketing Metrics Reference: Chapter 3 © 2011 Paul Farris and Management by the Numbers, Inc.

2. B REAKEVEN R EVIEW 2 Breakeven Review MBTN | Management by the Numbers Definitions BE (units) = Fixed Costs / (Selling Price – Variable Cost) or Fixed Costs / Unit Margin BE ($) = Fixed Costs / ((Selling Price – Variable Cost) / Selling Price) or Fixed Costs / Margin % To convert from revenue (currency) to units or vice versa: Revenue Breakeven = Breakeven in Units * Unit Price Breakeven in Units = Revenue Breakeven / Unit Price The Breakeven Point is selling enough to just cover fixed costs. Unit Breakeven is unit sales required to cover fixed costs Revenue Breakeven is sales revenue required to cover fixed costs

3. T ARGET P ROFITS 3 Target Profits MBTN | Management by the Numbers Definitions Target Volume in Units = (Fixed Costs + Profit Objective) / (SP – VC) Target Volume in Dollars = (Fixed Costs + Profit Objective) / ((SP-VC) / SP) Just as with the breakeven formulas, notice that multiplying the first formula by the selling price yields the second formula. Thus… Target Revenues = Unit Target Volume * Selling Price Companies don’t want to just breakeven on costs, they want to earn profits. We can calculate how many units have to be sold in order to breakeven on costs and to produce a particular level of profit. But What About Profits?

4. T ARGET P ROFIT : E XAMPLES 4 Target Profit: Examples MBTN | Management by the Numbers Question 1: Mickey’s Mousetraps wants to calculate how many of its “Magic Mouse Trappers” it needs to sell in order to realize a profit objective* of $30,000. The product sells for $20, it costs $5 per unit to make, and the company’s fixed costs are $30,000. Answer: We know that Target Volume (units) = (FC + Profit Objective) / (SP - VC) Therefore, substituting in our values: Target Volume (units) = ($30,000 + $30,000) / ($20 - $5) = 4000 mousetraps *Note: A profit objective may sometimes be described as a contribution objective. Generally, a contribution objective will not consider covering fixed costs whereas as a profit objective will. However, depending on the context, they may be used interchangeably, especially if describing the contribution a particular product line makes toward a company’s overall profitability.

5. T ARGET P ROFIT : E XAMPLES 5 Target Profit: Examples MBTN | Management by the Numbers Question 2: Now Mickey’s Mousetraps wants to calculate how many dollars worth of its “Deluxe Mighty Mouse Trappers’” it needs to sell in order to realize a profit objective of $60,000. The product sells for $40, it costs $10 per unit to make, and the company’s fixed costs are $30,000. Answer: We know Target Volume (Revs) = (FC + Profit Objective) / ((SP - VC) / SP) Therefore, substituting in our values: Target Volume (revenues) = ($30,000 + $60,000) / (($40 - $10) / $40) = ($90,000 / 0.75) = $120,000 = 3000 mousetraps

6. R EVIEW 6 Review MBTN | Management by the Numbers The objective of break-even calculations is to determine how many units or dollars worth of a product need to be sold to cover all costs. The objective of target volume calculations is to determine how many units or dollars worth of a product need to be sold not just to cover costs, but to achieve a certain profit objective as well. Continue for a few sample problems... Summarizing Target Profit and Target Volume...

7. C ONTRIBUTION : S AMPLE P ROBLEMS 7 Target Profit: Sample Problems MBTN | Management by the Numbers Question 1: Swiss entrepreneur Herr Zeitgeist buys watch faces from Italy for 5 Euros, buys watch mechanisms for 15 Euros from Spain, and hires assembly in Portugal for 10 Euros per watch. His only other expense is 100,000 Euros he pays the Zuricher Flughafen ad agency to place ads in in- flight magazines to build the Zeitgeist brand. Herr Zeitgeist sells each watch for 50 Euros to airport duty-free shops, that earn an 80% margin on the sale of each watch. If his profit objective is 40,000 Euros, how many watches must he sell? Answer: We know that Target Volume (units) = (FC + Profit Objective) / (SP - VC) From the problem, Variable Costs = 5 + 15 + 10 = 30 Euros per watch Therefore, substituting in our values: Target Volume (units) = (100,000 + 40,000) / (50 – 30) = 140,000 / 20 = 7,000 watches

8. C ONTRIBUTION : S AMPLE P ROBLEMS 8 Target Profit: Sample Problems MBTN | Management by the Numbers Question 2: Ms. Sprinkle runs a donut shop called “It’s in the hole!” She calculated the cost of the ingredients to be $0.05 per donut. Her rent and other overhead expenses total $2,000 per month. She sells her donuts for $0.25 each. If she sold 100,000 donuts in the last month, what were her profits? Answer: We know that Target Volume (units) = (FC + Profit) / (SP - VC) Therefore, substituting in our values: 100,000 units = ($2,000 + Profit) / (0.25 – 0.05) 100,000 units = ($2,000 + Profit) / (0.20) $20,000 = $2000 + Profit Profit = $18,000! That’s a lot of donuts! [Alt. Calculation] Profit = 100,000 * (.25 -.05) - $2,000 = $18,000

9. C ONTRIBUTION : S AMPLE P ROBLEMS 9 Target Profit: Sample Problems MBTN | Management by the Numbers Question 3: Now Ms. Sprinkle wants to know her profits for a particular level of sales revenues. As before, she calculated the cost of the ingredients to be $0.05 per donut. Her rent and other overhead expenses total $2,000 per month. She sells her donuts for $0.25 each. If she sold $10,000 of donuts last month, what were her profits? Answer: We know Target Volume (Revs) = (FC + Profit) / ((SP - VC) / SP) Therefore, substituting in our values: $10,000 = ($2,000 + Profit) / ((0.25 – 0.05) / 0.25) $10,000 = ($2,000 + Profit) / (0.80) $8,000 = $2000 + Profit Profit = $6,000

10. P RICE – V OLUME I NTERACTIONS 10 Price – Volume Interactions MBTN | Management by the Numbers While static relationships like the target volume and target profit equations provide a sound framework for estimating sales targets, price points, and budget allocations, often it is necessary for a manager to test various pieces of these equations in the quest for improving profitability. Price-volume relationships are elusive to pinpoint. Continue for a few examples that illustrate these concepts. But the world is not static...

11. P RICE – V OLUME I NTERACTIONS : E XAMPLES 11 Price – Volume Interaction: Examples MBTN | Management by the Numbers Question 1: Sam moved from Texas to Maine last year and opened a cowboy hat store. The store became quite popular. Sam’s financials for last year were: Year 1 Cowboy Hat Sales:1,000 units Sales Price per hat:$75 Variable Cost per hat:$20 Unit Contribution: $55 Year 1 Total Contribution:$55,000 Customers seemed so happy with the “cowboy look” that Sam wondered whether they would pay more for his hats. If, in Year 2, Sam raised the price of his hats to $100 each, how much could his volume drop before he would generate less contribution than in Year 1?

12. P RICE – V OLUME I NTERACTIONS : E XAMPLES 12 Price – Volume Interaction: Examples MBTN | Management by the Numbers Answer: Sam needs to calculate his Year 2 unit contribution, which is his new selling price [$100] less his variable cost [still $20], or $80. Then he can determine the number of units he needs to sell to meet the same total contribution of $55,000. Year 1 Total Contribution: $55,000 Year 1 Volume: 1,000 Year 2 (New) Unit Contribution:$80 Year 2 (New) Target Volume:688 [$55,000 / $80] Percentage Decrease: 31.2% [(1000 – 688) / (1000)] Therefore, Sam can allow his sales to decline by 31% before his price increase actually hurts his total contribution. The figure can also be obtained by dividing the old unit contribution by the new [$55 / $80 = 0.6875] and subtracting the result from 1 as the percentage increase in contribution is offset by the same percentage decrease in volume. [1 – 0.6875 = 0.3125 = 31.25%]

13. P RICE – V OLUME I NTERACTIONS : E XAMPLES 13 Price – Volume Interaction: Examples MBTN | Management by the Numbers Question 2: Sam’s sister, Lena, upon hearing of her brother’s success, decided to move to Maine to compete against him. She believes that if she sells “cowgirl” hats, she can eventually achieve higher sales than Sam. Lena has the following first year targets: Total Cowgirl Hat Sales:700 units Variable Cost per hat:$20 Total Contribution Goal:110% of Sam’s Year 1 (110% of $55,000) In addition, Lena is spending $5,000 on billboard advertising, so the locals will know that “authentic” Texas headwear isn’t for guys only. Given these costs and goals, what must Lena charge for her cowgirl hats?

14. P RICE – V OLUME I NTERACTIONS : E XAMPLES 14 Price – Volume Interaction: Examples MBTN | Management by the Numbers Answer: Lena must cover her contribution goal and her billboard advertising expense with her cowgirl hat sales: Contribution goal: $60,500 [$55,000 x 110%] Billboard advertising:$5,000 [Fixed Cost] Total Goal: $65,500 Lena can divide this total goal by the number of hats she hopes to sell to get a contribution per hat, to which she will add her variable costs per hat to arrive at a necessary sales price: Contribution per hat:$93.57 ($65,500 / 700 hats) Variable Costs: $20 Necessary Sales Price:$113.57 (contribution per hat + VC per hat) Note: One can also obtain the sales price by adding the total goal and the total variable costs, then dividing by the number of units. ($65,500 + $14,000) / 700 = $113.57

15. P RICE – V OLUME I NTERACTIONS : E XAMPLES 15 Price – Volume Interaction: Examples MBTN | Management by the Numbers Question 3: Lena managed to meet her goals for the previous year. For Year 2, she believes an advertising blitz will allow her to drastically increase her sales as ‘cowgirl’ hats become even more fashionable. She also plans on doubling her total contribution and slightly cutting her sales price. Lena’ year 2 projections are: Total advertising: $20,000 Cowgirl hat unit sales price:$100 Total contribution goal: $100,000 What percentage increase in sales must Lena achieve to meet her Year 2 goals?

16. P RICE – V OLUME I NTERACTIONS : E XAMPLES 16 Price – Volume Interaction: Examples MBTN | Management by the Numbers Answer: Lena needs to cover her increased advertising expense and her higher contribution goal with a lower unit contribution margin: Total Advertising: $20,000 Total Contribution Goal: $100,000 Total FC + Contribution Goal:$120,000 Unit Contribution: $80 (SP of $100 – VC of $20) Necessary Sales: 1,500 ($120,000 / $80) Percentage Increase: 114% [((1,500 – 700) / 700) x 100] Lena would need her total sales to more than double to meet her goals! Perhaps Lena’s projections are too aggressive? It boils down to whether the increase in advertising and decrease in selling price will more than double demand and estimating the impact of these factors is beyond the scope of this module!

17. Marketing Metrics by Farris, Bendle, Pfeifer and Reibstein, 2 nd edition, pages 65-108 (Chapter 3). - And - Pricing I – Linear Demand (advanced MBTN module). This module introduces one approach to estimating the relationship between price and volume. B REAKEVEN – F URTHER R EFERENCE 17 Profit Dynamics - Further Reference MBTN | Management by the Numbers