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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.
• 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
BREAKEVEN REVIEW
Breakeven Review
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
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But What About Profits?
• 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.
TARGET PROFITS
Target Profits
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
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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:
TARGET PROFIT: EXAMPLES
Target Profit: Examples
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.
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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:
TARGET PROFIT: EXAMPLES
Target Profit: Examples
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
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REVIEW
Review
Summarizing Target Profit and Target Volume...
• 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 . . .
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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 inflight 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?
CONTRIBUTION: SAMPLE PROBLEMS
Target Profit: Sample Problems
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
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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:
CONTRIBUTION: SAMPLE PROBLEMS
Target Profit: Sample Problems
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
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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:
CONTRIBUTION: SAMPLE PROBLEMS
Target Profit: Sample Problems
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
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But the world is not static...
• 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.
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PRICE – VOLUME INTERACTIONS
Price – Volume Interactions
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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:
Sales Price per hat:
Variable Cost per hat:
Unit Contribution:
Year 1 Total Contribution:
1,000 units
$75
$20
$55
$55,000
PRICE – VOLUME INTERACTIONS: EXAMPLES
Price – Volume Interaction: Examples
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?
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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:
Year 1 Volume:
Year 2 (New) Unit Contribution:
Year 2 (New) Target Volume:
Percentage Decrease:
$55,000
1,000
$80
688 [$55,000 / $80]
31.2% [(1000 – 688) / (1000)]
PRICE – VOLUME INTERACTIONS: EXAMPLES
Price – Volume Interaction: Examples
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%]
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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:
Variable Cost per hat:
Total Contribution Goal:
700 units
$20
110% of Sam‟s Year 1
(110% of $55,000)
PRICE – VOLUME INTERACTIONS: EXAMPLES
Price – Volume Interaction: Examples
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?
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Answer: Lena must cover her contribution goal and her billboard
advertising expense with her cowgirl hat sales:
Contribution goal:
Billboard advertising:
Total Goal:
$60,500
$5,000
$65,500
[$55,000 x 110%]
[Fixed Cost]
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:
Variable Costs:
Necessary Sales Price:
PRICE – VOLUME INTERACTIONS: EXAMPLES
Price – Volume Interaction: Examples
$93.57 ($65,500 / 700 hats)
$20
$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
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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:
Cowgirl hat unit sales price:
Total contribution goal:
$20,000
$100
$100,000
PRICE – VOLUME INTERACTIONS: EXAMPLES
Price – Volume Interaction: Examples
What percentage increase in sales must Lena
achieve to meet her Year 2 goals?
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Answer: Lena needs to cover her increased advertising expense and her
higher contribution goal with a lower unit contribution margin:
Total Advertising:
Total Contribution Goal:
Total FC + Contribution Goal:
Unit Contribution:
Necessary Sales:
Percentage Increase:
$20,000
$100,000
$120,000
$80
(SP of $100 – VC of $20)
1,500 ($120,000 / $80)
114% [((1,500 – 700) / 700) x 100]
Lena would need her total sales to more than double to meet
her goals!
PRICE – VOLUME INTERACTIONS: EXAMPLES
Price – Volume Interaction: Examples
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!
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Marketing Metrics by Farris, Bendle, Pfeifer and
Reibstein, 2nd 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.
MBTN | Management by the Numbers
BREAKEVEN – FURTHER REFERENCE
Profit Dynamics - Further Reference
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