Contribution BreakEven

1
Contribution Break-Even
Fixed Costs Variable Costs
2
Fixed- Variable-Cost Formulas

• Fixed Costs Total Costs Variable Costs
• Variable Costs Total Costs Fixed Costs
• Total Costs Fixed Costs Variable Costs
• Total Variable Costs Unit variable costs
  Units Sold
• Unit Variable Costs Total Variable Costs /
  Units Sold
• Total Revenue Unit Selling Price Units Sold
• Average Costs Total Costs / Units Sold
• Profits Total Revenues Total Cost

3
Fixed Costs

• Are the costs of production that stay the same
• Examples rent for facilities, management
  salaries, interest on loans.
• Dont change with volume sold (up to some limit).
• Dont change regardless of whether you produce a
  lot, a little bit, or even if you produce zero.

Source University of South Carolina, Arnold
School of Public Health, Dept. of Health Services
Policy and Management, Economics Interactive
Tutorials
4
Variable Costs

• Vary as you produce more or less.
• Examples construction materials, packaging,
  sales commissions
• Are unit costs that remain more or less constant
  on a unit basis
• In other words, total variable costs increase at
  a constant rate with increases in units produced
  and sold
• Producing more adds to Total Variable Costs.
  Producing less reduces them.

Source University of South Carolina, Arnold
School of Public Health, Dept. of Health Services
Policy and Management, Economics Interactive
Tutorials
5
Total Costs

• What it costs to operate at some particular rate
  of output.
• Total Costs Fixed Costs Variable Costs

Source University of South Carolina, Arnold
School of Public Health, Dept. of Health Services
Policy and Management, Economics Interactive
Tutorials
6
Truth or Consequences Fixed or Variable?
Fixed 1____ 2____ 3____ 4____ 5____ 6____ 7
____ 8____
Variable 1____ 2____ 3____ 4____ 5____ 6____
7____ 8____
Do the costs vary as you produce more/less?

• Rent for office space
• Packaging Material
• Sales Force Base Salaries
• Sales Force Commission
• TV Advertisement
• Shipping charges
• CEOs limo lease payment
• Warranty expenses

Click to see each answer
7
Total vs. Fixed vs. Variable

• Number of TVs   Total Cost       0          
  1000       1           4500       2          
  7500       3         10000       4        
  12000       5         14500       6        
  17500       7         21000       8        
  25000       9         30000

Fixed Cost  1000
Fixed Cost  1000  1000  1000  1000 
1000  1000  1000  1000  1000  1000
How much is the fixed cost?
Source University of South Carolina, Arnold
School of Public Health, Dept. of Health Services
Policy and Management, Economics Interactive
Tutorials
8
Total vs. Fixed vs. Variable
Variable Cost   0   3500   6500   9000  
11000   13500   16500   20000   24000   29000

• Number of TVs   Total Cost       0          
  1000       1           4500       2          
  7500       3         10000       4        
  12000       5         14500       6        
  17500       7         21000       8        
  25000       9         30000

How much is the variable cost?
Source University of South Carolina, Arnold
School of Public Health, Dept. of Health Services
Policy and Management, Economics Interactive
Tutorials
9
Distinguish variable from fixed costs to see how
total costs will increase with units sold.
Total Revenues
Total Fixed Costs Total Variable Costs Total
Costs
Total Costs
Total Variable Costs (change at a constant rate)
Total costs ()
Total Fixed Costs (dont change with units sold)
0
Units
Click to continue at each pause...
Variable costs increase with unit volume
(production and sales) Fixed costs dont so,
over the short-term, fixed costs may be sunk
costs.
And of course Total Revenues Total Costs
Profits (losses)
Def Sunk Costs
10
Sunk Costs

• Sunk costs are investment costs incurred before a
  certain activity takes place which cannot be
  recovered by the possible sale of the asset they
  produced.

Source Economics Web Institute
Return
11
Variable Costs, Average Costs
Units Sold 1 10 100 1,000
Fixed Costs 500 500 500 500
Variable costs Packaging 2 20 200
2,000 Material 3 30 300 3,000
Total Costs 505 550
1,000 5,500
Average Costs 505 55 10
5.50
Unit Variable Cost 5 5 5
5
Average Costs Total Costs / Units Sold Total
costs Fixed Costs (unit variable costs
units sold)
In this example, as the number of units sold
increases, fixed costs stay fixed at 500, unit
variable costs remain constant at 5, total
variable costs increase with each additional unit
sold, and the average cost per unit decreases as
more units are sold.
12
A Digression for those Remembering Economics 101
Marginal Costs and Variable Costs

• Almost the same concept marginal costs refer to
  what it costs to produce an additional unit
  variable cost analysis usually assumes constant
  marginal cost.
• Over a wide range of output, the unit variable
  costs may not change (as in previous slides
  example). Therefore the marginal costs of
  producing an additional unit and the variable
  costs will be the same.
• Over some range, variable costs might change
  (discounts from suppliers for a larger order of
  packaging materials, for example), but still
  would not be fixed costs.

13
Marginal Costs
Marginal cost is the difference between one rate
of output and another.
You may take the difference between the total
costs or the variable costs. The two ways result
in the same answer.
Marginal Cost   NA   3500   3000
  2500   2000
Variable Cost   0  3500  6500 
9000 11000

• of Total
• TVs    Cost  0          1000
  1          4500  2          7500  3        
  10000  4         12000  

Source University of South Carolina, Arnold
School of Public Health, Dept. of Health Services
Policy and Management, Economics Interactive
Tutorials
14
Marginal Costs
The difference between one rate of output and
another.
In other words

• The marginal cost of changing from one rate of
  output to another is how much total cost
  increases when the output rate goes up.
• When the output rate changes, the fixed cost
  doesn't change. That's why it's called "fixed."
  The variable cost is what changes, so the
  difference in total cost is just the difference
  in the variable cost.
• When there are only fixed costs, marginal costs
  will be zero, and any increase of production
  does not change costs.
• If there are only proportionally-growing variable
  costs, marginal costs will be equal to variable
  costs.

Source University of South Carolina, Arnold
School of Public Health, Dept. of Health Services
Policy and Management, Economics Interactive
Tutorials
15
Marginal Costs
The difference between one rate of output and
another.
Here's the table with all the variable and
marginal costs
Source University of South Carolina, Arnold
School of Public Health, Dept. of Health Services
Policy and Management, Economics Interactive
Tutorials
16
Marginal Costs
Here's the cost data in a graph
? Total Cost ? Fixed Cost ? Variable Cost ?
Marginal Cost
TVs per Year
Source University of South Carolina, Arnold
School of Public Health, Dept. of Health Services
Policy and Management, Economics Interactive
Tutorials
17
Marginal Costs

• Total cost and variable cost are cumulative.
  That's why they go up and up.
• Fixed cost is not cumulative because it's fixed
  at 1000, regardless of the output rate.
• Variable cost parallels total cost, always below
  it by 1000.

• Marginal cost on this graph is the difference in
  cost between the given output rate and the next
  lower one. Marginal cost dips for the first few
  TVs, indicating increasing returns to scale.
  ("Scale" means size, which here means output
  rate.) After the fourth TV, diminishing returns
  to scale set in, and marginal cost per added TV
  rises. The total cost curve bends down a bit for
  output rates from 0 to 4, because the marginal
  cost is falling. For output rates from 4 to 9,
  marginal cost is increasing, so the total cost
  curve bends up a bit.

Supplemental descriptions and information
regarding Marginal Costs available at
http//www.amosweb.com/cgi-bin/wpd_prv.pl?fcddsp
keymarginalcost
Source University of South Carolina, Arnold
School of Public Health, Dept. of Health Services
Policy and Management, Economics Interactive
Tutorials
18
For Tests 2 and 3

• Test 2 will include the information in this
  presentation up to this slide, i.e. Fixed Costs,
  Variable Costs, Unit Variable Costs, Total
  Variable Costs, Total Costs, Marginal Costs, and
  Profits. But the test will not include the
  information on the following slides.
• Test 3 will include the information on the
  following slides in the remainder of this
  presentation, i.e. Contribution and Break-Even

19
Decisions That Might Be Affected By Unit
Contribution

• Will our unit prices cover unit variable costs?
• Target unit volumes will the additional
  contribution cover our fixed costs and make a
  profit?
• We want to sell 10,000 units. Will the
  contribution cover our fixed costs?
• How much can we afford to pay marketing to sell
  an additional unit?
• If an advertisement costs 1,000, how many units
  will we need to sell to make it worthwhile?

20
Formulas for Contribution
Unit Contribution Selling Price per unit
Variable Costs per unit Unit Contribution Total
Contribution/Units Sold Total Contribution
Total Revenues Total Variable Costs Total
Contribution Unit Contribution Units
Sold Total Variable Costs Unit Variable Costs
Units Sold Total Revenues Selling Price per
unit Units Sold
Formulas for Break-Even
Unit Break-even Fixed Costs / Unit Contribution
Unit Break-even Fixed Costs / (Selling Price
Variable Cost per unit) Break-even Fixed
Costs / ((Selling Price unit Variable
Cost)/Selling Price) Break-even Fixed Costs
/ (Unit Contribution / Selling Price)
Break-even Unit Break-even Selling Price
21
Contribution
Total Contribution Total Revenues - Total
Variable Costs
Total Revenues
Total Contribution
Net Income
Total variable costs and revenues ()
Total Variable Costs
Fixed costs dont figure in when
calculating Contribution
0
Units
Click to continue at each pause...
Unit Contribution Selling Price per unit
Variable Costs per unit Think for a moment about
why this quantity might be meaningful to a
company.
Unit Contribution Selling Price per unit
Variable Costs per unit This is significant
because it measures a net income of funds to a
company as additional units are sold.
22
Unit Contribution Examples
Unit Contribution Selling Price per unit
Variable Costs per unit Unit Contribution Total
Contribution/Units Sold Total Contribution
Total Revenues Total Variable Costs Total
Contribution Unit Contribution Units
Sold Total Variable Costs Unit Variable Costs
Units Sold Total Revenues Selling Price per
unit Units Sold
Unit Contribution Selling Price per unit
Variable Costs per unit
If a firm receives 12 revenue from each unit it
sells, and pays 5 per unit in variable costs,
then what is the contribution of each unit?
(click for answer)
Unit Contribution SP per unit VC per
unit Unit Contribution 12 - 5 Unit
Contribution 7
23
Unit Contribution Examples
Unit Contribution Selling Price per unit
Variable Costs per unit Unit Contribution Total
Contribution/Units Sold Total Contribution
Total Revenues Total Variable Costs Total
Contribution Unit Contribution Units
Sold Total Variable Costs Unit Variable Costs
Units Sold Total Revenues Selling Price per
unit Units Sold
Unit Contribution Selling Price per unit
Variable Costs per unit
If a firm realizes 50 in total contribution by
selling 10 units of a product at a selling price
of 20, what is the variable cost per unit?
(click for answer)
Total Contribution Unit Contribution Units
Sold 50 Unit Contribution 10 Unit
Contribution 5 Unit Contribution Selling
Price per unit Variable Cost per unit 5 20
- Unit Variable Cost Unit Variable Cost 20 -
5 Unit Variable Cost 15
Or 200 - 50 150 150/10 15
Unit Var. Costs
24
Unit Contribution Examples
Unit Contribution Selling Price per unit
Variable Costs per unit Unit Contribution Total
Contribution/Units Sold Total Contribution
Total Revenues Total Variable Costs Total
Contribution Unit Contribution Units
Sold Total Variable Costs Unit Variable Costs
Units Sold Total Revenues Selling Price per
unit Units Sold
Unit Contribution Selling Price per unit
Variable Costs per unit
If a firm receives 100 revenue from selling 5
units of a product, and pays 25 in total
variable costs, then what is the contribution of
each unit? (click for answer)
Total Revenues Selling Price per unit Units
Sold 100 SP 5 Selling Price 20 Total
Variable Costs Unit Variable Costs Units
Sold 25 Unit Variable Costs 5 Unit Variable
Costs 5 Unit Contribution SP per unit VC
per unit Unit Contribution 20 - 5 Unit
Contribution 15
Or 100 - 25 75 75/5 15
25
The Break-even Point

• Definition the volume of sales needed to at
  least cover all your costs.
• Break-even means zero profit, but not a loss.

• Once you know what your variable costs are, as
  well as your overall fixed costs for the
  business, you can determine your breakeven point.
• You can also compute the new breakeven point that
  you'd need to meet if you decided to increase
  your fixed costs (for example, if you undertook a
  major expansion project or bought some new office
  equipment).

Source Business Owners Toolkit
26
Break-even Formulas
Unit Break-even Fixed Costs / Unit Contribution
Unit Break-even Fixed Costs / (Selling Price
Variable Cost per unit) Break-even Fixed
Costs / ((Selling Price unit Variable
Cost)/Selling Price) Break-even Fixed Costs
/ (Unit Contribution / Selling Price) Notice
that multiplying the first formula by the selling
price yields the second formula. Thus Unit
Break-even Selling Price Break-even
27
The Break-even Point
Total Revenues
Total Fixed Costs Total Variable Costs Total
Costs
Total Costs
Total Variable Costs (change at a constant rate)
Total costs ()
Total Fixed Costs (dont change with units sold)
0
Units
Click to continue at each pause...
The Break-even Point is where Total Costs
Total Revenues
28
Two Types of Break-even

• Unit break-even how many unit sales have to be
  made to cover fixed costs?
• Dollar break-even what level of dollar sales
  are required to break even?

Dollar Break-even Break-even in units Unit
Price Break-even in Units Dollar Break-even /
Unit Price
29
A Few Examples
BE (units) FC / (SP-VC) BE () FC / ((SP -
VC)/SP)
A
Mickeys Mousetraps wants to know how many of its
Magic Mouse Trappers it needs to sell in order
to break-even on costs. The product sells for
20, it costs 5 per unit to make, and the
companys fixed costs are 30,000.
BE (units) FC / (SP VC) BE (units) 30,000
/ (20 - 5) 2000 mousetraps
30
A Few Examples
BE (units) FC / (SP-VC) BE () FC / ((SP -
VC)/SP)
A
Mickeys Mousetraps wants to know how many
dollars worth of its Deluxe Mighty Mouse
Trappers it needs to sell in order to break-even
on costs. The product sells for 40, it costs
10 per unit to make, and the companys fixed
costs are 30,000.
BE () FC / ((SP VC)/SP) BE () 30,000 /
((40 - 10)/40) (30,000 / 0.75) 40,000
31
Sample Problem
BE (units) FC / (SP-VC) BE () FC / ((SP -
VC)/SP)
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, earning the retailer an
80 margin. How many watches must he sell to
break-even?
Click for answer
The formula for break-even in units is BE
(units) FC / (SP-VC) By reading the information
provided, we see that fixed costs are 100,000
Euros, and variable costs are 51510 30 Euros
per watch. BE (units) 100,000 / (50 30)
100,000 / 20 5,000 watches