break even analysis

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Break-Even Analysis

Greg Hiatt

May 5, 2002



Defined:

Break-even analysis examines thecost tradeoffs associated with

demand volume.



Overview:Break-Even Analysis

• Benefits

• Defining Page

• Getting Started• Break-even Analysis

– Break-even point

– Comparing variables• Algebraic Approach

• Graphical Approach



Benefits and Uses:

• The evaluation to determinenecessary levels of service or

production to avoid loss.

• Comparing different variables todetermine best case scenario.



Defining Page:

• USP = Unit Selling Price

• UVC = Unit Variable costs

• FC = Fixed Costs

• Q = Quantity of output unitssold (and manufactured)



Defining Page:Cont.

• OI = Operating Income

• TR = Total Revenue

• TC = Total Cost

• USP = Unit Selling Price



Getting Started:

• Determination of which equationmethod to use:

– Basic equation – Contribution margin equation

– Graphical display



Break-even analysis:Break-even point

• John sells a product for $10 and itcost $5 to produce (UVC) and hasfixed cost (FC) of $25,000 per year

• How much will he need to sell tobreak-even?

• How much will he need to sell tomake $1000?



Algebraic approach:Basic equation

Revenues – Variable cost – Fixed cost = OI

(USP x Q) – (UVC x Q) – FC = OI

$10Q - $5Q –

$25,000 = $ 0.00$5Q = $25,000

Q = 5,000

What quantity demand will earn $1,000?$10Q - $5Q - $25,000 = $ 1,000

$5Q = $26,000

Q = 5,200



Algebraic approach:Contribution Margin equation

(USP – UVC) x Q = FC + OI

Q = FC + OI

UMCQ = $25,000 + 0

$5

Q = 5,000

What quantity needs sold to make $1,000?

Q = $25,000 + $1,000

$5

Q = 5,200



Graphical analysis:

Dollars

70,000

60,000

50,000

40,000

30,000

20,000

10,000 Break-even point

0

1000 2000 3000 4000 5000 6000

Quantity

Total RevenueLine

Total Cost

Line



Graphical analysis:Cont.

Dollars

70,000

60,000

50,000

40,000

30,000

20,000

10,000 Break-even point

0

1000 2000 3000 4000 5000 6000

Quantity

Total Cost

Line

Total RevenueLine



Scenario 1:Break-even Analysis Simplified

• When total revenue is equal to totalcost the process is at the break-even

point.

TC = TR



Break-even Analysis:Comparing different variables

• Company XYZ has to choosebetween two machines to purchase.The selling price is $10 per unit.

• Machine A: annual cost of $3000 withper unit cost (VC) of $5.

• Machine B: annual cost of $8000 withper unit cost (VC) of $2.



Break-even analysis:Comparative analysis Part 1

• Determine break-even point for Machine A and Machine B.

• Where: V = FC

SP - VC



Break-even analysis:Part 1, Cont.

Machine A:

v = $3,000

$10 - $5= 600 units

Machine B:

v = $8,000$10 - $2

= 1000 units



Part 1: Comparison

• Compare the two results todetermine minimum quantity sold.

• Part 1 shows:

– 600 units are the minimum.

–

Demand of 600 you would chooseMachine A.



Part 2: Comparison

Finding point of indifference betweenMachine A and Machine B will givethe quantity demand required toselect Machine B over Machine A.

Machine A = Machine B

FC + VC = FC + VC$3,000 + $5 Q = $8,000 + $2Q

$3Q = $5,000

Q = 1667



Part 2: ComparisonCont.

• Knowing the point of indifference wewill choose:

• Machine A when quantity demandedis between 600 and 1667.

• Machine B when quantity demandedexceeds 1667.



Part 2: ComparisonGraphically displayed

Dollars

21,000

18,000

15,000

12,000

9,000

6,000

3,000

0

500 1000 1500 2000 2500 3000

Quantity

Machine A

Machine B



Part 2: ComparisonGraphically displayed Cont.

Dollars

21,000

18,000

15,000

12,000

9,000

6,000

3,000 Point of indifference

0

500 1000 1500 2000 2500 3000

Quantity

Machine A

Machine B



Exercise 1:

• Company ABC sell widgets for $30 aunit.

• Their fixed cost is$100,000

•

Their variable cost is $10 per unit.

• What is the break-even point usingthe basic algebraic approach?



Exercise 1:Answer

Revenues – Variable cost - Fixed cost = OI

(USP x Q) –

(UVC x Q) –

FC = OI$30Q - $10Q – $100,00 = $ 0.00

$20Q = $100,000

Q = 5,000



Exercise 2:

• Company DEF has a choice of twomachines to purchase. They bothmake the same product which sells

for $10.• Machine A has FC of $5,000 and a per

unit cost of $5.

•

Machine B has FC of $15,000 and aper unit cost of $1.

• Under what conditions would you

select Machine A?



Exercise 2:Answer

Step 1: Break-even analysis on bothoptions.

Machine A:

v = $5,000

$10 - $5

= 1000 units

Machine B:v = $15,000

$10 - $1

= 1667 units



Exercise 2:Answer Cont.

Machine A = Machine B

FC + VC = FC + VC

$5,000 + $5 Q = $15,000 + $1Q$4Q = $10,000

Q = 2500

• Machine A should be purchased if expected demand is between 1000and 2500 units per year.



Summary:

• Break-even analysis can be aneffective tool in determining the cost

effectiveness of a product.

• Required quantities to avoid loss.

• Use as a comparison tool for makinga decision.



Bibliography:

Russel, Roberta S., and Bernard W.Taylor III. Operations Management.

Upper Saddle River, NJ: Pentice-Hall,2000.

Horngren, Charles T., George Foster,and Srikant M. Datar. Cost Account.

10th ed. Upper Saddle River, NJ:Pentice-Hall, 2000.

break even analysis

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