Break-Even Analysis

Break-even Analysis – performed to determine the value of a variable that makes two elements equal.

In economic terms: determining a parameter such that revenue equals cost.

The study parameter might be:• Production Volume

• Percentage of capacity

• Labor rate

• Replacement cost

• Etc.

Break-Even AnalysisCost Function:

Fixed Cost (FC) – that cost which does not vary based on production volume. Includes building, insurance, fixed overhead (e.g. Engineering staff), equipment recovery cost, information systems, etc.

Variable Cost (VC) – that cost which varies as production volume varies. Includes direct labor, materials, warranty, utilities (power consumption), marketing, etc.

Break-Even AnalysisCost Function – cont.:

Total Cost = Fixed Cost + Variable Cost

Cost presented as a function of production volume.

Total Cost Function

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Break-Even AnalysisBreakeven Point

What is the breakeven point in terms of Production volume?

Breakeven Analysis

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Break-Even AnalysisBreakeven Point –cont.

FC = $10,000

VC = $5000(per 1000 units)

Revenue = $8000(per 1000 units)

Let Q = Production Volume (000s)

QBE = Production Volume (000s)

at the Breakeven point

Total Cost = Revenue

$10,000 + $5000*QBE = $8000 *QBE

QBE = 10,000/3000 = 3.333 (000s) = 3333 units

Breakeven Analysis

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Break-Even AnalysisSensitivity Analysis

Impact of reducing or increasing one factor while holding the other constant.

Example:

What is the QBE if VC varies from $4000 to $6000?

Variable Cost Fixed Cost Revenue QBE(1000s of unit)

$4,000 $10,000 $8,000 2.50$4,500 $10,000 $8,000 2.86$5,000 $10,000 $8,000 3.33$5,500 $10,000 $8,000 4.00$6,000 $10,000 $8,000 5.00

Break-Even AnalysisIn-Class Exercise

Your starting salary upon graduation is $50,000 / year.

The state takes 6%, the Feds take 21%, 7.5% Social Security and Medicare takes another 3%.

Using good tax advice, you are able to reduce your total taxes by 20%.

How many months do you work for free (in other words, what is the breakeven point in months between taxes and salary)?

Break-Even AnalysisIn-Class Exercise

Break-Even AnalysisBreakeven analysis between two alternatives:

If demand for the product is 1,000 units a month, which alternative should you choose? 3,000 units a month?

Breakeven Analysis - Between Alternatvies

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Break-Even AnalysisBreakeven analysis between two alternatives:

What is the breakeven point?

FC(1) = $10,000

FC(2) = $15,000

VC(1) = $5000 / (000s units)

VC(2) = $2000 / (000s units)

$10,000 + $5000*QBE = $15,000 + $2000* QBE

$3000 * QBE = $5000

QBE = 1.66 (000s units)

Breakeven Analysis - Between Alternatvies

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Break-Even AnalysisBreakeven analysis AW approach:

Two alternatives exist for a machining process. Alternative 1 has an initial cost of $10,000 and a salvage value of $1000 after 5 years. Alternative 1 also has a variable cost of $1/unit of product produced and an annual maintenance of $1000.

Alternative 2 has an initial cost of $15,000 and a salvage value of $2,000 after 7 years. Alternative 2 also has a variable cost of $0.80/unit of product produced and an annual maint. cost of $1200.

What is the breakeven point in annual production volume? Assume a MARR of 10%.

Break-Even AnalysisBreakeven analysis AW approach:

Let x = annual production volume.

AW1 = -$10,000 (A/P, 10%,5) + $1000(A/F,10%,5) - $1000 – 1.0x

AW1 = -$10,000(.2638) + $1000(.1638) - $1000 -$1.0xAW1 = -$3474.2 - $1.0x

AW2 = -$15,000 (A/P, 10%,7) + $2000(A/F,10%,7) - $1200 – .8x

AW2 = -$15,000(.20541) + $2000(.10541) - $1200 - $.8x

AW2 = -$4070.3 - $.8x

-$3474.2 - $1.0x = -$4070.3 - $.8xx = 2980.5