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MER 439 - Design of Thermal Fluid Systems

BreakEven Analysis

Professor AndersonSpring 2012

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Breakeven Analysis

Break even analysis is used to determine the volume of products that must be produced to maximize profitability.

Also called Cost-Volume-Profit (CVP) analysis.

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Breakeven Analysis

Fixed Costs - (FC) These are the costs that don’t vary with output. Examples: rent, depreciation, advertising, building maintenance, etc.

Variable Costs - (VC) These are the costs that do vary with output. Examples: direct and indirect labor costs, direct and indirect material costs.

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Breakeven Analysis

Total Cost: TC = VC + FC

Total Revenue (TR) is the unit selling

price multiplied by the quantity sold.

TR= P*Q

P = Price, Q = Quantity Sold

Linear Model - assume TR, VC and FC are linear. To sell more units, the selling price must be reduced.

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Breakeven AnalysisDemand Curve - Shows the relationship between the quantity of unit sold and the selling price.

$0

$200

$400

$600

$800

$1,000

$1,200

0 100 200 300 400 500 600

Quantity Sold per Year

Sel

ling P

rice

per

Unit

, ($

)Demand Curve

Total Revenue Area

Generally:

Q = (b- P)/m

or

P = b - mQ

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Breakeven AnalysisReal Demand Curves:

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Breakeven AnalysisBreakeven Point - the point of intersection between the TR and TC curves.

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Breakeven Analysis ExampleA company produces an electronic timing switch that is used in consumer and commercial products made by several other manufacturing firms. The fixed cost is $73,000 per month and the variable cost is $83 per unit. The selling price per unit is P = $180-0.02Q (where Q = Quantity Sold).Make a TR plot and determine:

(a) Volumes at which breakeven occurs. (range of profitable demand).(b) The optimal volume for this product

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Breakeven Analysis Example

$0

$100

$200

$300

$400

$500

0 1000 2000 3000 4000 5000

Quantity Sold per Month

Cost

an

d R

even

ue

in k

$

TC TRFC VC

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Breakeven Analysis Example

Profit (or Loss) = TR - TC

= (180-0.02Q)Q-(73000+83Q)

= 97Q - 0.02Q2-73000

Set Profit = 0 to find bounds:

Q1 = 932 and Q2 = 3912 units per month

Set d(Profit)/dQ = 0 to find max:

Qmax = 2425 units per month

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Project 4 - Economic AnalysisPerform a break-even analysis to determine the number of units that must be sold per year. The marketing department has provided some information about the expected product demand versus price:

.

Price $1 $2 $3 $4 $5 $6 $7 $8 $9 $10

Sell Quant.

(in 1000) 100 90 80 70 60 50 40 30 20 10

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Project 4 - Economic Analysis

The fixed costs (FC) for this project are expected to be $100,000 per year.

Estimate your design cost: Estimate your raw costs (E). Estimate material cost as 25 cents per cubic inch.

(injection molding) The boiler cost will be 50 cents. Include estimates of any other materials you use. Multiply your raw costs by 200% to account for labor

and overhead to get a variable cost per unit VC = E(2.0)

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Project 4 - Economic Analysis

Prepare a total cost and revenue break-even graph and determine your break even pricing and sales requirements.

Next determine the product price that will maximize profit.

Assuming these sales estimates and prices are good for at least 10 years, estimate the amount of money that we can afford to put into initial R&D costs if we want to realize a 12% rate of return on the project. Prepare a plot of initial R&D budget versus product price for a 12% rate of return.

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Project 4 - Economic AnalysisWe may have an opportunity to take advantage of low labor costs in Elbonia. Child labor laws and environmental compliance issues are non-existent in Elbonia. If we go to Elbobnia, our fixed and raw costs will be half what is quoted above. The labor and overhead cost in Elbonia is also significantly less expensive (VC = E*1.1). Should we pursue this opportunity?