Break-Even Analysis

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# Break-Even Analysis - PowerPoint PPT Presentation

Break-Even Analysis. Study of interrelationships among a firm’s sales, costs, and operating profit at various levels of output Break-even point is the Q where TR = TC ( Q 1 to Q 2 on graph). \$’s. TC. TR. Profit. Q. Q 1. Q 2. Linear Break-Even Analysis.

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## Break-Even Analysis

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Presentation Transcript
Break-Even Analysis
• Study of interrelationships among a firm’s sales, costs, and operating profit at various levels of output
• Break-even point is the Q where TR = TC (Q1 to Q2 on graph)

\$’s

TC

TR

Profit

Q

Q1

Q2

Linear Break-Even Analysis
• Over small enough range of output levels TR and TC may be linear, assuming
• Constant selling price (MR)
• Constant marginal cost (MC)
• Firm produces only one product
• No time lags between investment and resulting revenue stream
Graphic Solution Method

TR

• Draw a line through origin with a slope of P (product price) to represent TR function
• Draw a line that intersects vertical axis at level of fixed cost and has a slope of MC
• Intersection of TC and TR is break-even point

\$’s

TC

MC

1 unit Q

FC

P

Q

1 unit Q

Break-even point

Algebraic Solution
• Equate total revenue and total cost functions and solve for Q

TR = P x Q

TC = FC + (VC x Q)

TR = TC

P x QB = FC + VC x QB

(P x QB) – (VC x QB) = FC

QB (P – VC) = FC

QB = FC/(P – VC), or in terms of total dollar sales,

PQ = (FxP)/(P-VC) = ((FxP)/P)/((P-VC)/P) = F/((P/P) – (VC/P))

= F/(1-VC/P)

Related Concepts
• Profit contribution = P – VC
• The amount per unit of sale contributed to fixed costs and profit
• Target volume = (FC + Profit)/(P – VC)
• Output at which a targeted total profit would be achieved
Example 1 – how many Christmas trees need to be sold
• Wholesale price per tree is \$8.00
• Fixed cost is \$30,000
• Variable cost per tree is \$5.00
• Solution

Q(break-even) = F/(P – VC) = \$30,000/(\$8 - \$5)

= \$30,000/\$3 = 10,000 trees

Example 2 – two production methods to accomplish same task
• Method I : TC1 = FC1 + VC1 x Q
• Method II : TC2 = FC2 + VC2 x Q
• At break-even point:

FC1 + (VC1 x Q) = FC2 + (VC2 x Q)

(VC1 x Q) – (VC2 x Q) = FC2 – FC1

Q x (VC1 – VC2) = FC2 – FC1

Q = (FC2 – FC1)/(VC1 – VC2)

• Bowsaw
• Fixed cost is \$5.00
• Variable cost is \$0.40 per
• Chainsaw
• Fixed cost is \$305
• Variable cost is \$0.10 per tree
• Solution

Q(break-even) = (\$305 - \$5)/(\$0.40 - \$0.10)

= 300/.30 = 1,000 trees

Fixed costs per acre:

Land . . . . . . . \$300

Site prep . . . . 100

Annual . . . . 60

Set-up . . . . . 5

Total . . . . 465

Variable costs per 100 seedlings

Seedlings . . . . \$ 5

Planting . . . . 20

Total . . . . 25

Example 3: Continued

TC = 465 + 25 x (# trees per A/100)

Example 3: Continued