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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
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
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
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
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
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
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
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)

example 2 continued bowsaw or chainsaw to cut christmas trees
Example 2 continued: bowsaw or chainsaw to cut Christmas trees
  • 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

example 3 continued
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 continued11
Example 3: Continued
  • See Excel spreadsheet