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.

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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 (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)

Example 2 continued: bowsaw or chainsaw to cut Christmas trees 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: Optimal planting density No. Trees per A @ 5 years Yield in cords @ rotation Total Revenue @$24/cord 300 21.3 511 400 23.4 562 500 25.2 605 600 26.7 641 700 28.0 672 800 29.1 698 900 30.1 722

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

Example 3: Continued See Excel spreadsheet