2. 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 Q2on graph)
TR
TC
Q
$’s
Profit
Q1 Q2
3. 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
4. Graphic Solution Method
• 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
TR
TC
FC
Break-even
point
MC
P
1 unit Q
1 unit Q Q
$’s
5. 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)
6. 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
7. 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
8. 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)
