1. 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

2. 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

3. Graphic Solution MethodTR
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

4. 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)

5. 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

6. 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

7. 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)

8. 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 - $5)/($ $0.10)
= 300/.30 = 1,000 trees

9. Example 3: Optimal planting density
No. Trees per 5 years
Yield in rotation
Total
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

10. Example 3: Continued Fixed costs per acre:
Land $300
Site prep
Annual
Set-up
Total
Variable costs per 100 seedlings
Seedlings $ 5
Planting
Total
TC = x (# trees per A/100)

11. Example 3: Continued
See Excel spreadsheet