• 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
Q
1
Profit
Q
2
TC
TR
Q

• 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

• 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
TR
MC
1 unit Q
FC
P
1 unit Q
Break-even point
TC
Q

• Equate total revenue and total cost functions and solve for Q
TR = P x Q
TC = FC + (VC x Q)
TR = TC
P x Q
B
= FC + VC x Q
B
(P x Q
B
) – (VC x Q
B
) = FC
Q
B
(P – VC) = FC
Q
B
= 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)

• 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

• 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

• Method I : TC
1
• Method II : TC
2
= FC
= FC
• At break-even point:
1
2
+ VC
1
+ VC
2 x Q x Q
FC
1
+ (VC
1 x Q) = FC
2
+ (VC
2 x Q)
(VC
1 x Q) – (VC
2 x Q) = FC
2
– FC
1
Q x (VC
1
– VC
2
) = FC
2
– FC
1
Q = (FC
2
– FC
1
)/(VC
1
– VC
2
)

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

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