Break-Even Method of Investment Analysis no. 3.759

F A R M & R A N C H S E R I E S
ECONOMICS
Break-Even Method of Investment Analysis no. 3.759
by P.H. Gutierrez and N.L. Dalsted 1 (7/08)
Break-even analysis
is a useful tool to study the
relationship between fixed costs,
Quick Facts...
variable costs and returns. A
break-even point defines when
an investment will generate
A break-even point defines when
a positive return and can be
an investment will generate a
determined graphically or with
positive return.
simple mathematics. Break-even
analysis computes the volume
Fixed costs are not directly
of production at a given price
related to the level of production.
necessary to cover all costs.
Break-even price analysis computes Figure 1: Graph form of break-even analysis.
Variable costs change in direct
the price necessary at a given level of production to cover all costs. To explain
relation to vol ume of output.
how break-even analysis works, it is necessary to define the cost items.
Fixed costs, incurred after the decision to enter into a business activity is
Total fixed costs do not change
made, are not directly related to the level of production. Fixed costs include, but
as the level of produc tion
are not limited to, depreciation on equipment, interest costs, taxes and general
increases.
overhead expenses. Total fixed costs are the sum of the fixed costs.
Variable costs change in direct relation to volume of output. They may
include cost of goods sold or production expenses such as labor and power
costs, feed, fuel, veterinary, irrigation and other expenses directly related to the
production of a com modity or investment in a capital asset. Total variable costs
(TVC) are the sum of the variable costs for the specified level of production or
output. Average vari able costs are the variable costs per unit of output or of TVC
divided by units of output.
Total fixed costs are shown in Figure 1 by the broken horizontal line.
Total fixed costs do not change as the level of production increases. Total variable
costs of production are indicated by the broken line sloping upward, which
illustrates that total variable costs increase directly as production increases.
The total cost line is the sum of the total fixed costs and total variable
costs. The total cost line paral lels the total variable cost line, but it begins at the
level of the total fixed cost line.
The total income line is the gross value of the output. This is shown
as a dotted line, starting at the lower left of the graph and slanting upward. At
any point, the total income line is equivalent to the num ber of units produced
multiplied by the price per unit.
The key point (break-even point) is the intersec tion of the total cost line
 Colorado State University Extension. 9/92.
Reviewed 7/08.
and the total income line (Point P). A vertical line down from this point shows the
www.ext.colostate.edu
level of production necessary to cover all costs. Production greater than this level
generates positive revenue; losses are incurred at lower levels of produc tion.

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Mathematical Explanation
The graphic method of analysis helps the reader understand the concept
of the break-even point. How ever, graphing the cost and income lines is
laborious. The break-even point is found faster and more accu rately with the
following formula:

B-E = F / (S - V)
where:

B-E = break-even point (units of production),

F = total fixed costs,

V = variable costs per unit of production,

S = savings or additional returns per unit of pro duction, and

The mathematical approach is best presented using examples.
Example 1
A farmer wants to buy a new com bine rather than hire a custom
harvester. The total fixed costs for the desired com bine are $21,270 per year. The
variable costs (not counting the operator’s labor) are $8.75 per hour. The farmer
can harvest 5 acres per hour. The custom harvester charges $16.00 per acre. How
many acres must be harvested per year to break-even?
Fixed costs (F) = $21,270
Savings (S) = $16/A
Variable costs (V) = $8.75/hr / 5 A/hr = $1.75/A
B-E = $21,270 / ($16/A - $1.75/A) = $21,270 / $14.25/A = 1,493 Acres
Example 2
Break-even analysis can be easily extend ed to consid er other changes.
If the farm operator can save two addition al bushels of wheat per acre more
than the custom harvester, what would be the break-even point if wheat is worth
$4/bushel?
Additional income = $4/bu * 2 bu/A = $8/A
B-E = $21,270 / ($16/A + $8/A - $1.75/A) = $21,270 / $22.25/A = 956
Acres
Example 3
A farmer raising 1,200 acres of wheat per year considers purchasing a
combine. How much additional return (to land, capital labor, management and
risk) would result?
Additional return = (savings or additional income) - (fixed costs +
variable costs)
Additional profit = [ $16/A + ($4/bu * 2 bu/A) ] x 1200 A = $21,270 + [
($8.75/hr / 5 A/hr) x 1200 A] = $28,800-$23,370 = $5,430
Thus, the farmer would generate another $5,430 in additional return by
purchasing the combine. A farmer harvesting only 900 acres would probably
choose not to buy the combine because the acreage is below the break-even point
of 956 acres. The farmer may want to evaluate the purchase of a smaller or used
combine.
Additional Situations
Two additional situations are presented as follows:
Problem 1. If the fixed costs for the combine are $12,000 per year, no
additional yield is expected, vari able costs are $7 per hour and the farmer can
combine 4 acres per hour, what is the new break-even point?

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Problem 2. If 900 acres are harvested, what is the effect on the farmer’s
profits?
Solutions

Fixed costs = $12,000

Savings = $16/A

Variable costs = $7/hr / 4 A/hr = $1.75/A
Problem 1:

B-E = $12,000 / ($16/A - $1.75/A) = $12,000 / $14.25/A = 842

Acres
Problem 2:

Additional profit = ($16/A x 900 A) - [$12,000 + ($7/hr / 4 A/hr

x 900 A = $14,000 - $13,575 = $825 increase
Appraisal of Break-Even Analysis
The main advantage of break-even analysis is that it points out the
relationship between cost, production volume and returns. It can be extended to
show how changes in fixed cost-variable cost relationships, in commodity prices,
or in revenues, will affect profit levels and break-even points. Limitations of
break-even analysis include:
• It is best suited to the analysis of one product at a time;
• It may be difficult to classify a cost as all variable or all fixed; and
• There may be a tendency to continue to use a break-even analysis after
the cost and income functions have changed.
Break-even analysis is most useful when used with partial budgeting
or capital budgeting techniques. The major benefit to using break-even analysis
is that it indicates the lowest amount of business activity neces sary to prevent
losses.
1 P.H. Gutierrez, former Colorado State
University Extension farm/ranch management
economist and associate professor; N.L.
Colorado State University, U.S. Department of Agriculture, and Colorado counties cooperating.
Dalsted, Extension farm/ranch management
CSU Extension programs are available to all without discrimination. No endorsement of products
specialist and professor; agricultural and
mentioned is intended nor is criticism implied of products not mentioned.
resource economics.

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