Chapter 8
Breakeven Analysis for Profit
Planning
Breakeven Analysis
• Breakeven analysis (cost-volume-profit
analysis): approach to profit planning that
requires derivation of various relationships
among revenue, fixed costs, and variable
costs in order to determine units of
production or volume of sales dollars at which
firm “breaks even” (where total revenues
equal total of fixed and variable costs)
Assumptions of Breakeven Analysis
1. Costs can be reasonably subdivided into fixed
and variable components.
2. All cost-volume-profit relationships are linear.
3. Sales prices will not change with changes in
volume.
Assumptions of Breakeven Anaylsis
1. Costs can be reasonably subdivided into
fixed and variable components.
– Fixed costs (i.e. depreciation expenses, salaries,
rental expenses, etc.) and variable costs (i.e. cost
of direct labor and materials used) can be easily
identified in most cases.
– Semivariable expenses can be problematic, but
can nonetheless be separated into fixed and
variable components for analysis purposes.
Assumptions of Breakeven Analysis
2. All cost-volume-profit relationships are
linear.
– Assumption holds so long as analysis is confined
to reasonable range of operations.
– If level of operations are doubled, relationship
may be different.
Assumptions of Breakeven Analysis
3. Sales prices will not change with changes in
volume.
– Economic theory states that one would normally
expect price increase to be accompanied by
decrease in sales volume and vice versa.
– Assumption holds so long as analysis is confined
to reasonable range of prices.
Breakeven Applications
• Four major applications:
1.
2.
3.
4.
New product decisions
Pricing decisions
Modernization or automation decisions.
Expansion decisions.
Breakeven Applications
1. New product decisions
– Determine sales volume required for firm (or
individual product) to break even, given expected
sales and expected costs
2. Pricing decisions
– Study the effect of changing price and volume
relationships on total profits
Breakeven Analysis
3. Modernization or automation decisions
– Analyze profit implications of a modernization or
automation program
–
In this case, firm substitutes fixed costs (i.e. capital equipment
costs) for variable costs (i.e. direct labor)
4. Expansion decisions
– Study aggregate effect of general expansion in
production and sales
–
In this case, relationships between total dollar dales for all
products and total dollar costs for all products are examined in
order to indentify potential changes in these relationships
The Breakeven Technique
• Simplified example
– Peter Porter’s Porsche Plant is a small business
that assembles and markets improved racing
suspension for Porsches
• Fixed costs estimate: $1,650
• Variable costs estimate: $350
• Selling price per package:$500
The Breakeven Technique
• At what point will new product break even?
Revenue = Fixed costs + Variable costs
– Requires determining quantity of items to be
produced and sold
– Let X be equal to unknown breakeven quantity
$500X = $1,650 + $350X
– $500X = total revenue produced by selling X items
– $1,650 = total fixed costs
– $350X = total variable costs incurred by producing X items
The Breakeven Technique
• Solve the equation
$500X = $1,650 + $350X
$150X = $1,650
X = 11 units
• Thus, 11 units is the breakeven point for this
product.
• As a computational check, simply substitute X=11 into the
breakeven equation.
The Breakeven Technique
Operating Leverage
• Contribution margin: difference between selling price
and variable cost; represents contribution made by each
unit sold toward covering fixed costs and making profit
– For Peter, contribution margin is $150.
– This is key to breakeven problem.
• Once enough units sold to cover fixed costs (11 units),
each unit then makes direct contribution to profits.
• Once above breakeven point, relatively small percentage
increase in number of units sold will produce relatively
large percentage increase in profit.
The Breakeven Technique
• Operating Leverage
– If firm produces 12 units, it will then earn $150 in profit.
$500[12] - $350[12] - $1,650 = $150
– Increase in production of 1 unit, or 8.3% (1/12=8.3%), will
result in profit of $300 (100% increase).
– Additional increase of 1 unit will increase profits to $450
(50% increase).
– As production moves further and further above breakeven
point, operating leverage effect becomes less dramatic in
terms of percentage increase in profits generated.
The Breakeven Technique
• Operating Leverage
– Implications of operating leverage concept:
• As firm incurs higher levels of fixed costs due to use of more
capital equipment (becomes more capital intensive), it
normally incurs lower levels of variable costs (becomes less
labor intensive).
• Once fixed costs are covered, any available contribution
margin will make direct contribution to profit.
• If firm falls short of covering its fixed costs, loss will be
incurred.
• The higher the degree of operating leverage, the higher
probability that loss may be incurred, and the higher the
risk.
The Breakeven Technique
• Additional Breakeven Applications
1. Determine breakeven point in terms of aggregate
sales dollars for a multiproduct operation.
– Set up breakeven equation in terms of percentage
relationships.
– Porter wants to expand his operation to full-time
business carrying full line of specialized racing
equipment.
• Variable cost estimate: 70% of sales ($350/$500 = 70%)
• Contribution margin per unit: 30% ($150/$500 = 30%)
• Fixed costs estimate: $30,000
The Breakeven Technique
• Additional Breakeven Applications
1. (continued)
– Solve new equation:
Revenue (R) = Fixed costs + Variable costs
R = $30,000 +0.7R
0.3R = $30,000
R = $100,000
– Thus, new operation will break even at sales level
of $100,000.
The Breakeven Technique
•
Additional Breakeven Applications
2. Determine sales dollars (or units) required to
earn given level of profit
– Porter is concerned with sales volume required
to earn $3,000 in profit
•
•
Add required profit to right-hand side of original
equation
X now equals number of units required to earn
$3,000 profit
The Breakeven Technique
•
Additional Breakeven Applications
2. (continued)
Revenue = Fixed costs + Variable costs + Required profit
$500X = $1,650 + $350X + $3,000
$150X = $4,650
X = 31 units
– Porter must sell 31 units, or $15,500 worth of
suspensions ($500 x 31 = $15,500).
The Breakeven Technique
•
Additional Breakeven Applications
3. Determine pricing decisions.
– Porter wants to know what price he will have to
charge for given number of orders and
predetermined level of profit.
– If Porter sells 20 units, what price should he
charge to earn $3,000 in profit?
The Breakeven Technique
•
Additional Breakeven Applications
3. (continued)
– Solve in terms of selling price (X = sales price):
Revenue = Fixed costs + Variable costs + Required profit
20X = $1,650 + $350 (20) + $3,000
20X = $1.650 + $7,000 + $3,000
20X = $11,650
X = $582.50
– Selling price of $582.50 will yield required profit.
Breakeven Charts
•
See exhibit 8.1 for graphic representation of
breakeven problem posed by Peter Porter’s
Porsche Plant
1. Illustrates key assumptions of breakeven
analysis
– Revenue and total cost are treated as simple linear
functions of number of units produced and sold.
– Profit or loss is difference between revenue and total
cost.
– Breakeven point occurs where revenue equals total
cost.
Breakeven Charts
•
Exhibit 8.1 (continued)
2. Provides simple visual interpretation of effect of
changing cost-volume-profit relationships
–
–
Incurring additional fixed costs shifts horizontal fixed-cost line
upward, thus raising total-cost line parallel to itself and causing
breakeven point to rise.
“Substitute” additional fixed costs (i.e. additional depreciation
for improved capital equipment) for low levels of variable cost
(i.e. less direct labor and material waste):
–
–
–
Horizontal fixed-cost line moves upward, but total-cost line
becomes less steep due to lower levels of variable cost
Higher breakeven level and higher contribution margin (revenue
per unit less variable cost per unit)
At levels of operation sufficiently above breakeven point, profits are
much higher, while near or below breakeven, profits are less or
losses are greater.
Breakeven Charts
•
Exhibit 8.1 (continued)
2. (continued)
–
–
–
–
Porter buys additional capital equipment to produce racing
suspensions, causing annual fixed costs to rise to $1,920.
Variable costs per unit decline to $340.
New contribution margin is $160 per unit
New breakeven point:
Revenue = Fixed costs + Variable costs
$500X = $1,920 + $340X
$160X = $1,920
X = 12 units
Breakeven Charts
• See exhibit 8.2
• At new level of operation, breakeven point is one
unit higher than old level.
– At high levels of operation (30 units), profits under new
cost-volume-profit relationships are $2,880 (compared to
$2,850 under old relationships)
– At lower levels, (20 units), profits for new system are
$1,280 (compared to $1,350 for old system)
– At loss levels (5 units), new relationships produce loss of
$1,120 (compared to $900 under old relationships)
– An increase in level of fixed costs must be justified by
expectation of level of operations substantially in excess
of breakeven level.
Breakeven Charts
• Determine point at which new relationships
produce same profit as old relationships.
R – FC – VC = R – FC – VC
$500X - $1,650 - $350X = $500X - $1,920 - $340X
$270 = $10X
X = 27 units
– At 27 units of production, profits are same under either
alternative.
• Under first alternative:
Profit = ($500) (27) - $1,650 – ($350) (27) = $2,400
• Under revised alternative:
Profit = ($500) (27) - $1,920 - ($340) (27) = $2,400
Breakeven Charts
• See exhibit 8.3: profit as function of units
produced and sold is graphed for each
alternative
– Above 27 units, second alternative will produce
larger profits than first alternative.
– Below 27 units, first alternative will produce
higher profits (in profit zone) or lower losses (in
loss zone) than second alternative.
Nonlinear Breakeven Analysis
• Empirical studies of cost behavior over wide ranges of output suggest that
average variable cost per unit declines over some range and then begins
to increase.
• See exhibit 8.4
– Total cost function for wide ranges of output looks like a
curve
• Total cost curve increases at decreasing rate over some range and
then begins to increase at increasing rate.
– Revenue function more nearly resembles a curve than a
straight line over wide ranges of output.
• If sales volume continues to expand over very wide range, sales
price per unit must eventually decline in order to achieve everincreasing sales.
Nonlinear Breakeven Analysis
•
Two key factors of exhibit 8.4
1. Two breakeven points in nonlinear case.
–
–
Lower breakeven point occurs at point where rising revenue
curve crosses rising total cost curve.
Upper breakeven point occurs at very high output level where
declining revenue curve crosses now rapidly increasing total cost
curve
2. Planning plant capacity
–
–
•
Maximum profit point represents point of maximum separation
of revenue and cost curves.
This is optimal production level: production at either higher or
lower levels of output will result in lower profits
Developing equation for curves is almost impossible, but
can be ignored for practical purposes.