Chapter Four
Cost–Volume–Profit Analysis
CVP Analysis
• Estimates how changes in costs, sales,
volume, and price affect a company’s
profit.
• Powerful tool for planning and decision
making.
• Most versatile and widely applicable tools
used by managerial accountants to help
managers make better decisions
Break-Even Point
• Point where Total Revenue = Total Costs
• Use contribution margin income statement to
calculate the Break-even point.
• Break-even point can be calculated in
number of units and sales dollars.
• Once fixed costs have been covered, net
income will increase by the per unit
contribution margin for each additional unit
sold
Contribution Margin
• CM = Revenue – Variable Costs
• CM represents the amount available to
cover fixed expenses and thereafter
provides profits.
• CM can be calculated in total or per unit.
• CMU = Selling Price – Var. Cost per Unit
Contribution Margin
Income Statement
Sales Revenue
(Variable Costs)
Contribution Margin
(Fixed Costs)
Operating Income
*When using this format, costs include
product as well as period costs.
• Whittier Company plans to sell 1,000
mowers at $400 each in the coming year.
Product costs include:
– Direct materials per mower
– Direct labor per mower
– Variable factory OH per mower
– Total fixed factory OH
$180
$100
$25
$15,000
– Variable selling expense is a commission of
$20 per mower; fixed selling and admin
expenses totals $30,000
Contribution Margin
Income Statement
Sales ($400 * 1,000)
Variable cost ($325 * 1,000)
Contribution margin
Fixed costs
Operating income
$400,000
(325,000)
$ 75,000
( 45,000)
$ 30,000
*CM per unit = $400 – 325 = $75
**VC per unit = $180 + 100 + 25 + 20
***FC = $15,000 + $30,000 = $45,000
Break-even Point in Units
Sales – VC - FC = Operating Income
• At break-even point, operating income =
$0.
• Calculate BE point in units using previous
example:
Sales – VC – FC = Income
$400X - $325X - $45,000 = $0
$400X - $325X = $45,000
$45,000 / $75X
X = 600 mowers
Break-even Point in Units
• Operating income equation can be
rearranged as follows to calculate number
of units at breakeven
• BE units = Total FC / (SP – VC per unit)
• Looking back at previous example
• =$45,000 / ($400 - $325)
Break-even Point
in Sales Dollars
• Unit sold measure is converted into sales
dollars
# of units sold * sales price per unit = sales revenue
• Sales revenue needed in order to breakeven
=600 mowers * $400 = $240,000
Variable Cost Ratio
&
Contribution Margin Ratio
• VC Ratio = VC expressed as % of sales
dollars
• CM Ratio = CM expressed as % of sales
dollars
• VC Ratio + CM Ratio = 100%
• If VC Ratio = 70%, then CM Ratio = ? %
Variable Cost Ratio
• Variable Cost Ratio – proportion of each
sales dollar that must be used to cover
variable costs
• Can be calculated using total data or unit
data
VC Ratio = VC per unit / SP per unit
• VC Ratio = $325 / $400
• VC Ratio = 81.25%
Contribution Margin Ratio
• Percentage of sales dollars remaining
after variable costs are covered
• Proportion of each sales dollar available to
cover fixed costs and provide for profit
CM Ratio = CM per unit / SP per unit
• CM Ratio = $75 / $400
• CM Ratio = 18.75%
Break-even Point
in Sales Dollars
BE Sales = FC / CM Ratio
• BE Sales = $45,000 / 18.75%
• BE Sales = $240,000
Calculating Sales Needed to Earn a
Target Operating Income
• Whittier sells mowers at $400 each.
Variable cost per unit is $325 and total
fixed cost is $45,000.
• Calculate sales that Whittier must make to
earn an operating income of $37,500
Sales – VC – FC = Operating Income
$400X - $325X - $45,000 = $37,500
$75X = $82,500
X = $82,500 / $75
X = 1,100
What happens if a company
sells more than one product?
Whittier Company
• Decides to offer two models of lawn mowers:
mulching mower (SP = $400) & riding lawn
mower (SP = $800)
Mulching
Mower
(1,200 units,
60%)
Riding Mower
(800 units,
40%)
Total
(2,000 units)
Sales
$480,000
$640,000
$1,120,000
Less: Variable Expenses
( 390,000)
( 480,000)
(
Contribution Margin
$ 90,000
$160,000
$ 250,000
Less: Fixed expenses
(
(
(
70,000)
Product Margin
$ 60,000
$
180,000
Less: Common fixed
expenses
Operating Income
30,000)
40,000)
$ 120,000
870,000)
(
$
26,250)
153,750
Weighted-Average
Contribution Margin per Unit
• In the real world, a company sells more than one
product.
• Have to find weight-average contribution margin:
• Several ways to calculate, but one way is-total contribution margin divided by the total
units: $250,000/2,000 = $125
• Use $125 to find break-even point for company.
– $125X – 70,000 – 26,250 = $0
– $125X = $96,250
– X = $96,250/$125
– X = 770 units
• How many mulching mowers?
– 770 * 60% = 462
• How many riding mowers?
– 770 * 40% = 308
Margin of Safety
• The units sold or revenue earned above
the break-even volume.
• “Wiggle room”
= Actual or Target Sales – Breakeven Sales
Example
Whittier Company
• Break-even Point = 600 units or $240,000
sales dollars
• Target Point = 1,000 units or $400,000
sales dollars
Margin of Safety:
• Units = 1,000 – 600 = 400 units
• Sales dollars = $400,000 – 240,000 =
$160,000
Operating Leverage
• Concerned with the relative mix of fixed
costs and variable costs in an
organization.
• As variable costs decrease, the unit CM
increases, making the contribution of each
unit sold that much greater.
• Degree of OL = CM / Operating Income
Operating Leverage
• Whittier plans to sell 1,000 mowers at
$400 each and has VC per unit of $325
and FC of $45,000. Operating income at
that level of sales is $30,000.
– OL = $75,000 / $30,000 = 2.5
• Use of OL:
Degree of OL * % change in sales = %
change in income
• If company sales increase 20%, but how
much income increase?
– 2.5 * 20% = 50%