Chapter 18
Identify how changes in volume affect costs
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Total variable costs change in direct proportion to changes in the volume of activity◦ If activity increases, so does the cost
Unit variable cost remains constant
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Units produce
d
Direct materials cost per
unit
Total direct
materials cost
100 $25 $2,500
200 $25 5,000
300 $25 7,500
400 $25 10,000
500 $25 12,500
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Do not change over wide ranges in volume Examples:
◦ Straight-line depreciation◦ Salaries
Fixed cost per unit is inversely proportional to activity◦ The more activity, the less the fixed cost per unit
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Have both a fixed and variable component Example:
◦ Utilities that charge a set fee per month, plus a charge for usage
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$0
$500
$1,000
$1,500
$2,000
$2,500
$3,000
$3,500
$4,000
$4,500
$0 $10,000 $20,000 $30,000 $40,000
Total Sales
Sal
es C
om
pen
sati
on
9
Variable
Fixed
Method to separate mixed costs into variable and fixed components
Select the highest level and the lowest level of activity over a period of time
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Change in total cost
Change in activity
Total mixed cost
Total variable cost
Variable cost per
unit
Total fixed costs
minus #2#2
#1#1
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Number of units
Variable cost per
unit
Total mixed cost
Total fixed costs
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Variable cost per unit
Change in total cost
Change in activity
$4,400 - $4,000
1400 - 900
Variable cost per unit
Variable cost per unit
$0.80 per inspection$0.80 per inspection
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Total fixed costs
Total mixed cost
minus
Total variable cost
$4,000
minus
900 inspections x $0.80
Total fixed costs
$3,280$3,280Total fixed costs
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Number of inspections
$0.80 per inspection
Total mixed cost
$3,280
$0.80 per inspection$0.80 per inspection
1,000 inspections
1,000 inspections
$3,280
$4,080$4,080
Band of volume: ◦ Where total fixed costs remain constant and
variable cost per unit remains constant Outside the relevant range, costs can differ
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Use CVP analysis to compute breakeven points
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Sales level at which operating income is zero◦ Sales above breakeven result in a profit◦ Sales below breakeven result in a loss
Two methods:◦ Income statement approach◦ Contribution margin approach
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Sales – Variable costs – Fixed costs = Operating income
Sales – Variable costs – Fixed costs = Operating income
Selling price per
unit x units sold
Selling price per
unit x units sold
Variable cost per unit x
units sold
Variable cost per unit x
units sold
Fixed costsFixed costs
Operating incomeOperating income
Set to zero
Solve for units sold
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Sales revenue per unit
Variable costs per
unit
Contribution margin per unit
Fixed costsFixed costs
Contribution margin per unit
Contribution margin per unit
Breakeven point in
units
Breakeven point in
units
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Sales revenue
Contribution margin
ratio
Contribution margin
Fixed costs
Contribution margin ratio
Breakeven point in sales
dollars
Use CVP analysis for profit planning, and graph the CVP relations
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Fixed costs + Desired operating income
Contribution margin ratio
Target sales in dollars
Target sales in dollars
$0
$5,000
$10,000
$15,000
$20,000
0 500 1,000 1,500
Volume of Units
Do
llars
Revenues
26
•
$0
$5,000
$10,000
$15,000
$20,000
0 500 1,000 1,500
Volume of Units
Do
lla
rs
RevenuesFixed costs
27
28
$0
$5,000
$10,000
$15,000
$20,000
0 500 1,000 1,500
Volume of Units
Do
lla
rs RevenuesFixed costsTotal cost
$0
$5,000
$10,000
$15,000
$20,000
0 500 1,000 1,500
Volume of Units
Do
llars
29
Breakeven point
Profit
Loss
Use CVP methods to perform sensitivity analysis
Management tool to predict how changes in sale prices, cost or volume affects profits
“What if?” analysis
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All would impact breakeven point
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Cause Effect Result
Change Contribution margin
Breakeven point
Selling price increases Increase Decrease
Selling price decreases Decrease Increase
Variable cost per unit increases Decrease Increase
Variable cost per unit decreases
Increase Decrease
Fixed costs increase No effect Increase
Fixed costs decrease No effect Decrease
Excess of expected sales over breakeven sales
Cushion company can absorb without incurring a loss
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Expected sales in units
Expected sales in units
Breakeven sales in unitsBreakeven
sales in units
Margin of safety in
units
Margin of safety in
units
Expected sales in dollars
Breakeven sales in dollars
Margin of safety in dollars
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Sales price per unit
Variable costs per
unit
Contribution margin per
unit
Fixed costsFixed costs
Contribution margin per unit
Contribution margin per unit
Breakeven point in
units
Breakeven point in
units
$230 $70 $160
$112,000
$160
700 students
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Decreased Sales price
per unit
Decreased Sales price
per unit
Variable costs per
unit
Variable costs per
unit
Decreased Contribution margin per
unit
Decreased Contribution margin per
unit
Fixed costsFixed costs
Contribution margin per unit
Contribution margin per unit
New Breakeven point in
units
New Breakeven point in
units
$200$200 $70 $130$130
$112,000
$130
862 students
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Sales price per unit
Sales price per unit
Decreased variable costs per
unit
Decreased variable costs per
unit
Increased Contribution margin per
unit
Increased Contribution margin per
unit
Fixed costsFixed costs
Contribution margin per unit
Contribution margin per unit
New Breakeven point in
units
New Breakeven point in
units
$50$50 $180$180
$112,000
$180
623 students
$230
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Sales price per unit
Variable costs per
unit
Contribution margin per
unit
Decreased fixed costsDecreased fixed costs
Contribution margin per unit
Contribution margin per unit
Breakeven point in
units
Breakeven point in
units
$230 $70 $160
$102,000$102,000
$160
638 students
Calculate the breakeven point for multiple product lines or services
Selling prices and variable costs differ for each product◦ Different contribution to profits
Weighted-average contribution margin computed
Sales mix provides weights◦ Combination of products that make up total sales
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Calculate weighted average contribution margin per unit
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Product A Product B Total
Sales price per unit $100 $150
Variable cost per unit 58 60
Contribution margin per unit 42 90
Sales mix per unit 5 3 8
Contribution margin 210 270 480
Weighted average contribution margin $60
A company has two products with the sales prices and variable costs per unit indicated
in the table
The sales mix weight is multiplied by the
product’s contribution margin
Last year, the company sold 5,000 units of A and 3,000 units of B. This results in a sale
mix of 5:3
The sales mix weights are added as well as
the products’ contribution margins
$480 divided by 8 results in a weighted average contribution
margin of $60
Calculate breakeven point for the package of products
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Fixed costsFixed costs
Weighted average contribution margin per unit
Weighted average contribution margin per unit
$600,000
$60
10,000 units
assumed
Calculate the breakeven point for each product line◦ Multiply the package breakeven point by each
product line’s proportion of the sales mix
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Breakeven point Product A
10,000 x 5/8 6,250 units
Breakeven point Product B
10,000 x 3/8 3,750 units