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© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
Cost-Volume-Profit Analysis
Chapter
19
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
CVP analysis is used to answer questionssuch as: How much must I sell to earn my desired income? How will income be affected
if I reduce selling prices toincrease sales volume?
What will happen toprofitability if I expandcapacity?
CVP analysis is used to answer questionssuch as: How much must I sell to earn my desired income? How will income be affected
if I reduce selling prices toincrease sales volume?
What will happen toprofitability if I expandcapacity?
Questions Addressed byCost-Volume-Profit Analysis
Questions Addressed byCost-Volume-Profit Analysis
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
Number of Local Calls
Mon
thly
Bas
ic
Tel
epho
ne B
ill
Total fixed costs remain unchangedwhen activity changes.
Your monthly basictelephone bill probablydoes not change when
you make more local calls.
Total Fixed CostTotal Fixed Cost
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Number of Local Calls
Mon
thly
Bas
ic T
elep
hone
B
ill p
er L
ocal
Cal
l
Fixed costs per unit declineas activity increases.
Your average cost perlocal call decreases as
more local calls are made.
Fixed Cost Per UnitFixed Cost Per Unit
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Minutes Talked
Tot
al L
ong
Dis
tanc
eT
elep
hone
Bill
Total variable costs changewhen activity changes.
Your total long distancetelephone bill is basedon how many minutes
you talk.
Total Variable CostTotal Variable Cost
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Minutes Talked
Per
Min
ute
Tel
epho
ne C
harg
e
Variable costs per unit do not changeas activity increases.
The cost per long distanceminute talked is constant.
For example, 10cents per minute.
Variable Cost Per UnitVariable Cost Per Unit
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Summary of Variable and Fixed Cost Behavior
Cost In Total Per Unit
Variable Changes as activity level
changes.Remains the same over wide
ranges of activity.
FixedRemains the same even
when activity level changes.Dereases as activity level
increases.
Cost Behavior SummaryCost Behavior Summary
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Mixed costs contain a fixed portion that is incurred even when facility is unused, and a variable portion that increases with usage.
Example: monthly electric utility charge Fixed service fee Variable charge per
kilowatt hour used
Mixed CostsMixed Costs
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Variable
Utility Charge
Activity (Kilowatt Hours)
To
tal
Uti
lity
Co
st
Total mixed cost
Fixed Monthly
Utility Charge
Slope isvariable cost
per unitof activity.
Mixed CostsMixed Costs
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Activity
Co
st
Total cost remainsconstant within anarrow range of
activity.
Stair-Step CostsStair-Step Costs
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Activity
Co
st
Total cost increases to a new higher cost for the
next higher range of activity.
Stair-Step CostsStair-Step Costs
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To
tal
Co
st
Relevant Range
A straight line closely (constant unit variable cost)approximates a
curvilinear variablecost line within
the relevant range.
Volume of Output
CurvilinearCost Function
Curvilinear CostsCurvilinear Costs
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
Let’s extend our
knowledge of
cost behavior to
CVP analysis.
Cost-Volume-Profit(CVP) Analysis
Cost-Volume-Profit(CVP) Analysis
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
The break-even point (expressed in units of product or dollars of sales) is the unique sales level at which a company neither
earns a profit nor incurs a loss.
Computing Break-Even PointComputing Break-Even Point
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Contribution margin is amount by which revenue exceeds the variable costs of producing the revenue.
Contribution margin is amount by which revenue exceeds the variable costs of producing the revenue.
Total Unit
Sales Revenue (2,000 units) 100,000$ 50$
Less: Variable costs 60,000 30
Contribution margin 40,000$ 20$
Less: Fixed costs 30,000
Operating income 10,000$
Computing Break-Even PointComputing Break-Even Point
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How much contribution margin must this company have to cover its fixed costs (break even)?
How much contribution margin must this company have to cover its fixed costs (break even)?
Total Unit
Sales Revenue (2,000 units) 100,000$ 50$
Less: Variable costs 60,000 30
Contribution margin 40,000$ 20$
Less: Fixed costs 30,000
Operating income 10,000$
Computing Break-Even PointComputing Break-Even Point
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
How much contribution margin must this company have to cover its fixed costs (break even)?
Answer: $30,000
How much contribution margin must this company have to cover its fixed costs (break even)?
Answer: $30,000
Total Unit
Sales Revenue (2,000 units) 100,000$ 50$
Less: Variable costs 60,000 30
Contribution margin 40,000$ 20$
Less: Fixed costs 30,000
Operating income 10,000$
Computing Break-Even PointComputing Break-Even Point
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
How many units must this company sell to cover its fixed costs (break even)?
How many units must this company sell to cover its fixed costs (break even)?
Total Unit
Sales Revenue (2,000 units) 100,000$ 50$
Less: Variable costs 60,000 30
Contribution margin 40,000$ 20$
Less: Fixed costs 30,000
Operating income 10,000$
Computing Break-Even PointComputing Break-Even Point
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
How many units must this company sell to cover its fixed costs (break even)?
Answer: $30,000 ÷ $20 per unit = 1,500 units
How many units must this company sell to cover its fixed costs (break even)?
Answer: $30,000 ÷ $20 per unit = 1,500 units
Total Unit
Sales Revenue (2,000 units) 100,000$ 50$
Less: Variable costs 60,000 30
Contribution margin 40,000$ 20$
Less: Fixed costs 30,000
Operating income 10,000$
Computing Break-Even PointComputing Break-Even Point
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We have just seen one of the basic CVP relationships – the break-even computation.
Break-even point in units = Fixed costs
Contribution margin per unit
Finding the Break-Even Point
Unit sales price less unit variable cost($20 in previous example)
Formula for ComputingBreak-Even Sales (in Units)
Formula for ComputingBreak-Even Sales (in Units)
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The break-even formula may also be expressed in sales dollars.
Break-even point in dollars = Fixed costs
Contribution margin ratio
Unit sales price Unit variable cost
Formula for ComputingBreak-Even Sales (in Dollars)
Formula for ComputingBreak-Even Sales (in Dollars)
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to
break even?
a. 100,000 units
b. 40,000 units
c. 200,000 units
d. 66,667 units
ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to
break even?
a. 100,000 units
b. 40,000 units
c. 200,000 units
d. 66,667 units
Computing Break-Even SalesQuestion 1
Computing Break-Even SalesQuestion 1
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to
break even?
a. 100,000 units
b. 40,000 units
c. 200,000 units
d. 66,667 units
ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to
break even?
a. 100,000 units
b. 40,000 units
c. 200,000 units
d. 66,667 units
Unit contribution = $5.00 - $3.00 = $2.00
Fixed costsUnit contribution =
$200,000$2.00 per unit
= 100,000 units
Computing Break-Even SalesQuestion 1
Computing Break-Even SalesQuestion 1
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
Use the contribution margin ratio formula to determine the amount of sales revenue ABC must
have to break even. All information remains unchanged: fixed costs are $200,000; unit sales
price is $5.00; and unit variable cost is $3.00.
a. $200,000
b. $300,000
c. $400,000
d. $500,000
Use the contribution margin ratio formula to determine the amount of sales revenue ABC must
have to break even. All information remains unchanged: fixed costs are $200,000; unit sales
price is $5.00; and unit variable cost is $3.00.
a. $200,000
b. $300,000
c. $400,000
d. $500,000
Computing Break-Even SalesQuestion 2
Computing Break-Even SalesQuestion 2
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
Use the contribution margin ratio formula to determine the amount of sales revenue ABC must
have to break even. All information remains unchanged: fixed costs are $200,000; unit sales
price is $5.00; and unit variable cost is $3.00.
a. $200,000
b. $300,000
c. $400,000
d. $500,000
Use the contribution margin ratio formula to determine the amount of sales revenue ABC must
have to break even. All information remains unchanged: fixed costs are $200,000; unit sales
price is $5.00; and unit variable cost is $3.00.
a. $200,000
b. $300,000
c. $400,000
d. $500,000
Unit contribution = $5.00 - $3.00 = $2.00
Contribution margin ratio = $2.00 ÷ $5.00 = .40
Break-even revenue = $200,000 ÷ .4 = $500,000
Computing Break-Even SalesQuestion 2
Computing Break-Even SalesQuestion 2
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
Volume in Units
Co
sts
and
Rev
enu
ein
Do
llar
sRevenue
Starting at the origin, draw the total revenueline with a slope equal to the unit sales price.
Total fixed cost
Total fixed costextends horizontallyfrom the vertical axis.
Preparing a CVP GraphPreparing a CVP Graph
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Total cost
Volume in Units
Co
sts
and
Rev
enu
ein
Do
llar
s
Total fixed cost
Break-even Point
Profit
Loss
Draw the total cost line with a slopeequal to the unit variable cost. Revenue
Preparing a CVP GraphPreparing a CVP Graph
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Break-even formulas may be adjusted to show the sales volume needed to earn
any amount of operating income.
Break-even formulas may be adjusted to show the sales volume needed to earn
any amount of operating income.
Unit sales = Fixed costs + Target incomeContribution margin per unit
Dollar sales = Fixed costs + Target income
Contribution margin ratio
Computing Sales Needed to Achieve Target Operating Income
Computing Sales Needed to Achieve Target Operating Income
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to earn operating income of $40,000?
a. 100,000 units
b. 120,000 units
c. 80,000 units
d. 200,000 units
ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to earn operating income of $40,000?
a. 100,000 units
b. 120,000 units
c. 80,000 units
d. 200,000 units
Computing Sales Needed to Achieve Target Operating Income
Computing Sales Needed to Achieve Target Operating Income
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to earn operating income of $40,000?
a. 100,000 units
b. 120,000 units
c. 80,000 units
d. 200,000 units
ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to earn operating income of $40,000?
a. 100,000 units
b. 120,000 units
c. 80,000 units
d. 200,000 units = 120,000 units
Unit contribution = $5.00 - $3.00 = $2.00
Fixed costs + Target income Unit contribution
$200,000 + $40,000 $2.00 per unit
Computing Sales Needed to Achieve Target Operating Income
Computing Sales Needed to Achieve Target Operating Income
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
Margin of safety is the amount by which sales may decline before reaching break-even sales:
Margin of safety provides a quick means of estimating operating income at any level of sales:
Margin of safety = Actual sales - Break-even sales
Operating Margin Contribution Income of safety margin ratio= ×
What is our Margin of Safety?What is our Margin of Safety?
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Oxco’s contribution margin ratio is 40 percent. If sales are $100,000 and break-even sales are $80,000, what is operating
income?
Operating Margin Contribution Income of safety margin ratio= ×
Operating Income = $20,000 × .40 = $8,000
What is our Margin of Safety?What is our Margin of Safety?
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
Once break-even is reached, every additional dollar of contribution margin becomes operating income:
Oxco expects sales to increase by $15,000. How much will operating income increase?
Change in operating income = $15,000 × .40 = $6,000
Change in Change in Contributionoperating income sales volume margin ratio= ×
What Change in Operating Income Do We Anticipate?
What Change in Operating Income Do We Anticipate?
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
Business Applications of CVPBusiness Applications of CVP
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
Total Per Unit PercentSales (500 bikes) 250,000$ 500$ 100%Less: variable expenses 150,000 300 60%Contribution margin 100,000$ 200$ 40%
Less: fixed expenses 80,000 Operating income 20,000$
Consider the following information developed by the accountant at CyclCo, a
bicycle retailer:
Business Applications of CVPBusiness Applications of CVP
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
Should CyclCo spend $12,000 on advertising to increase sales by 10 percent?
Total Per Unit PercentSales (500 bikes) 250,000$ 500$ 100%Less: variable expenses 150,000 300 60%Contribution margin 100,000$ 200$ 40%
Less: fixed expenses 80,000 Operating income 20,000$
Business Applications of CVPBusiness Applications of CVP
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
500 550Bikes Bikes
Sales 250,000$ 275,000$ Less: variable expenses 150,000 165,000 Contribution margin 100,000$ 110,000$ Less: fixed expenses 80,000 92,000 Operating income 20,000$ 18,000$
550 × $300
$80K + $12K
No, income is decreased.
550 × $500
Business Applications of CVPBusiness Applications of CVP
Should CyclCo spend $12,000 on advertising to increase sales by 10 percent?
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
500Bikes
Sales 250,000$ Less: variable expenses 150,000 Contribution margin 100,000$ Less: fixed expenses 80,000 Operating income 20,000$
Now, in combination with the advertising, CyclCo is considering a 10 percent price reduction that willincrease sales by 25 percent. What is the income effect?
Business Applications of CVPBusiness Applications of CVP
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
500 625Bikes Bikes
Sales 250,000$ 281,250$ Less: variable expenses 150,000 187,500 Contribution margin 100,000$ 93,750$ Less: fixed expenses 80,000 92,000 Operating income 20,000$ 1,750$
625 × $300
$80K + $12K
Income is decreased even more.
625 × $450
Now, in combination with the advertising, CyclCo is considering a 10 percent price reduction that willincrease sales by 25 percent. What is the income effect?
1.25 × 500
Business Applications of CVPBusiness Applications of CVP
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
500Bikes
Sales 250,000$ Less: variable expenses 150,000 Contribution margin 100,000$ Less: fixed expenses 80,000 Operating income 20,000$
Business Applications of CVPBusiness Applications of CVPNow, in combination with advertising and a price cut, CyclCo
will replace $50,000 in sales salaries with a $25 per bike commission, increasing sales by 50 percent above the
original 500 bikes. What is the effect on income?
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
500 750Bikes Bikes
Sales 250,000$ 337,500$ Less: variable expenses 150,000 243,750 Contribution margin 100,000$ 93,750$ Less: fixed expenses 80,000 42,000 Operating income 20,000$ 51,750$
The combination of advertising, a price cut,and change in compensation increases income.
750 × $325
$92K - $50K
750 × $450
Business Applications of CVPBusiness Applications of CVPNow, in combination with advertising and a price cut, CyclCo
will replace $50,000 in sales salaries with a $25 per bike commission, increasing sales by 50 percent above the
original 500 bikes. What is the effect on income?
1.5 × 500
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
Different products with different contribution margins.
Determining semivariablecost elements.
Complying with theassumptions of CVP analysis.
Additional Considerations in CVPAdditional Considerations in CVP
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
Sales mix is the relative combination in whicha company’s different products are sold.
Different products have different selling prices, costs, and contribution margins.
If CyclCo sells bikes and carts, howwill we deal with break-even analysis?
Sales mix is the relative combination in whicha company’s different products are sold.
Different products have different selling prices, costs, and contribution margins.
If CyclCo sells bikes and carts, howwill we deal with break-even analysis?
CVP Analysis When a Company Sells Many Products
CVP Analysis When a Company Sells Many Products
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
CyclCo provides us with the following information:
Bikes Carts TotalSales 250,000$ 100% 300,000$ 100% 550,000$ 100%Var. exp. 150,000 60% 135,000 45% 285,000 52%Contrib. margin 100,000$ 40% 165,000$ 55% 265,000$ 48%
Fixed exp. 170,000 Net income 95,000$
CVP Analysis When a Company Sells Many Products
CVP Analysis When a Company Sells Many Products
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
The overall contribution margin ratio is:
$265,000 $550,000
= 48% (rounded)
Bikes Carts TotalSales 250,000$ 100% 300,000$ 100% 550,000$ 100%Var. exp. 150,000 60% 135,000 45% 285,000 52%Contrib. margin 100,000$ 40% 165,000$ 55% 265,000$ 48%
Fixed exp. 170,000 Net income 95,000$
CVP Analysis When a Company Sells Many Products
CVP Analysis When a Company Sells Many Products
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
Break-even in sales dollars is:
$170,000 .48
= $354,167 (rounded)
Bikes Carts TotalSales 250,000$ 100% 300,000$ 100% 550,000$ 100%Var. exp. 150,000 60% 135,000 45% 285,000 52%Contrib. margin 100,000$ 40% 165,000$ 55% 265,000$ 48%
Fixed exp. 170,000 Operating income 95,000$
CVP Analysis When a Company Sells Many Products
CVP Analysis When a Company Sells Many Products
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
OwlCo recorded the following production activity and maintenance costs for two months:
Using these two levels of activity, compute: the variable cost per unit. the total fixed cost. total cost formula.
Units Cost
High activity level 9,000 9,700$Low activity level 5,000 6,100 Change 4,000 3,600$
The High-Low MethodThe High-Low Method
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Units Cost
High activity level 9,000 9,700$Low activity level 5,000 6,100 Change 4,000 3,600$
Unit variable cost = = = $0.90 per unitin cost
in units$3,600 4,000
The High-Low MethodThe High-Low Method
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
Units Cost
High activity level 9,000 9,700$Low activity level 5,000 6,100 Change 4,000 3,600$
Unit variable cost = = = $0.90 per unit
Fixed cost = Total cost – Total variable cost
in costin units
$3,600 4,000
The High-Low MethodThe High-Low Method
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
Units Cost
High activity level 9,000 9,700$Low activity level 5,000 6,100 Change 4,000 3,600$
Unit variable cost = = = $0.90 per unit
Fixed cost = Total cost – Total variable cost
Fixed cost = $9,700 – ($0.90 per unit × 9,000 units)
Fixed cost = $9,700 – $8,100 = $1,600
in costin units
$3,600 4,000
The High-Low MethodThe High-Low Method
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
Units Cost
High activity level 9,000 9,700$Low activity level 5,000 6,100 Change 4,000 3,600$
Unit variable cost = = = $0.90 per unit
Fixed cost = Total cost – Total variable cost
Fixed cost = $9,700 – ($0.90 per unit × 9,000 units)
Fixed cost = $9,700 – $8,100 = $1,600 Total cost = $1,600 + $.90 per unit
in costin units
$3,600 4,000
The High-Low MethodThe High-Low Method
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
If sales commissions are $10,000 when 80,000 units are sold and $14,000 when 120,000 units are sold, what is the variable portion of sales commission per
unit sold?
a. $.08 per unit
b. $.10 per unit
c. $.12 per unit
d. $.125 per unit
If sales commissions are $10,000 when 80,000 units are sold and $14,000 when 120,000 units are sold, what is the variable portion of sales commission per
unit sold?
a. $.08 per unit
b. $.10 per unit
c. $.12 per unit
d. $.125 per unit
The High-Low MethodQuestion 1
The High-Low MethodQuestion 1
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
If sales commissions are $10,000 when 80,000 units are sold and $14,000 when 120,000 units are sold, what is the variable portion of sales commission per
unit sold?
a. $.08 per unit
b. $.10 per unit
c. $.12 per unit
d. $.125 per unit
If sales commissions are $10,000 when 80,000 units are sold and $14,000 when 120,000 units are sold, what is the variable portion of sales commission per
unit sold?
a. $.08 per unit
b. $.10 per unit
c. $.12 per unit
d. $.125 per unit $4,000 ÷ 40,000 units = $.10 per unit
Units Cost
High level 120,000 14,000$Low level 80,000 10,000 Change 40,000 4,000$
The High-Low MethodQuestion 1
The High-Low MethodQuestion 1
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
If sales commissions are $10,000 when 80,000 units are sold and $14,000 when 120,000 units are sold, what is the fixed portion of the sales commission?
a. $ 2,000
b. $ 4,000
c. $10,000
d. $12,000
If sales commissions are $10,000 when 80,000 units are sold and $14,000 when 120,000 units are sold, what is the fixed portion of the sales commission?
a. $ 2,000
b. $ 4,000
c. $10,000
d. $12,000
The High-Low MethodQuestion 2
The High-Low MethodQuestion 2
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
If sales commissions are $10,000 when 80,000 units are sold and $14,000 when 120,000 units are sold, what is the fixed portion of the sales commission?
a. $ 2,000
b. $ 4,000
c. $10,000
d. $12,000
If sales commissions are $10,000 when 80,000 units are sold and $14,000 when 120,000 units are sold, what is the fixed portion of the sales commission?
a. $ 2,000
b. $ 4,000
c. $10,000
d. $12,000
Total cost = Total fixed cost + Total variable cost
$14,000 = Total fixed cost +($.10 × 120,000 units)
Total fixed cost = $14,000 - $12,000
Total fixed cost = $2,000
The High-Low MethodQuestion 2
The High-Low MethodQuestion 2
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
A limited range of activity, called the relevant range, where CVP relationships are linear. Unit selling price remains constant. Unit variable costs remain constant. Total fixed costs remain constant.
Sales mix remains constant. Production = sales (no inventory changes).
Assumptions Underlying CVP Analysis
Assumptions Underlying CVP Analysis
© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin
End of Chapter 19End of Chapter 19