Cost Voume Profit

8/7/2019 Cost Voume Profit

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3/19/2011 Slide # 1

Cost ManagementMeasuring, Monitoring, and Motivating Performance

Cost-Volume-Profit Analysis


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3/19/2011 Slide # 2

Chapter 3: Cost-Volume-Profit Analysis

Learning objectives Q1: What is cost-volume-profit (CVP) analysis, and how is it

used for decision making?

Q2: How are CVP calculations performed for a single

product? Q3: How are CVP calculations performed for multiple

products?

Q4: What is the breakeven point?

Q5: What assumptions and limitations should managersconsider when using CVP analysis?

Q6: How are the margin of safety and operating leverageused to assess operational risk?


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3/19/2011 Slide # 3

units

$

Total Costs (TC)

Total Revenue (TR)

Q1,Q4: CVP Analysis and the Breakeven Point

The breakeven point (BEP) is where total revenueequal total costs.

CVP analysis looks at the relationship betweenselling prices, sales volumes, costs, and profits.

BEP in units

BEP insales $


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3/19/2011 Slide # 4

Q1: How is CVP Analysis Used?

CVP analysis can determine, both in units and insales dollars:

the volume required to break even

the volume required to achieve target profit levels the effects of discretionary expenditures

the selling price or costs required to achieve

target volume levels CVP analysis helps analyze the sensitivity of profits

to changes in selling prices, costs, volume andsales mix.


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3/19/2011 Slide # 7

Bills Briefcases makes high quality cases for laptops that sell for $200.The variable costs per briefcase are $80, and the total fixed costs are$360,000. Find the BEP in units and in sales $ for this company.

Q2: Breakeven Point Calculations

BEP in unitsF

P V

!

$360,000

$200 /unit $80 /unit!

$360,0003,000 units

$120/unit! !

( ) /F

P V P!

$360,000$600,000

60%! !

BEP in sales $ 0FCMR

! $360,000($200 $80)/ $200

!


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3/19/2011 Slide # 8

units

$1000s TC

TR

3000

$600

Q2: CVP Graph

Draw a CVP graph for Bills Briefcases. What is the pretax profit if Billsells 4100 briefcases? If he sells 2200 briefcases? Recall that P=$200, V= $80, and F= $360,000.

$360

41002200

Profit at 4100 units =$120 x 4100 - $360,000.

$132,000

-$96,000

Profit at 2200 units = $120 x 2200 - $360,000.

More easily: 4100 units is 1100 units past BEP,so profit = $120 x 1100 units; 2200 units is 800units before BEP, so loss = $120 x 800 units.


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3/19/2011 Slide # 9

How many briefcases does Bill need to sell to reach a target pretaxprofit of $240,000? What level of sales revenue is this? Recall that P=$200, V= $80, and F= $360,000.

Q2: CVP Calculations

Units needed to

reach targetpretax profit

rofitF

P V

!

$360,000 $240,000

$120/unit

!

5,000 units!

$600,000$1,000,000

60%! !

( ) /

F

P V P!

Sales $ required

to reach targetpretax profit

$ 0,000F

CMR

!

Of course, 5,000 units x$200/unit = $1,000,000,

too.But sometimes you onlyknow the CMR and not

the selling price perunit, so this is still avaluable formula.


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3/19/2011 Slide # 10

How many briefcases does Bill need to sell to reach a target after-taxprofit of $319,200 if the tax rate is 30%? What level of sales revenue isthis? Recall that P= $200, V= $80, and F= $360,000.

Q2: CVP Calculations

First convert the target after-tax profit to its target pretax profit:

After-tax profit $319,200Pretax profit $456,000(1 Tax rate) (1 0.3)

! ! !

Units needed toreach target

pretax profit

$360,000 $456,0006,800 units

$120/unit

! !

Sales $ neededto reach target

pretax profit

$360,000 $456,000$1,360,000

60%

! !


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3/19/2011 Slide # 11

Suppose that Bills marketing department says that he can sell 6,000briefcases if the selling price is reduced to $170. Bills target pretaxprofit is $210,000. Determine the highest level that his variable costscan so that he can make his target. Recall that F= $360,000.

Q1,2: Using CVP to Determine Target Cost Levels

Use the CVP formula for units, but solve for V:

Q = 6,000 units $360,000 $210,000

$170/unit V

!

If Bill can reduce his variable costs to $75/unit, he can meet his goal.

$75/unitV !

$360,000 $210,000$170/ it $95/ it

6,000 its

V

! !


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3/19/2011 Slide # 12

Q5: Uncertainties in Bills Decision

After this analysis, Bill needs to consider severalissues before deciding to lower his price to$170/unit.

How reliable are his marketing departments estimates?

Is a $5/unit decrease in variable costs feasible?

Will this decrease in variable costs affect product quality?

If 6,000 briefcases is within his plants capacity but lowerthan his current sales level, will the increased productionaffect employee morale or productivity?


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3/19/2011 Slide # 13

Q1: Using CVP to Compare Alternatives

CVP analysis can compare alternative coststructures or selling prices.

high salary/low commission vs. lower salary/highercommission for sales persons

highly automated production process with low variablecosts per unit vs. lower technology process with highervariable costs per unit and lower fixed costs.

The indifference point between alternatives is thelevel of sales (in units or sales $) where the profits ofthe alternatives are equal.

broad advertising campaign with higher selling prices vs.minimal advertising and lower selling prices


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3/19/2011 Slide # 14

Currently Bills salespersons have salaries totaling $80,000 (includedin F of $360,000) and earn a 5% commission on each unit ($10 perbriefcase). He is considering an alternative compensation arrangementwhere the salaries are decreased to $35,000 and the commission isincreased to 20% ($40 per briefcase). Compute the BEP in units underthe proposed alternative. Recall that P= $200 and V= $80 currently.

Q1,2: Using CVP to Compare Alternatives

First compute Fand Vunder the proposed plan:

F= $360,000 - $45,000 decrease in salaries = $315,000

V= $80 + $30 increase in commission = $110

Then compute Q under the proposed plan:

Unitsneeded tobreakeven

0FQ

P V

! !

$315,0003,500 units

$200 /unit - $110/unit! !


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3/19/2011 Slide # 15

Q1: Determining the Indifference Point

Compute the volume of sales, in units, for which Bill is indifferentbetween the two alternatives.

The indifference point in units is the Q for which the profit equationsof the two alternatives are equal.

Current Plan Proposed PlanContribution margin per unit $120 $90

Total fixed costs $360,000 $315,000

Profit (current plan) = $120Q - $360,000

Profit (proposed plan) = $90Q - $315,000

$120Q - $360,000 = $90Q - $315,000

$30Q = $45,000 Q = 1,500 units


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3/19/2011 Slide # 16

Q1,2: CVP Graphs of the Indifference Point

Draw a CVP graph for Bills that displays the costs under bothalternatives. Notice that the total revenue line for both alternatives isthe same, but the total cost lines are different.

TC-current plan

TR

units

$1000s

3000

$600

$360

3500

$315

TC-proposed plan

1500

BEP for thecurrent plan

BEP for theproposed plan

indifference point between the plans


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3/19/2011 Slide # 17

TC-current plan

TR

units

$1000s

3000

$600

Q1,2: Comparing Alternatives

$360

3500

$315

TC-proposed plan

1500

The current plan breaks even before the proposed plan.

At 1500 units, the plans have the same total cost.

Each unit soldprovides a larger

contribution to profitsunder the current

plan.


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3/19/2011 Slide # 18


Hopefully Bill is currently selling more than 1500briefcases, because profits are negative underBOTH plans at this point.

Therefore, it seems the current plan is preferable tothe proposed plan.

However, . . .

The total costs of the current plan are less than thethose of the proposed plan at sales levels past1500 briefcases.


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3/19/2011 Slide # 19


. . . this may not be true because the level of futuresales is always uncertain.

What if the briefcases were a new product line?

The plans may create different estimates of thelikelihood of various sales levels.

Estimates of sales levels may be highly uncertain. The lower fixed costs of the proposed plan may be

safer.

Salespersons may have an incentive to sell moreunits under the proposed plan.


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3/19/2011 Slide # 20

Q3: CVP Analysis for Multiple Products

When a company sells more than one product theCVP calculations must be adjusted for the salesmix. The sales mix should be stated as a proportion

of total units sold when performing CVP

calculations for in units.

of total revenues when performing CVP

calculations in sales $.


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3/19/2011 Slide # 21

Q3: Sales Mix Computations

The weighted average contribution margin is theweighted sum of the products contribution margins:ni 1 i iP! where i is product is % of total sales

in units, CMi is product is contributionmargin, and n= the number ofproducts.

ni=1 i i

CM CMK!where Ki is product is % of totalsales revenues, CMRi is product iscontribution margin ratio, and n=the number of products.

The weighted average contribution margin ratio isthe weighted sum of the products contribution

margin ratios:


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3/19/2011 Slide # 22

Peggys Kitchen Wares sells three sizes of frying pans. Next year shehopes to sell a total of 10,000 pans. Peggys total fixed costs are$40,800. Each products selling price and variable costs is givenbelow. Find the BEP in units for this company.

Q3: Multiple Product Breakeven Point

Small Medium Large Total

Expected sales in units 2,000 5,000 3,000 10,000

Selling price per unit $10.00 $15.00 $18.00

Variable costs per unit $4.00 $8.00 $11.00

Contribution margin per unit $6.00 $7.00 $7.00

First note the sales mix in units is 20%:50%:30%, respectively; thencompute the weighted average contribution margin:

CM = 20%x$6 + 50%x$7 + 30%x$7 = $6.80


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3/19/2011 Slide # 23


But 6,000 units is not really the BEP in units; the BEP is only 6,000 units ifthe sales mix remains the same.

Next, compute the BEP in terms of total units:Total unitsneeded tobreakeven

0FQ

P V

! !

$40,8006,000 units

$6.80/unit! !

The BEP should be stated in terms of how many of each unit must be sold:

Units re uired to brea even:Small ans 0 , 00

edium ans 0 ,000

ar e ans 0 ,800

6,000


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3/19/2011 Slide # 24

Find the BEP in sales $ for Peggys Kitchen Wares. The total revenueand total variable cost information below is based on the expectedsales mix.


First compute the weighted average contribution margin ratio:

WACMR = (20/149)x60% + (75/149)x46.7% + (54/149)x38.9% =

ma Medium arge ota

xpected sa es in units 2,000 5,000 3,000 10,000

ota revenue 20,000 75,000 54,000 149,000

ota variab e costs 8,000 40,000 33,000 81,000

ota contribution margin 12,000 35,000 21,000 68,000

Contribution margin ratio 60.0% 46.7% 38.9% 45.6%


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3/19/2011 Slide # 25


Next compute the BEP in sales $:

. . . = 45.6%, of course! Depending on how the giveninformation is structured, it may be easier to compute theCMR as Total contribution margin/Total revenue.

BEP in sales $ 0FCMR

!

$40, 00 $89,4740.456

! ! *

* If you sum the number of units of each size pan requiredat breakeven times its selling price you get $89,400. Theextra $74 in the answer above comes from rounding the

contribution margin ratio to three decimals.


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3/19/2011 Slide # 26

Q6: Margin of Safety

The margin of safety is a measure of how far pastthe breakeven point a company is operating, orplans to operate. It can be measured 3 ways.

margin of

safety in units

actual or estimated units of

activity BEP in units

=

margin ofsafety in $

actual or estimated sales $ BEP in sales $

=

margin ofsafety

percentage

= argin of safety in units

ctual or estimated units

argin of safety in $

ctual or estimated sales $!


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3/19/2011 Slide # 28

Q6: Degree of Operating Leverage

The degree of operating leverage measures theextent to which the cost function is comprised offixed costs.

A high degree of operating leverage indicates a

high proportion of fixed costs. Businesses operating at a high degree of operating

leverage

but enjoy profits that rise more quickly when salesincrease.

face higher risk of loss when sales decrease,


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3/19/2011 Slide # 29


The degree of operating leverage can be computed3 ways.

Contribution margin

Profit

i ed costs+1

Profit

1

Margin of safety percentage

degree of

operating =

leverage


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3/19/2011 Slide # 30

Suppose that Bills Briefcases has budgeted next years sales at 5,000units. Compute Bills degree of operating leverage. Recall that P=$200, V= $80, F= $360,000, and the margin of safety percentage at5,000 units is 40%.


First, compute contribution margin and profit at 5,000 units:

Profit = $600,000 - $360,000 = $240,000

$600,000Degree of operating le erage = = 2.5

$240,000

Contribution margin = ($200 - $80) x 5,000 = $600,000

1or, degree of operating le erage = = 2.5

40%

$360,000or, degree of operating le erage = + 1 = 2.5$240,000


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3/19/2011 Slide # 32

Q5: Assumptions in CVP Analysis

CVP analysis assumes that costs and revenues arelinear within a relevant range of activity.

Linear total revenues means that selling prices per unitare constant and the sales mix does not change.

If volume discounts are received from suppliers, thenvariable costs per unit are not constant.

Offering volume discounts to customers violates this assumption.

Linear total costs means total fixed costs are constantand variable costs per unit are constant.

If worker productivity changes as activity levels change,then variable costs per unit are not constant.


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3/19/2011 Slide # 33

Q5: Assumptions in CVP Analysis

These assumptions may induce a small relevantrange.

Results of CVP calculations must be checked to see ifthey fall within the relevant range.

Nonlinear analysis techniques are available.

Linear CVP analysis may be inappropriate if thelinearity assumptions hold only over small rangesof activity.

For example, regression analysis, along with nonlineartransformations of the data, can be used to estimatenonlinear cost and revenue functions.

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