Cost Volume Profit Revised March 3 08

8/3/2019 Cost Volume Profit Revised March 3 08

http://slidepdf.com/reader/full/cost-volume-profit-revised-march-3-08 1/68

COST VOLUME PROFIT

Richard E. McDermott Ph.D.



Costs Volume Profit

In this chapter we study what happens to bothcost and profit as volume changes.The tools we will use will be helpful in thedevelopment of flexible budgets.I am going to begin by giving you some basicdefinitions.

I will then give you what I feel are the bestformulas to use in working the problems youwill be assigned.



Definitions

Variable Costs: Costs that vary in total, directlyand proportionately, with changes inproduction (also called activity level).

If the activity level increases by 50%, variablecosts increase by 50%.



Examples of Variable Costs

Direct laborDirect materialsVariable overhead



Definitions

Mixed Costs: costs that contain both a fixedand a variable element.Mixed cost change in total, but not

proportionately, with changes in the activitylevel.An example of a mixed cost might bemaintenance cost on a taxi.

Maintenance costs increase as miles increase.Even if the truck is never driven, however, it is agood idea to change the oil every three months tokeep it from degenerating.



Separating Fixed and VariableCosts

If you will look at a general ledger, you willnever find accounts labeled ―variable labor‖ or ―fixed labor‖ or ―variable overhead‖ or ―fixed

overhead.‖ In order to perform cost volume profit analysis,therefore, it is usually necessary to separatefixed and variable costs.

There are three methods to do this:Scatter graph methodHigh-low methodLeast squares method

The best method is theleast squares method,but since the authordoes not teach it we willnot cover it either.



Definitions

Fixed Costs: Costs that do not change withincreases or decreases in production volume.It is important to add, there is usually a relevantrange.For example, a plant may be built to manufacture1 to 10,000 shoes per month.Fixed costs would not change within this ―relevant

range.‖ If a company wanted to manufacture 12,000shoes per month, however, there of course wouldbe a new relevant range and the fixed costs might

increase.



Examples of Fixed Costs

Rent on a factoryDepreciation – straight-line methodHeating and air-conditioning expenseHousekeeping

It is important to emphasize that what might be a

fixed cost in one factory, could be a variable cost inanother, depending upon the way the firm doesbusiness.



Other Definitions

Contribution Margin: Revenue (or unit price)minus total variable costs (or unit variablecosts).

Example:Contribution Margin IncomeStatement

Sales $100,000Less variable costs 60,000Contribution margin $40,000Less fixed costs 30,000Income from

operations

$10,000

Note thatcontributionmargin is

what is leftafter payingvariablecosts.



Notation

I will use the following notation when referringto contribution margin:

CMu = contribution margin per unit of produce,

calculated as follows: Price – Variable Cost PerUnit = Cmu.CMt = contribution margin total calculated asfollows: Total Sales – Total Variable Costs = CMtCMr = contribution margin ratio calculated asfollows: CMt/Total Sales or CMu/Price.



Tip for Examination

In any problem where the only change isvolume (i.e. variable costs per unit, and fixedcosts do not change), then the impact of the

change on operating income can be calculatedsimply by calculating the change in totalcontribution margin.The change in total contribution margin willequal the change in operating income.We will illustrate this in a moment.



Here Are Some Formulas I Wouldlike You to Learn

PX – VX – F = P

whereP = unit priceX = volume of units soldV = variable cost per unitF = total fixed priceP = operating income or profit



Breakeven

Breakeven is defined as the point where thefirm neither makes nor loses money.The formula for breakeven is:PX – VX – F = 0Let us illustrate the solution for breakeven withan example.



Example

Morris Electronics makes calculators.The market dictates a price of $30 for a modelwith their particular features.Variable costs per unit are $16, total fixedcosts are $200,000.What is the breakeven point in units for sales

of the calculators?



Solution

PX - VX – F = 030X – 16X – 200,000 = 014X = 200,000X = 14,285.714286calculators

Income statement

Sales $428,571

Variable cost 228,571

Contributionmargin

$200,000

Fixed cost 200,000

Operatingincome

$0

Note that at breakeven, contribution margin equals fixedcosts.



New Problem

Most companies are not in the business tobreakeven.Assume that Morris Electronics wants to make$50,000.How many calculators will they have to sell toachieve that objective?

We are solving for ―target sales‖



Solution

PX - VX – F = P

30X – 16 X – 200,000 = 50,00014X = 250,000

X = 17,857.14285 calculatorsWhat if we want to know the sales dollarvolume to break even?17,857.14285 x 30 = $535,714



Deriving an Alternate Formula

PX – VX – F = PSimplifying the equationX(P – V) – F = PBut we know that price per units minus variable costper unit equals the contribution marginSince (P – V) = CMu(CMu)(X) = F + PX = (F + P)/CMu when we want to know target sales

in units for a specific level of profitsIf we are solving for target sales at breakeven, P = 0soX = F/CMu

Formulas for target sales with a profit and no profit (breake



Example Problem

Let us use the same data from MorrisElectronics, where the company wants to earna $50,000 profit.

X = (F + P)/CMuX = (200,000 + 50,000)/14X = 250,000/14X = 17,857.142858 units breakevenOrSale at breakeven = 17,857.142858 x 30 =$535,714



Now Finding Breakeven SalesDollar Volume

We can either multiply 17,857.142858 times thesales price of $30, or use this formulaS = (F + P)/CMr where S = sales dollars, CMrstands for contribution margin ratio, and thecontribution margin ratio is defined thus:CMr = Total Contribution Margin/SalesOr CMr = Unit Contribution Margin/Price

CMr in this problem is 14/30 = .466667So sales in dollars = (200,000 + 50,000)/.466667=$535,714



Therefore the Formula ForBreakeven Would Be:

S = (F + P)/CMrOrS = (F + 0)/CMr

OrS = F/CMrTwo formulas to get the same answers!

To get breakeven in dollars use F/CMr whereCMr is the contribution margin ration(contribution margin divided by sales).



Let Us Solve Another Problem

Assume that Morris Electronics can onlymanufacture 15,000 units a year.The variable cost is $16 per unit, and fixedcosts are $200,000 per year.Assuming that they want to earn $50,000 peryear, what must the price be to obtain their net

profit objective?



Solution

PX – VX – F = P(15,000) – 16(15,000) – 200,000 = 50,00015,000P – 240,000 – 200,000 = 50,00015,000P = 490,000P = $32.6667To check:$490,000 – 240,000 – 200,000 = $50,000



Alternate Formulas

We could have used:X = (F + )/CMu to solve for breakeven in unitswhere of course is 0OrS = (F + )/CMr to solve for breakeven in salesdollars to get the same results (again at

breakeven is 0).In this case, S is of course sales dollars.



Income Statements

Sales $xxx

Cost of Goods Sold xxxGross Margin xxx

Administrative andSelling Expense

xxx

Income xx

Traditional income statement CVP Income Statement

Sales $xxx

Variable Costs xxxContribution Margin xxx

Fixed Costs xxx

Income xx

A better income statement to use for internal reporting,especially when management wants to do CVP analysis,is the CVP income statement shown above.



Income Statements

It is better, because it gives us the figures needed forCVP analysis.

FASB still requires the traditional income statement forexternal reporting, however.



One More Concept . . .

Margin of Safety: The difference betweenactual or expected sales and sales at thebreak even point.

The formula is:Actual (expected) sales – breakeven sales =margin of safety in dollars.



Problem

Johnson Foundry currently sells $1,500,000 ofproduct a year.Their breakeven point is $1,250,000.What is their margin of safety?$1,500,000 – $1,250,000 = $250,000



Separating Fixed and VariableCosts

One method (a very inaccurate method) ofseparating fixed and variable costs is the high-lowmethod.

The method is inaccurate because it dependsupon only two data points, a high and low point.The small sample size, plus the fact that highand/or low points are often outliers caused byinaccurate readings make it inadvisable to use inthe real world.Nevertheless, since the book teaches it, so will I(sigh).



Steps

Use the following formula to determinevariable costs.

( )( )

high costs low costsvariablecosts per unit highactivity lowactivity



Steps

Calculate total variable cost and total costs athigh or low activity.Subtract total variable costs from total costs (athigh or low activity) to determine total fixedcosts.



Example

Community Hospital’s controller has providedyou with the following information. Using thehigh-low method, divide payroll into fixed and

variable costs. Chest Labor

X-rays Dollars

January 1,200 16,400

February 1,400 18,800

March 900 12,800

April 875 12,500

May 1,300 17,600

June 1,350 18,200

High

Low



Solution

( )high costs low costsvariablecosts per unit high activity lowactivity

$18,800 $12,500$12/

1, 400 875

xray

1. Calculate variable costs using this formula.



Solution

2. Calculate variable costs at high or low (we willuse high here).$12 variable cost per x-ray x 875 x-rays =

$10,5003. Subtract variable costs at high or low (we willuse low here) from total costs to get fixed costs.

$12,500 total costs – 10,500 variable costs =$2,000 fixed costsSummary: variable costs = $12 per unit andfixed costs = $2,000 per period (per month in

this case)



Question

Given this data what would be the total cost at1,145 x-rays?Variable costs = $12 x 1,145 = $13,740Fixed costs = $2,000Total costs at 1,145 x-rays = $15,740

The best method, the least squares methodcan beworked using Excel or a financial calculator. Ifyouwant to learn how to do it on a financialcalculator, look in the hp 10bII instruction book



Brief Exercise 5-1

Monthly costs for two levels of production aregiven below. From this information determinewhich costs are variable, fixed, and mixed, and

give the reason for each answer.Cost 3000 units 6000 units

Indirect labor $10,000 $20,000

Supervisory salaries $5,000 $5,000

Maintenance 4,000 7,000



Brief Exercise 5-1

Cost 3000 units 6000 unitsIndirect labor $10,000 $20,000

Supervisory salaries $5,000 $5,000Maintenance 4,000 7,000

Indirect labor is obviously variable, as it varies proportionally

with volume. When volume doubles, costs double.



Brief Exercise 5-1



Supervisory salaries are obviously fixed, since they stay the sa

At different levels of production.



Brief Exercise 5-1



Maintenance salaries are mixed, since they increase,

but not proportional to increase in production volume.



Brief Exercise 5-2

For Loder Company, the relevant range ofproduction is 40% to 80% of capacity.At 40% of capacity, variable cost is $4000 and

fixed cost $6,000.Diagram the behavior of each costs within therelevant range assuming the behavior is linear.



Brief Exercise 5-2

To create these graphs I used Excel.



Brief Exercise 5-3

For Hunt Company, a mixed cost is $20,000plus $16 per direct labor hour.Diagram the behavior of the cost using

increments of 500 hours up to 2,500 hours onthe horizontal access, and increments of$20,000 up to $80,000 on the vertical axis

Note to students: I think the question would have been clearer if the author had said “fixed cost is $20,000 plus$16 per direct labor hour.”



Brief Exercise 5-3



Exercise 5-2

Kozy Enterprises is considering manufacturinga new product.It projects the costs of direct materials and

rents for a range of output as shown on thefollowing slide.



Output in Units Rent Expense Direct Materials1000 5000 4000

2000 5000 6000

3000 5000 7800

4000 7000 8000

5000 7000 10,000

6000 7000 12,000

7000 7000 14,000

8000 7000 16,000

9000 7000 18,00010,000 10,000 23,000

11,000 10,000 28,000

12,000 10,000 36,000



Exercise 5-2

Relevant Range



Exercise 5-2

The relevant range is 4,000 – 9,000 units ofoutput since a straight-line relationship existsfor both direct materials and rent within this

range.



Exercise 5-4

Identify each of the following costs as variable,fixed, or mixed.Wood used in production of furniture —variable

Fuel used in delivery trucks – variableStraight-line depreciation on factory buildings – fixedScrews used in production of furniture – variableSales staff salaries – fixedSales commissions – variableProperty taxes – fixed



Exercise 5-4

Insurance on buildings – fixedHourly wages of furniture craftsman – fixedSalaries of factory supervisor – fixedUtilities expense – mixedTelephone bill – mixed



Brief Exercise 5-8

Larisa Company has a unit selling price of$520, variable costs per unit of $286, and fixedcost of $187,200.

Compute the breakeven in units using themathematical equation and contributionmargin per unit.



Mathematical Equation

PX – VX – F = 520X – 286X – 187,200 = 0234X = 187,200X = 800



Contribution Margin Per Unit

Breakeven = F/CMu187,200/(520 – 286)187,200/234X = 800 units



Brief Exercise 5-9

Turgro Corp. had total variable cost of$180,000 total fixed costs of $160,000, andtotal revenues of $300,000.

Compute the required sales in dollars to breakeven.



Brief Exercise 5-9

We know that at breakeven, fixed costs =contribution margin.Since fixed costs are $160,000 then the

contribution margin must be $160,000We know that CMr is CMt/Sales (CMt = totalcontribution margin from income statement)

From the data given in the problem we knowthe CMr is (300,000 – 180,000)/300,000 =40%So when CMt is $160,000, then sales must be$160,000/.40 = $400,000



Brief Exercise 5-10

For MeriDen Company, variable costs are 60%of sales and fixed costs are $195,000.Management’s net income goal is $75,000.

Compute the required sales in dollars neededto achieve management’s target net income if $75,000.

Use the contribution margin approach.



Brief Exercise 5-10

S (target sales) = (F + )/CMrS = (195,000 + 75,000)/.40

How did I get .40 for CMr? One trick to remember

is that contribution margin ratio is (1 – variableexpense ratio)Thus CMr is 1 - .60 = .40

S = $270,000/.40S = $675,000



Exercise 5-8

Green with Envy provides environmentallyfriendly lawn services for homeowners.Its operating costs are as follows:

Depreciation = $1,500/monthAdvertising = $200/monthInsurance = $2,000/monthWeed and feed materials = $13/lawn

Direct labor = $12/lawnFuel = $2/lawn

Compute breakeven in units and dollars.



Exercise 5-8

Fixed costs are $1,500 + $200 + $2,000 =$3,700 per monthVariable costs are $13 + $12 + $2 = $27 perlawnPX - VX - F = 060X – 27X – 3,700 = 033X = 112.12 lawnsBreakeven sales dollars = 112.12 x 60 =$6,727.27



Exercise 5-10 (Not assigned)

During the month of March, New Day Spaservices 570 clients at an average price of$120. During the month, fixed costs were

$21,000 and variable costs were 65% of sales.What was the contribution margin . . .

In dollarsPer unitAnd as a ratio?



Contribution Margin

Sales (570 x $120) $68,400

Variable costs (.65 x $68,400) 44,460

Contribution margin $23,940

In dollars . . .

Per unit . . .

$23,940/570= $42

As a ratio . . .

42/120 = .35



Breakeven Point

Breakeven in $ = F/CMrBreakeven in $ = $21,000/.35 = $60,000Breakeven in Units = F/CMuBreakeven in Units = $21,000/$42Breakeven in Units = 500



Exercise 5-14

Lynn Company had $150,000 of net income in2008 when selling price per unit was $150.Variable costs were $90.

Fixed costs were $570,000.Management expects per-unit data and totalfixed cost to remain the same in 2009.

Management is under pressure to increase netincome by $60,000 in 2009.



Exercise 5-14

Compute the number of units sold in 2008PX – VX – F = P

150X – 90X – 570,000 = 150,00060X = 720,000X = 12,000 units



Exercise 5-14

Question: How many units would have had tohave been sold in 2009 to reach thestockholder’s desired profit level? Target sales in units = PPX – VX – F = P150X – 90X - $570,000 = ($150,000 +$60,000)

60X = $570,000 + $150,000 + $60,00060X = $780,000X = 13,000 units



Exercise 5-14

Assume Lynn Company sells he same numberof units in 2009 as it did in 2008.What would the selling price have to be in

order to reach the stockholder’s desired profitlevel?PX – VX – F = P

12,000P – (90)(12,000) – 570,000 = 210,00012,000P = 1,860,000P = $155



The End!

Cost Volume Profit Revised March 3 08

Documents

Transcript of Cost Volume Profit Revised March 3 08