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Week Seven
C-V-P Analysis
Cost-Volume-Profit Analysis
CVP analysis is a method for analyzing how operatingdecisions and marketing decisions affect profit
Managers use CVP analysis to guide strategic decision
e.g. a decision about which feature to add to an existingproduct; how much to advertise, whether to expand intonew markets, and how to price the product.
These decision can affect SP, VC, FC units sold and OI
CVP analysis helps managers in making decision by
estimating the expected profitability of the choicesQ. What are the assumption of C-V-P analysis
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CVP analysis can be used in:
Setting prices for products and services
Determining whether to introduce a new product orservice
Replacing a piece of equipment
Determining breakeven point
Making Make-or-buy (i.e., sourcing) decisions
Determining the best product mix
Performing strategic what-if (sensitivity) analysis
Strategic Role of CVP Analysis
CVP analysis can help a firm choose its strategic position
and execute its strategy by providing an understanding of
how changes in sales volume affect costs and profits
This process is most important for cost leadership firmsduring the manufacturing stage
Differentiation firms use CVP analysis to assessprofitability and desirability of new products and features
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Profit Targets and Sales Revenue
The equation and contribution margin methods can be usedto determine the sales volume needed to achieve a targetprofit.
i.e. how many units must be sold to earn a certain amountof operating income.
Using equation method-
To calculate revenues needed to earn a certain amountof operating income -
Sales = Variable expenses + Fixed expenses + Profits
Using contribution margin method
To calculate the quantity must be sold to earn a target profit
OR
Q = [ (FC + TP) / CMPU ]
To calculate revenues needed to earn a certain amount ofoperating income
ORRevenues = [ (FC + TP) / CM% ]
Fixed expenses + Target profitUnit contribution margin
=Unit sales to attain
the target profit
Fixed expenses + Target profitContribution margin ratio
=Unit sales to attain
the target profit
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Risk and Uncertainty in DecisionMaking
Strategic decisions invariably involve riskand uncertainty
Risk differ from uncertainty.
Under risk the probability distribution of variables areknown, whereas, under uncertainty they are not known.
Q. What are the concepts managers apply to deal with risk
and uncertainty in the context of CVP?
Margin of safety (MS)
Is the unit sold (revenue earned) or expected to be sold
(revenue expected to be earned) above the break-evenvolume.
MS in unit = (Sales in unit BEP in unit)
It is a crude measures of risk
because there are unknown events that can lowersales below the expected level.
It states the amount by which sales can drop before
losses begin to incurred
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Operating Leverage (OL):
Operating leverage provides information concerning therelationship between a companys variable and fixed costs.
Give indication how sensitive net income is to percentagechange in sales.
OL act as multiplier
Generally, companies that are highly labor intensive tend tohave higher variable costs and lower fixed costs, and thus,low operating leverage. The reverse is also true for capitalintensive companies.
Degree of OL = CM / Profit
A higher DOL value indicates a higher risk in the sensethat a given change in sales will have a relatively greater
% impact on profits
Firms with a higher OL will experience greater reductionsin profits as sales decrease.
The DOL can be thought of as the extent to which fixedcosts characterize the cost structure of an organization:
the higher the percentage of fixed costs, the higher theDOL (and therefore the higher the operating risk)
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Characteristics of a highly leveraged company
Generally have high contribution margin since theirvariable costs tend to be lower. However, the higher fixedcosts would mean that the BEP would also be high.
If selling price is relatively stable, the volume of saleswould have high impact on profit/loss. A small increase insales volume can have a major impact on profit/loss withina given relevant range.
It is important to reduce operational leverage duringperiods of economic distress
Actual sales500 Bikes
Sales 250,000$
Less: variable expenses 150,000
Contribution margin 100,000
Less: fixed expenses 80,000
Net income 20,000$
$100,000$20,000 = 5
Example: Assume following information is gathered fromBicycle division of Racing Bicycle company.
At Racing Bicycle co., the degree of
operating leverage is =
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If sales are higher (in certain percentage) then theexpected/projected sales, then it has effect on the percentagechange in profits.
% change in profits= DOL x % change in sales
For example-with an operating leverage of 5, if Racing increasesits sales by 10%, net operating income would increase by 50%.
Percent increase in sales 10%
Degree of operating leverage 5
Percent increase in profits 50%Heres the verification!
Actual sales
(500)
Increased
sales (550)
Sales 250,000$ 275,000$
Less variable expenses 150,000 165,000Contribution margin 100,000 110,000
Less fixed expenses 80,000 80,000
Net operating income 20,000$ 30,000$
10% increase in sales from
$250,000 to $275,000 . . .
. . . results in a 50% increase in
income from $20,000 to $30,000.
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Sensitivity Analysis
Sensitivity analysis is a what-if technique that manager use toexamine-
how a result will change if the original predicted data are notachieved (due to uncertainty) or if an underlying assumptionchanges.
Therefore, this analysis is the calculation of an amount givendifferent levels of a factor that influences that amount
In the context of CVP analysis, sensitivity analysis answer suchquestion as-
What will operating income be if the units sold decreased say by5% from the originally predicted?
What will operating income be if variable cost per unit increasesay by 10% from the originally predicted?
Multiple Product CVP Analysis
What is multiple product CVP Analysis?
method for analyzing how operating decisions andmarketing decisions affect profit when company sell
multiple products
Assumptions required:
Sales mix (i.e. ratio of products sold) is assumed constant
Fixed costs is not directly related to a particular product.
Basic approach to deal with multi-product situation is -
Determine the Total Sales dollars and Total quantity ofunits to be sold as well as the Sales and Units Sales of
the individual products
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Setting up the problem
The challenge of Multiple product CVP analysis is diminishedwhen you set up the problem correctly.
Create CM income statement for each product
Create a total column that is a summation of the differentproducts
Example: Setting up the problem
Assume that a company sells two products: Product A andProduct B. The sales prices are $10 for product A and $15for product B. Variable costs per unit are $8 for Product Aand $9 for Product B. The company has total fixed costs of$5,000. Assume the company expects to sell 1,500 units ofProduct A and 500 units of Product B.
UNITS 1,500 500 2,000
Product A Product B TOTAL
Sales $ 15,000 $ 7,500 $ 22,500
Variable costs $ (12,000) $ (4,500) $ (16,500)
Contribution Margin $ 3,000 $ 3,000 $ 6,000
Fixed Costs $ (5,000)
Net Income $ 1,000
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Weighted Average CM and CM%Weighted Average CM
Take the Total CM from total column ($6,000 in example) anddivide by total units (2,000 in example).
In example this gives a Weighted Average CM of $3 per unit.UNITS 1,500 500 2,000
Product A Product B TOTAL
Sales $ 15,000 $ 7,500 $ 22,500
Variable costs $ (12,000) $ (4,500) $ (16,500)
Contribution Margin $ 3,000 $ 3,000 $ 6,000
Fixed Costs $ (5,000)
Net Income $ 1,000
Weighted Average CM is
$6,000/2,000 units = $3/unit
Weighted Average CM%
Take the CM from the TOTAL column ($6,000 in example) anddivide by the Sales from the total column ($22,500 in example).
$6,000 / $22,500 = 26.67% (.2667)
UNITS 1,500 500 2,000
Product A Product B TOTAL
Sales $ 15,000 $ 7,500 $ 22,500
Variable costs $ (12,000) $ (4,500) $ (16,500)
Contribution Margin $ 3,000 $ 3,000 $ 6,000
Fixed Costs $ (5,000)
Net Income $ 1,000
Weighted Average CM%
$6,000 / $22,500 = 26.67%
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Calculating the Breakeven Point in Units Use the formula you already know, but use weighted average
CM:
Breakeven units = (FC + Targeted Profit) / Wt. avg. CM
This gives the TOTAL number of units to be sold at the breakevenpoint. Then determine how many of Product A and Product B will besold at the breakeven point.
UNITS 1,500 500 2,000
Product A Product B TOTAL
Sales $ 15,000 $ 7,500 $ 22,500
Variable costs $ (12,000) $ (4,500) $ (16,500)
Contribution Margin $ 3,000 $ 3,000 $ 6,000
Fixed Costs $ (5,000)
Net Income $ 1,000
Breakeven Units:
(5000 + 0) / 3 = 1,667 (rounded)
The Allocation to Determine Units of EachProduct Sold at the Breakeven Point
Allocate Total Units to each product Based on ExpectedUnits Proportion
Must assume that the company will continue to sell the products
in fixed proportions.
In this example company sell 1,500 units of Product A and 500units of Product B.
So the proportion of units of Product A is 1,500/2,000 and theproportion of units of Product B is 500/2,000.
Take the total units to be sold at the breakeven point (1,667)and multiply by each products proportion
PRODUCT A: 1,667 * (1,500/2,000) = 1250 units
PRODUCT B: 1,667 * (500/2,000) = 417 units
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Calculating the Breakeven Point in
Sales Dollars Can be determined the breakeven point in Sales Dollars two
ways:
1. Calculate the Breakeven point in units and then multiply by thesales price per unit
2. Using the CM % method, directly calculate the Breakeven Point inSales Dollars
Multiply Breakeven Units by the sales price per unit
We know that the company will sell 1,250 units of Product A and 417units of Product B. Therefore,
Breakeven Sales Dollars of Product A:
1,250 * $10 per unit = $12,500
Breakeven Sales Dollars of Product B:
417 * $15 per unit = $6,255
Directly Calculate the Breakeven Sales Dollars Using CM %
Using the data from the Total column the Contribution Margin %
is 26.67%.
Using the Breakeven formula -determine the breakeven salesdollars for the company as a whole: (FC + Targeted Profit)/CM%
($5,000+0) / 26.67% = $18,748
Now allocation percentages of Sales Dollars for the individualproducts (based on given sales data) and Calculate SalesDollars using Proportions:
Product A: $18,748 * ($15,000 / $22,500) = $12,499
Product B: $18,748 * ($7,500 / $22,500) = $6,249
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Alternative Way to Deal withMultiple-Product CVP Analysis
Alternative approach to deal with multiple products situationis-
Convert the multi-product problem into a single-productproblem i.e.
identify the expected sales mix (in units) of the products.
Sales mix is the relative proportion in which a companys
products are sold. Different products have different selling prices, cost
structures, and contribution margins.
Determining sales Mix:
Can be measured in unit sold or in proportion of revenue.
But for CVP analysis, better to use sales mix expressed inunits.
e.g. say, sales mix of product X and Y is 3:2 whichmeans that it is expected to sell 3 units of X for ever 2units of Y.
After determining sales mix, firm can define the product it sellas package containing units X and Y.
By defining the product as package multiple product problemis converted into single product
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Now next step is to determine package contribution marginto calculate package BEP in units.
to calculate this the sales mix, individual product priceand variable cost are needed.
Therefore,
BE package = FC / Package contribution Margin
Limitation of the approach:
Complexity of the approach increase when the numberof product increases
ABC co. Produces and sells three types of yoga-trainingproducts: Video tapes, Basic equipment set and Yoga Mat. Lastyear Co. Sold 10,000 videos; 5,000 equipment sets and yoga
mats 20,000. Information on the three products is as follows:
Total fixed costs are $118,350
Required:
What is the sales mix of videos, equipment sets and yoga mats?
Calculate the BEQ of each product
Video Equipment Set Yoga Mat
Price $ 12.00 $ 15.00 $18
Variable cost perunit
4.00 6.00 $13
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Multiple-Product Break- Even
Analysis Example 11.9 Solution: R- 1 & 2
Product Sellingprice
VC CM Sales Mix Total CM
Videos $12 $4 $8 2 $16
Equip Sets 15 6 9 1 9
Yoga Mats 18 13 5 4 20
BE package ($118,350/$45) = 2,630
BE videos 2 x 2,630 = 5,260
Be Equip Sets 1 x 2,630 = 2,630
BE Yoga Mats 4 x 2,630 = 10,520
Conventional CVP Analysis andActivity-Based Costing (ABC)
Major limitation of traditional CVP Exclusive use of unit level activity cost drivers, i.e. does not
consider other categories of cost drivers
High probability of significant errors in cost estimation andprediction
ABC-costs are divided into units and non-units basedcategories
Therefore Activity based CVP is the expansion ofconventional CVP approach to incorporate non-unit activitycost drivers
Difficult to develop graphical relationships
Good way to begin is to make use of a contribution statementthat incorporates a hierarchy of cost drivers
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Note that :
If the assumption is made that say, total batch-level costsare fixed relative to the number of batches, bothapproaches will produce the same result
On the other hand, if the activity cost pool is a mixed cost,the ABC approach will provide a more accurate estimate ofcost because the traditional CVP approach treats all
activity costs that do not vary with output volume, (such asmachine setup, materials handling, inspection, andengineering, as fixed)
CVP Analysis in Service and Non-profit Organisations
To apply CVP analysis in service and nonprofitorganisation-
need to focus on measuring their output, which isdifferent from the tangible units sold.
Example of output measures in various service and nonprofitindustries:
Industry Measure of Output
Airlines Passenger miles
Hotels/motels Room-nights occupied
Hospitals Patient days
Universities Student credit-hours
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