CostVolumeProfit Relationships

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Cost-Volume-Profit Relationships
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COST VOLUME PROFIT ANALYSIS

• HELPFUL TO UNDERSTAND THE RELATIONSHIP AMONG
  VARIABLE COSTS, FIXED COSTS AND PROFIT
• BASIC ASSUMPTIONS
• SELLING PRICE IS CONSTANT
• COSTS ARE LINEAR AND CAN BE DIVIDED INTO FIXED
  AND VARIABLE FIXED ELEMENT CONSTANT OVER THE
  RELEVANT RANGE UNIT VARIABLE COST CONSTANT OVER
  RELEVANT RANGE
• SALES MIX IS CONSTANT
• INVENTORIES STAY AT THE SAME LEVEL

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• Contribution Margin (CM) is the amount remaining
  from sales revenue after variable expenses have
  been deducted

• CM goes to cover fixed expenses.

• After covering fixed costs, any remaining CM
  contributes to income

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The Contribution Approach
For each additional unit Wind sells, 200 more
in contribution margin will help to cover fixed
expenses and profit.
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The Contribution Approach
Each month Wind must generate at least 80,000 in
total CM to break even.
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The Contribution Approach

• The break-even point can be defined either as
• The point where total sales revenue equals total
  expenses (variable and fixed).
• The point where total contribution margin equals
  total fixed expenses.

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CONTRIBUTION MARGIN RATIO
CMR CONTRIBUTION MARGIN RATIO CM /
SALES OR cmu/p VCR VARIABLE COST RATIO
VC/SALES OR vcu/p CMR VCR
1 EFFECT OF CHANGE IN FIXED COSTS? EFFECT OF
CHANGE IN VARIABLE COSTS? EFFECT OF CHANGE IN
SELLING PRICE?
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PROFIT ANALYSIS

• AT BREAKEVEN PROFIT 0
• BEFORE BREAKEVEN LOSS AFTER BREAKEVEN PROFIT
• CM COVERS FIXED COST UPTO BREAKEVEN POINT
• AFTER BREAKEVEN POINT INCREASE IN CM WILL
  INCREASE NET INCOME
• CM FC INCOME BEFORE TAX

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Changes in Fixed Costs and Sales Volume

• Wind is currently selling 500 bikes per month.
  Selling price per bike is 500, variable cost per
  bike is 300 and the fixed costs are 80,000 per
  month. The companys sales manager believes that
  an increase of 10,000 in the monthly advertising
  budget would increase bike sales to 540 units.
• Should we authorize the requested increase in the
  advertising budget?
• If sales increase by 50,000, what will be the
  increase in total contribution margin?

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Changes in Fixed Costs and Sales Volume
80,000 10,000 advertising 90,000
Sales increased by 20,000, but net income
decreased by 2,000.
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Changes in Fixed Costs and Sales Volume
The Shortcut Solution
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Break-Even Analysis

• Break-even analysis can be approached in two
  ways
• Equation method
• Contribution margin method.

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Equation Method
Profits(before tax) Sales (Variable
expenses Fixed expenses)
OR
Sales Variable expenses Fixed expenses
Profits (before tax)
At the break-even point profits equal zero.
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DERIVATION OF EQUATIONS
SALES VARIABLE COSTSFIXED COSTS PROFIT pq
vcu q FC AT BREAKEVEN PROFIT 0 pqvcu
q FC q (p-vcu) FC q FC / (p - vcu) OR
qFC/ cmu CM SALES - TOTAL VC VC SALES - CM
INCLUDE VARIABLE PRODUCTION AND SELLING
EXPENSES cmuCONTRIBUTION MARGIN PER UNIT p -
vcuCM/q vcu VARIABLE COST PER UNIT VC/ q q
number of units
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Equation Method
Here is the information from Wind Bicycle Co.
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Equation Method

• We calculate the break-even point as follows

Sales Variable expenses Fixed expenses
Profits
500q 300q 80,000 0 Where q
Number of bikes sold 500 Unit sales
price 300 Unit variable expenses 80,000
Total fixed expenses
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Equation Method

• We can also use the following equation to compute
  the break-even point in sales dollars.

Sales Variable expenses Fixed expenses
Profits
X 0.60X 80,000 0
Where X Total sales dollars 0.60
Variable expenses as a percentage
of sales 80,000 Total fixed expenses
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Equation Method

• We can also use the following equation to compute
  the break-even point in sales dollars.

Sales Variable expenses Fixed expenses
Profits
X 0.60X 80,000 0
0.40X 80,000 X 200,000
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Contribution Margin Method
The contribution margin method is a variation of
the equation method.
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CVP Graph
Profit Area
Dollars
Break-even point
Loss Area
Units
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Target Profit Analysis
Suppose Wind Co. wants to know how many bikes
must be sold to earn a profit of 100,000. We
can use our CVP formula to determine the sales
volume needed to achieve a target net profit
figure.
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The CVP Equation
Sales Variable expenses Fixed expenses
Profits
500Q 300Q 80,000 100,000 200Q
180,000 Q 900 bikes
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The Contribution Margin Approach
We can determine the number of bikes that must
be sold to earn a profit of 100,000 using the
contribution margin approach.
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The Margin of Safety
Excess of budgeted (or actual) sales over the
break-even volume of sales. The amount by which
sales can drop before losses begin to be incurred.
Margin of safety Total sales - Break-even
sales
Lets calculate the margin of safety for Wind.
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The Margin of Safety
Wind has a break-even point of 200,000. If
actual sales are 250,000, the margin of safety
is 50,000 or 100 bikes.
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The Margin of Safety
The margin of safety can be expressed as 20
percent of sales.(50,000 250,000)
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MARGIN OF SAFETY
EXCESS OF SALES (EITHER ACTUAL OR FORECASTED )
OVER THE BREAKEVEN SALES I.E., THE BUFFER
AMOUNT MoS ACTUAL OR BUDGETED SALES -
BREAKEVEN SALES MoS MoS / ACTUAL OR
BUDGETED SALES BREAKEVEN SALES IN SINGLE PRODUCT
SETTING SALES VC FC WHERE VCR x
SALES THEN 1-x CMR SALES
x SALES FC (1-x) SALES FC THAT IS
CMRSALES FC SALES AT BREAKEVEN FC/ CMR
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Operating Leverage

• A measure of how sensitive net income is to
  percentage changes in sales.
• With high leverage, a small percentage increase
  in sales can produce a much larger percentage
  increase in net income.

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Operating Leverage
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Operating Leverage
With a measure of operating leverage of 5, if
Wind increases its sales by 10, net income
would increase by 50.
Heres the proof!
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Operating Leverage
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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COST STRUCTURE AND PROFITABILITY

• HIGH VARIABLE COSTS LEAD TO LOWER CM AND LESS
  VULNERABLE IN CRISIS TIME
• HIGH FIXED COSTS CAUSE HIGHER BREAKEVEN POINT
  AFTER THE BREAKEVEN POINT PROFITS INCREASE FASTER
  THAN THE HIGH VARIABLE COST COMPANY
• DEGREE OF OPERATING LEVERAGE CONTRIBUTION
  MARGIN / NET INCOME
• FOR A GIVEN CHANGE IN SALES, INCOME WILL
  INCREASE BY ( INCREASE IN SALES DEGREE OF
  OPERATING LEVERAGE)
• DEGREE OF OPERATING LEVERAGE DECREASES AS THE
  SALES MOVE AWAY FROM THE BREAKEVEN POINT
• IF VARIABLE COSTS ARE HIGH DEGREE OF OPERATING
  LEVERAGE LOW AND VICE VERSA

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The Concept of Sales Mix

• Sales mix is the relative proportions in which a
  companys products are sold.
• Different products have different selling prices,
  cost structures, and contribution margins.
• Lets assume Wind sells bikes and carts and see
  how we deal with break-even analysis.

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The Concept of Sales Mix
Wind Bicycle Co. provides us with the following
information
265,000 550,000
48 (rounded)
170,000 0.48
354,167 (rounded)
WEIGHTED CMR
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• SALES MIX OF TOTAL SALES FOR EVERY PRODUCT
• THREE PRODUCTS A , B, C
• SALES OF a, b , c where a sales of
  product a / total sales etc.
• CMa CM OF PRODUCT A, B OR C
• WEIGHTED CMR a CMR of product A b CMR of
  product B c CMR of product C
• BREAKEVEN IN MULTIPLE PRODUCT S FC/ WEIGHTED CMR
• TO FIND HOW MANY UNITS MUST BE SOLD AT BREAKEVEN
  (OR FOR TARGET INCOME)
• 1.FIND BREAKEVEN IN MULTIPLE PRODUCTS
• 2.COMPUTE EACH PRODUCTS SALES AMOUNT BY
  MULTIPLYING THE SALES RATIO BREAKEVEN SALES
• 3.FIND THE BREAKEVEN SALE SHARE OF EACH PRODUCT
• 4.DIVIDE EACH PRODUCTS SHARE OF BREAKEVEN SALES
  BY THE UNIT PRICE OF EACH PRODUCT TO GET THE
  NUMBER OF UNITS TO BE SOLD OF EACH PRODUCT IN
  ORDER TO BREAKEVEN OR FOR TARGET INCOME

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