ACA 212 STRATEGIC COST MANAGEMENT

Lesson 4 Cost-Volume-Profit Analysis

Learning Objectives:
At the end of the lesson, students should be able to answer the following questions:
1. Why is variable costing more useful than absorption costing in determining the break-even-point and doing cost
volume process analysis?
2. How is the break-even point determined in using the formula approach, graph approach, and income statement
approach?
3. How can a company use cost-volume-profit (CVP) analysis?
4. How do break-even and CVP analysis differ between single-product and multiproduct firms?
5. How are margin of safety and operating leverage concepts used in business?
6. What are the underlying assumptions of CVP analysis?

LECTURE NOTES

I. TERMINOLOGIES

Break-even chart - a graph that depicts the relationships among revenue, volume, variable costs, fixed costs, and profits
(or losses)
TC=TR Break-even point (BEP) - the level of activity, in units or pesos, at which total revenues equal total costs
CM Contribution margin - the difference between selling price and variable cost per unit or in total for the level of activity; it
Sales - VC indicates the amount of each revenue peso remaining after variable costs have been covered and going toward
the coverage of fixed costs and the generation of profits
CMr Contribution margin ratio - the proportion of each revenue peso remaining after variable costs have been covered;
computed as contribution margin divided by revenue
Cost-volume-profit (CVP) analysis - a procedure that examines changes in costs and volume levels and the resulting
effects on net income (profits)
DOL Degree of operating leverage - a factor that indicates how a percentage change in sales, from the existing or current
CM / OI or NI level, will affect company profits; it is calculated as contribution margin divided by net income; it is equal to (1 ÷
margin of safety percentage)
Incremental analysis - a process of evaluating changes that focuses only on the factors that differ from one course of
action or decision to another
MOS Margin of safety - the excess of the budgeted or actual sales of a company over its break-even point; it can be calculated
in units or pesos or as a percentage; it is equal to (1 ÷ degree of operating leverage)
Operating leverage - the proportionate relationship between a company’s variable and fixed costs
Profit-volume graph - a visual representation of the amount of profit or loss associated with each level of sales
VCr Variable cost ratio - the proportion of each revenue peso represented by variable costs; computed as variable costs
VC / Sales divided by sales or as (1 – contribution margin ratio)

II. TOPIC OUTLINE

A. The Break-Even Point.

1. The break-even point is the level of activity, in units or pesos, at which total revenues equal total costs.
2. Several simplifying assumptions must be made concerning revenue and cost functions.
a. Relevant range: The company is assumed to be operating within the relevant range of activity specified in
determining the revenue and cost information used in each of the following assumptions.

TOTAL REVENUE
P TOTAL COST
BEP
SALES
L
UNIT SOLD
 b. Revenue: Total revenue fluctuates in direct proportion to the level of activity or volume while revenue per
unit is assumed to remain constant, and fluctuations in per unit revenue for factors such as quantity
discounts are ignored.
c. Variable costs: Total variable costs fluctuate in direct proportion to level of activity or volume. Variable costs
per unit are assumed to remain constant within the relevant range. Variable production costs include direct
material, direct labor, and variable overhead; variable selling cost includes charges for items such as
commissions and shipping; and variable administrative costs may exist in areas such as purchasing.
d. Fixed costs: Total fixed costs are assumed to remain constant within the relevant range. Fixed cost per unit
decreases as volume increases, and it increases as volume decreases. Fixed costs include both fixed factory
overhead and fixed selling and administrative expenses.
e. Mixed costs: Mixed costs must be separated into their variable and fixed elements before they can be used
in CVP analysis. Any method (such as regression analysis) that validly separates these costs in relation to one
or more predictors may be used. After they are separated, the variable and fixed cost components of the
mixed cost take on the assumed characteristics previously mentioned.
3. Contribution margin (CM) is defined as the difference between selling price and variable cost per unit or in total
for a specific level of activity; it indicates the amount of revenue that remains after all variable costs have been
covered and goes toward the coverage of fixed costs and the generation of profits.

B. Formula Approach to Breakeven

1. The formula approach uses an algebraic equation to calculate the exact break-even point.
2. Sales activity, rather than production, is the focus for the relevant range.
3. Algebraic break-even computations use an equation that represents the variable costing income statement and
shows the relationships among revenue, fixed cost, variable cost, volume, and profit as follows:
R(X) – VC(X) – FC = P
where R = revenue (selling price) per unit
Sales xxx X = number of units sold or to be sold
(VC) xxx R(X) = total revenue
CM xxx FC = total fixed cost
(FC) xxx VC = variable cost per unit
IO xxx
VC(X) = total variable cost
P = profit
a. The equation represents an income statement, so P can be set equal to zero for the formula to indicate a
break-even situation.
b. The break-even point in units can be found by solving the equation for X:
X = FC ÷ (R – VC)
c. Break-even point volume is equal to total fixed cost divided by the revenue per unit minus the variable cost
per unit.
d. The formula can be abbreviated as follows using contribution margin to find the break-even point:
X = FC ÷ CM
where CM = contribution margin per unit
4. The break-even point can be expressed in either units or pesos of revenue.
a. The break-even point in sales pesos can be found by multiplying the break-even point in units by the selling
price per unit.
b. The break-even point in sales dollars can also be found by dividing total fixed cost by the contribution
margin ratio.
Sales = FC ÷ (1 – VC%)
or
Sales = FC ÷ CM%
where VC% = the percentage relationship of variable cost to sales
CM% = the percentage relationship of contribution margin to sales

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 Spu
(VCu)
CMu CM per unit (CMu) CMu
CMr c. Contribution margin (CM) ratio is the proportion of each revenue dollar remaining after variable costs have
been covered; it is computed as contribution margin divided by sales. Contribution margin ratio is often
termed contribution rate. CM / Sales or CMu / SPu
d. The variable cost (VC) ratio is the proportion of each revenue dollar represented by variable costs; it is
computed as variable costs divided by sales or as (1 – contribution margin ratio).
5. The break-even point provides a starting point for planning future operations.
a. Managers want to earn profits, not just cover costs, so the break-even point formula can be used by
substituting an amount other than zero for the profit (P) term.
b. This substitution converts break-even analysis to cost-volume-profit analysis.

C. CVP Analysis
1. Cost-volume-profit analysis is a procedure that examines changes in costs and volume levels and the resulting
effects on net income (profits).
a. CVP analysis can be used to calculate the sales volume necessary to achieve a desired target profit on a
before or after-tax basis
2. Managers can use CVP to plan and control more effectively since the technique allows them to concentrate on
the relationships between revenues, costs, volume changes, taxes, and profits.
a. The CVP model can be expressed through a formula or as a graph.
b. All costs—regardless of whether they are product, period, variable, or fixed—are considered in the CVP
model.
c. The same basic CVP model and calculations can be applied to a single- or multiproduct business.

3. Using Cost-Volume-Profit Analysis

a. CVP analysis requires the substitution of known amounts in the formula to determine an unknown amount.
The formula mirrors the income statement for selling price per unit, variable cost per unit, unit volumes, and
fixed costs to find the amount of profit generated under given conditions. In this context, profits are used to
refer to operating profits before extraordinary and other nonoperating, nonrecurring items.
b. A significant application of CVP analysis is the setting of a desired target profit and focusing on the
relationships between it and specified income statement amounts to find an unknown.
i. Volume is a common unknown in such applications since managers want to achieve a particular amount
of profit and need to know what quantity of sales must be generated to accomplish this objective.
ii. Selling price is not as common an unknown as volume since selling price is usually market-related rather
than being set solely by company management.
c. Profits may be stated as either fixed or variable amount and on either a before-tax or after-tax basis.

4. Fixed Amount of Profit

a. Each peso of contribution margin is a peso of profit after the break-even point is reached.
i. The formula to compute target profit before tax is as follows:
R(X) – VC(X) – FC = PBT
or
R(X) – VC(X) = FC + PBT
or
CM(X) = FC + PBT
or
X = (FC + PBT) ÷ CM
where PBT = fixed amount of profit before taxes
ii. The formula to compute target profit after taxes is as follows:
PBT – [(TR) (PBT)] = PAT
and
R(X) – VC(X) – FC – [(TR) (PBT)] = PAT

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 where PBT = fixed amount of profit before tax
PAT = fixed amount of profit after tax
TR = tax rate
PBT is further defined as:
PBT – (1 – TR) = PAT
or
PBT = PAT ÷ (1 – TR)

substituting into the formula

R(X) – VC(X) – FC = PBT
or
R(X) – VC(X) = FC + PBT
or
(R – VC)(X) = FC + [PAT ÷ (1 – TR)]
or
CM(X) = FC + [PAT ÷ (1 – TR)]

5. Set Amount of Profit Per Unit

a. Managers may wish to analyze profit as a set amount per unit.
b. This treats profits similarly to a variable cost.
c. A set amount of profit can be stated on either a before tax or after-tax basis or as either a percentage of
revenues or a per unit amount.
d. Set amount of profit per unit before tax
i. The adjusted CVP formula for computing the necessary unit sales volume to earn a specified amount of
profit before tax per unit is as follows:
R(X) - VC(X) - FC = PuBT(X)
or
R(X) - VC(X) - PuBT(X) = FC
or
CM(X) - PuBT(X) = FC
or
X = FC ÷ (CM – PuBT)
e. Analysis of a set amount of profit per unit after tax
i. The adjusted CVP formula for computing the necessary unit sales volume to earn a specified amount of
profit after tax per unit is as follows:
R(X) - VC(X) - FC – {(TR) [PuBT(X)]} = PuAT(X)
where PuAT = amount of profit per unit after tax
or
X = FC ÷ (CM – PuBT)
where PuBT = variable amount profit per unit before taxes

D. The Graph Approach to Breakeven

1. A break-even chart is a graph that depicts the relationships among revenues, volume, and costs.
2. The BEP is located at the point where the total cost and total revenue lines intersect.
3. The traditional approach to graphical break-even analysis is a break-even chart that does not show contribution
margin.
4. The profit-volume graph is a visual representation of the amount of profit or loss associated with each level of
sales.
a. The horizontal axis on the PV graph represents unit sales volume and the vertical axis represents dollars.
b. Amounts shown above the horizontal axis are positive and represent profits, while amounts below the
horizontal axis are negative and represent losses.
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 E. The Income Statement Approach
1. The income statement approach to CVP analysis allows the preparation of pro forma (budgeted) statements
from available information.
2. Income statements can be used to prove the accuracy of computations made the CVP formula, or the
statements can be prepared simply to determine the impact of various sales levels on profit after taxes (net
income).

F. Incremental Analysis for Short-Run Changes

1. The break-even point may increase or decrease, depending on the particular changes that occur in the revenue
and cost factors.
a. The break-even point will increase if there is an increase in total fixed cost or a decrease in unit (or
percentage) contribution margin.
b. A decrease in contribution margin could arise due to a reduction in selling price, an increase in variable unit
cost, or a combination of the two.
c. The break-even point will decrease if there is a decrease in total fixed cost or an increase in unit (or
percentage) contribution margin.
d. Any factor that causes a change in the break-even point will also cause a shift in total profits or losses at any
activity level.
2. Incremental analysis is a process of evaluating changes that focuses only on the factors that differ from one
course of action or decision to another.

G. CVP Analysis in a Multiproduct Environment

1. A constant product sales mix or, alternatively, an average contribution margin ratio must be assumed in order to
perform CVP analysis in a multiproduct company.
2. The constant sales mix assumption can be referred to as the “bag” (or “basket”) assumption, with sales mix
representing a bag of products that are sold together.
3. The computation of a weighted average contribution margin ratio for the bag of products being sold is necessary
under the constant sales mix assumption.
4. Any shift in the sales mix proportion of products will change the weighted average contribution margin and the
break-even point.

MOS H. Margin of Safety SALES WILL GO DOWN WITHOUT INCURRING LOSSES

1. The margin of safety is the excess of the budgeted or actual sales of a company over its break-even sales; it can
be calculated in units or dollars or as a percentage; it is equal to (1 ÷ degree of operating leverage).
2. The margin of safety is the amount that sales can drop before reaching the break-even point and, thus, provides
a certain amount of “cushion” from losses.
3. The following formulas are applicable:
a. Margin of safety in units = Actual units – Break-even units units - BE units
b. Margin of safety in Php = Actual sales Php – Break-even sales in Php sales - BE sales
c. Margin of safety % = Margin of safety in units ÷ Actual unit sales MOS unit / unit sales Actual sales 500k
(or) BE sales ( 400k)
MOS sale / sales MOS 100K
d. Margin of safety % = Margin of safety in Php ÷ Actual sales Php
4. The margin of safety calculation allows management to determine how close to a danger level the company is
operating, and thus provides an indication of risk. MOS / SALES if nag baba ang sales mo ng 15% lang meaning pasok
= 100K / 500K sa 20% so bale safe ka parin sa loss.pero pag nag lagpas na ng
I. Operating Leverage MOS % = 20% 20% ang binaba meaning ang laki na nh loss mo.
1. Operating leverage is the proportionate relationship between a company’s variable and fixed costs.
2. Low operating leverage and a relatively low break-even point are found in companies that are highly labor-
intensive, have high variable costs, and low fixed costs.
a. Companies with low operating leverage can experience wide swings in volume levels and still show a profit.

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 b. An exception is a sports team, which is highly labor-intensive, but whose labor costs are fixed.
3. High operating leverage and a relatively high break-even point are found in companies that have low variable
costs and high fixed costs.
a. Companies will face this type of cost structure and become more dependent on volume to add profits as
they become more automated.
b. A company’s cost structure, or the relative composition of its fixed and variable costs, strongly influences
the degree to which its profits respond to changes in volume.
c. Companies with high operating leverage also have high contribution margin ratios.

DOL 4. The degree of operating leverage is a factor that indicates how a percentage change in sales, from the existing
CM / OI or current level, will affect company profits; it is calculated as contribution margin divided by net income; it is
SALES equal to (1 ÷ margin of safety percentage). The calculation providing the degree of operating leverage factor is:
(VC) a. Degree of operating leverage = Contribution margin ÷ Profit before tax
CM b. The calculation assumes that fixed costs do not increase when sales increase.
(FC)
OI c. The degree of operating leverage decreases the farther a company moves from its break-even point; when
the margin of safety is small, the degree of operating leverage is large.

J. Underlying Assumptions of CVP Analysis

1. CVP analysis is a short-run model that focuses on relationships among selling price, variable costs, fixed costs,
volume, and profits.
2. CVP is useful as a planning tool that can provide information about the impact on profits when changes are
made in the cost structure or in sales levels.
a. The CVP model, like other human-made models, is an abstraction of reality and, as such, does not reveal all
the forces at work. It reflects reality but does not duplicate it.
b. CVP is a tool that focuses on the short run partially because of the assumptions that underlie the
calculations.
c. The assumptions are necessary, but they limit the accuracy of the results.
3. The underlying assumptions are:
a. The revenue and cost behavior patterns are constant per unit and linear within the relevant range.
b. Total contribution margin is linear within the relevant range and increases proportionally with output.
c. Total fixed cost is a constant amount within the relevant range.
d. Mixed costs can be accurately separated into their fixed and variable elements. While accuracy of separation
may be questioned, reliable estimates can be developed from the use of the high-low method or least
squares regression analysis.
e. Sales and production are equal; thus, there is no material fluctuation in inventory levels. This assumption is
necessary because of the allocation of fixed costs to inventory at potentially different rates each year.
f. In a multiproduct firm, the sales mix will remain constant. If this assumption were not made, no useful
weighted average contribution margin could be calculated for the company.
g. Labor productivity, production technology, and market conditions will not change. Any such changes would
change costs correspondingly, and possibly selling prices would change, invalidating the first three
assumptions.

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