
The Breakeven Point

The breakeven point (BEP) is the level of activity, in units
or dollars, at which total revenues equal total costs.

The following list summarizes the basic simplifying assumptions
about revenue and cost functions:

Relevant Range: A primary assumption is
that the company is operating within the relevant range of activity specified in determining the revenue and cost information
used in each of the following assumptions.

Revenue: Total revenue fluctuates in direct
proportion to units sold, while revenue per unit is assumed to remain constant; fluctuations in perunit revenue for factors
such as quantity discounts are ignored.

Variable Costs: Total variable costs fluctuate
in direct proportion to level of activity or volume. Variable costs per unit remain constant within the relevant range. Variable
costs exist in all functional business areas including production, distribution, selling, and administration.

Fixed Costs: Total fixed costs 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.

Mixed Costs: Mixed costs must be separated
into their variable and fixed elements before they can be used in breakeven analysis. Any method that validly separates these
costs in relation to one or more predictors may be used.

Contribution margin (CM) id defined as selling price per
unit minus all variable production, selling, and administrative costs per unit.

Total contribution margin fluctuates in direct proportion
to sales volume.

The formula approach to breakeven uses an algebraic equation
to calculate the breakeven point.

The answer to the equation is not always acceptable and
may need to be rounded to a whole number.

Breakeven volume is equal to total fixed cost divided by
the difference between revenue per unit and variable cost per unit.

Algebraic breakeven computations use an equation that represents
the income statement and groups costs by behavior to show 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
X = number of units sold or to be sold
R(X) = total revenue
FC = total fixed cost
VC = variable cost per unit
VC(X) = total variable cost
P = beforetax profit

The equation represents an income statement, so P can be
set equal to zero for the formula to indicate a breakeven situation.

The breakeven point in units can be found by solving the
equation for X:
X = FC ¸ (R – VC)

The contribution margin ratio (CM%) is contribution margin
divided by revenue; indicates what proportion of selling price remains after variable casts have been covered.

The BEP can be expresses in either units or dollars of revenue:
(1) the BEP in sales dollars can be found by multiplying the BEP in units by the selling price per unit, or (2) the BEP in
sales dollars can also be found by dividing total fixed cost by the CM%
X$ = FC ¸ CM%
Where X$ = breakeven point in sales dollars
CM% = contribution margin ratio = (R – VC) ¸ R

CVP Analysis (See text Exhibits 62, 63, 64, and 65.)

Costvolumeprofit analysis is a process of examining the
relationships among revenues, costs, and profits for a relevant range of activity and for a particular time frame. The technique
is applicable in all economic sectors (manufacturing, wholesaling, retailing, and service industries) since the same types
of managerial functions are performed in each type of organization.

CVP analysis uses the same algebraic income statement formula
that is used for the calculation of the breakeven point, but includes a profit amount.

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.

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.

Profits may be stated either as a fixed or variable amount
and on either a beforetax or aftertax basis.

The amount of profit may be specified – after the
breakeven point is reached, each dollar of contribution margin is a dollar of profit.

The formula would appear as follows for a fixed amount of
profit before taxes:
In units: R(X) – VC(X) = FC + PBT
In sales dollars: X$ = (FC + PBT) ¸ CM%
Where PBT = specified amount of profit before tax

The formula would appear as follows for a fixed amount of
profit after taxes:
R(X) – VC(X) – FC = PBT
And [(PBT)(TR)] = Tax Expense
PBT – [(TR)(PBT)] = PAT
Where TR = tax rate
PAT = specified amount of profit after tax

Managers may want desired profit to be equal to a specified
variable amount of sales.

The formula would appear as follows for a variable amount
of profit before taxes:
R(X) – VC(X) – FC = PuBT(X)
Where PuBT(X) = desired profit per unit before taxes

The formula would appear as follows for a variable amount
of profit after taxes:
R(X) – VC(X) – FC = PuBT(X)
And PuBT(X) [(1TR0] = PuAT
So X = FC ¸ (CM – PuBT)
Where PuAT(X) = desired profit per unit after tax

CVP Analysis in a Multiproduct Environment (See text Exhibit
66)

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.

The constant sales mix assumption compares the sales mix
to a bag or package of items that are sold together.

The computation of a weighted average contribution margin
ratio for the bag of products being sold is necessary under the constant sales mix assumption.

Any shift in the sales mix proportion of products will change
the weighted average contribution margin and the breakeven point.

Underlying Assumption of CVP Analysis

The CVP model is a useful planning tool that can provide
information on the impact on profits when changes are made in the costing system or in sales levels.

The CVP model, like other humanmade 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.

CVP is a tool that focuses on the shortrun partially because
of the assumptions that underlie the calculations.

The assumptions are necessary, but they limit the accuracy
of the results.

The underlying assumptions are:

All variable cost revenue behavior patterns are constant
per unit and linear within the relevant range.

Total contribution margin is linear within the relevant
range and increases proportionally with output.

Total fixed cost is a constant amount within the relevant
range.

Mixed costs can be accurately separated into their fixed
and variable elements. Such accuracy is especially unrealistic, but reliable estimates can be developed from the highlow
method or least squares regression analysis

Sales and production are equal; thus, there is no material
fluctuation in inventory levels. This assumption is necessary because otherwise fixed costs might be allocated to inventory
at different rates each year. The assumption is more realistic as more firms start to utilize JIT inventory systems.

There will be no capacity additions during the period under
consideration. If such additions were made, fixed ( and possible variable) costs would change, invalidating the first three
assumptions.

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 for CVP
analysis.

Either there is no inflation or, inflation affects all cost
factors equally. Or. If factors are affected unequally, the appropriate effects are incorporated into the CVP figures.

Labor productivity, production technology, and market conditions
will not change. If any of these factors changed, costs would change correspondingly, and it is possible that selling prices
would change, invalidating the first three assumptions.

Costs and Quality

Cost, price, and volume work handinhand with a fourth
factor, quality.

The quality specifications of a product and its components
will play an important part in influencing costs, and quality products are typically able to command higher selling prices.

Consideration of the implications of quality changes on
cost, price, and volume should assist managers in concentrating their attention on the long run more than on the short run.

Analyzing Effects of ShortRun Operational Changes

Many decisions are made on the basis of incremental analysis,
which encompasses the concept of relevant costing, which allows managers to focus on pertinent facts and disregard extraneous
data.

While relevant costing decisions are often viewed by managers
as shortrun, each decision also has vital longrun implications.

The Concepts of Relevance and Relevant Costing

Relevant costs are costs that are pertinent to or logically
associated with a specific problem or decision and that differ between alternatives.

Two prevailing rules for shortrun decision making are that

most variable costs are treated as relevant and

most fixed costs are not.

Relevant costing is a process that allows managers to focus
on pertinent facts and disregard extraneous information by comparing, to the extent possible and practical, the differential,
incremental revenues and incremental costs of alternative decisions.

Relevant information supports decision making, and information
is relevant when it is logically related to the decision.

Incremental revenue is the additional revenue resulting
form a contemplated sale of a quantity of output.

Incremental cost is the additional cost of producing or
selling a contemplated quantity of output.

Opportunity cost represents the benefit foregone when one
course of action is chosen over another.

The difference between the incremental revenue and incremental
costs of a particular alternative is the positive or negative incremental benefit of that course of action.

Management can compare the incremental benefits of various
alternatives to decide on the most profitable or least costly alternative or set of alternatives.

Sunk costs are the historical or past cost that is associated
with the acquisition of an asset or a resource and that have no future recovery value.

Relevant Costs in Scarce Resource Decisions

A scarce resource is an item that is essential to production
activity but that is available only in a limited quantity.

Scarce resources create constraints on producing goods or
providing services and can include money, machine hours, skilled labor hours, raw materials, and production capacity.

Management may desire and be able to obtain a greater abundance
of a scarce resource in the long run, but management must make the best current use of the scarce resources it has in the
short run.

The determination of the best use of a scarce resource requires
that specific company objectives be recognized.

The outcome of a scarce resource decision will always indicate
that a single type of product should be manufactured and sold when one limiting factor is involved.

One method of solving problems that have several limiting
factors is linear programming, which finds the optimal allocation of scarce resources when there is one objective and multiple
restrictions on achieving that objective.

Company management must consider qualitative aspects of
the problem in addition to the quantitative ones.

Relevant Costs in Sales Mix and Sales Price Decisions

Sales mix is the relative combination of quantities of sales
of the various products that make up the total sales of a company.

Some important factors that affect the appropriate sales
mix are (1) product selling prices and (2) advertising expenditures. A change in one or both of these factors may cause a
company’s sales mix to shift.

Managers must constantly monitor the relative selling prices
of company products, both in respect to each other as well as to competitor’s prices.

Total contribution margin must be maximized in order to
maximize profit.

Unit contribution margin and sales volume should be evaluated
together when profitability is assessed.

The sales volume of a product or service is normally directly
related to its selling price. When the selling price is increased and demand is elastic with respect to price, demand for
the product or service decreases.

In deciding to raise or lower prices, the relevant quantitative
factors include:

prospective or new contribution margin per unit of product;

both shortterm and longterm changes in product demand
and production volume caused by the price increase or decrease; and

best use of any scarce resources.

Relevant qualitative factors that are related to price change
decisions are:

influence on customer goodwill;

customer product loyalty; and

competitor’s reactions.

Special order pricing is the process of setting a sales
price for manufacturing or service jobs that are outside the company’s normal production or service realm.

Relevant Costs in Product Line Decisions

Operating results of multiproduct environments are frequently
presented in a format that indicates separate product lines in order to expedite performance evaluations.

Managers, in reviewing such disaggregated statements, must
distinguish relevant from irrelevant information in a manner that relates to the individual product lines.

A common cost is a cost that cannot be associated with a
particular cost object and is incurred because of general production activity.

Product margin represents the excess of a product’s
revenues over both its direct variable expenses and any avoidable fixed expenses related to the product.

It is the amount remaining to cover unavoidable direct fixed
expenses and common costs and then to provide profits.

The product margin is the appropriate figure on which to
base continuation or elimination decisions since it measures the segment’s contribution to the coverage of indirect
and unavoidable costs.

Graphic Approaches to Breakeven Analysis – Appendix
1

A breakeven graph is a graphical depiction of the relationships
among revenues, variable costs, fixed costs, and profits (or losses). (See text Exhibit 615)

The following steps are required in preparing a breakeven
graph.

Label the xaxis as volume and the yaxis as dollars.

Plot the variable cost line with a slope equal to total
perunit variable cost.

Plot the revenue line with its slope equal to the unit sales
price.

To graph total cost, add a line parallel to the total variable
cost line.

The breakeven point is located where the revenue and total
cost lines intersect.

The format of the breakeven graph allows the following important
observations to be made.

Contribution margin is created by the excess of revenues
over variable costs. If variable costs are greater than revenues, no quantity of volume will ever allow a profit to be made.

Total contribution margin is always equal to total fixed
cost plus profit or minus loss.

Contribution margin must exceed fixed costs before profits
can be generated.

The profitvolume (PV) graph is a graphical presentation
of the profit or loss associated with each level of sales.

The horizontal axis on the PV graph represents unit sales
volume and the vertical axis represents dollars.

Amounts shown above the horizontal axis are positive and
represent profits, while amounts below the horizontal axis are negative and represent losses.

An Overview of Absorption and Variable Costing – Appendix
2

Absorption costing is a cost accumulation method that treats
the costs of all manufacturing components (direct materials, direct labor, variable overhead, and fixed overhead) as inventoriable,
or product, costs; also known as full costing. (See text Exhibit 617)

Total variable product costs increase with each additional
product made or service rendered, and are therefore considered to be product costs and are inventoried until the product or
service is sold.

Fixed overhead does not vary with units of production or
level of service; it provides the manufacturing capacity necessary for production to occur. Production could not take place
without the incurrence of fixed overhead, so fixed overhead is considered to be inventoriable under absorption costing.

Absorption costing presents expenses on an income statement
according to their functional classification. A functional classification is a grouping of costs incurred for the same basic
purpose.

Variable costing is a cost accumulation method that includes
only variable production costs (direct materials, direct labor, and variable overhead) as product or inventoriable costs and
treats fixed overhead as a period cost; also known as direct costing. (See text Exhibit 618)

A variable costing income statement or management report
separates costs by cost behavior, although it may present expenses by functional classification within the behavioral categories.

Cost of goods sold is more appropriately called variable
cost of goods sold since it is composed of only the variable production costs related to the units sold.

Product contribution margin is revenue minus variable cost
of goods sold.

Total contribution margin is revenue minus all variable
costs regardless of the area (production or nonproduction) of incurrence.

The accounting profession has unofficially disallowed the
use of variable costing as a generally accepted inventory valuation method for external reporting purposes.

Linear Programming – Appendix 3

Linear programming (LP) is a method used to solve problems
with one objective and multiple limiting factors; it determines the optimal allocation of scarce resources when the objective
and the restrictions on achieving that objective can be stated as linear equations.

The objective function is the mathematical equation that
states the maximization or minimization goal of a linear programming problem.

A constraint is a restriction on the ability to reach an
objective.

A feasible solution is an answer to a linear programming
problem that does not violate any of the problem constraints.

The optimal solution is the solution to a linear programming
problem that provides the best answer to the allocation problem without violating any problem constraints.

Simplex is an iterative technique used to solve multivariable,
multiconstraint linear programming problems; usually requires the aid of a computer.
Bibliography:
