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Cost & management Accounting II
CHAPTER ONE
Cost-Volume-Profit Analysis, Absorption, and Variable Costing
1.1 Absorption versus Direct Costing
Direct costing and absorption costing are two quantitative accounting models that are used by the
decision makers of the firm for two different purposes — for internal and for external
reporting. The direct costing model takes all the fixed cost to the income statement immediately.
The absorption costing model assigns the fixed cost to units produced during the period. The two
costing systems can produce different periodic income numbers if production and sales volume
fluctuate, i.e. differ from each other. Absorption costing and variable costing are methods used to
value companies' work in progress and inventory, for accounting purposes. Absorption
costing includes all the costs associated with the manufacturing of a product. Variable costing
includes the variable costs directly incurred in production and none of the fixed costs. For
reporting purposes, absorption costing is required under the International Accounting Standards
Board’s (IASB’s) International Financial Reporting Standards (IFRS). Absorption vs. variable
costing will only be a factor for companies that expense costs of goods sold (COGS) on their
income statement. Although any company can use both methods for different reasons, public
companies are required to use absorption costing due to their IFRS accounting obligations.
In the field of accounting, variable costing (direct costing) and absorption costing (full costing)
are two different methods of applying production costs to products or services. The difference
between the two methods is in the treatment of fixed manufacturing overhead costs. Under the
direct costing method, fixed manufacturing overhead costs are expensed during the period in
which they are incurred. Under the full costing method, fixed manufacturing overhead costs are
expensed when the product is sold.
Key Notes
 Absorption costing includes all of the direct costs associated with manufacturing a product.
 Variable costing can exclude some direct fixed costs.
 Absorption costing entails allocating fixed overhead costs to all units produced for an
accounting period.

 Variable costing includes all of the variable direct costs in COGS but excludes direct, fixed
overhead costs.
 Variable costing can provide a clearer picture of per-unit cost and inventory value because it
excludes the fixed overhead cost.
Direct and Indirect Costs
Before looking at absorption versus variable costing, it's important to understand the difference
between direct and indirect costs on the income statement. Direct costs are usually associated
with COGS, which affects a company’s gross profit and gross profit margin. Indirect costs are
associated with the operating expenses of a company. These costs heavily influence operating
profit and the operating profit margin.
Some of the direct costs associated with manufacturing a product include wages for workers
physically manufacturing a product, the raw materials used in producing a product, and direct
overhead costs involved in manufacturing a product.
Indirect expenses are not directly associated with manufacturing. These can include:
 Research and development
 Some depreciation
 Amortization of intangibles
 Selling expenses
 Marketing expenses
 Administrative expenses
 Other expenses
Absorption Costing
Absorption costing is also known as full costing. Public companies are required to use the
absorption costing method in cost accounting management for their COGS. Many private
companies also use this method because it is IFRS-compliant whereas variable costing isn't.
Absorption costing involves allocating all of the direct costs associated with manufacturing a
product to COGS. This includes any variable costs directly associated with manufacturing, i.e.

Cost of raw materials
Hourly cost of labor
Salaries of manufacturing workers
Variable costs of electricity used to run a plant in manufacturing mode
This also includes any direct fixed costs, such as:
The mortgage payment on a building used for manufacturing
Insurance on a manufacturing property
Depreciation on a manufacturing machine
Depending on a company’s level of transparency, an income statement using absorption costing
may break out variable direct costs and fixed direct costs into two line items or combine them
together to report a comprehensive COG. In any case, the variable direct costs and fixed direct
costs are subtracted from revenue to arrive at the gross profit.
Using the absorption costing method will increase COGS and thus decrease gross profit per unit
produced. This means companies will have a higher breakeven price on production per unit. It
also means that customers will pay a slightly higher retail price. Furthermore, it means that
companies will likely show a lower gross profit margin.
The impact of absorption costing will depend on the business. For example, a company has to
pay its manufacturing property mortgage payments every month regardless of whether it
produces 1,000 products or no products at all. A company may see an increase in gross profit
after paying off a mortgage or finishing the depreciation schedule on a piece of manufacturing
equipment. These are considerations cost accountants must closely manage when using
absorption costing.
The absorption costing method is typically the standard for most companies with COGS. It is
required for compliance with IFRS. Auditors and financial stakeholders will require it for
external reporting. Depending on the type of business structure, small businesses may also be
required to use absorption costing for their tax reporting.

A main advantage of absorption costing is that it is IFRS-compliant. That means that's the only method needed if it's
what a company prefers to use. If a company prefers the variable costing method for management decision-making
purposes, it may also be required to use the absorption costing method for reporting purposes.
Variable Costing
Some companies may choose to use the variable costing method. With variable costing, all of the
variable direct costs are included in COGS. The fixed direct costs are allocated to operating
expenses rather than COGS. The types of fixed direct costs are the same whether a company uses
absorption or variable costing:
 A mortgage payment on a building used for manufacturing
 Insurance on a manufacturing property
 Depreciation on a manufacturing machine
Variable costing will result in a lower breakeven price per unit using COGS. This can make it
somewhat more difficult to determine the ideal pricing for a product. Variable costing leads in to
slightly higher gross profit. In turn, that result in a slightly higher gross profit margin compared
to absorption costing.
Keep in mind; companies using the cash method may not need to recognize some of their
expenses as immediately with variable costing since they are not tied to revenue recognition.
This can be an advantage.
The reason variable costing isn't allowed for external reporting is because it doesn't follow the IFRS matching
principle. It fails to recognize certain inventory costs in the same period in which revenue is generated by the
expenses, like fixed overhead.

Key Differences
Both costing methods can be used by management to make manufacturing decisions. For internal
accounting purposes, both can also be used to value work in progress and finished inventory. The
overall difference between absorption costing and variable costing concerns how each accounts
for fixed manufacturing overhead costs.
Here's a summary of their differences.
Absorption Costing
Variable Costing
Method
Applies all direct costs, fixed
overhead, and variable
manufacturing overhead to
the cost of a product
Only variable costs are applied
to the cost of a product; fixed
overhead costs are expensed in
the period in which they occur
Use
Calculates a per-unit cost of
fixed overhead
Determines a lump-sum for
fixed overhead costs
Inventory
Inventory value includes
direct material, direct labor,
and all overhead
Inventory value does not include
fixed overhead
Accounting
Can cloud picture of
company profitability for an
accounting period because
all fixed costs are not
deducted from revenues
(unless all inventory is sold)
Doesn't match expenses to
revenue (with regard to
inventory) in the same
accounting period; may result in
a more realistic inventory value
and actual profit since unsold
stock doesn't absorb fixed
overhead costs
Reporting
Acceptable costing method
under IFRS
Not an acceptable costing
method under IFRS

Absorption Costing vs. Variable Costing Example
Let's say that ABC Company manufactures and sells 20,000 units of its product yearly. A single
product includes these costs:
 Direct materials: $3 per unit
 Direct labor: $5 per unit
 Variable manufacturing overhead: $2 per unit
 Fixed manufacturing overhead: $35,000 per year, which computes to a $1.75 per unit cost
($35,000/20,000 annual units)
Under the absorption costing method, per unit cost of product would be:
$3 + $5 + $2 + $1.75 = $11.75
Under the variable costing method, per unit cost of product would be:
$3 + $5 + $2 = $10
Is Variable Costing More Useful Than Absorption Costing?
It can be, especially for management decision-making concerning break-even analysis to derive
the number of product units needed to be sold to reach profitability.
What Are the Advantages of Variable Costing?
Unlike absorption costing, variable costing doesn't add fixed overhead costs into the price of a
product and therefore can give a clearer picture of costs. By assigning these fixed costs to cost of
production as absorption costing does, they're hidden in inventory and don't appear on the
income statement.
What Are the Disadvantages of Variable Costing?
While it's a valuable management tool, it isn't IFRS-compliant and can't be used for external
reporting by public companies. Therefore, if a company uses variable costing, it may also have to
use absorption costing (which is IFRS-compliant).

The Bottom Line
Most companies will use the absorption costing method if they have COGS. What's more, for
external reporting purposes, it may be required because it's the only method that complies with
IFRS. Companies may decide that absorption costing alone is more efficient to use.
Depending on a company’s business model and reporting requirements, it may be beneficial to
use the variable costing method, or at least calculate it in dashboard reporting. Managers should
be aware that both absorption costing and variable costing are options when reviewing their
company’s COGS cost accounting process.
If a company has high direct, fixed overhead costs it can make a big impact on the per unit price.
Companies that use variable costing may be able to allocate high monthly direct, fixed costs to
operating expenses. This could result in a more reasonable per unit price in some cases.
However, most companies may need to transition to absorption costing at some point, which can
be important to factor into short-term and long-term decision making.
1.2 The Concept of Profit Contribution
The difference, therefore, between contribution and profit is that contribution shows the
difference between the sales price and variable costs for specific products. This then contributes
to the fixed costs, and goes towards the profit of the business. Contribution profit means an
amount equal to the direct revenues of the Division less direct operating expenses before any
allocation of corporate overheads as calculated by the Company.
How do you calculate profit contribution?
Contribution margin is calculated as Revenue - Variable Costs. The contribution margin ratio is
calculated as (Revenue - Variable Costs) / Revenue.

In any retail or manufacturing business, it is important to know how much each unit sold
contributes to the business's profit. This is commonly referred to as the "contribution margin."
This is part of cost volume profit analysis, a management accounting technique that allows
businesses to understand their profit levels at varying levels of production. By calculating the
contribution margin, a manager can determine which products are most profitable and make
production decisions accordingly. It is easy to calculate the profit contribution of a product by
following several basic steps.
Step 1
Write down the unit price. This is the price at which each unit is sold; it is not the unit cost or the
unit profit.
Step 2
Calculate the unit variable cost. This is calculated by first determining the total variable costs for
all the products. Variable costs are all the costs that increase proportionately to an increase in
production. They include material costs, direct labor costs and any other costs that increase as
production increases. Variable costs include all costs that are not fixed costs, such as equipment,
indirect labor and real estate. Add all of the variable costs and divide the total by the number of
units produced. This will give you the unit variable cost. Write this number down.
Step 3
Subtract the unit variable cost from the unit price. This figure gives you the contribution margin
of each unit, which tells you how much one unit contributes to the profit. Write down the unit
contribution margin. For example, if your unit price is $5 and your unit variable cost is $2, then
each unit that you produce will contribute $3 toward profits.
Step 4
Multiply the unit contribution margin by the number of units produced. This will give you the
total contribution margin for all units. This is useful if you want to know how much your total
production is contributing to profits.

TIP
Profit contribution is a tool intended to help make management decisions. You should use the
information that you calculate to make recommendations for the business, such as increasing
production, ending production of a product with a low contribution margin or reducing variable
costs to achieve a higher profit contribution.
WARNING
The contribution to profit does not necessarily mean that there is a profit. The contribution first
must cover fixed costs. Only after covering fixed costs, or reaching the break-even point, will a
profit actually is made. Knowing the contribution margin is essential for calculating the break-
even point.
For example, let’s look at how this might work in practice with a sporting goods company.
Imagine that a basketball costs £20, with variable costs per unit of £8. So, to find the contribution
margin ratio, we can use the following formula:
20 – 8 / 20 = 0.6
What does that mean? Essentially, it indicates that for this company, the contribution margin for
every £1 of revenue is 60 cents.
Now, let’s look at another example. Imagine the same company sold around £50,000 worth of
basketballs within a given period, with variable costs of £20,000. However, the company also
has fixed costs of £40,000. We can use the contribution margin formula to find out what this
means for their bottom line:
50,000 – 20,000 = 30,000

While the contribution margin is £30,000, the business’s fixed costs (premises, staffing,
insurance, etc.) mean that the company is making a net loss of £10,000. As a result, they need to
decrease their fixed expenses or boost prices if they want to remain solvent and stay afloat.
1.3 Cost-volume-profit (CVP) analysis: understanding the concepts of break-
even and margin of safety
CVP analysis looks at the effect of sales volume variations on costs and operating profit. The
analysis is based on the classification of expenses as variable (expenses that vary in direct
proportion to sales volume) or fixed (expenses that remain unchanged over the long term,
irrespective of the sales volume). Accordingly, operating income is defined as follows:
Operating Income = Sales – Variable Costs – Fixed Costs
A CVP analysis is used to determine the sales volume required to achieve a specified profit level.
Therefore, the analysis reveals the break-even point where the sales volume yields a net
operating income of zero and the sales cutoff amount that generates the first dollar of profit.
Cost-volume profit analysis is an essential tool used to guide managerial, financial and
investment decisions.
COST-VOLUME PROFIT ANALYSIS
Contribution Margin and Contribution Margin Percentage
The first step required to perform a CVP analysis is to display the revenue and expense line
items in a Contribution Margin Income Statement and compute the Contribution Margin Ratio.
A simplified Contribution Margin Income Statement classifies the line items and ratios as
follows:

Contribution Margin Income Statement
Table 1 Contribution Margin Income Statement
Statement Item Amount Percent of Income
Sales $100 100%
(Deduction) Variable Costs $60 60%
(Total) Contribution Margin $40 40%*
(Deduction) Fixed Costs $30 30%
(Total) Operating Income $10 10%
* Contribution Margin Percentage
The method relies on the following assumptions:
 Sales price per unit is constant (i.e. each unit is sold at the same price);
 Variable costs per unit are constant (i.e. each unit costs the same amount);
 Total fixed costs are constant (i.e. costs such as rent, property taxes or insurance do not vary with
sales over the long term);
 Everything produced is sold;
 Costs are only affected because activity changes.
The equation: Operating Income = Sales – Variable Costs – Fixed Costs
Sales = units sold X price per unit

Variable Costs = units sold X cost per unit
The first equation above can be expanded to highlight the components of each line item:
Operating Income = (units sold X price per unit) – (units sold X cost per unit) – Fixed Cost
The contribution margin is defined as Sales – Variable Costs. Therefore,
Contribution Margin ($) = (units sold X price per unit) – (units sold X cost per unit)
And the Contribution Margin Percentage (CM %) is computed as follows:
CM% = Contribution Margin ($) / Sales ($)
Accordingly, the following is another way to express the relationship between contribution
margin, CM percentage, and sales:
Contribution Margin $ = Sales $ X Contribution Margin %
The contribution margin percentage indicates the portion each dollar of sales generates to pay
for fixed expenses (in our example, each dollar of sales generates $.40 that is available to cover
the fixed costs).
As variable costs change in direct proportion (i.e. in %) of revenue, the contribution margin also
changes in direct proportion to revenues, However, the contribution margin percentage remains
the same. Example:
Revenues $100 – (20 units X $5)
Var. Costs $60 – 60% (20 units X 60%)
CM $40 – 40%
If revenues double:
Revenues $200 – (40 units X $5)
Fixed Costs $120 – 60% (40 units X 60%)
CM $80 – 40%

Targeted Profit
CVP analysis is conducted to determine a revenue level required to achieve a specified profit.
The revenue may be expressed in number of units sold or in dollar amounts.
Income Statement
Table 2 Income Statement
Statement Item Amount Percent of Income
Sales (20 units X $5) $100 100%
(Deduction) Variable Costs (20 units X $3) ($60) (60%)
(Total) Contribution Margin $40 40%
(Deduction) Fixed Costs ($30) (30%)
(Total) Operating Income $10 10%
The equation above demonstrates 100 percent of income ($100) minus how much sales is required to achieve a $20 profit?
This can be answered by finding the number of units sold or the sales dollar amount.
1. Required number of units sold:
Profit = Revenues – Variable Costs – Fixed Costs
$20 = (Units Sold X $5) – (Units Sold X $3) – $30
$50 = (Units Sold X $5) – (Units Sold X $3)
Sales deducted from Variable Costs is the definition of contribution margin
$50 = (Units Sold) X ($5-$3)
($5-$3=$2 which is the $ contribution margin per unit)
$50/$2 = 25 Units sold needed to achieve $20 in profit
revenues doubling to $200 and deducting fixed costs of $120, that results in $80 contribution margin.

Units sold to achieve targeted profit = (Fixed Costs + Targeted Profit)
Contribution margin dollar per unit
Verification:
Income Statement
Table 3 Income Statement
Statement Item Dollar Amount Percent of Income
Sales (25 units X $5) $125 100%
(Deduction) Variable Costs (25 units X $3) ($75) (60%)
(Total) Contribution Margin (25 units X $2) $50 40%
(Deduction) Fixed Costs ($30) (30%)
(Total) Targeted Operating Income $20 10%
1. Note: while Operating Income doubled, (from $10 to $20) only 5 additional units sold (+25%)
were required as only variable costs changed while fixed costs remained at $30.
2. Required sales dollar amount
Profit $ = sales $ – Variable Costs $ – Fixed Costs $
and
Sales $ – Variable Costs $ = Contribution Margin $
So,
Profit $ = Contribution Margin $ – Fixed Costs $
We saw earlier that Contribution
Margin $ can be expressed as:
Sales X Contribution Margin %

Contribution Margin $ = (Sales $ x Contribution Margin %)
Profit $ = (Sales $ x Contribution Margin %) – Fixed Costs $
Profit $ + Fixed Costs $ = (Sales $ x Contribution Margin %)
(Targeted Profit $ + Fixed Expense $) / Contribution Margin % = Sales $
Verification:
Sales required achieving $20 in targeted profit:
($20 + $30) / 40% = $125
The example equation reads: $20 + $30, divided by 40 percent equals $12
CVP formulas to be remembered:
 Required sales based on units sold to yield a targeted operating income:
Required number of units sold For Targeted Profit =
(Fixed Costs Dollar + Targeted Profit Dollar)
Contribution Margin Dollar per Unit
 Required sales based on contribution margin percentage to yield a targeted operating income:
Required Dollar Sales for Targeted Profit =
(Fixed Costs Dollar + Targeted Profit Dollar)
Contribution Margin Percentage
Break-even Point
The break-even point is reached when total costs and total revenues are equal, generating no gain
or loss (Operating Income of $0). Business operators use the calculation to determine how many
product units they need to sell at a given price point to break even or to produce the first dollar of
profit.
Break-even analysis is also used in cost/profit analyses to verify how much incremental sales (or
revenue) are needed to justify new investments.
The following graph illustrates the break-even point based on the number of covers sold in a
restaurant

A line graph with covers sold on the x axis. The x axis starts at 0, and has increment markers in
intervals of 50, increasing to a maximum of 400. There is a label for loss indicated from the start
of the x axis (0) to the fifth interval marker (250). There is a label for profit indicated on the x
axis starting after the 250 marker. The Y axis is labeled for revenues, also starting at 0,
incrementing by one thousand dollars every marker, to a maximum of six thousand dollars.
There are four lines graphed. One of which is a line representing total sales, which increases at
linear rate, starting point (0, $0), and ending point (400, $6000). Another line represents the total
costs, which also increases at a linear rate. Its starting point is (0, $2500), and its ending point is
(400, $5000). The total sales and total costs lines that are graphed intersect at the point (250,
$4000) which is labeled as the breakeven point. The intersection of these two lines emphasize (as
the x axis profit label does, which was mentioned earlier in this description) that profit occurs
after 250 covers are sold. A fixed cost line is represented in this graph as well. Starting point ( 0 ,
$2500), and ending point (400, $2500). This shows that fixed costs are static and not dependent
on covers sold. The last line represents variable costs, starting point (0, $0) and ending point
(400, $2500). Notice the ending point of the total costs line equals the fixed cost and variable
cost totals.

 The Sales line starts at the origin (0 revenue for 0 covers) and grows in direct proportion to the
number of covers sold;
 Variable costs grow in direct proportion to Sales but at a slower rate. The line starts at the origin
since no variable cost arises if no sale occurs;
 The Fixed Costs line remains flat (unchanged irrespective of the number of covers sold). The
operation incurs Fixed Costs such as rent whether the operation operates (is open for business) or
not;
 Total Cost grows at the same rate as Variable Costs. The Total Cost minimum is represented by
the Fixed Costs line;
 The Break-Even point occurs where the Total Sales line crosses the Total Costs line. In this
illustration, the operation starts being profitable when selling exceeds 250 covers.
Computing the Break-Even Point
Computing the break-even point is equivalent to finding the sales that yield a targeted profit of
zero.
Example
The average check (selling price per cover) for the Roadside Exotic BBQ Restaurant is $16. The
restaurant averages 85 covers sold a day or 2,250 covers per month. The restaurant currently
loses money as indicated in the following statement:
Roadside Exotic BBQ Restaurant
Income Statement
Table 4 Income Statement for an Exotic Barbecue Restaurant
Sales (2,250 Covers x $16) $40,800 100%
(Deduction) Variable Costs ($29,376) (72%)
(Total) Contribution Margin $11,424 28%
(Deduction) Fixed Costs ($13,464) (30%)
(Total) Operating Income ($2,040) (5%

The owner wants to know the sales volume required in terms of both dollars ($) and the number
of covers for the restaurant to break even considering its current expense structure.
1. Required number of covers sold
Required number of covers sold = (Fixed Costs Dollar + Targeted Profit Dollar)
Contribution Margin Dollar per Unit
In this case,
 Targeted Profit = zero (definition of Break-even)
 Contribution Margin per unit: $16 X 28% (CM%) = $4.48
Fixed Cost Dollar
Contribution Margin Dollar /unit =$13,464
$4.48 = 3,005.36 (3,006) covers or100.18 (101) covers
per day.
Verification
Roadside Exotic BBQ Restaurant
Income Statement
Table 5 Income Statement of an Exotic Barbecue Restaurant
Sales (3,005.36 Covers x$16) $48,086 100%
(Deduction) Variable Costs ($34,622) (72%)
(Total) Contribution Margin $13,464 28%
(Deduction) Fixed Costs ($13,464) (28%)
(Total) Operating Income ($0) (0%)

2 Required Sales
Sales $ = Targeted Profit $ + Fixed Expense $
Contribution Margin %
Since targeted profit is zero, the formula for the Break-Even Sales is:
Fixed Expense $ = $13,464 = $48,086
Contribution Margin % 28%
Break-Even formulas to be remembered:
Break-Even number of Units sold
Break-Even number of units sold =
(Fixed Costs Dollar / Contribution Margin Dollar per unit)
Break-Even Sales
Break-Even Sales $ =
(Fixed Costs Dollar / Contribution Margin Percentage)
Summary
The break-even point calculation allows food service operators to calculate the number of covers
(or units sold) or total sales needed to cover all costs of the operation given the level of business
generated. Once the break-even point is met, additional revenue (or sales) starts to generate a
profit, which is typically at least one purpose of running a business. Cost volume profit analysis
allows the food service operator to calculate similar figures but with a targeted profit in mind.
This CVP analysis is an essential tool in guiding managerial, financial and investment decisions
for current operations or future business ideas or plans.

1.4 Cost Volume Profit Analysis under Absorption Costing
When the production level exceeds the sales level, absorption costing income will be higher than
variable costing income because some of the fixed factory overhead incurred during the period
will be deferred into inventory rather than going to the income statement. Since no fixed
overhead is inventoried under variable costing, there will be more dollars of expense on the
income statement under variable costing than there will be under absorption costing. When the
production level is less than the sales level, some of the fixed overhead deferred in previous
periods will be charged against income as part of cost of goods sold under absorption costing in
addition to the current period fixed overhead. Thus, there will be greater income charges under
absorption costing than under variable, resulting in a smaller income amount.
1.5 The use of linear, curvilinear and step functions and how their calculations
are used to analyze cost behavior
What Is a Linear Cost Function?
A linear cost function is a mathematical method used by businesses to determine the total costs
associated with a specific amount of production. This method of cost estimation can be done
whenever the cost for each unit produced remains the same no matter how many units are
produced. When that is the case, the linear cost function can be calculated by adding the variable
cost, which is the cost per unit multiplied by the units produced, to the fixed costs. Performing
this equation will give the total cost for a production order, thus enabling businesses to budget
accordingly and make decisions on production amounts.
Managers of businesses that focus on some kind of production or manufacturing must be aware
of costs at all times. Simply counting up all of the costs after production is done can lead to
major problems if the costs exceed what was expected. For that reason, managers must develop
methods of cost estimation that are accurate and reliable. One simple method of cost estimation
involves the use of a linear cost function.

Using a linear cost function requires a basic understanding of how functions work. A function is
a mathematical equation that is performed on any set of values that then produces a
corresponding set of values. These values can be placed on a graph to study the relationship
between them when the function is performed. If the function produces a straight line on the
graph when the values are entered, it is known as a linear function.
For an example of how a linear cost function is utilized to estimate production costs, imagine
that a company decides to fill out an order of 1,000 widgets that cost $50 US Dollars (USD) each
to produce. Multiplying these two numbers produces the variable costs in this function, which
turn out to be $50,000 USD. In addition to that total, it takes $3,000 USD to simply get the
factory up and running for any type of production. Those costs, which are the fixed costs in this
equation, are added to the variable costs to leave a total of $53,000 USD for this particular order.
It is important to note that the linear cost function in this case works because the widgets always
cost the same amount to produce. If a graph was produced with the amount of widgets produced
on one axis and the total costs on the other, it would reveal a straight line. This process would
not work if the individual cost to make each widget varied depending on the size of the order.
What is a Curvilinear Cost?
Definition: A curvilinear cost, also called a nonlinear cost, is an expense that increases at an
inconsistent rate as production volume increases. In other words, this is an irregular cost that
increases at different rates as total output increases.
Unlike variable costs that increase at a constant rate as production increases, curvilinear costs
have not set parameters. They tend to increase drastically at lower levels of production, flatten
out at mid-levels, and increase again at higher levels of output. These irregular cost increases
make the curvilinear cost curve look like an “s” when charted on a graph with the x axis
representing volume in units and the y axis representing total costs. Compare this to a variable
cost curve that simply consists of a straight line from zero to infinity.

Generally, nonlinear costs are made up of groups of expenses. For example, total direct labor for
hourly workers is an irregular expense. At lower levels of production, few hourly workers are
needed, so the costs are low. When production levels get into the mid-level, more workers are
needed. The costs increase, but more efficiency are also added which allows the same number of
workers to increase output. Once the production reaches the highest levels of output, more
workers are needed increasing the total labor costs.
As you can see, this nonlinear line looks like the classic “s” on a graph. Production costs increase
at low levels, taper off in mid-levels, and rise again at the highest levels of output. Quite often
management graphs the curvilinear cost lines with the step-wise incremental cost lines.
Management uses these cost curves to plan operations and calculate key ratios like the break-
even point in units. Management can also use these curves to judge whether current levels of
production are sustainable over the long term and make an estimated decisions about hiring a
new workforce or expanding capacity.
What is Step functions cost?
Step costs are expenses that are constant for a given level of activity, but increase or decrease
once a threshold is crossed. Step costs change disproportionately when production levels of a
manufacturer, or activity levels of any enterprise, increase or decrease.
Step costs, also called stair-step costs, are costs that do not change in direct proportion to
increasing levels of activity. In other words, step costs are constant at a certain activity level but
increase or decrease when an activity threshold is met.
Step costs are extremely important to consider when a company is about to reach a new activity
level. If neglected, they can cause a business to miss out on profits.
John operates a company that produces pens. A machine costing $15,000 is capable of producing
up to 1,000 pens. Assume that there are no additional costs related to producing pens (no raw
materials, labor, etc.). As such, the cost of machinery is an example of a step cost. The
information is illustrated below:

As shown in the illustration, the cost of machinery closely resembles steps. At a production of
500 or 750 pens, only one machine is required. The total cost is, therefore, $15,000. However, at
the production of 1,500, the company must purchase an additional machine to expand its
production capacity. At a production of 1,500 pens, the total cost is $30,000 ($15,000 x 2
machines). Therefore, it is an example of a step cost: costs that are constant at a certain level of
activity and rise or decrease when a certain activity threshold is met.
Importance of Step Costs
Step costs are extremely important to consider when a company is about to reach a new activity
level. If neglected, they can cause a business to lose unnecessary profits.
Assume that John initially forecasted that the demand for pens would be 1,050 next year.
Additionally, assume that each pen can be sold for $20.
To an individual who does not understand step costs, they may recommend purchasing two
machines to meet the demand for 1,050 pens. The revenues generated from 1,050 pens are
$21,000 (1,050 x $20). However, total costs (two machines) are $30,000. The purchase of the

second machine that would only generate revenue for the sale of 50 additional pens would make
the company much less profitable.
To an individual who understands step costs, they would recommend purchasing one machine
and producing 1,000 pens and not 1,050. The revenues generated from 1,000 pens are $20,000
(1,000 x $20) and the total costs (one machine) are $15,000. The company would be generating
$5,000 in profits at the given production level.
As shown above, investing in an additional machine would cause the company to lose profits!
Therefore, it is key to consider whether incurring a step cost would be accretive to profits or not.
In the example above, an additional 50 pens (revenues of $100) would be generated through a
second machine costing $15,000. In such a scenario, it would not be worthwhile for the company
to incur the additional cost to produce an additional 50 pens. Example: Consider a company
with a cost structure in the production of widgets as follows:

Assuming that the sale price of widgets is $30 and the company currently utilizes three machines
and sells 125 widgets. Would you recommend the company to continue utilizing three machines
or to cut down to two and only sell 100 widgets (the production capacity for two machines)?
Three machines with sales of 125 widgets
The total costs for the three machines are $3,000. The sales generated from 125 widgets are
$3,750 (125 x $30). Therefore, the profit is $750.
Two machines with sales of 100 widgets
The total costs for the two machines are $2,000. The sales generated from 100 widgets are
$3,000 (100 x $30). Therefore, the profit is $1,000.
Therefore, the company should only operate two machines and produce 100 widgets.
Step Costs in the News
Step costs are common – the cost of a new production facility, the cost of a new machine,
supervision costs, marketing costs, etc., are all step costs.
For example, on July 17, 2019, FortisBC announced the completion of a $400-million expansion
project that increased the company’s capacity from 35,000 a ton to 250,000 a ton. As such, the
facility expansion project by FortisBC is a step cost.
1.6 The concepts of cost units, cost centers and profit centers
A cost center is a company's department that supervises all the costs of the company. A profit
center is a company's department that is responsible for the profits of the company. Cost units, on
the other hand, are determined by the final product or output, as well as current trade practices.
The cost unit is defined as the unit of product, service, time, activity, or combination in relation
to which cost is estimated.

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