**MANAGEMENT ACCOUNTING:
CONCEPTS AND TECHNIQUES**

**By Dennis Caplan**

**PART 2: MICROECONOMIC
FOUNDATIONS OF MANAGEMENT ACCOUNTING**

**CHAPTER 7: COST-VOLUME-PROFIT **

**Chapter Contents:**

- The Basic Profit Equation

- Assumptions in CVP Analysis

- Target Costing

- Leverage

- Examples

**The Basic Profit Equation:**

Cost-Volume-Profit analysis (CVP) relates the firm’s cost structure to sales volume and profitability. A formula that facilitates CVP analysis can be easily derived as follows:

**Profit =
Sales – Costs**

Ž Profit = Sales – (Variable Costs + Fixed Costs)

Ž Profit + Fixed Costs = Sales – Variable Costs

Ž Profit + Fixed Costs = Units Sold x (Unit Sales Price – Unit Variable Cost)

This formula is henceforth called
the **Basic
Profit Equation** and is abbreviated:

**P + FC = Q x (SP – VC) **

**Contribution margin** is defined as

**Sales – Variable Costs**

The **unit contribution margin** is defined
as

**Unit Sales Price – Unit Variable Cost**

Typically, the Basic Profit
Equation is used to solve one equation in one unknown, where the unknown can be
any of the elements of the equation. For example, given an understanding of the
firm’s cost structure and an estimate of sales volume for the coming period,
the equation predicts profits for the period. As another example, given the
firm’s cost structure, the equation indicates the required sales volume **Q** to achieve a targeted level of
profits **P**. If targeted profits are
zero, the equation simplifies to

**Q = FC ÷ Unit Contribution Margin **

In this case, **Q** indicates the required sales volume
to break even, and the exercise is called **breakeven analysis**.

CPV analysis can be depicted graphically. The graph below shows total revenue (SP x Q) as a function of sales volume (Q), when the unit sales price (SP) is $12.

The following graph shows the total cost function when fixed costs (FC) are $4,000 and the variable cost per unit (VC) is $5.

The following graph combines the revenue and cost functions depicted in the previous two graphs into a single graph.

The intersection of the revenue line and the total cost line indicates the breakeven volume, which in this example, occurs between 571 and 572 units. To the left of this point, the company incurs a loss. To the right of this point, the company generates profits. The amount of profit or loss can be measured as the vertical distance between the revenue line and the total cost line.

**Assumptions in CVP
Analysis:**

The Basic Profit Equation relies on a number of simplifying assumptions.

- Only one product is sold. However, multiple products
can be accommodated by using an average sales mix and restating
**Q**,**SP**and**VC**in terms of a representative bundle of products. For example, a hot dog vendor might calculate that the “average” customer buys two hot dogs, one bag of chips, and two-thirds of a beverage.**Q**is the number of customers, and**SP**and**VC**refer to the sales price and variable cost for this “average” customer order.

- If the equation is applied to a manufacturer, beginning inventory is assumed equal to zero, and production is assumed equal to sales. Relaxing these assumptions requires additional structure on the equation, including specifying an inventory flow assumption (e.g., FIFO or LIFO) and the extent to which the matching principle is honored for manufacturing costs.

- The analysis is confined to the
**relevant range**. In other words, fixed costs remain unchanged in total, and variable costs remain unchanged per unit, over the range of**Q**under consideration.

**Target Costing:**

A relatively recent innovation in
product planning and design is called **target costing**. In the context of the Basic
Profit Equation, target costing sets a goal for profits, and solves for the
unit variable cost required to achieve those profits. The design and
manufacturing engineers are then assigned the task of building the product for
a unit cost not to exceed the target. This approach differs from a more
traditional product design approach, in which design engineers (possibly with
input from merchandisers) design innovative products, manufacturing engineers
then determine how to make the products, cost accountants then determine the
manufacturing costs, and finally, merchandisers and sales personnel set sales
prices. Hence, setting the sales price comes last in the traditional approach,
but it comes first in target costing.

Target costing is appropriate
when **SP** and **Q **are predictable, but are not choice variables, such as might
occur in well-established competitive markets. In such a setting, merchandisers
might know the price that they want to charge for the product, and can probably
estimate the sales volume that will be achieved at that price. Target costing
has been used successfully by a number of companies including

**Leverage****:**

There is often a trade-off between fixed cost inputs and variable cost inputs. For example, in the manufacturing sector, a company can build its own factory (thereby operating with relatively high fixed costs but relatively low variable costs) or outsource production (operating with relatively low fixed costs but relatively high variable costs). A merchandising company can pay its sales force a flat salary (relatively higher fixed costs) or rely to some extent on sales commissions (relatively higher variable costs). A restaurant can purchase the equipment to launder table cloths and towels, or it can hire a laundry service.

A company that has relatively
high fixed costs is more highly leveraged than a company with relatively high
variable costs. Higher fixed costs result in greater downside risk: as **Q** falls below the breakeven point, the
company loses money more quickly than a company with less leverage. On the
other hand, the company’s lower variable costs result in a higher unit contribution
margin, which means that as **Q** rises
above the breakeven point, the more highly-leveraged company is more
profitable.

There is an ongoing trend for companies to outsource support functions and other “non-core” activities to third party suppliers and providers. Usually, outsourcing reduces the leverage of the company by eliminating the fixed costs associated with conducting those activities inside the firm. When the activities are outsourced, the contractual payments to the outsource providers usually contain a large variable cost component and a relatively small or no fixed cost component.

**Examples:**

**Breakeven:** Steve Poplack owns a service station in

How many inspections would Steve have
to perform monthly to break even from this part of his business?

Q = FC ÷ Unit
Contribution Margin

Q = $6,000 ÷ ($40 - $10) = 200 inspections

**Targeted
profits, solving for volume: **Refer to
the information in the previous question. How many inspections would Steve have
to perform monthly to generate a profit of $3,000 from this part of his
business?

P + FC = Q x (SP – VC)

$3,000 + $6,000 = Q x
($40 - $10)

Q = 300 inspections

**Targeted
profits, solving for sales price: **Alice
Waters (age 9) runs a lemonade stand in the summer in

P + FC = Q x (SP – VC)

$200 + $20 = 100 x (SP - $2)

SP = $4.20 per glass

**Contribution
margin: **Refer to the previous
question. What price would

Total CM = Q x (SP –
VC)

$200 = 100 x (SP - $2.00)

SP = $4.00 per glass

**Target
costing: **Refer to the information
about

P + FC = Q x (SP – VC)

$200 + $20 = 110 x ($3 – VC)

VC = $1