5.1: Introduction to Cost Volume Profit Analysis

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Businesses focus on profitability and look for ways to improve operational performance by analyzing projected or actual financial information. One relatively simple strategy is to look at cost behavior, which is how costs respond to changes in sales volume. Knowing how costs behave helps managers forecast operating income based on sales volume. This insight also helps managers estimate costs related to the decisions they make in the business.

Cost Classifications

Costs are classified as variable, fixed, or mixed.

A variable cost is an expenditure directly associated with a sale. For each sale of a unit of product or service, one unit of variable cost is incurred.

The following are three examples. The sale of one manufactured desk for $200 includes the direct materials and direct labor costs combined of $100. The sale of one pizza for $10 has the variable cost of $3 for the cost of the ingredients. The rental of one room night at a hotel for $80 has the variable cost $5 for the guests’ breakfast that is included. There is only a variable cost if there is sale. The more sales there are, the more total variable cost there is.

The following table illustrates the cost behavior of a variable cost using the pizza example.

Number of pizzas sold	Variable cost per pizza	Total variable cost for all pizzas sold
200	$3	$600
400	3	1,200
600	3	1,800
800	3	2,400

Variable cost behavior is summarized as follows:

Variable cost per unit is the same regardless of number of units sold Example: Regardless whether 200 or 800 pizzas are sold, the cost of making each pizza is $3.
Total variable cost increases (or decreases) as the number of units sold increases (or decreases)
Example: Total variable cost is $600 for 200 pizzas sold and increases to $2,400 for 800 pizzas.
The more pizzas sold, the more the total variable cost is.

Fixed costs remain the same in terms of their total dollar amount, regardless of the number of units sold. These are general expenditures that cannot be traced to any one item sold and may include electricity, insurance, depreciation, salary, and rent expenses.

Fixed costs are considered within a relevant range. The costs remain the same regardless of the number of units sold until capacity has been reached, at which time the company cannot produce or sell any more without spending money for expansion. We will assume for our examples that the business is operating within its relevant range.

The following table illustrates fixed and variable cost behaviors using the pizza example.

Number of pizzas sold	Total fixed costs	Fixed cost per pizza	Variable cost per pizza	Total variable costs
200	$480	$2.40	$3.00	$600
400	480	1.20	3.00	1,200
600	480	0.80	3.00	1,800
800	480	0.60	3.00	2,400

Total fixed costs remain the same regardless of the level of sales. Example: Regardless whether 200 or 800 pizzas are sold, total fixed cost is $480.
Fixed cost per unit decreases (increases) as the number of units sold increases (decreases)
Example: Fixed cost per unit is $2.40 for 200 pizzas sold and decreases to $.60 each for 800 pizzas.

The term leverage relates to fixed costs in terms of their ability to generate sales. Since a company is committed to paying them, it wants to maximize the value from doing so. The goal is to “get the most bang for your buck” for the fixed amount the company must pay each period. Leverage is taking advantage of fixed costs to generate sales. The more sales, the better fixed costs have been leveraged.

The table that follows summarizes the cost totals for the four quantities/ batches of pizza sold.

Number of pizzas sold (batch)	Total cost of the batch of pizzas	Cost per pizza using unit costs	Cost per pizza using total cost
200	$600 + $480 = $1,080	$2.40 + $3.00 = $5.40	$1,080 / 200 pizzas = $5.40
400	1,200 + 480 = 1,680	1.20 + 3.00 = 4.20	1,680 / 400 pizzas = 4.20
600	1,800 + 480 = 2,280	0.80 + 3.00 = 3.80	2,280 / 600 pizzas = 3.80
800	2,400 + 480 = 2,880	0.60 + 3.00 = 3.60	2,880 / 800 pizzas = 3.60

The total cost of a batch of pizzas equals total variable cost plus total fixed cost. The cost per pizza in each batch can be determined in two ways: (1) fixed cost per pizza plus variable cost per pizza or (2) total cost per batch divided by the number of pizzas in the batch. Both calculations produce the same result.

The batch of 800 units generates the most sales dollars from its fixed costs and therefore leverages them most effectively. The more highly leveraged, the lower the fixed cost per unit. In this case, the $480 is spread over more units, so each unit picks up a lower amount of that $480. And the lower the fixed cost per unit, the lower the total cost per unit, which is a desirable goal.

Mixed costs have both a fixed and a variable component. There is typically a base amount that is incurred even if there are no sales at all. There is also an incremental amount assigned to each unit sold.

The following are three examples of mixed costs. A prepaid cell phone plan might include a base rate of $30 for1G of data and $5 for each additional 300 megabytes of data. A sales person might earn a base salary of $25,000 per year plus $3 for each unit of product he sells. Equipment rental may cost $8,000 per year plus $1 for each hour used over 10,000 hours.

For purposes of analysis, mixed costs are separated into their fixed and variable components. The high-low estimation method may be used to break out the costs by looking at the total sales in dollars and the total cost of those sales for several periods, such as months. The month with the highest activity level and the month with the lowest activity level are selected for the calculation.

The high-low method of separating costs is illustrated using the following information over a six-month period.

Month	Units sold	Total cost
January	1,400	$52,700
February	2,100	61,200
March	2,900 highest	69,800
April	2,500	66,400
May	1,100 lowest	48,200
June	1,800	56,900

Since the fixed cost does not change with the number of sales, the difference between the total costs of the month with the most units sold (March) and the month with the fewest units sold (May) must be variable costs. Therefore, using data from these two months,

Variable cost per unit =

Difference in total cost / Difference in units sold

(69,800 – 48,200) / (2,900 – 1,100)

Variable cost per unit =

$21,600 / 1,800 units sold = $12

Now that the variable cost per unit is known to be $12, the fixed costs can be determined by used either the March (highest sales) or May (lowest sales) using the following equation:

Total cost – variable costs = fixed costs
March:	$69,800 – ($12 per unit x 2,900 units sold) = $69,800 - $34,800 = $35,000
May:	$48,200 – ($12 per unit x 1,100 units sold) = $48,200 - $13,200 = $35,000

The high-low method estimates that variable cost per unit is $12 and fixed costs are $35,000.