## Variable and Fixed Costs

### Learning Outcomes

• Understand the relationship between fixed, variable, mixed and total costs

Total costs can be classified as variable, fixed, or mixed.

## Variable Costs

A variable cost is an expenditure directly correlated with the sale or manufacture of goods or services. For each sale of a unit of product or service, one unit of variable cost is incurred.

For example, assume you work for a company that assembles blank journals from two components: (1) leather bindings at $5.00 each and (2) blank pages at$1.00 each.

Your company hires college students as independent contractors to assemble the books, paying them $2.00 for each journal assembled. Workers are expected to produce up to 25 journals per hour, so the hourly rate is respectable if the student works steadily. The company, BlankBooks, Inc., sells the journals to a wholesaler for$10.00 each. The wholesaler delivers them to retail outlets. The retail outlet pays $15 and sells them to the consumer for$19.99.

In addition to the cost of the binding, the blank pages, and the direct labor, the company pays its salespeople a 3% commission for each book sold. That means there is an additional variable cost per unit of $0.30 (thirty cents), making the total variable costs =$5.00 + $1.00 +$2.00 + $0.30 =$8.30.

If your company makes no books, the variable costs are $0. One book manufactured =$8.30 in variable costs, ten books = $83.00 in variable costs, one hundred books =$830.00 in variable costs, and so on.

 Number of units manufactured Direct Materials @ $6 per unit Direct Labor @$2 per unit Commission @ 3% of sales price Total Variable Costs 0 $0.00$0.00 $0.00$0.00 10 $60.00$20.00 $3.00$83.00 100 $600.00$200.00 $30.00$830.00 200 $1,200.00$400.00 $60.00$1,660.00
Note that variable costs per unit are the same no matter how many units are manufactured. That’s really the definition of a variable cost. It varies by unit and therefore increases as production increases.

Review your understanding of variable costs:

You can view the transcript for “Variable Costs” here (opens in new window).

## Fixed Costs

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

Also, fixed costs remain the same regardless of the number of units manufactured until capacity has been reached, at which time the company cannot produce or sell any more without spending money for expansion. In that case, fixed costs will probably jump dramatically because expenditures like rent and additional salaries don’t increase incrementally. For instance, leasing a second factory to double output from 1,500 units to 3,000 units doubles the monthly rent, even if it only produces ten more units—or even zero units.

Review the concept of fixed costs:

You can view the transcript for “Fixed Costs” here (opens in new window).

Here is a video explanation of the relevant range with regard to fixed costs:

The following table illustrates fixed and variable cost behaviors using the book example and assuming that the number of units manufactured all fit within our current existing operating capacity.

 Number of units manufactured (relevant range = 0 to 1,000 units) Total Fixed Costs Fixed Costs per unit 0 $3,400.00 N/A 10$3,400.00 $340.00 100$3,400.00 $34.00 200$3,400.00 $17.00 Notice that fixed costs per unit go down as we produce more units. Since we categorize costs as either fixed or variable, the combination of the two gives us total costs for various levels of production.  Number of units manufactured Total Variable Costs @$8.30 per unit Total Fixed Costs Total Costs Total Costs per unit 0 $0.00$3,400.00 $3,400.00 N/A 10$83.00 $3,400.00$3,483.00 $348.30 100$830.00 $3,400.00$4,230.00 $42.30 200$1,660.00 $3,400.00$5,060.00 $25.30 This is the formula: (#units * VC/unit) + FC = Total Costs Where the number of units times the variable cost (VC) per unit gives us total variable costs. Total variable costs plus fixed costs (FC) gives us total cost. Total cost per unit goes down as fixed cost per unit goes down. You can see that at a production of 200 units, the total unit cost is still way above the$10 per unit price our wholesalers are willing to pay. Remember that the finished product price of $19.99 is set by the market—what the buyers are willing to pay. The wholesaler who buys from us in bulk and then distributes across the country wants to make a profit as well. One student working 80 hours per month should be able to produce 2,000 units, but our maximum output will be determined by other factors as well, such as how many units the retailers can sell in a month and how much raw material we can obtain. Absent those constraints though, if we have room for, say, ten workers at a time in our little production facility, our output is relatively unlimited (10 workers X 30 days per month X 24 hours in a day X 25 units per hour = 180,000 units). ## Mixed Costs 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 for 1G of data and $5 for each additional 300 megabytes of data. A salesperson might earn a base salary of$25,000 per year plus $3 for each unit of the product she 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. Normally, you know the fixed and variable cost components of whatever contract you might have that has resulted in a mixed cost, but if you didn’t, you could calculate the fixed and variable components. For instance, the high-low estimation method breaks out the costs by looking at the total sales in dollars and the total cost of those sales for several periods by selecting the period with the highest activity level and the period with the lowest activity level. The high-low method of separating costs is illustrated using the following information over a six-month period.  Month Units manufactured Total Mixed Cost January 1,400$52,700 February 2,100 $61,200 March 2,900$69,800 Highest total units April 2,500 $66,400 May 1,100$48,200 Lowest total units June 1,800 $56,900 Since the fixed cost component 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) will estimate variable costs. Difference in total cost ($69,800 – $48,200) =$21,600

Difference in total units (2,900 – 1,100) = 1,800

Variable cost per unit = $21,600 / 1,800 units sold =$12

Now that you have determined the variable cost per unit to be $12, you can calculate the fixed costs by using either March (highest sales) or May (lowest sales): Total cost – variable costs = fixed costs For March, the total cost for this particular expense item was$69,800.

Our estimate of variable costs would be $34,800 = ($12 per unit x 2,900 units).

Subtracting variable costs from total mixed costs gives us $35,000 ($69,800 – $34,800). Therefore, using the high-low method, we estimate the variable cost per unit is$12 and fixed costs are \$35,000.

If we graph the data points we have and then apply a best-fit line to the data, we can see that our formula looks reasonable within a relevant range. The blue Xs are our data points, and the dashed line is what our formula predicts based on various levels of output.

Step costs are another version of fixed costs. A step cost occurs when a variable or fixed cost crosses the boundary of the relevant range, making it jump up suddenly. If the relevant range is fairly wide, accountants may refer to the increasing cost as a “step-fixed” cost. If the relevant range is fairly narrow, it could be called a “step-variable” cost (see video below). In any case, like mixed costs, a step cost is a variation of the basic behavior categories of fixed or variable.

You can view the transcript for “Step Variable Costs” here (opens in new window).