# Variable Costs

In management accounting, variable costs are cost items whose total cost varies proportionately with some underlying activity level such as total units, labor hours, machine hours, etc.

Variable costs, fixed costs and mixed costs are three categories into which cost items are classified based on the relationship between their total cost and activity level.

Variable costs are defined with reference to a cost driver. A cost driver (also called activity base) is a variable such as quantity produced, direct labor hours, machine hours, kilometers travelled, etc. which drives the increase in total variable cost.

The relationship between total variable costs TVC and activity level Q can be expressed using the following mathematical equation:

TVC = v × Q

Where v is a constant which equals the variable cost per unit of cost driver; for example, cost per machine hour, cost per labor hour, etc.

Average variable cost per unit is the total variable costs divided by total output. Variable cost ratio is the ratio of variable cost ratio to sales. It is important to identify variable costs because they are important in break-even analysis, variable costing and budgeting.

Typical examples of variable costs include:

- Direct labor: For example, if a typical worker takes 30 minutes in manufacturing a unit and the hourly wage rate is $20, total labor cost will be $10 per 1 unit, $20 for 2 units, $30 for 3 units and so on.
- Direct materials: For example, if $5 of raw materials are used in 1 unit; total variable cost of 1, 2, 3 and n units will be $5, $10, $15 and n × $5 respectively.
- Sales commissions: For example, if salespeople are paid 10% of the sales they generate as commissions, total commissions cost will change in direct proportion to change in units sold.

## Numerical Example

Braavos Metro has rented 50 diesel generators from Power Solutions, Inc. to provide power backup at its 50 metro stations in case of a power outage.

Payments that Braavos Metro makes to Power Solutions, Inc. include:

- $20,000 per month on account of dedicated maintenance team.
- $0.5 per kilowatt hour as compensation for fuel consumed.
- $10 for each time each generator is triggered into operation due to power outage.
- A charge of $300 for periodic servicing of the generator i.e. engine oil, air filter, etc.

Identify which of the costs are variable and work out the company’s total variable cost in the following scenarios: (a) there are 30 power outages at each station in a month lasting 1 hour in which 20 kilowatt hours are consumed at each of the 50 locations, (b) there are 50 power outages at each station lasting 2 hours each in which 45 kilowatt hours are consumed by the system.

### Solution

The $20,000 paid for dedicated maintenance team is a fixed cost because it stays constant regardless of actual generator operation hours. The $300 charge on account of periodic maintenance is a semi-fixed cost because it changes after each 250 hours of operation for each generator. The per-kilowatt hour charge of $0.5 and the setup charge of $10 per generator are variable costs.

We can write the following equation for total variable cost:

TVC = $0.5 × K + $10 × P

Where K is the number of kilowatt hours consumed and P is the number of power outages.

We can find the total variable costs under the two scenarios are as follows:

TVC in Scenario A

= 50 × ($0.5 × 20 × 30 + $10 × 30)

= $45,000

TVC in Scenario B

= 50 × ($0.5 × 45 × 50 + $10 × 45)

= $78,750

In this example, there are two cost drivers (i.e. activity bases), namely kilowatt hours and number of power outages and the variable cost must be broken down into the constituent components to correctly project and forecast it.

It would be wrong to define the total rented power costs based on some single cost driver or even the ultimate units of sales i.e. passengers served.

by Obaidullah Jan, ACA, CFA and last modified on

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