# Behavior of Costs

Costs can be classified as fixed or variable costs on the basis of their behavior to the change in level of production/activity.

## Fixed costs

Those costs which are not related to the level of production/ activity or which remain constant for a period irrespective of the level of production/ activity are classified as fixed costs.

Examples of fixed costs include depreciation expense, monthly rent, salaries of administrative staff etc.

## Variable costs

Those costs which are related to the level of production/ activity and which vary or change with the change in level of production/ activity are classified as variable costs.

Examples of variable costs include materials used in the production, wages etc.

## Fixed vs variable costs

The following example further clarifies the behavior of fixed and variable costs with change in volume of production.

 Units Produced Fixed Costs Variable Costs @ \$2 per unit Total Costs A B C = A x  \$2 D = A + B 500 2,500 1,000 3,500 1000 2,500 2,000 4,500 1500 2,500 3,000 5,500 2000 2,500 4,000 6,500 2500 2,500 5,000 7,500 3000 2,500 6,000 8,500 3500 2,500 7,000 9,500 4000 2,500 8,000 10,500

It can be seen that fixed cost graph is a horizontal line which means that total fixed cost is constant and is not affected by change in the production level. Whereas variable cost graph shows an increase in total variable cost with increase in the production level.

## Step fixed costs

Step fixed costs are those costs which remain constant or do not change within a certain range of production level/ activity, but will change to new constant value if the production/ activity falls out of this range of production level/ activity. Step fixed costs will increase to a new constant value or fall to a new constant value depending on whether the upper limit or the lower limit of that production level/ activity, respectively is breached. This concept is best seen with an example.

### Example: Step fixed costs

ABC Company is a manufacturing concern involved in the production of footballs. ABC uses machinery acquired on operating lease for a monthly rental of \$ 800. Monthly production capacity of the machinery is 5,000 footballs. Workout monthly rental cost in each of the following cases:

1. If planned production is 3,000 footballs.
2. If planned production is 4,000 footballs.
3. If planned production is 5,000 footballs.
4. If planned production is 6,000 footballs.
5. If planned production is 12,000 footballs.

Answer: Monthly rental cost depends on the number of machineries used. If the production is not more than 5,000 footballs, rental cost will be a constant of \$ 800. When the production exceeds 5,000 footballs, rental cost would change to a new constant value of \$ 1,600 (2 machineries x \$ 800 per machine). Rental cost in each of the above cases would be:

1. \$ 800        (1 machine x \$ 800 per machine)
2. \$ 800        (1 machine x \$ 800 per machine)
3. \$ 800        (1 machine x \$ 800 per machine)
4. \$ 1,600     (2 machines x \$ 800 per machine)
5. \$ 2,400     (3 machines x \$ 800 per machine)

## Semi variable costs

Semi variable costs are a mixture of fixed costs and variable costs. It has two components:

• One that varies with the change in level of production/ activity (variable component).
• One that remains constant and is not dependent on the level of production/ activity (fixed component).

The total cost function (y = a + bx) can be used to estimate costs at different activity levels and is particularly useful in forecasting and decision making. If fixed component and variable component are unknown, the total cost function can be constructed using high low method or linear regression analysis.

### Formula: Semi variable cost

y = a + bx

Where:

y = total semi variable cost or total cost

a = fixed component of the semi variable cost

b = variable component of the semi variable cost

x = number of units of output or the volume of activity

### Example: Semi variable cost

A telephone bill has two components;

• Line rent of \$ 200 per month (fixed component)
• Call charges of \$ 2 per minute of phone call (variable component)

Work out total cost and cost per minute of telephone usage for each month if 500, 1000 and 1500 minutes were used in the months of January, February and March respectively.