Mixed Cost or Semi-variable Cost:

• Define and explain mixed or semi-variable cost. Give examples of mixed costs.
• Analyze mixed cost using high-low point method.

Definition and explanation of mixed or semi variable cost:

A mixed cost is one that contains both variable and fixed cost elements. Mixed cost is also known as semi variable cost. Examples of mixed costs include electricity and telephone bills. A portion of these expenses are usually consists line rent. Line rent normally is fixed for each month. Variable portion consists units consumed or calls made. The relationship between mixed cost and level of activity can be expressed by the following equation or formula:

Y = a + bX

In this equation,

• Y = The total mixed cost
• a = The total fixed cost
• b = The variable cost per unit
• X = The level of activity

The equation makes it very easy to calculate what the total mixed cost would be for any level of activity within the relevant range For example, Suppose that the company expects to produce 800 units and company has to pay a fixed cost of \$25,000 and a variable manufacturing cost is \$3.00 per unit. The total mixed cost would be calculated as follows:

Y = a + bX

Y = \$25,000 + (\$3.00 × 800 units)

= \$27,400

A characteristic of mixed cost that needs to be understood is that we usually have to separate fixed and variable components of the total mixed cost.

The analysis of mixed costs:

In practice the mixed costs are very common. For example the cost of providing X-ray services to patients is a mixed cost. There are substantial fixed costs for equipment depreciation and for salaries for radiologist and technicians, but there are also variable costs for X-ray film, power and supplies. Maintenance costs of machineries and plants are also mixed costs. Companies incur costs for renting maintenance facilities and for keeping skilled mechanics on the payroll, but the costs of replacement parts, lubricating oil, tires, and so forth are variable with respect to how often and how far the machineries and plants are used.

The fixed portion of the mixed cost represents the basic, minimum cost of just having a service available for use. The variable portion represents the cost incurred for actual consumption of the service. The variable element varies in proportion to the amount of service that is consumed .

High and Low Point Method- Separation of Fixed and Variable Components of Mixed or Semi-variable Cost:

The fixed and variable elements of a mixed cost can be estimated by using high and low point method. To analyze mixed costs with the high and low point method, we begin by identifying the period with the lowest level activity and the period with the highest level of activity. The period with lowest level of activity is selected as first point and the period with the highest activity is selected as the second point. Consequently the formula becomes:

Variable Costs = (Y2 − Y1) ÷ (X2 − X1)

• Y2 = Cost at the high level of activity
• Y1 = Cost at the low level of activity
• X1 = High activity level
• X2 = Low activity level

Formula can also be written as:

Variable cost = Change in cost / Change in activity

Therefore, when high and low point method is used, the variable cost is estimated by dividing the difference in cost between the high and low activity levels by the change in activity between those two points. We can apply high and low point method on the following data to spare fixed and variable costs.

 Month Activity Level: (Hours Worked) Mixed Cost (Maintenance Cost) January February March April May June July 5,600 7,100 5,000 6,500 7,300 8,000 6,200 \$7,900 8,500 7,400 8,200 9,100 9,800 7,800

Using the high and low point method we first identify the period with the highest and lowest activity-in the following data June and March. We then use the activity and cost data from these two periods to estimate the variable cost component as follows:

 Activity Levels Patient Maintenance Cost High activity level (June) Low activity level (March) 8,000 5,000 \$9,800 7,400

Variable Cost = Change in Cost / Change in Activity

\$2,400 / 3,000 hours

= \$ 0.80 Per hour

Variable rate is \$0.80 per unit according to above calculation under high and low point method. We can now determine the amount of fixed cost as follows:

Fixed cost element = Total cost − variable cost element

\$9,800 − (\$0.80 per unit × 8,000 hours)

= \$3,400

Both the elements, variable and fixed , have now been isolated. The cost of maintenance can now be expressed as \$3,400 per month plus \$0.80 per hour. The cost of maintenance can also be expressed in terms of the equation for a straight line as follows:

Y = \$3,400 + \$0.80X

Some times the high and low levels of activity don’t coincide with the high and low amounts of cost. For example, the period that has the highest level of activity may not have the highest amount of cost. Nevertheless, the highest and lowest levels of activity are always used to analyze a mixed cost under the high and low point method. the reason is that the analyst would like to use data that reflect the greatest possible variation in activity.

Limitations and Disadvantages of High and Low Point Method:

The high and low point method is easy to apply and its simplicity is its main advantage, but it suffers from a major defect. It utilizes only two points and generally two points are not enough to produce accurate results in cost analysis work. Additionally, Periods in which the activity level is unusually low or unusually high will tend to produce inaccurate results. A cost formula that is estimated solely using data from these unusual periods may seriously misrepresent the true cost relationship that holds during normal periods.