# Semi-variable cost

The concept of semi-variable cost (also referred to as semi-fixed cost) is often used to project financial performance at various scales of production, where it is an expense which contains both a fixed-cost component and a variable-cost component. It is related to the scale of production within the business where there is a fixed cost which remains constant across all scales of production whilst the variable cost increases proportionally to production levels.

Adopting the example of a factory, fixed costs can include the leasing of the factory building and insurance whilst the variable costs can be listed as overtime pay and purchasing of the raw materials.

## Calculating semi-variable costs

In the simplest case, where cost is linear in output, the equation for the total semi-variable cost is as follows:

Y = a + bX

where

Y = Total cost
a = Total fixed cost
b = Variable cost per unit
X = Output produced

## Example of calculating the total cost using the semi-variable cost equation

A factory costs £5000 per week to produce goods at a minimum level and due to high demand it has to produce for an extra 20 hours in the week. Including the wages, utility bills, raw materials etc. the extra cost per hour (the variable cost) is £300.

Y = Total cost
a = £5000
b = £300
X = 20 hours
Total cost = 5000 + (300x20)

The total cost would be £11,000 to run the factory for this particular week.

## The high-low method to separate the components of a semi-variable cost equation

A relatively common method used by managers and accountants alike to estimate the variable and fixed cost components is the high-low method. By identifying the time period where production is at its highest and lowest and inputting the figures into the high–low equation we can separate out the variable and fixed costs.

Variable Costs = (Y2 − Y1) ÷ (X2 − X1)
Y1 = Cost at the low level of activity
Y2 = Cost at the high level of activity
X1 = Low activity level
X2 = High activity level
Y1= 3500
Y2 = 5600
X1 = 4000
X2 = 7000
Variable costs = (5600-3000) / (7000-4000)
Variable costs = 2100/3000
Variable cost = 0.7

Using the original semi-variable cost equation

Y = a + bX
7000 = Fixed cost + (0.7x5600)
Fixed cost = 7000 – 3920
Fixed cost = £3080

The equation to calculate the semi-variable cost in this example is as follows;

VC = 3080 + (b*0.7)

## Advantages and disadvantages of using the high-low method in calculating semi-variable costs

A major advantage of the high-low method is that it is relatively simple to calculate; this enables an estimate for the fixed costs and variable costs can be found in a short time, with only basic mathematics and no expensive programs to run the calculations, allowing for the firm to invest their finite resources elsewhere. This is particularly useful for smaller firms which do not that the budget to afford external, more qualified accountants.

As this particular method only uses the highest and lowest figures it means individuals in companies can simply research the data in the company database (as the total costs and scale of production would be widely available to employees or easily attainable); this would allow all employees in the business to calculate the semi-variable costs and its components easily resulting in them having a better understanding of how the company performs and its expenses.

However, the high-low method can only produce an estimate; as it only uses two sets of data, the highest and lowest at that, it can be largely unreliable as often firms can have high variances in production levels and this method would not be able to capture the average activity levels, causing an incorrect figure to be found. There are more accurate methods such as the least-squares regression, although this is much more complex to use.

A major drawback of the high-low method is that no foreign factors are taken into account. Once a level of production has been reached the firm would have to purchase additional assets such as machines or employees in order to attain the increase in production levels; the disadvantage of calculating semi-variable costs through this particular method is that it would underestimate the cost as it does not separate the fixed and variable costs, leading to the increase in expenditure being neglected and resulting in incorrect forecasts. This could lead to the firms bottom line eroding as the individual would estimate lower costs than what it would occur and profits would be lower than expected.