## Methods of Cost Estimation

We will consider following cost estimation methods commonly utilized, namely:

1. High Low Activity method
2. Account Analysis
3. Engineering Analysis
4. Visual Fit (Scatter graph) method
5. Simple linear regression analysis
6. Learning curve Theory

High – Low method

Here, cost estimation is based on the relationship between past cost and past level of activity. Variable cost is based on the relationship between costs at the highest level of activity and the lowest level of activity. The difference in cost between high and low activity level is taken to be the total variable cost from which the unit variable cost can be computed by dividing it by the change in output level. This is indicated below:

Total Variable Cost = Cost at high activity level – Cost at low activity level

Therefore,

Unit Variable cost = Variable cost = Cost at high level activity – cost at low level activity

Output Units Units at high activity level – units at low activity level

The variable cost per unit so calculated forms the ‘b’of the straight line equation mentioned earlier. By substituting ‘ b’ into the equation, we can obtain ‘a’, the fixed cost.

Account Analysis (Inspection of Accounts)

Using account analysis, the accountant examines and classifies each ledger account as variable, fixed or mixed. Mixed accounts are broken down into their variable and fixed components. They base these classifications on experience, inspection of cost behaviour for several past periods or intuitive feelings of the manager.

Example

Management has estimated Shs.1,090 variable costs, Shs.1,430 fixed costs to make 100 units using 500 machine hours. Since machine hours drives variable costs in our example, the variable cost stated as

Then we get the total cost equation as

Y = ,1430 +2.18 x

Where y = total cost

x = number of machine hours

For 550 machine hours

Total cost = Shs.1,430 + Shs. 2.18 (550) = 1,430 + 1,999 = Shs.2,629

This analysis should determine whether any factors apart from output machine hours are influencing total cost.

A danger in using this method lies in the fact that many managers may assume a cost’s behaviour without further analysis. This is because the method is highly subjective.

Engineering method

This method is based on a detailed study of each operation where careful specification is made for materials, labour and equipment necessary to produce a product. It involves identifying the level of input required of an activity in form of raw material and labour while total cost is based on the cost of each input. This approach is applicable where no past data exists. The main setback of the approach is that it requires a complex analysis of all the constituents of an activity and the requirements of an activity in terms of costs detailed into materials, labour, overheads and time.

Visual fit (scatter graph method)

Cost estimation is based on past data regarding the dependent variable and the cost driver. The past data on cost levels and the output levels) is plotted on a graph( called a scatter graph )and a line of best fit is drawn as shown in the diagram . A line of best fit is a line drawn so as to cover the most points possible on a scatter graph. Its intersection with the vertical axis indicates the fixed cost while the gradient indicates the variable cost per unit.

Regression analysis

It involves estimating the cost function using past data or the dependent and the independent variables. The cost function is based on the regression of the relevant variables. The cost function will depend on the relationship between the dependant variable and the independent variable. The dependent variable will constitute the relevant cost which may be service, variable cost, overhead cost e.t.c. The independent variable will be the cost drivers where the cost drivers will be labour hours, units of labour or raw materials, units of output e.t.c.

In regression analysis, a regression model of the form y= a + bx for a simple regression is obtained. For a multiple regression, a regression model of the form Y = a + b1x1 +b2x2 + bnxn is obtained

#### Where a is fixed cost, x1,x2,xn are cost drivers x1,x2,x3 upto xn.

b1,b2 bn are changes in cost with the change in value of cost driver i.e. variable cost per unit of change in x1,x2,xn

y is the dependant variable (Total cost)

Note that a simple regression produces a cost function of the form y = a + bx so that we only have only one variable cost per unit (b) and only one independent variable (cost driver) x..

However, a multiple regression produces a cost function of the form

y = a + b1,x1+ b2, x2 + bn,xn so that we have several variable costs per

unit (b1,b2,bn) and several independent variables (x1,x2,xn)