# Methods of cost estimation

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

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.
Based on performance, you have been provided with the following information regarding ABC
Ltd for the year ended 31 December 2004:

To get the fixed cost a, substitute ‘b’ into the straight line equation as follows:

When labour hours (X) = 800, service cost (total cost, Y) = shs.200,000
Therefore, from the Straight Line equation, Y = a + bX

200,000 = a + (100) 800
200,000 = a + 80,000
a = 200,000 – 80,000
a = 120,000

Therefore, fixed costs = Shs.120,000

NB: Even if we used the 2nd set of labour hours and service costs, were would still get he same
When labour hours (X) = 300, service cost (total cost, Y) = Shs.150,000.

Therefore,
50,000 = a + 100(300)
a = 150,000 – 30,000
= Shs.120,000

Therefore, the cost equation is:
Y = 120,000 + 100X

This equation can be used to estimate or predict the total costs: For example, when the activity level is, say, at 1000 labour hours, then the total cost would be:

y = 120,000 + 1000(100)
= 120,000 + 100,000
= Shs.220,000

Evans, the Managing Director of Mambo Company, has asked for information about the cost behavior of manufacturing overhead costs. Specifically, he wants to know how much overhead cost is fixed and how much is variable. The following data are the only records available.

Required:
Using the high-low method, determine the overhead cost equation. Use machine-hours as your
cost driver

Solution:
Note that in most cases, you are required to identify the cost driver. For instance, in our case, the cost driver is the machine hours and not overhead cost. Overhead cost cannot be a cost driver. It is a cost by itself.

To get the fixed cost a, substitute ‘b’ into the straight line equation as follows:

When machine hours (Y) = Shs.1,000, Overhead cost (total cost, Y) = shs.19,950
Therefore from the Straight Line equation, Y = a + bX

High low method of cost estimation is easy to use and is liked by many as it is handy when a quick rough estimate is required. However, it does not consider all observations and thus outlier cases may distort the model. It is only suitable with a single predictor and, in addition, It assumes that the relationship between the X and Y variables is linear and exists. The probable error of estimation can not be measured.
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 behavior for several past periods or intuitive feelings of the manager.
>>> Illustration
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 2.18(1090/500)

For 550 machine hours
Total cost, Y = 1,430 + 2.18(550)
= 1,430 + 1,199
= Shs.2,629

This analysis should determine whether any factors apart from output machine hours are
influencing total cost.
The accounts analysis method is easy to use and useful when a quick cost forecast is required. However, it assumes that what occurred in the past will be reflected in the future. This calls for further analysis.
The model’s reliability and validity cannot be determined as we cannot measure the size of probable error in forecasts made i.e. it lacks statistical vigor. The method is highly subjective as different managers will classify some costs differently.
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. It can also be defined as ‘a straight line used as a best approximation of a summary of all the points in a scatter-plot’. Its intersection with the vertical axis indicates the fixed cost while the gradient indicates the variable cost per unit.
This method takes into account all observations and is easy to apply. However, it cannot be used with two or more independent variables and is subjective to some extent as different lines of best fit may be drawn by different analysts.
>>> Illustration IV
Assume a firm has total costs of 8m, 4m and 1m respectively when the output units are 400,000, 200,000 and 0 respectively. Estimate its cost equation using the visual fit method.

On the basis of the existing data, fixed cost is Shs 1m and the variable cost per unit is 20. On the basis of the developed model, estimates can be made regarding future cost. When the activity level is 600,000 units, total cost will be estimated as:

REGRESSION ANALYSIS

Regression analysis has a mathematical base of all regression lines that could be drawn to represent the data. The least square regression line of Y on X is that line for which the sum of squares of vertical deviations of all the points from the line is least. It involves estimating the cost function using past data or the dependent and the independent variables. The dependent variable will constitute the relevant cost, which may be service, variable cost, overhead cost, etc.. 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, etc..
In regression analysis, a regression model of the form Y = a + bX for a simple regression is obtained. This formal model measures the average amount of deviation of the dependent variable that is associated with unit changes in the amount of the independent variable. For a multiple regression, a regression model of the form Y = a + b1X1 + b2 X2 + …….. + bnXn is obtained
Where a is fixed cost,
X1, X2, Xn are cost drivers X1, X2, X3 up to Xn _
bl, 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, X3

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 + b1X1 + b2 X2 + +
bnXn so that we have several variable costs per unit (bl, b2 bn) and several independent variables
(X1, X2, X3)
The general formulas used to compute a and b are as listed below. The equations are solved simultaneously to obtain the values.

Assumptions of the regression analysis
(a) There exists a cause and effect relationship between the variables. That is, a change in the independent variable causes a change in the dependent variable.

(b) There is good evidence of correlation. In this case, linearity of costs exists. Correlation is the degree of relationship between variables which seek to determine how well linear or other equations, explain or describe, the relationship between variables

(c) The historical data used covers a large level of activity level

(d) Only one independent variable or activity base affects costs. This is in the case of simple regression analysis where only one independent variable exists.
>>> Illustration
The following data relates to MAKB Company limited for the half year period just ended.

Required:
Determine the business fixed and variable costs for its manufacturing overheads and thus write down the cost equation in the form of Y=a + bX.
Approach I

Approach II (substituting the figures obtained from the table in the formula)