Management and Cost Accounting: Cost Estimation and Cost Behaviour

Management and Cost Accounting Introduction

This material is prepared for use with Management and Cost Accounting in South Africa 1e by Colin Drury (ISBN 9781473773943), ) 2023 Colin Drury.
This section falls under Part Two: Cost accumulation for inventory valuation and profit measurement.
The specific focus is Chapter 3: Cost Estimation and Cost Behaviour.

Learning Objectives

After studying this chapter, students should be able to perform the following:

Identify and describe the different methods of estimating costs.
Calculate regression equations using three specific techniques: high-low, scattergraph, and least-squares.
Explain, calculate, and interpret the coefficient of determination test of reliability.
Explain the meaning and significance of the term correlation coefficient.
Identify and explain the six specific steps required to estimate cost functions from past data.

General Principles Applying to Estimating Cost Functions

Regression Equation (Cost Function): This is defined as a measure of past relationships between a dependent variable and potential independent variables.
Dependent Variable ( $y$ ): Usually represents the total cost to be predicted.
Independent Variables ( $x$ ): These are the cost drivers or activity measures.
Simple Regression: Refers to the relationship between the dependent variable and a single independent variable.
The mathematical form of the cost function is typically expressed as: $y = a + bx$ - Where $a$ represents the vertical intercept (total fixed costs). - Where $b$ represents the slope of the line (variable cost per unit of activity).

Cost Estimation Methods

There are five primary methods utilized for estimating costs:

Engineering Methods

Definition: This method involves an analysis based on direct observations of physical quantities required for an activity, which are subsequently converted into cost estimates.
Utility: It is particularly useful for estimating the costs of repetitive processes where input-output relationships are clearly and precisely defined.
Applications: This method is appropriate for estimating costs associated with: - Direct labour - Materials - Machine time

Inspection of Accounts Method

Process: A departmental manager and an accountant collaborate to inspect each item of expenditure within the accounts for a specific period.
Classification: Each item is classified into one of three categories: 1. Fixed 2. Variable 3. Semi-variable

Graphical or Scattergraph Method

Process: This method involves plotting the total costs for each activity level on a graph.
Fitting the Line: A straight line is fitted to the scatter of plotted points using visual approximation.

High–low Method

Process: This involves selecting the periods characterized by the highest and lowest activity levels.
Comparison: It compares the changes in costs that result from the difference between these two levels to determine the variable cost per unit.
Example Calculation: - Activity level: $5\,000\,\text{units}$ - Total cost ( $y$ ): $R22\,000$ - Variable cost: $R10\,000$ - Non-variable (fixed) cost calculation: $R22\,000 - R10\,000 = R12\,000$ - The resulting cost function is derived from these points.

Least-squares Method

Definition: A mathematical method used to find the "line of best fit," represented by the equation $y = a + bx$ .
Calculation Status: Note that the transcript explicitly states "THESE CALCULATIONS ARE NOT REQUIRED!" for the purposes of the specific exercise, though the method remains a core concept.
Purpose: It provides a precise cost function based on minimizing the sum of the squares of the vertical deviations from each data point to the line.

Tests of Reliability

Purpose: These tests indicate how reliable potential cost drivers are in predicting the dependent variable (total cost).

Simplistic Approaches

Visual Inspection: The most simplistic approach is to plot the data for each potential cost driver and examine the distances of the points from the straight line derived from the visual fit.
Coefficient of Determination ( $r^2$ ): A more formal simplistic approach involving the computation of the coefficient of variation, known as $r^2$ .

Correlation Coefficient ( $r$ )

Definition: $r$ is the coefficient of correlation.
Interpretation: The value of $r^2$ (coefficient of determination) explains the proportion of the variation in the dependent variable explained by the independent variable.
Data Interpretation Example: Using data from provided tables, if an analysis yields a specific result, it might mean: "This means $88.61\%$ of the variation in total cost is explained by variations in the activity base."

Relevant Range and Non-Linear Cost Functions

The Relevant Range: It is the range of activity levels for which the cost function is valid.
Warning: It may be misleading to use a cost function to estimate costs for activities that fall outside the range of observations used to define that specific cost function.

Summary of Steps Involved in Estimating Cost Functions

The process of estimating cost functions from past data involves six essential steps:

Select the dependent variable ( $y$ ): Identify the cost record to be predicted.
Select the potential cost drivers: Identify independent variables that cause variations in the dependent variable.
Collect data on the dependent variable and cost drivers: Gather historical information.
Plot the observations on a graph: Use a scattergraph to visualize the relationship.
Estimate the cost function: Use methods like High-Low or Least-Squares to determine $y = a + bx$ .
Test the reliability of the cost function: Use tests like $r^2$ to ensure the cost driver is a good predictor.

Cost Estimation When the Learning Effect is Present

Learning Curve Effect: When employees perform new tasks, they are likely to take less time as they become more familiar and experienced with the task.
Impact on Costing: As humans learn, the time (and thus the related labor cost) per unit decreases over time at a predictable rate.