DEPARTMENT OF ACCOUNTING AND FINANCE

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1 Mt Kenya University P.O. Box Thika Web: DEPARTMENT OF ACCOUNTING AND FINANCE COURSE CODE: DAF1305 COURSE TITLE: MANAGEMENT ACCOUNTING Instructional Material for BBM- Distance Learning

2 DAF1305: MANAGEMENT ACCOUNTING Contact Hours: 30 Pre-requisites: DBM 114 and DBM 121 Purpose: To provide the student with the knowledge of important concepts and techniques needed by managers in planning, control, management and decision making in business organization Expected Learning Outcomes of the Course: By the end of the course unit the learners should be able to:- i) Explain the importance of management accounting in the management of organizations ii) iii) Apply management accounting techniques to solve various management dilemmas Explain the importance of budgeting and responsibility accounting in management of organizations Course Content: Nature, Purpose and scope of Management Accounting; Decision Making environments and techniques; Cost Behavior; Cost Estimation; Relevant costing; Cost-Volume- Profit Analysis; Variable and absorption costing; Master Budget and Responsibility Accounting Course Outline WEEK 1 Chapter: INTRODUCTION; Nature, Purpose and Scope of Management Accounting Sub Topics: Definitions- Managerial Accounting, Cost Accounting, Financial Accounting Objectives of Management Accounting Difference between Management and Financial Accounting Role of management accounting in management process Week 2 Chapter: DECISION MAKING Sub Topics: Decision Making Process Decision Making Conditions Decision Making Techniques- Maximin, Maximax, Laplace and Minimax regret criteria; Expected values, standard deviation, coefficient of variation Week 3 Chapter: COST BEHAVIOUR Variable /fixed costs Direct/indirect costs Controllable /uncontrollable costs Week 4 CHAPTER: COST ESTIMATION Cost Estimation Methods- Accounts analysis (Accounts inspection method), The two point method (High-Low Method), Regression analysis (least-square method), Engineering methods ii

3 Week 5 Chapter: Cost Volume Profit Analysis Sub Topics: Cost Volume Profit Analysis Assumption of CVP analysis The Break- Even Point B. E. P in Graphical Form B. E. P in Mathematical Formula Margin of safety Limitations of CVP analysis Week 6&7 Chapter: COSTING METHODS; Absorption Costing and Marginal Costing Sub Topics: Absorption Costing Marginal Costing Marginal / Variable Costing Vs Absorption Costing A comparison of the impact of variable costing and absorption costing on profit Week 8 Chapter: RELEVANT COSTING The concept of cost relevance to decision making Relevant and irrelevant costs Week: 9 & 10 Chapter: BUDGETING Sub Topics: The role and rationale of budgeting- Functions of budgets, Advantages of budgets Types of budgets Mechanics of budgeting Stages in the budgeting process Steps in developing a master budget Course Assessment Examination - 70%; Continuous Assessment Test (CATS) - 20%; Assignments - 10%; Total - 100% Recommended Text Books: i) Horngren C.T and Foster, G: (2003), Cost Accounting: A Managerial Emphasis, (11 th Edition) ii) Hansen (2008); Management Accounting; Cengage Learning ( Thompson ) Text Books for further Reading: i) Horngren C.T Sundrem G L and Stratton W. O; (1996), An introduction to Management Accounting, (10 th International Edition), Prentice Hall International Inc Note: Sit in CATs cover work up to week 7 in the course outline iii

4 Table of Contents Page 1.0 Chapter One: Nature, Purpose and Scope of Management Accounting Definitions Objectives of Management Accounting Difference between Management and Financial Accounting Role of management accounting in management process Review Questions Chapter Two: Decision Making Decision Making Process Decision Making Conditions Decision Making Techniques Maximin, Maximax, Laplace and Minimax regret criteria Expected values, standard deviation and coefficient of variation Review Questions Chapter Three: Cost Behaviour Variable/ Fixed Costs Direct/ Indirect Costs Controllable/ Uncontrollable costs Chapter Four Cost Estimation Methods Accounts analysis (Accounts inspection method) The two point method (High-Low Method) Regression analysis (least-square method) Graphical Method Engineering methods Review Questions Chapter Five: Cost Volume Profit Analysis Cost Volume Profit Analysis Assumption of CVP analysis The Break- Even Point B. E. P in Graphical Form B. E. P in Mathematical Formula Margin of safety Limitations of CVP analysis Review Questions.41 iv

5 6.0 Chapter Six: Costing Methods Definitions Presentation of data under Marginal Costing and Absorption Costing Reconciliation Statement for Marginal Costing and Absorption Costing Profit Marginal / Variable Costing Vs Absorption Costing Review Questions Chapter Seven: Relevant Costing The Concept of Cost Relevance to Decision Making Assumptions of Relevant costs Qualitative and Quantitative factors in Decision Making Review Questions Chapter Eight: Budgeting The role and rationale of budgeting Types of budgets Mechanics of budgeting Steps in developing a master budget Review Questions.70 Sample Exam Papers..71 v

6 1.0 CHAPTER ONE: NATURE AND PURPOSE OF MANAGEMENT ACCOUNTING Learning Objectives By the end of this chapter the learner should be able to: i) Distinguish between managerial accounting, cost accounting and financial accounting ii) State objectives of management accounting iii) Describe the management accounting system iv) Explain the role of management accounting in management process 1.1 Definitions Managerial Accounting Management accounting is the application of the professional knowledge and skills in preparation and presentation of accounting information in such a way as to assist management in formulation of policies and planning and control of the operations of undertakings. It measures and reports financial and non-financial information that helps managers make decision to fulfill the goals of an organization. It is focused on internal reporting. It is concerned with the provision of information to people within the organization so as to help them make decision and improve efficiency and effectiveness of existing operations. Management accounting provides information required by management for such purposes as:- 1. Formulation of policies 2. Planning and controlling activities of the enterprises 3. Decision making on alternative causes of action. 4. Disclosure to those external to the entity 5. Disclosure to employees 6. Safeguarding assets The above involves participative management to ensure that there is effective:- 1. Formulation of long tern plans to meet objectives 2. Formulation of short term operation plans 3. Recording of actual transactions 1

7 4. Corrective actions required to bring future actual transactions into line. 5. Obtaining and controlling finance 6. Reviewing and reporting on systems and operations Cost Accounting Cost accounting measures and reports financial and non-financial information that relates to the cost of acquiring or consuming resources by an organization, it includes those parts of management and financial accounting where information cost is collected or analyzed. It provides information both managerial accounting and financial accounting. Financial Accounting It focuses on reporting to external parties. It measures and records business transactions and provides financial statements that are based on generally accepted accounting principles. It is defines as that part of accounting which covers the classification and recording actual transactions of an entity in monetary terms in accordance with established concepts, principles, accounting standards and legal requirements and present as accurate view as possible of the effect of those transactions over a period of time and at the end of that time. Note: - All the above three branches of the accounting should be integrated into the company s reporting system where: Financial accounting maintains records of each transaction and helps control the firm s assets and liabilities e.g. plant, equipment, stock, debtors and creditors. It satisfies the legal and taxation requirements and also provides input into the costing system. Cost accounting analyses the financial data into more detail and provides a lot of other information used for control It also provides key data such as stock valuation and cost of sale which are fed back into the financial accounting system so that accounts can be finalized. Managerial accounting gets information from financial and cost accounting system and uses this and other available information in order to advice management on matters such as cost control, pricing, investment decisions and planning. 2

8 1.2 Objectives of Management Accounting 1. Planning All organization should plan a head in order that they can set objectives and decide how they can meet them. Management accounting uses past data to predict the future 2. Control The production of the company internal accounts enable the firm to concentrate on achieving its objectives by identifying which areas are performing and which are not. The use of management by exception reports enables control to be exercised where it is most useful. 3. Organization There is a direct relationship between the organizational structure and the management accounting system. Management accounting system should therefore produce the right information at the right cost, at the right time. 4. Communication The existence of budgetary and management accounting system is an important part of communication process. Plans are outlined to managers so that they are fully aware of what is required of them and the management accountant tells them whether or not the desired results are achieved. 5 Motivation The use of budget and achievable targets motivates the employees to work hard so as to achieve these targets. 3

9 1.3Difference between Management and Financial Accounting 1. Legal requirements It is a legal requirement for a public limited company to produce annual financial accounts regardless of whether or not management regards this information as useful. However it is optional for management accounting to prepare this statement. 2. Financial accounts Financial accounts must be prepared to conform to legal requirements and generally accepted accounting principles established by regulatory bodies. These requirements are essential to ensure consistency and formality that is needed for external financial statement. In contrast management accountings are not required to adhere to generally accepted accounting principles when providing managerial information for internal purposes. 3. Time dimensions Financial accounting reports what has happened in the past in an organization where as management accounting is concerned with both past and future information. Management requires details of expected future cost and revenues. 4. Reporting frequency Financial accounting is published annually while management accounting requires information frequently so as to make decisions. 5. Focus on individual parts or segments of the business Financial accounting report focuses on all parts of the business whereas management accounting focuses on a small part of the business. 6. Type of information Management a c c o u n t i n g i n c l u d e s n o n m o n e t a r y a n d m o n e t a r y i n f o r m a t i o n w h i l e financial accounting includes monetary information only. Management accounting includes quantities of materials as well as monetary cost of material, number of employees as well as Labor cost etc. Financial accounting records this information in monetary terms only. 4

10 1.4 Role of management accounting in management process i) To allocate and accumulate data and provide reliable results for internal and external profit reporting ii) To provide relevant information to help managers make better decisions iii) To provide information for planning, iv) To provide information for control and v) To provide information for performance measurement Review Questions i) What is the basic difference between financial and managerial accounting? ii) What are the key attributes of a good management accounting system? iii) Discuss the role of management accounting in the management process? iv) Explain the objectives of management accounting Suggested References for Further Reading i) Horngren et. al., 2009, Introduction to Management Accounting, 14 th Ed, Dorling Kindersley, New Delhi Pg ii) Garisson R. H., and Noreen E. W., 1997 Managerial Accounting, 8th Ed, MacGrraw-Hill, New York, Pg

11 2.0 CHAPTER TWO: DECISION MAKING Learning Objectives By the end of this chapter the learner should be able to: i) Describe the decision making process ii) Identify the decision making conditions iii) Illustrate various decision making techniques 2.1 Decision Making Process Information generated by management accounting is judged based on its ultimate effect on the outcome of decisions, an understanding of the decision making process is therefore imperative precedent to understanding management accounting. The Decision-Making, Planning and Control Process 1. Identify objectives 2. Search for alternative course of action Planning process 3. Gather data about alternatives 4. Select alternative course of action 5. Implement the Decision Control process 6. Compare actual and planned outcomes 7. Respond to divergencies from plan 6

12 The figure above represents a decision making process. Planning involves making choices between alternatives and is primarily a decision making activity. The final two stages represents the control process which s a process of measuring and correcting actual performance to ensure that the alternatives that are chosen and the plans for implementing them are carried out. 1. Identifying objectives Objectives provide a direction aim or guide and are therefore a prerequisite to any decision before any good decision can be made. Thus specification of organizational goals or objectives is the first step in the decision making process. The overriding objective of the firm is the maximization of shareholder s value or maximization of future cash flows (though controversy still exists). Some authors have argued that people have a limited capacity for understanding and can only deal with limited amount of information at a time (bounded rationality), they tend to search fro solutions until the first acceptable solution is found and no attempt is made to find the best or optimal solution this is referred to satisficing. 2. The search for alternative course of action These are strategies that might enable the objectives to be achieved. To maximize future cash flows management identifies potential opportunities and threats in its environment and takes appropriate steps to grow the cash flows. The potential courses of action include developing new products for existing markets, new products for new markets, or new markets for existing products. The search for alternatives involves acquisition of information concerning the future opportunities and environments 3. Gather data about alternatives With the alternative courses of action selected, assessment should be made on the ability of the company to establish adequate flows for each of the alternative activity for various states of outcome. Strategic decisions that have a profound effect on the firms future position are made based on collected data, it is therefore imperative that adequate data is gathered about the firm s future capabilities and the environment in which it operates. Operation decisions or short term decisions which are a concern of lower level also need collection of necessary data such as selling prices of competitors, estimated demand etc when data have been gathered management must decide on which course of action to take. 7

13 4. Select alternative course of action In practice decision making involve choosing of competing alternative courses of action and selecting the alternative that best satisfies the objectives of the organization. Assuming that the objective of the organization is the maximization of future cash flows, an incremental analysis of the net cash benefits is applied to rank the alternatives, so that the alternative with the greatest benefits is chosen, subject to consideration of other qualitative factors. 5. Implement the Decision The selected course of action should be implemented as part of the budgetary process. The budget is a financial plan for implementing the various decisions that the management has made. The budgets for various decisions are expressed in terms of cash inflows and outflows revenues and expenses and merged together into a master budget that brings out the budgeted profit and loss statement, cash flow statement and balance sheet. The budgeting process communicates to everyone in the organization the part that they should play in implementing management s decisions. 6. Compare actual and planned outcomes and responding to divergencies from plan The managerial function of control consists of measurement reporting and subsequent correction of performance in an attempt to ensure that the firm s objectives and plans are achieved. Performance reports consisting of a comparison of actual outcomes with budgeted or planned outcomes are produced and presented to management (feedback). These reports highlight activities that don not conform to plans so that management can focus they scarce time on those activities (management by exception). Effective control ensures that corrective action is taken so that actual outcomes conform to planed outcomes. This is indicated by the feedback loops linking stages 7and 5 and 7 and Decision Making Conditions i) Decision making under certainty When the decision maker knows with reasonable certainty about what the available alternatives are, and what conditions are associated with each alternative; then a state of certainty is said to exist. In making a choice under conditions of certainty, there is less ambiguity and there is a relatively lower chance of making a bad decision 8

14 For example, Kenya Airways needs to buy ten jumbo jets. The decision is from whom to buy. Kenya Airways has three choices: Airbus, Boeing and McDonnell Douglas. Each of these companies are known for their quality products. Kenya Airways can choose from any of these alternatives. ii) Decision making under risk In some situations, a manager is able to estimate the level of probability at which certain variables could occur. The ability to estimate may be due to experience, incomplete but reliable information or, in some cases, an accurate report. When estimates are made, a degree of risk is involved. However some amount of information about the situation is available. The situation requires estimating the probability that one or more known variables might influence the decision being made. iii) Decision making under uncertainty A condition of uncertainty exists when a manager is faced with reaching a decision with no historical data concerning the variables and/or unknowns and their probability of occurrence. v) Decision under conditions of perfect information Making decisions under conditions perfect information is straight forward because there exist no unknowns. 2.3 Decision Making Techniques 2.3.1Maximin, maximax, laplace and minimax regret criteria Maximin: A pessimistic approach that takes into account the worst possible outcome for each decision outcome alternative. Determine the worst possible payoff for each alternative and choose the alternative that has the best of worst outcome. This guarantees a minimum outcome. Possible Future demand with probabilities Decision Alternatives Low(0.3) Moderate (0.5) High(0.2) Small Facility $10 $10 $10 Medium Facility Large Facility (4)

15 Maximin Solution: minimum payoff for each of the decision alternatives is: $10, $7 and $(4). Solution: build small ($10). Maximax: An optimistic approach that takes into account the best possible outcome for each decision outcome alternative. Determine the best possible payoff for each alternative and choose the alternative that has the best of best outcome. Only takes into account the best possible payoff. Maximax Solution: Best payoffs are $10, $12 and $16. Solution: build large ($16). Laplace: Determine the average payoff for each alternative; choose the alternative with the best average best weighted payoff. This approach treats the states of nature as equally likely. Laplace Solution: first find the row totals; then divide each of these amounts by the number of states of nature. Solution: build medium. Decision Alternatives Row Total Row Average Small Facility $30 $10 Medium Facility Large Facility 14 $4.67 Minimax Regret Determine the worst regret for each alternative; choose the alternative with the best worst regret. This approach seeks to minimize the difference between the payoff that is realized and the best payoff for each state of nature. Minimax Regret Solution: first prepare a table of opportunity regrets (subtract every payoff in each column from the best payoff in that column); second, identify the worst regret for each alternative; third, select the best of the worst regrets. Regrets Decision Alternatives Low Moderate High Worst Small Facility 0 (10-10) $2(12-10) $6(16-10) $6 Medium Facility 3 (10-7) 0(12-12) 4(16-12) 4 Large Facility 14(10-(4) 10(12-2) 0(16-16) 14 Solution: build medium ($4) 10

16 Expected monetary value: This is the weighted average of each state with the probabilities being the weights the best weighted average is chosen Expected Monetary Values solution Small Facility.30(10) +.50(10) +.20(10) = $10.00 Medium Facility.30(7) +.50(12) +.20(12) = $10.50 Large Facility.30(-4) +.50(2) +.20(16) = $ 3.00 Solution: build medium ($10.50) Expected opportunity loss: The opportunity loss is computed by taking the difference between the optimal decision for each state of nature and the other decision alternatives. Opportunity Loss Table Regrets Decision Alternatives Low Moderate High Small Facility 0 $2 $6 Medium Facility Large Facility Expected opportunity loss solution Small Facility.30(0) +.50(2) +.20(6) = $4.6 Medium Facility.30(3) +.50(0) +.20(4) = $1.7 Large Facility.30(14) +.50(10) +.20(0) = $ 9.2 Solution: build medium ($1.7) Probability distributions expected values and standard deviation and coefficient of variation The presentation of a probability distribution for each alternative course of action provides useful additional information to management by indicating the degree of uncertainty that exists for each alternative course of action. The expected value of a decision represents the long-run average outcome that is expected to occur f a particular course of action is undertaken many times. The standard deviation is the conventional measure of dispersion or variability, while the coefficient of variation is the relative variation expressed as the standard deviation divided by the expected value (mean) Example: a manager is considering whether to make product A of B but only one product can be produced. An estimation of the possible sales demand for each product gives the following probability distribution of the profits for each product. 11

17 Product A Outcome (1) Estimated probability (2) Weighted (1) (2) Profits of 6, Profits of 7, ,400 Profits of 8, ,200 Profits of 9, ,800 Profits of 10, ,000 =1.0 Expected value = 8,000 Product B Outcome (1) Estimated probability (2) Weighted (1) (2) Profits of 4, Profits of 6, Profits of 8, ,200 Profits of 10, ,500 Profits of 12, ,400 =1.0 Expected value = 8,900 Which product should the company make? Expected values are obtained by getting the sum of the weighted outcomes of each product (see above) The standard deviation is given as: n σ = ( Xi X ) 2 (Pi) i =1 (1) Profits (2) Deviation from expected Product A (3) Deviation squared (4) probability (5) Weighted amount (3) (4) value (A i - A ) (A i - A ) 2 6,000-2,000 4,000, ,000 7,000-1,000 1,000, ,000 8, ,000 1,000 1,000, ,000 10,000 2,000 4,000, ,000 Sum of sqd dev 1,200,000 σ

18 (1) Profits (2) Deviation from expected Product B (3) Deviation squared (4) probability (5) Weighted amount (3) (4) value (B i - B ) (B i - B ) 2 4,000-4,900 24,010, ,200,500 6,000-2,900 8,410, ,000 8, , ,000 10,000 1,100 1,210, ,000 12,000 3,100 9,610, ,922,000 Sum of sqd dev 4,590,000 σ Coefficient of variation is expressed as σ/ A, thus for A, C V is /8000 = or 13.7% and that of B is /8900 = or 24.1%. A is therefore more variable than B. the decision on whether to pick A or B depends on the risk attitude of the decision maker. However assuming risk aversion the manager would go for product A. 13

19 Review Questions i) A yatch company has developed a new cabin cruiser which they earmarked for the medium to large board market. A market analysis has a 30% probability of annual sales being 5000 boats, and a 40% probability of 4000 annual sales. This company can go into limited production while available costs are sh.10,000 per boat and a fixed cost and sh.800,000 annually. Alternatively they can go into full production where variable cost are sh.9000 per boat and fixed costs are sh.5,000,000 annually, if the new boat is to be sold for shs.11,000 should the ii) company go to limited or full scale production when the objective is to maximized expected profits (use a tree diagram) Describe the decision making process i) Drury c., 2008, Management and Cost Accounting, Cangage Learning, New York Pg 2-50 ii) Horngren et. al., 2009, Introduction to Management Accounting, 14 th Ed, Dorling Kindersley, New Delhi Pg

20 3.0 CHAPTER THREE: COST BEHAVIOUR Learning Objectives By the end of this chapter the learner should be able to: i) Describe the decision making process ii) Identify the decision making conditions iii) Illustrate various decision making techniques i) Cost behavior This is classification of cost according to variability based on the level of output. Cost can be variable, fixed or mixed. Variable costs are the ones which vary in total in direct proportions to changes in the related activity level or volume e.g. material costs, direct labor costs, purchases price, sales commissions etc. Fixed costs are costs that remain in total for a given time period despite wide changes in the related level of activity e.g. rent, depreciation, management salaries etc Figure 1: Total costs Total costs V. C. 5,000 F. C. Slope = V.C.e.g. $50 per kilo of four Constant or intercept of $5,000 2, Output Cost behavior is best seen through a cost function. A cost function is a mathematical expression describing how cost changes with changes in the level of activity. The behavior depicted in figure 1 can be summarized by the following cost function; y = $5, x Where y represents total costs and x the kilos of floor milled 15

21 Figure 2: Unit costs Unit costs $50 per Kilo V. C. F. C. 2,000 4,000 6,000 Output Unit fixed reduce as output increases as illustrated below: Units produced Fixed cost per unit 1 5, , ,000 1 NB: 1. since fixed costs are not constant per unit they should be used with caution for decision making. iv) in practice fixed costs are not constant over the full range of activity, they may increase in steps as shown below: Total Costs Output 16

22 Mixed costs or semi variable cost contain both variable and fixed components and therefore are partly affected by production in the level of activities e.g. consumption or elasticity. As shown in the figure below: Total Costs Output ii) According to the degree of traceability to the final product Under this classification costs can be direct costs or indirect costs. A direct cost is that cost which can be traced in total to the product of services that is being costed. E.g. direct material, labor and expenses which are also referred to as prime costs. Individual costs are cost that cannot be traced directly and in full to the product or service or department e.g. indirect materials, labor, expenses etc. Indirect costs are referred to as overheads which include indirect materials, labor expenses. Total cost is therefore prime costs plus overheads. I.e. the total cost is given as: iii) According to controllability Direct materials XXX Direct labor XXX Prime cost XXX Overheads XXX Total cost XXX Controllable costs - These are the costs which can be influenced by the action of a specified member of an undertaking. A business organisation is usually divided into a 17

23 number of responsibility centres and an executive heads each such centre. Controllable costs incurred in a particular responsibility centre can be influenced by the action of the executive heading that responsibility centre. For example, Direct costs comprising direct labour, direct material, direct expenses and some of the overheads are generally controllable by the shop level management. Uncontrollable costs - Costs which cannot be influenced by the action of a specified member of an undertaking are known as uncontrollable costs. For example, expenditure incurred by, say, the Tool Room is controllable by the foreman in charge of that section but the share of the tool-room expenditure which is apportioned to a machine shop is not to be controlled by the machine shop foreman The distinction between controllable and uncontrollable costs is not very sharp and is sometimes left to individual judgement. In fact no cost is uncontrollable; it is only in relation to a particular individual that we may specify a particular cost to be either controllable or uncontrollable 18

24 4.0 CHAPTER FOUR: COSTS ESTIMATION METHODS By the end of this chapter the learner should be able to: i) Describe the methods used to estimate costs ii) Illustrate various cost estimation methods 4.1 Cost Estimation Methods The following methods used to estimate cost. i. Accounts analysis (Accounts inspection method) ii. The two point method (High-Low Method) iii. Regression analysis (least-square method) iv. Graphical method v. Engineering methods Accounts analysis or inspection of accounts This requires that departmental managers and accountants to inspect each item of expenditure within the accounts and then classifying each of these items as wholly fixed, wholly variable or mixed variable. A simple average unit cost figure is selected for this items that are categorized as fixed and also variable. Mixed costs are decomposed into their fixed and variable components and the departmental manager and the accountant agree on a cost function that best describes the cost behavior. Illustration: The following cost information has been obtained from the latest monthly accounts for an output level of 10,000 units for the manufacturing department of ABC Company. Item Direct materials Ksh 100,000 Direct labor 140,000 Indirect Labor 30,000 Depreciation 15,000 Repairs and maintenance 10, ,000 19

25 An analysis of each of the accounts reveals the following as the variable and non-variable elements of the accounts Item Unit Variable cost Total nonvariable cost Direct materials Direct labor Indirect Labor 30,000 Depreciation 15,000 Repairs and maintenance ,000 Total ,000 The cost function is therefore y = 50,000 + Ksh 24.50x. Exercise: Estimate the total cost of producing 10,000 units The two point method (High-Low) Or Range Method This consists of selecting the periods of highest and lowest activity levels and comparing the change in the cost that results from the two levels i.e. the period with the highest level of output and the period with the lowest level of output. The two points are then used to find the equation which is given by; y = a + bx where; b = the gradient or slope, given by the difference between costs associated with the highest and lowest observation of dependent variable divided by the difference between highest and lowest observation of cost driver. Illustration: Assume that the product manager of ABC Ltd is concerned about the apparent fluctuations in efficiency and therefore work done by employees which are related to the volume. The result of this in most 12 weeks research carried out is as shown below; Week 1. Machine hours(cost driver) 68 Indirect labor costs $1, , ,

26 , , , , y = a + b x machine hour (x) labor costs(y) Highest 96 1,456 Lowest Slope coefficient b = Diff btw costs associated with highest & lowest cos t driver Diff btw highest & lowest cos t driver = $ = $14.92 To compute the constant, we solve for a in the equation y = a +bx using any of the values of x and y i.e. y = a +bx, a = y bx. Thus; a = 1456 ($ ) = $23.68 Therefore the High-low estimate of the cost function is y = a +bx = $ ($14.92 Machine hours) Exercise: (a) Find the indirect labor costs associated with 90 machine hours and (b) the machine hours that $1,000 of indirect labor cost would produce (a) If, x = 90 y = $ ($ ) = $1, (b) If, y = $1,000 $1000 = $ ($14.92x) 21

27 $14.92x = $1000 $23.68 x =976.32/14.92 = Regression Analysis (Ordinary Least Square Method) A regression equation identifies the relationship between dependent variable y and independent variable x. If the relationship has one dependants and one independent variable it is referred to as simple regression given by the function y = a + bx. a and b are computed by solving the following simultaneous equations; y = na + b x xy = a x + b x 2 Use the data from the previous example to compute the regression line and determine the labor cost associated with 80 machine hours Week Machine hours /cost driver (x) Indirect labor costs (y) x 2 x y $1,190 4,624 80, ,211 7, , ,004 3,844 62, ,184 66, ,600 46, ,456 9, , ,180 6,084 92, ,116 32, ,316 6, , ,032 8,836 97, ,624 51, ,304 46,224 Σ x=862 Σy=12,501 Σ x 2 = 64,900 Σxy=928,716 Solve for a and b in the simultaneous equations; y = na + b x... (1) 22

28 xy = a x + b x 2... (2), this gives; 12,501 = 12a + 862b (1) 928,716 = 862a + 64,900b (2) Multiply equation (1) by i.e. 64,900/862, this gives; 941, = ,900b.. (1) 928,716 = 862a + 64,900b.. (2) Subtract equation (2) form equation (1), and then solve for a this gives; 12, = 41,4803a a = 12, / = Insert this figure in either equation (1) or (2) to solve for b. Inserting in equation (1) gives; 12,501 = ( ) +862b 12,501 = 3, b = 862b b = /862 = The cost function is therefore y = $ ($10.31 Machine hours) If x = 80 then, y = $ ($ ) = $ a and b may also be computed using the following simplified expressions b = n xy x y n x 2 ( x)2 Using the above data, b =, while a = y n = b x n 11,144,592 10,775, , = 368,730 = ,756 a = 12, = =

29 Exercise: A hospital records show that the cost of carrying health checks in the last five accounting periods has been as follows; Period 1. No of patients seen 650 Total cost 17, , , , Required: Estimate the cost of carrying out health checks on 850 patients using i) Regression model ii) High low method Period No of patients seen Total cost x 2 x y , ,500 11,131, , ,600 16,732, ,650 1,587,600 23,499, , ,100 17,800, Σ x= ,360 Σy=89,915 1,322,500 Σ x 2 = 5,196,300 21,114,000 Σxy = 90,276,450 i) Regression analysis method An alternative formula of solving for a and b is: b = n xy x y n x 2 ( x) 2 y b x a = n n b = b = b = ,276,450 4,490 89, ,196, ,382, ,675,850 25,981,500 24,900,100 24

30 a = 89, a = ,495 = 15,488 The cost function is therefore; y = $15,488 + ($2.5 number of patients seen) The cost of carrying out health checks for 850 patients is y = $15,488 + ($ ) =$17,613 ii) High - low method x y Highest 1,260 18,650 Lowest , b = y / x = 1525/610 = 2.5 Filling in this value and solving for a, y = a + bx. 17,125 = a (650) 17,125 = a a = = $15,500 The cost function is therefore; y = $15,500 + ($2.5 number of patients seen) The cost of carrying out health checks for 850 patients is y = 15, = $17,625 25

31 4.1.4 Graphical or scatter graph method This method involves plotting on a graph the cost of each activity level the total cost is on represented on the vertical (y) axis and the activity level on the horizontal(x) axis. A straight line is fitted to the scatter of plotted points by visual approximation. The point at which the straight line cuts the vertical axis (y intercept) represents the non-variable costs or item a in the equation y = a + bx. The unit variable cost b is obtained by calculating the gradient of the straight line i.e. change in y/change in x 26

32 Indirectlabour costs Example: Consider data from the previous illustration on ABC ltd, plot the scatter graph and fit the line of best fit by visual approximation and estimate the cost 50 machine hours $1,600 $1,400 $1,200 $1,000 $800 $600 $400 $200 $ Machine hours(cost driver) Y-intercept (constant) and thus a is approx 300 while, b is given by y / x i.e. b = 1, = 200 = The cost function according to the graph method is therefore: y = (15.39 machine hours used) If x = 50, y = 300+ ( ) = KSh The graphical method is easy to use and it provides a useful visual indication of lack or correlation or erratic behavior of costs. It however suffers from the disadvantage of the determination of exactly where the straight line should lie, which is subjective with different people drawing different lines with different slopes therefore giving different cost estimated. To overcome this shortcoming, it is preferable to determine the line of best fit mathematically using the least squares method. 27

33 4.1.5 Engineering methods (work measurement method) This is based on the use of engineering analysis of technological relationship between inputs and outputs in physical terms e.g. methods studies or time and motion studies. The procedures for such analysis are to make an analysis based on direct observations of: i) The physical quantity required for an activity and then convert the final results into the cost estimate; Analyzing or breaking task into its constituent motion elements or operations ii) Determining time for each motion element or operation and several observations are made on different persons performing the task; the average of this gives the normal or base time required for each elements. iii) Time allowance is made for fatigue, resetting of tools, idleness in recent in the method of work. Motion study is the study of movement of work and machines in performing the operations. The objective of motion study is to eliminate unnecessary and wasteful motion by workers and machines operated by them. This method is useful in the estimating the cost of repetitive process where input and output relationship are clearly defined. For instance to set the direct labor standards, each operation is studied and an allowed time computed, usually after carrying out time and motion study. The most efficient methods of production, equipment and operating conditions are the standardized this is followed by time measurements to determine the standard hours required by an average worker to complete the job. Unavoidable delays such as machine breakdowns and routine maintenance are included in standard time while the wage rates are a mater of company policy or negotiation wit unions. The disadvantage is that the methods may be very expensive to apply in practice. Steps of cost estimation The following steps are followed while estimating costs. 1. Identify or select the dependent variable or the response variable. The cost to be predicted will depend in respond variables whose purpose is the reason for estimation. 2. Identify the independent variables also referred to as cost drivers, explanatory 28

34 variables or predictor variables. This is any factor whose change cause, a change in the dependent variable e.g. direct labor hours, direct labor cost, machine hours, numbers or limits numbers or production runs, number of customer order etc. 3. Gathers data on both dependent and independent variables. A sufficient number of past observations must be obtained to derive an acceptable cost function. This should be adjusted to reflect any change of circumstances e.g. inflation or change in the type of equipment being used. 4. Plot the data on the graph usually a scatter diagram. The graph will indicate the general relationship between dependent and independent variable and will give visual indication as whether there is a relationship or not. 5. Estimate the cost function. Either of the different methods learnt such as regression, high-low etc may be use 6. Evaluation of the cost function this may be done through goodness of ft methods such as the coefficient of determination. 29

35 Review Questions i) What is a cost driver ii) iii) iv) Explain how step costs can be fixed or variable depending on your perspective Explain how mixed costs are related to both fixed and variable costs How would account analysis be combined with engineering analysis? v) Mr. Galgallo, CEO of a granite tiles manufacturing firm in Kenya is troubled by fluctuations in productivity and wants to compute how manufacturing support costs are related to the various sizes of batches of output. The following data show the results of a random sample of 10 batches of one pattern of granite tiles: Sample Batch size (X) Support costs $ (Y) a) Using regression analysis measure the cost function of support costs and batch size b) Predict a support cost of a batch size of 25 c) Using the high- low method, repeat question a and b above vi) d) Should the manager use the high low or the regression method? Explain What can we learn from R 2 the coefficient of determination? i) Horngren et. al., 2009, Introduction to Management Accounting, 14 th Ed, Dorling Kindersley, New Delhi Pg ii) Garisson R. H., and Noreen E. W., 1997 Managerial Accounting, 8th Ed, MacGrraw-Hill, New York, Pg

36 Costs and revenue 5.0 CHAPTER FIVE: COST VOLUME PROFIT ANALYSIS Learning Objectives By the end of this chapter the learner should be able to: i) Explain the assumption of C.V.P analysis ii) Illustrate the Break- Even Point, in graphical form and in mathematical formula iii) Explain the margin of safety iv) Discuss the criticisms of C.V.P analysis 5.1 Cost Volume Profit Analysis Cost volume profit analysis examines the behavior of total revenues, total cost and operating income as changes occur in the output level, selling price, variable costs per unit and a fixed cost. 5.2 Assumption of CVP analysis 1. Cost revenue and volume relationship is valid only within a relevant range. A relevant range is the expected band of activity or volume in which a specified form of budgeted sales and cost relationship will be valid e.g. $1,600 $1,400 $1,200 $1,000 $800 $600 $400 $200 Relevant range $ Units sold) 2. The behavior of the total cost and total revenue functions have been reliable determined and is linear within the relevant range. 3. All costs can be divided into fixed and variable costs and therefore we decompose the total cost into their variable and fixed components. 4. Total fixed cost remains constant over the relevant range e.g. 31

37 5. Unit selling prices are constant. 6. Total variable cost is directly proportional to volume within the relevant range. 7. There is no change in the level of inventory 8. Efficiency and productivity remains constant. 9. Prices of factors of production remain constant. 10. No limiting factors exist, no constraints. 5.3 The Break Even Point It is a form of CVP analysis. It specifies a way of presenting and studying interrelationship between cost volume and profit. It establishes the relationship between revenues and costs with respect to volume. It shows the level of sales at which costs and revenue are in equilibrium. The equilibrium point is known as the break even point where total revenue equal to total costs i.e. no profit or loss. Break even point can either be shown graphically or computed mathematically. 5.4 B. E. P in Graphical Form The following steps are used: 1. The sales line Plot the sales volume on the horizontal axis. Sale volume can be in terms of shillings units, or as a percentage of capacity. 2. Cost and revenue lines Revenues, variable costs and fixed cost are represented on the vertical axis. 3. Fixed cost line They are down parallel to the horizontal axis. 32

38 Costs/Revenue Illustration: A tour company has fixed cost estimates costs of Ksh 60,000 a variable cost of Ksh 10 for each ticket sold and a proposed ticket sale price of Ksh 20. Use the graphical method to determine the break-even point (1) Sales volume (q) (2) Sales revenue (20 q) (3) Total costs {60,000 + (10 q)} (4) Variable costs (4) Operating profit = (2) - (3) 1,000 20,000 70,000 10,000-50,000 2,000 40,000 80,000 20,000-40,000 3,000 60,000 90,000 30,000-30,000 4,000 80, ,000 40,000-20,000 5, , ,000 50,000-10,000 6, , ,000 60, , , ,000 70,000 10,000 8, , ,000 80,000 20,000 9, , ,000 90,000 30,000 10, , , ,000 40,000 Break - Even Chart 280 Sales volume 240 Profit area 200 B.E.P. T. C Loss area V. C Sales volume F. C. 33

39 Cost/revenue Costs/Revenue Contribution Chart Sales volume B. E. P. Profit area Contribution Loss area F. C. 80 V. C Sales volume Profit Volume Graph 60,000 40,000 20,000 Loss area B. E. P. Profit area 0-20, ,000-60,000 Sales volume 5.5 B E P in Mathematical Formula B E P can be computed in terms of units or in terms of money value or sales volume or as a percentage of estimated sales. 34

40 Units sold will cover variable costs and leave a remainder known as contribution margin Selling price per unit variable cost per unit = contribution per unit Unit contribution units sold = total contribution B E P in units is given by: B.E.P.(units) = Fixed Costs Selling Pr ice per unit Variable Cost perunit = Fixed Costs Contribution B. E. P. (shs) = B. E. P. (shs) Selling price or B.E.P.(Shs) = Fixed Costs, where contribution margin ratio is: Contribution m arg in ratio C.M.R. = Selling Pr ice Variable Selling price cos ts Example: Assume that a company intends to sale product in the market, at a selling price of sh.9 per unit. The V C is shs.5 per unit and the T F C is sh.2000 Required: i. Compute the B E P in units and in shs. ii. Assume that the company intends to make a profit before tax of 20% of sales, determine the number of units that must be sold. iii. Assume that the corporate tax rate is 30% and the company has a target profit of 1640 after tax. Compute the number of units that must be sold to earn this target profit. iv. If the company expects to sale 600 units, compute the marginal of safety. Solution F. C. = Sh.2,000; S. P. = 9.00; V. C. = 5.00 i) B.E.P.(units) = 2,000 = 2,000 = 500 units B. E. P. (shs) = B. E. P. (shs) Selling price 35

41 = = 4,500 or 36

42 B.E.P.(Shs) = Fixed Costs Contribution m arg in ratio Fixed cos t = selling price var iable selling price = 2,000 = 2,000 = 2,000 = 4,500 cos t ii) PBT = Sales TC = 9q ( q) Since PBT = 0.2 of sales, then target PBT = q q = 9q ( q) 1.8q = 9q q 2000 = 9q 5q 1.8q 2000 = 2.2q q = 2000/2.2 = = Units Alternatively, let target before tax profit be Y and X be the number of units required to earn the target before tax profit. Then, X = F.C. + Y S.P. V.C Sales = S P Units sold = 9 X = 9X Thus, X = X / 9-5 Since Profit = 20% of 9X = 1.8X = X/4 4X = X 4X 1.8X = X = 2000 X = 2000/2.2 = units iii) PAT = 1640, 37

43 = PBT (1-Tax rate) = PBT = PBT 0.7 PBT = 1640/0.7 PBT = Sales TC 2343 = 9q ( q) 2343 = 9q q = 9q - 5q 4343 = 4q q = Alternatively assume the target after tax profit is Z, the number of units to earn the target after tax profit is given by: F.C. + Z 1 T X = S.P. V.C Where: T is the tax rate i.e. 1 T = = 0.7 X = (1640/0.7) / 9 5 = /4 = Margin of safety This is the amount by which actual sales may fall before incurring a loss. It measures the risk that the company might make a loss if it fails to achieve the target. A high margin of safety means a high profit expectation even if the budget or target is not achieved. Margin of safety is given by: Example M arg in of M arg in of safety = Expected sales B.E.P.sales 100, or Expected sales safety = Expected sales(units) B.E.P.units 100 Expected sales(units) = = 16.67%