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Cost behaviour marginal costing

This document discusses different types of costs and their classification. It begins by defining direct and indirect costs, as well as fixed and variable costs. Direct costs include direct materials, direct labor, and direct expenses that can be traced to a specific product. Indirect costs cannot be traced to a specific product. Fixed costs remain constant regardless of production volume, while variable costs change in proportion to production volume. It then discusses how costs are classified for different purposes, such as stock valuation, decision-making, and control. For stock valuation, costs are classified as product costs (included in inventory valuation) or period costs (expensed immediately). For decision-making, costs are classified as relevant (those that change with a decision

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New Module Topic-3 COST BEHAVIOUR • Direct and Indirect Costs • Fixed Costs • Variable and semi-variable costs • Marginal Costing • Operational Gearing or Leverage Costing: Is the process of determining the cost of doing something e.g. the cost of manufacturing an article. 3.0 Classification of costs: Costs can be classified as: (i) Direct costs, and (ii) Indirect costs (i) Direct Costs: These costs comprising direct material, direct labour and direct expenses and are those which can be directly identified with a job, a product or a service. Direct materials: consist of all those materials, which can be physically identified with a specific product e.g. timber in case of a chair. Direct labour: Consist of those labor costs which can be specifically traced to a particular product e.g. wages of carpenter in manufacturing a chair. Direct expenses: Cost of raising a machine for producing a specific product is an example of direct expense Direct material + direct labour + direct expenses = Prime Cost (ii) Indirect costs: All material, labour and expense expenditure which cannot be identified with the particular product are termed as indirect costs. The total of indirect costs is known as overhead which is normally separated into categories such as production overheads, Administrative overheads, selling and distribution overheads. • Prime cost + Production overheads = Factory cost • Factory cost + Administrative overheads + Selling and distribution overheads = Total cost 1
Elements of manufacturing cost In a manufacturing organization product costs consist of direct material, direct labour, direct expenses and manufacturing overheads. Manufacturing overhead: Include indirect material, indirect labour & indirect expenses such as depreciation of machinery, Rent, etc Indirect overheads are allocated to various products on some sensible basis. Indirect materials: If the materials are used for several products and is not identifiable with the specific product, it is known as indirect material such as welding rod. (It forms part of manufacturing overhead cost) Indirect labour: can not be specifically assigned to product such as foreman wages/salaries. This forms part of manufacturing overhead. Prime cost + manufacturing overhead= Total manufacturing cost Classification of costs on the basis of cost object(ive): 1. Costs for Stock Valuation 2. Cost for Decision-making and Planning 3. Cost for Control Costs for Stock Valuation: Un-expired costs are the resources acquired to contribute to future revenue. These are recorded as assets in the Balance Sheet. Expired costs: are expenses, which have been consumed in generating revenue and are shown in the P & L Account. Period costs: are those expenses (administration, selling & distribution) which are not included in the stock valuation and are treated as expenses in the period in which they are incurred. All non-manufacturing costs are period costs. Product costs: are those costs which are identified with goods produced / purchased and are attached to the product and are included in the stock valuation. All fixed costs are recorded as product cost. Classification for Decision–making and Planning Cost & Revenues behavior: Knowledge of how cost and revenues will vary with different levels of volume is essential for decision making. How costs react to changes in volume? Variable cost, fixed cost, semi–variable costs, semi– fixed costs, terms are used. 2
Variable cost: vary in direct proportion to the volume of activity Total variable costs are linear. A unit variable cost is constant Fixed costs: remain constant over wide ranges of activity for specified time period. Dep. on factory Building, lease charges, supervisors Salaries etc.. Unit fixed cost: decrease proportionality with the level of activity increased. Semi – Variable cost: include a cost which has both elements, a fixed and a variable, e.g. Hiring a loader, telephone expense etc. 3 2500 2000 1500 1000 500 Total variable cost 1000 2000 3000 4000 Level of Activity Unit variable cost 10 50 1000 2000 3000 4000 Level of Activity Total fixed cost Unit fixed cost
Semi–fixed or Step Costs: Are fixed for a given level of activity but eventually increase at same critical point Relevant and Irrelevant Costs & Revenues. Costs & revenues can be classified for decision – making as Relevant or Irrelevant. Relevant cost or revenues are those future cost / revenues which will be changed by decision making. Irrelevant cost & revenues are those which will not be affected by the decision, e.g. journey by car or by public transport-- road tax and insurance of car is irrelevant for taking decision, it is the fuel cost & wear & tear of the car vs. transport charges should be taken into account. Sunk costs: These are the costs, which have already incurred by a decision made in the past, which cannot be changed e.g. investment in machinery. Opportunity cost: Measuring benefits forgone in order to take alternative course of action. Incremental cost / revenues: There are additional costs/ revenue which arise from the production/ sale of additional units, called Incremental or differentiall cost / revenues. Marginal cost / revenues: Marginal cost / revenue represent the additional cost / revenue of one extra unit of output. Thus, the above classification of cost is helpful to the management in decision making. Classification of Costs for Control: The allocation of cost to products is inappropriate for cost control purposes. For control purposes costs and revenues are allocated to the individuals who are responsible for their performance. The system is known as responsibility accounting. It is based on the 4 Level of activity Total fixed cost (step)
recognition of individual areas of responsibility as specified in the firm’s organization structure. There are three types of responsibility centre: 1. Cost centre: where the manager is responsible for the expenses under his control 2. Profit Centre: where a manger is accountable for the sales revenue, expenses and profit. 3. Investment Centre: where a manager is responsible for capital investment decisions. Controllable and Non–controllable cost / Revenues Cost / Revenues allocated to responsibilities centre should be classified into controllable and non–controllable by the responsibility centre manager. A controllable cost: is one which is reasonably subject to regulation by the responsibility centre manager. In this the difference between budgeted and actual results is emphasized and corrective measures are taken. Non–controllable cost: is one for which the responsibility centre manager is not responsible as they are under the decision of his superiors. The comparison of budgeted costs and actual costs is made for the same level of activity. If it is different, the budget cost first be revised to the actual level of activity for comparison purposes, for this the understanding of behaviour of cost (variable, fixed) is important. Method of Isolating the variable and fixed component of Semi–variable cost 1. William’s Method or High – low Method The following steps are taken:- (i) A minimum and maximum volume of production is determined along with the total costs of each level (ii) The difference in total costs of minimum and maximum level is ascertained along with difference in minimum and maximum volume. (iii) Following formula is applied Variable cost per unit = Difference in total cost Difference in volume This is multiplied with the units of volume which will give total variable cost of each level, if deducted from the total semi–variable cost of that level will give the fixed cost of that level. 5
Example 3.1 Isolate the variable and fixed component of Semi – variable cost by Williams’s method. Volume of Production Semi – variable cost in unit Shs 100 8,300 200 12,300 300 16,300 400 20,300 500 24,300 Solution Minimum volume of Production 100 Maximum volume of Production 500 Total cost at minimum level 8,300 shs Total cost at maximum level 24,300 shs Difference in volume 500 – 100 = 400 units Difference in total cost 24,300 – 8,300 = Shs. 16,000 Variable cost per unit = 16,000 or shs 40/= 400 Units x variable Variable Semi-Variable Fixed cost i.e cost per unit cost Semi-variable minus Variable 100 x 40 4000 8300 4300 200 x 40 8000 12300 4300 300 x 40 12000 16300 4300 400 x 40 16000 20300 4300 500 x 40 20000 24300 4300 6
This method is not scientific as it assumes that observing the two extreme limits can draw straight line and the cost of the volumes of production between these two limits would lie on this straight line. The accurate result should not be expected from this method as there is a possibility of negative value of fixed costs, which would never be found in practice? This would change with the volume of production to the next level. Marginal Costing: Change in total cost on account of adding or subtracting one unit is known as marginal cost. Marginal cost is also known as variable cost. Variable cost = Direct material + Direct Labor + Variable direct expenses + variable indirect expenses We know that TC = VQ + F TC = Total costs VQ = Variable costs at a given Quantity Marginal cost per unit = V = TC – F Q Determination of Profit under marginal costing C = S – Vc C = Contribution S = Sales Vc = Variable cost Where: C = F + Pt F = Fixed cost Pt = Profit or S – Vc = F + Pt or S = F + Pt + Vc or F = C – Pt or S = C + Vc 7
Remember: Fixed costs under marginal costing are regarded as period cost (charged against the profit immediately rather than as a product cost (assigned to units produced) Procedure for Profit determination under marginal costing: (i) Sales value is compared to it variable costs and the difference between the two is called contribution. Only variable costs of units sold are taken into account. (ii) Fixed cost for the period is deducted from the contribution and the balance is known as profit. (iii) Units remaining unsold (i.e. stock) are valued at marginal cost. No portion of fixed cost is carried over to the next period through inventory valuation Example: 3.2 Guru Engineering Co. is manufacturing two products – A & B. The costs of manufacturing are as under:- A B Shs Shs Direct material per unit 60 80 Direct labour per unit 40 60 Selling price per unit 200 300 Output 2000 units 2000 units Total overheads are Shs 160,000 out of which Shs 120,000 are fixed and the rest are variable. The overheads are to be apportioned in the ratio of output. The closing stock is of 200 units in case of product A and 300 units in case of Product B. Find profit under Marginal costing 8
Solution Statement of cost and Profit (Marginal Approach) Sales A 1800 unit x 200 Sh 360,000 Sh 510,000 Sh 870,000 B 1700 unit x 300 Product A Product B Total Direct material 120,000 160,000 280,000 Direct Labour 80,000 120,000 200,000 Variable overheads 20,000 20,000 40,000 Total Variable Costs 220,000 300,000 520,000 Less: Closing stock 22,000 45,000 67,000 220,000 = Shs110 x 200 2000 300,000 = Shs 150 x 300 2000 Total Marginal Cost 198,000 255,000 453,000 Contribution 162,000 255,000 417,000 S-V Less: Fixed cost 120,000 Profit 297,000 9
Uses of Marginal Costing Example 3.3 Dropping a line or Product or Department These are three lines of production and their production cost per unit & selling price per unit is given below:- X Y Z £ £ £ Materials 20 25 40 Wages 15 19 24 Variable overheads 20 30 36 Fixed overheads 50 80 90 _______________________________ Total costs 105 154 190 Selling Price 125 220 290 ________________________________ Net Profit £ 20 66 100 ________________________________ Production in units 3000 2000 2500 The production manager wants to discontinue one line and guarantees that the production of other two lines shall rise by 50%. He wants to discontinue X as it is least profitable. (a) Do you agree to the scheme in principle? (b) If yes, do you think that line X should be discontinued? 10
Workings Fixed overheads X 3000 x £ 50 150,000 Y 2000 x £ 80 160,000 Z 2500 x £ 90 225,000 £ 535,000 Marginal cost per unit in £ X Y Z Materials 20 25 40 Wages 15 19 24 Variable overheads 20 30 36 ______________________________ Marginal cost 55 74 100 Selling Price 125 220 290 ______________________________ Contribution 70 146 190 =========================== Contribution Ratio 56.0% 66.36% 65.52% Now Let us consider the alternative arrangements:- (i) If all lines are continued Sales Marginal Contribution Cost Lines X 375,000 165,000 210,000 Y 440,000 148,000 292,000 Z 725,000 250,000 475,000 977,000 Less: Fixed cost 535,000 Profit £ 442,000 11
(ii) When X line is dropped the production of Y and Z would rise by 50% Sales Marginal Contribution £ £ £ Y 3000 x 220 660,000 222,000 438,000 Z 3750 x 290 1,087,500 3,750,000 712,500 1,150,500 Less: Fixed cost 535,000 Profit £ 615,500 (iii) When Y line is dropped, the production of X and Z would rise by 50% Units Sales Marginal Contribution X 4500 562,500 247,500 315,000 Z 3750 1,087,500 375,000 712,500 1,027,500 Less: Fixed cost 535,000 Profit 492,500 (iv) When Z lines is dropped the production X & Y would rise by 50% Units Sales Marginal Contribution X 4500 562,500 247,500 315,000 Y 3000 660,500 222,000 438,500 753,500 Less: Fixed cost 535,000 Profit 218,000 It is not true by dropping any one line the profit would rise, however by dropping X line the profit would rise from £ 442,000 to £ 615,500. Example 3.4 Introducing a New product / Line DSM Ltd. Produce a product X. Present level of production is 2000 units as against the installed capacity of 3000 units. The present cost structure is as under Materials Shs 200,000 Labour 100,000 Variable overheads 20,000 12
Fixed overheads including Dep 150,000 Fixed overheads include Shs 40,000 for depreciation. Product X is sold at Shs 300 per unit. It is proposed to manufacture product Y along with product X. The installed capacity of product Y will be 1500 unit. This will require a additional investment of Shs. 250,000 in machine over and above existing investment of Shs 500,000. At the start 1,000 units will be manufactured & sold at a price of Shs 200 each. Fixed overheads would be Shs 15,000 apart from 10% depreciation on machine. Shs. 50,000 will be required for working capital. The cost estimates of Y product Material Shs 100 Labour Shs 30 Variable overheads Shs 10 Is it advisable to introduce product Y? Solution Statement of Profitability of Each Product 2000 units 1000 units Existing product X New product Y Total Sales 600,000 200,000 800,000 Less: Marginal cost Material 200,000 100,000 300,000 Labour 100,000 30,000 130,000 Variable overheads 20,000 10,000 30,000 ________________________________________________________ Marginal cost 320,000 140,000 460,000 Contribution 280,000 60,000 340,000 Less: Fixed overheads including Dep. 150,000 40,000 190,000 ___________________________________________________ Net Profit 130,000 20,000 150,000 ================================================ Contribution Ratio 46.67% 30% 42.5% =============================================== Net Profit on Investment 26% 6.67% 18.75% Introduction of New product will not improve the profitability in terms of contribution ratio & Net Profit on Capital Employed. Example 3.5 Optimum Sales Mix 13
The directors of TAN PLANT Ltd. are considering the sales budget for the next year. You are required to present to the Board a Statement showing the Marginal Cost of each product and also to recommend which of the following sales – mix should be adopted: (i) 900 units of X and 600 units of Y (ii) 2000 units of X only (iii) 1500 units of Y only (iv) 1200 units of X and 600 units of Y. You are given the following information Product X Product Y Direct labour per hour @ Shs 50 20 hour 30hour Direct material Shs.2000 Shs.2500 Selling Price Shs.7000 Shs.10, 000 Overheads Fixed Shs1, 000, 000 Variable overheads 100% of Direct labour. Statement of Marginal cost per unit Product X Product Y Direct material 2000 2500 Direct labour 50 x 20 1000 ------ 50 x 30 ------ 1500 Variable overheads 1000 1500 Marginal cost 4000 5500 Selling price 7000 10,000 Contribution 3000 4500 Profitability of various Sales Mix (i) X 900 units and Y 600 units Product Sales Marginal Contribution X 6,300,000 3,600,000 2,700,000 Y 6,000,000 3,300,000 2,700,000 5,400,000 Less: fixed costs 1,000,000 Profit 4,400,000 14
(ii) 2000 units of X only Product Sales Marginal Contribution X 14,000,000 8,000,000 6,000,000 Less: fixed cost 1,000,000 Profit 5,000,000 (iii) 1500 units of Y only Product Sales Marginal Contribution Y 15,000,000 8,250,000 6,750,000 Less: fixed cost 1,000,000 Profit 5,750,000 (iv) 1200 units of X and 600 units of Y Product Sales Marginal Contribution X 8,400,000 4,800,000 3600,000 Y 6,000,000 3,300,000 2,700,000 6,300,000 Less: fixed costs 1,000,000 Profit 5,300,000 Sales mix (iii) is best however if the product X is discontinued and the demand for Y is reduced, the firm would have changed its sales mix. It is better to continue with both products and option (iv) is near to the best solution. Example 3.6 Use of marginal costing in achieving profit target A Co. has invested Shs.100, 000,000 in its factory and sets a goal of 15% annual return on investment. Fixed costs in the factory at present are Sh. 40,000,000 and variable cost is Shs 1500. In the past the firm produced and sold 50,000 units at shs. 2500 each and earned a net profit of shs 10,000,000. How can the management achieve their target profit by making changes in fixed costs, variable costs, quantity sold or increasing the selling price per unit? 15
Solution Target Profit = 100,000,000 x 15 100 = Shs. 15,000,000 (i) Change in fixed costs: S = Vc + C C = S – Vc F = C – Pt Vc = 50,000 units x 1500 = 75,000,000 S = 50,000 units x 2500 = 125,000,000 C = 125,000,000 – 75,000,000 = 50,000,000 F = 50,000,000 – 15,000,000 = 35,000,000 Present Fixed costs are 40,000,000. The management can achieve the target profit by reducing the Fixed cost by Shs 5,000,000 (ii) Change in Variable cost Vc = S – C C = F + Pt C = 40,000,000 + 15,000,000 = 55,000,000 Vc = 125,000,000 – 55,000,000 = 70,000,000 Variable cost per unit = 70,000,000 = Shs. 1400 50,000 It should be reduced to Shs 1400 per unit from Shs 1500 per unit (iii) Change in Quantity sold S – Vc = F + Pt S = P x Q Vc = V x Q Q (P – V) = C Q (2500 – 1500) = 55,000,000 16
Q = 55,000,000 or 55,000 units 1000 (iv) Change in selling price S = Vc + C PQ = Vc + C P = Vc + C Q P = 75,000,000 + 55,000,000 50,000 = 130,000,000 50,000 = Shs 2600 If the selling price could be raised to Shs 2600 Example 3.7 Dropping a line or a product There are three lines of product and their product cost per unit and selling price per unit are given below: X Y Z Material 180 260 300 Wages 70 90 100 Variable overheads 20 30 30 Fixed overheads 50 80 90 320 460 520 Selling price 400 600 610 Net profit 80 140 90 Production in units 4000 2000 5000 The manager wants to discontinue one line and guarantees that the production of other two lines shall rise by 50%. He wants to discontinue line X as it is least profitable Solution Total fixed cost X 4000 x 50 = 200,000 Y 2000 x 80 = 160,000 Z 500 x 90 = 450,000 810,000 17
(i) When all lines are continued Sales Marginal Contribution X 1,600,000 1,080,000 520,000 Y 1,200,000 760,000 440,000 Z 3,050,000 2,150,000 900,000 5,850,000 3,990,000 1,860,000 Less fixed cost 810,000 _____ Profit 1,050,000 ======= (ii) When line X is dropped the production in Y & Z will increase by 50% Product Sales M.C Contribution Y 1,800,000 1,140,000 660,000 X 4,575,000 3,225,000 1,350,000 2,010,000 Less fixed cost 810,000 ______ Profit 1,200,000 ===== (iii) When line Y is dropped the production of X & Z will increase by 50% Product Sales M.C Contribution X 2,400,000 1,620,000 780,000 Z 4,575,000 3,225,000 1,350,000 2,130,000 Less fixed cost 810,000 Profit 1,320,000 (iv) If Z line is dropped the production of X & Y will increase by 50% Product Sales M.C Contribution Y 2,400,000 1,620,000 780,000 X 1,000,000 1,140,000 660,000 1,440,000 Less fixed cost 810,000 18
Profit 630,000 To maximize profit, Y line should be dropped. Example 3.8 Introducing a New Product or line Simba Plastic limited produces a product X. The capacity of the plant is to produce 30,000 units. However at present 20,000 units are produced. The present cost is as under: Material Shs. 200,000,000 Labour 100,000,000 Variable overheads 20,000,000 Fixed overheads 150,000,000 Product X is sold at Shs 30,000 per unit. It is proposed to manufacture product Y along with product X. This will require additional investment of Shs. 250,000,000 to manufacture 15000 units of Y. Initially 10,000 units of Y can be manufactured and sold for 20,000 each. The cost estimates of Y product are:- Material Shs. 10,000 per unit, Labour Shs. 3000 per unit Variable overheads Shs. 1000per unit Fixed overheads Shs. 35,000,000 Is it advisable to introduce product Y? Solution: Existing Product New Product Total Sales 600,000,000 200,000,000 800,000,000 Less: Marginal costs Material 200,000,000 100,000,000 300,000,000 Labour 100,000,000 30,000,000 130,000,000 Variable overheads 20,000,000 10,000,000 30,000,000 Total marginal cost 320,000,000 140,000,000 460,000,000 ______________________________________________ Contribution 280,000,000 60,000,000 340,000,000 19
Less: fixed overhead 150,000,000 35,000,000 185,000,000 Net profit 130,000,000 25,000,000 155,000,000 Contribution ratio = C x 100 46.6% 30% 42.5% S Contribution ratio will decline. However total profit will increase. It would be better to increase the production of X product. Example 3.9 Accepting Special offer / Exploring new market. The Zenith Plastic is operating at 60% of it capacity. The cost position is as follows for producing 15000 units:- Material Shs 30,000 per unit Labour Shs. 15,000 per unit Variable overheads Shs. 5,000 per unit Fixed overheads Shs. 20,000 per unit or shs.300,000,000 Total FC 70,000 Profit 20,000 per unit Selling price Shs 90,000 per unit The import duty in the EA region has been abolished. A company in Kenya is willing to buy 10,000 units at a price of Shs. 60,000 each. However the extra production can not be sold in Tanzania. Would you recommend that the company should accept this offer? Solution: Statement of Marginal cost & contribution Existing Kenya order Total 15,000 unit 10,000 unit 25,000 unit Material 450,000,000 300,000,000 750,000,000 Labour 225,000,000 150,000,000 375,000,000 Variable overheads 75,000,000 50,000,000 125,000,000 Marginal cost 750,000,000 500,000,000 1,250,000,000 Sales 1,350,000,000 600,000,000 1,950,000,000 20
Contribution 600,000,000 100,000,000 700,000,000 Les: fixed cost 300,000,000 ---------- 300,000,000 Profit 300,000,000 100,000,000 400,000,000 Contribution ratio 44.44% 16.66% 35.89% Contribution ratio will decline after accepting the Kenya’s offer. However in absolute terms the profit margin will increase by Shs 100,000,000 so the Kenya’s offer should be taken on board, as this will help us to operate at full capacity. Operating Leverage Operating leverage influences the net operating income of the firm due to investing decision. The investments are made in fixed assets incurring fixed costs and incurring variable costs. In many cases due to investments in fixed assets, the variable costs are reduced considerably. So how much investment is to be made in each category is a planning function, which should be looked into carefully. Operating leverage is the extent to which a firms fixed costs contribute to total operating costs at different level of sales. The DOL measures the % change in NOI (%∆NOI) for a given % in change in sales (%∆S). The DOL is a Magnification factor. DOL exists because of fixed costs and fixed costs amplify changes in NOI for small changes in sales. DOL = Total Sales – Total Variable Costs or Total Sales – Total Variable Costs –Total Fixed Costs = Q (P-V) Q (P-V) – F DOL = %∆NOI %∆S Example 3.10 You have been provided with the following information concerning X Company and Y Company. X Company Shs Y Company Shs Sales 100,000 Sales 100,000 Fixed costs 50,000 per year Fixed costs 20,000 per year Variable costs 30% of sales Variable costs 60% of sales Compute 21
i. The degree of Operating Leverage ii. If the sales increase by 10% what would be the impact on NOI? X Company Y Company DOL = TS –TV DOL = TS –TV TS – TV– TF TS – TV– TF = 100,000 – 30,000 = 100,000 – 60,000 100,000 – 30,000 – 50,000 100,000 – 60,000 – 20,000 = 70,000 = 40,000 20,000 20,000 = 3.5 = 2.0 DOL = %∆NOI DOL = %∆NOI %∆S %∆S 3.5 = %∆NOI 2.0 = %∆NOI 10% 10% 35% = %∆NOI 20% = %∆NOI To Prove NOI of X C0. NOI=TS-VC-FC (before change in NOI) = 100,000-30,000-50,000 = 20,000 NOI= TS-VC-FC(new NOI) = 110,000-33,000-50,000 =27,000 ∆NOI =27,000-20,000 =7,000 %∆NOI=7,000 X 100 20,000 =35% Example 3.11 Light source makes bulbs and has F = shs.1, 000,000, V = shs.5 and P = shs.10 at a given Q = 250,000 units. Calculate the DOL and %∆NOI if the sales go up by 5%. DOL = Q (P-V) 22
Q (P-V) – F = 250,000 (10 – 5) 250,000 (10 – 5) – 1,000,000 = 5.0 DOL = %∆NOI %∆S 5.0 = %∆NOI 5% 5 x 5% = %∆NOI 25% = %∆NOI The DOL is a Magnification factor. DOL exists because of fixed costs and fixed costs amplify changes in NOI for small changes in sales. Example 3.12 A small company in Morogoro has a current NOI of shs. 200,000. Next year NOI is expected to be shs. 300,000 as sales are expected to go up by 25%, what is its DOL. %∆NOI = New NOI- Old NOI Old NOI = 300,000 – 200,000 X 100 200,000 = 50% DOL = %∆NOI %∆S = 50% 25% = 2.0 Example 3.13 Chagga Bros. make seat covers for cars and sell at shs.20,000 each with a variable cost of shs.12,000 each. Next year he expects 20% drop in sales and 50% drop in NOI due to lack of demand. Current level of sales is 112 set of seat covers. What is the level of fixed cost? 23
%∆S = - 20%; %∆NOI = - 50% DOL = %∆NOI %∆S = -50% -20% = 2.5 DOL = Q (P – V) Q (P – V) – F 2.5 = 112(20,000 – 12,000) 112(20,000 – 12,000) – F 2.5 = 896,000 896,000 – F -2.5F + 2.5 x 896,000 = 896,000 -2.5F + 2,240,000 = 896,000 -2.5F = -2,240,000 + 896,000 -2.5F = -1,344,000 F = 537,600 24

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Cost behaviour marginal costing

  • 1.
    New Module Topic-3COST BEHAVIOUR • Direct and Indirect Costs • Fixed Costs • Variable and semi-variable costs • Marginal Costing • Operational Gearing or Leverage Costing: Is the process of determining the cost of doing something e.g. the cost of manufacturing an article. 3.0 Classification of costs: Costs can be classified as: (i) Direct costs, and (ii) Indirect costs (i) Direct Costs: These costs comprising direct material, direct labour and direct expenses and are those which can be directly identified with a job, a product or a service. Direct materials: consist of all those materials, which can be physically identified with a specific product e.g. timber in case of a chair. Direct labour: Consist of those labor costs which can be specifically traced to a particular product e.g. wages of carpenter in manufacturing a chair. Direct expenses: Cost of raising a machine for producing a specific product is an example of direct expense Direct material + direct labour + direct expenses = Prime Cost (ii) Indirect costs: All material, labour and expense expenditure which cannot be identified with the particular product are termed as indirect costs. The total of indirect costs is known as overhead which is normally separated into categories such as production overheads, Administrative overheads, selling and distribution overheads. • Prime cost + Production overheads = Factory cost • Factory cost + Administrative overheads + Selling and distribution overheads = Total cost 1
  • 2.
    Elements of manufacturingcost In a manufacturing organization product costs consist of direct material, direct labour, direct expenses and manufacturing overheads. Manufacturing overhead: Include indirect material, indirect labour & indirect expenses such as depreciation of machinery, Rent, etc Indirect overheads are allocated to various products on some sensible basis. Indirect materials: If the materials are used for several products and is not identifiable with the specific product, it is known as indirect material such as welding rod. (It forms part of manufacturing overhead cost) Indirect labour: can not be specifically assigned to product such as foreman wages/salaries. This forms part of manufacturing overhead. Prime cost + manufacturing overhead= Total manufacturing cost Classification of costs on the basis of cost object(ive): 1. Costs for Stock Valuation 2. Cost for Decision-making and Planning 3. Cost for Control Costs for Stock Valuation: Un-expired costs are the resources acquired to contribute to future revenue. These are recorded as assets in the Balance Sheet. Expired costs: are expenses, which have been consumed in generating revenue and are shown in the P & L Account. Period costs: are those expenses (administration, selling & distribution) which are not included in the stock valuation and are treated as expenses in the period in which they are incurred. All non-manufacturing costs are period costs. Product costs: are those costs which are identified with goods produced / purchased and are attached to the product and are included in the stock valuation. All fixed costs are recorded as product cost. Classification for Decision–making and Planning Cost & Revenues behavior: Knowledge of how cost and revenues will vary with different levels of volume is essential for decision making. How costs react to changes in volume? Variable cost, fixed cost, semi–variable costs, semi– fixed costs, terms are used. 2
  • 3.
    Variable cost: varyin direct proportion to the volume of activity Total variable costs are linear. A unit variable cost is constant Fixed costs: remain constant over wide ranges of activity for specified time period. Dep. on factory Building, lease charges, supervisors Salaries etc.. Unit fixed cost: decrease proportionality with the level of activity increased. Semi – Variable cost: include a cost which has both elements, a fixed and a variable, e.g. Hiring a loader, telephone expense etc. 3 2500 2000 1500 1000 500 Total variable cost 1000 2000 3000 4000 Level of Activity Unit variable cost 10 50 1000 2000 3000 4000 Level of Activity Total fixed cost Unit fixed cost
  • 4.
    Semi–fixed or StepCosts: Are fixed for a given level of activity but eventually increase at same critical point Relevant and Irrelevant Costs & Revenues. Costs & revenues can be classified for decision – making as Relevant or Irrelevant. Relevant cost or revenues are those future cost / revenues which will be changed by decision making. Irrelevant cost & revenues are those which will not be affected by the decision, e.g. journey by car or by public transport-- road tax and insurance of car is irrelevant for taking decision, it is the fuel cost & wear & tear of the car vs. transport charges should be taken into account. Sunk costs: These are the costs, which have already incurred by a decision made in the past, which cannot be changed e.g. investment in machinery. Opportunity cost: Measuring benefits forgone in order to take alternative course of action. Incremental cost / revenues: There are additional costs/ revenue which arise from the production/ sale of additional units, called Incremental or differentiall cost / revenues. Marginal cost / revenues: Marginal cost / revenue represent the additional cost / revenue of one extra unit of output. Thus, the above classification of cost is helpful to the management in decision making. Classification of Costs for Control: The allocation of cost to products is inappropriate for cost control purposes. For control purposes costs and revenues are allocated to the individuals who are responsible for their performance. The system is known as responsibility accounting. It is based on the 4 Level of activity Total fixed cost (step)
  • 5.
    recognition of individualareas of responsibility as specified in the firm’s organization structure. There are three types of responsibility centre: 1. Cost centre: where the manager is responsible for the expenses under his control 2. Profit Centre: where a manger is accountable for the sales revenue, expenses and profit. 3. Investment Centre: where a manager is responsible for capital investment decisions. Controllable and Non–controllable cost / Revenues Cost / Revenues allocated to responsibilities centre should be classified into controllable and non–controllable by the responsibility centre manager. A controllable cost: is one which is reasonably subject to regulation by the responsibility centre manager. In this the difference between budgeted and actual results is emphasized and corrective measures are taken. Non–controllable cost: is one for which the responsibility centre manager is not responsible as they are under the decision of his superiors. The comparison of budgeted costs and actual costs is made for the same level of activity. If it is different, the budget cost first be revised to the actual level of activity for comparison purposes, for this the understanding of behaviour of cost (variable, fixed) is important. Method of Isolating the variable and fixed component of Semi–variable cost 1. William’s Method or High – low Method The following steps are taken:- (i) A minimum and maximum volume of production is determined along with the total costs of each level (ii) The difference in total costs of minimum and maximum level is ascertained along with difference in minimum and maximum volume. (iii) Following formula is applied Variable cost per unit = Difference in total cost Difference in volume This is multiplied with the units of volume which will give total variable cost of each level, if deducted from the total semi–variable cost of that level will give the fixed cost of that level. 5
  • 6.
    Example 3.1 Isolate thevariable and fixed component of Semi – variable cost by Williams’s method. Volume of Production Semi – variable cost in unit Shs 100 8,300 200 12,300 300 16,300 400 20,300 500 24,300 Solution Minimum volume of Production 100 Maximum volume of Production 500 Total cost at minimum level 8,300 shs Total cost at maximum level 24,300 shs Difference in volume 500 – 100 = 400 units Difference in total cost 24,300 – 8,300 = Shs. 16,000 Variable cost per unit = 16,000 or shs 40/= 400 Units x variable Variable Semi-Variable Fixed cost i.e cost per unit cost Semi-variable minus Variable 100 x 40 4000 8300 4300 200 x 40 8000 12300 4300 300 x 40 12000 16300 4300 400 x 40 16000 20300 4300 500 x 40 20000 24300 4300 6
  • 7.
    This method isnot scientific as it assumes that observing the two extreme limits can draw straight line and the cost of the volumes of production between these two limits would lie on this straight line. The accurate result should not be expected from this method as there is a possibility of negative value of fixed costs, which would never be found in practice? This would change with the volume of production to the next level. Marginal Costing: Change in total cost on account of adding or subtracting one unit is known as marginal cost. Marginal cost is also known as variable cost. Variable cost = Direct material + Direct Labor + Variable direct expenses + variable indirect expenses We know that TC = VQ + F TC = Total costs VQ = Variable costs at a given Quantity Marginal cost per unit = V = TC – F Q Determination of Profit under marginal costing C = S – Vc C = Contribution S = Sales Vc = Variable cost Where: C = F + Pt F = Fixed cost Pt = Profit or S – Vc = F + Pt or S = F + Pt + Vc or F = C – Pt or S = C + Vc 7
  • 8.
    Remember: Fixed costs undermarginal costing are regarded as period cost (charged against the profit immediately rather than as a product cost (assigned to units produced) Procedure for Profit determination under marginal costing: (i) Sales value is compared to it variable costs and the difference between the two is called contribution. Only variable costs of units sold are taken into account. (ii) Fixed cost for the period is deducted from the contribution and the balance is known as profit. (iii) Units remaining unsold (i.e. stock) are valued at marginal cost. No portion of fixed cost is carried over to the next period through inventory valuation Example: 3.2 Guru Engineering Co. is manufacturing two products – A & B. The costs of manufacturing are as under:- A B Shs Shs Direct material per unit 60 80 Direct labour per unit 40 60 Selling price per unit 200 300 Output 2000 units 2000 units Total overheads are Shs 160,000 out of which Shs 120,000 are fixed and the rest are variable. The overheads are to be apportioned in the ratio of output. The closing stock is of 200 units in case of product A and 300 units in case of Product B. Find profit under Marginal costing 8
  • 9.
    Solution Statement of costand Profit (Marginal Approach) Sales A 1800 unit x 200 Sh 360,000 Sh 510,000 Sh 870,000 B 1700 unit x 300 Product A Product B Total Direct material 120,000 160,000 280,000 Direct Labour 80,000 120,000 200,000 Variable overheads 20,000 20,000 40,000 Total Variable Costs 220,000 300,000 520,000 Less: Closing stock 22,000 45,000 67,000 220,000 = Shs110 x 200 2000 300,000 = Shs 150 x 300 2000 Total Marginal Cost 198,000 255,000 453,000 Contribution 162,000 255,000 417,000 S-V Less: Fixed cost 120,000 Profit 297,000 9
  • 10.
    Uses of MarginalCosting Example 3.3 Dropping a line or Product or Department These are three lines of production and their production cost per unit & selling price per unit is given below:- X Y Z £ £ £ Materials 20 25 40 Wages 15 19 24 Variable overheads 20 30 36 Fixed overheads 50 80 90 _______________________________ Total costs 105 154 190 Selling Price 125 220 290 ________________________________ Net Profit £ 20 66 100 ________________________________ Production in units 3000 2000 2500 The production manager wants to discontinue one line and guarantees that the production of other two lines shall rise by 50%. He wants to discontinue X as it is least profitable. (a) Do you agree to the scheme in principle? (b) If yes, do you think that line X should be discontinued? 10
  • 11.
    Workings Fixed overheads X 3000x £ 50 150,000 Y 2000 x £ 80 160,000 Z 2500 x £ 90 225,000 £ 535,000 Marginal cost per unit in £ X Y Z Materials 20 25 40 Wages 15 19 24 Variable overheads 20 30 36 ______________________________ Marginal cost 55 74 100 Selling Price 125 220 290 ______________________________ Contribution 70 146 190 =========================== Contribution Ratio 56.0% 66.36% 65.52% Now Let us consider the alternative arrangements:- (i) If all lines are continued Sales Marginal Contribution Cost Lines X 375,000 165,000 210,000 Y 440,000 148,000 292,000 Z 725,000 250,000 475,000 977,000 Less: Fixed cost 535,000 Profit £ 442,000 11
  • 12.
    (ii) When Xline is dropped the production of Y and Z would rise by 50% Sales Marginal Contribution £ £ £ Y 3000 x 220 660,000 222,000 438,000 Z 3750 x 290 1,087,500 3,750,000 712,500 1,150,500 Less: Fixed cost 535,000 Profit £ 615,500 (iii) When Y line is dropped, the production of X and Z would rise by 50% Units Sales Marginal Contribution X 4500 562,500 247,500 315,000 Z 3750 1,087,500 375,000 712,500 1,027,500 Less: Fixed cost 535,000 Profit 492,500 (iv) When Z lines is dropped the production X & Y would rise by 50% Units Sales Marginal Contribution X 4500 562,500 247,500 315,000 Y 3000 660,500 222,000 438,500 753,500 Less: Fixed cost 535,000 Profit 218,000 It is not true by dropping any one line the profit would rise, however by dropping X line the profit would rise from £ 442,000 to £ 615,500. Example 3.4 Introducing a New product / Line DSM Ltd. Produce a product X. Present level of production is 2000 units as against the installed capacity of 3000 units. The present cost structure is as under Materials Shs 200,000 Labour 100,000 Variable overheads 20,000 12
  • 13.
    Fixed overheads includingDep 150,000 Fixed overheads include Shs 40,000 for depreciation. Product X is sold at Shs 300 per unit. It is proposed to manufacture product Y along with product X. The installed capacity of product Y will be 1500 unit. This will require a additional investment of Shs. 250,000 in machine over and above existing investment of Shs 500,000. At the start 1,000 units will be manufactured & sold at a price of Shs 200 each. Fixed overheads would be Shs 15,000 apart from 10% depreciation on machine. Shs. 50,000 will be required for working capital. The cost estimates of Y product Material Shs 100 Labour Shs 30 Variable overheads Shs 10 Is it advisable to introduce product Y? Solution Statement of Profitability of Each Product 2000 units 1000 units Existing product X New product Y Total Sales 600,000 200,000 800,000 Less: Marginal cost Material 200,000 100,000 300,000 Labour 100,000 30,000 130,000 Variable overheads 20,000 10,000 30,000 ________________________________________________________ Marginal cost 320,000 140,000 460,000 Contribution 280,000 60,000 340,000 Less: Fixed overheads including Dep. 150,000 40,000 190,000 ___________________________________________________ Net Profit 130,000 20,000 150,000 ================================================ Contribution Ratio 46.67% 30% 42.5% =============================================== Net Profit on Investment 26% 6.67% 18.75% Introduction of New product will not improve the profitability in terms of contribution ratio & Net Profit on Capital Employed. Example 3.5 Optimum Sales Mix 13
  • 14.
    The directors ofTAN PLANT Ltd. are considering the sales budget for the next year. You are required to present to the Board a Statement showing the Marginal Cost of each product and also to recommend which of the following sales – mix should be adopted: (i) 900 units of X and 600 units of Y (ii) 2000 units of X only (iii) 1500 units of Y only (iv) 1200 units of X and 600 units of Y. You are given the following information Product X Product Y Direct labour per hour @ Shs 50 20 hour 30hour Direct material Shs.2000 Shs.2500 Selling Price Shs.7000 Shs.10, 000 Overheads Fixed Shs1, 000, 000 Variable overheads 100% of Direct labour. Statement of Marginal cost per unit Product X Product Y Direct material 2000 2500 Direct labour 50 x 20 1000 ------ 50 x 30 ------ 1500 Variable overheads 1000 1500 Marginal cost 4000 5500 Selling price 7000 10,000 Contribution 3000 4500 Profitability of various Sales Mix (i) X 900 units and Y 600 units Product Sales Marginal Contribution X 6,300,000 3,600,000 2,700,000 Y 6,000,000 3,300,000 2,700,000 5,400,000 Less: fixed costs 1,000,000 Profit 4,400,000 14
  • 15.
    (ii) 2000 unitsof X only Product Sales Marginal Contribution X 14,000,000 8,000,000 6,000,000 Less: fixed cost 1,000,000 Profit 5,000,000 (iii) 1500 units of Y only Product Sales Marginal Contribution Y 15,000,000 8,250,000 6,750,000 Less: fixed cost 1,000,000 Profit 5,750,000 (iv) 1200 units of X and 600 units of Y Product Sales Marginal Contribution X 8,400,000 4,800,000 3600,000 Y 6,000,000 3,300,000 2,700,000 6,300,000 Less: fixed costs 1,000,000 Profit 5,300,000 Sales mix (iii) is best however if the product X is discontinued and the demand for Y is reduced, the firm would have changed its sales mix. It is better to continue with both products and option (iv) is near to the best solution. Example 3.6 Use of marginal costing in achieving profit target A Co. has invested Shs.100, 000,000 in its factory and sets a goal of 15% annual return on investment. Fixed costs in the factory at present are Sh. 40,000,000 and variable cost is Shs 1500. In the past the firm produced and sold 50,000 units at shs. 2500 each and earned a net profit of shs 10,000,000. How can the management achieve their target profit by making changes in fixed costs, variable costs, quantity sold or increasing the selling price per unit? 15
  • 16.
    Solution Target Profit =100,000,000 x 15 100 = Shs. 15,000,000 (i) Change in fixed costs: S = Vc + C C = S – Vc F = C – Pt Vc = 50,000 units x 1500 = 75,000,000 S = 50,000 units x 2500 = 125,000,000 C = 125,000,000 – 75,000,000 = 50,000,000 F = 50,000,000 – 15,000,000 = 35,000,000 Present Fixed costs are 40,000,000. The management can achieve the target profit by reducing the Fixed cost by Shs 5,000,000 (ii) Change in Variable cost Vc = S – C C = F + Pt C = 40,000,000 + 15,000,000 = 55,000,000 Vc = 125,000,000 – 55,000,000 = 70,000,000 Variable cost per unit = 70,000,000 = Shs. 1400 50,000 It should be reduced to Shs 1400 per unit from Shs 1500 per unit (iii) Change in Quantity sold S – Vc = F + Pt S = P x Q Vc = V x Q Q (P – V) = C Q (2500 – 1500) = 55,000,000 16
  • 17.
    Q = 55,000,000or 55,000 units 1000 (iv) Change in selling price S = Vc + C PQ = Vc + C P = Vc + C Q P = 75,000,000 + 55,000,000 50,000 = 130,000,000 50,000 = Shs 2600 If the selling price could be raised to Shs 2600 Example 3.7 Dropping a line or a product There are three lines of product and their product cost per unit and selling price per unit are given below: X Y Z Material 180 260 300 Wages 70 90 100 Variable overheads 20 30 30 Fixed overheads 50 80 90 320 460 520 Selling price 400 600 610 Net profit 80 140 90 Production in units 4000 2000 5000 The manager wants to discontinue one line and guarantees that the production of other two lines shall rise by 50%. He wants to discontinue line X as it is least profitable Solution Total fixed cost X 4000 x 50 = 200,000 Y 2000 x 80 = 160,000 Z 500 x 90 = 450,000 810,000 17
  • 18.
    (i) When alllines are continued Sales Marginal Contribution X 1,600,000 1,080,000 520,000 Y 1,200,000 760,000 440,000 Z 3,050,000 2,150,000 900,000 5,850,000 3,990,000 1,860,000 Less fixed cost 810,000 _____ Profit 1,050,000 ======= (ii) When line X is dropped the production in Y & Z will increase by 50% Product Sales M.C Contribution Y 1,800,000 1,140,000 660,000 X 4,575,000 3,225,000 1,350,000 2,010,000 Less fixed cost 810,000 ______ Profit 1,200,000 ===== (iii) When line Y is dropped the production of X & Z will increase by 50% Product Sales M.C Contribution X 2,400,000 1,620,000 780,000 Z 4,575,000 3,225,000 1,350,000 2,130,000 Less fixed cost 810,000 Profit 1,320,000 (iv) If Z line is dropped the production of X & Y will increase by 50% Product Sales M.C Contribution Y 2,400,000 1,620,000 780,000 X 1,000,000 1,140,000 660,000 1,440,000 Less fixed cost 810,000 18
  • 19.
    Profit 630,000 To maximizeprofit, Y line should be dropped. Example 3.8 Introducing a New Product or line Simba Plastic limited produces a product X. The capacity of the plant is to produce 30,000 units. However at present 20,000 units are produced. The present cost is as under: Material Shs. 200,000,000 Labour 100,000,000 Variable overheads 20,000,000 Fixed overheads 150,000,000 Product X is sold at Shs 30,000 per unit. It is proposed to manufacture product Y along with product X. This will require additional investment of Shs. 250,000,000 to manufacture 15000 units of Y. Initially 10,000 units of Y can be manufactured and sold for 20,000 each. The cost estimates of Y product are:- Material Shs. 10,000 per unit, Labour Shs. 3000 per unit Variable overheads Shs. 1000per unit Fixed overheads Shs. 35,000,000 Is it advisable to introduce product Y? Solution: Existing Product New Product Total Sales 600,000,000 200,000,000 800,000,000 Less: Marginal costs Material 200,000,000 100,000,000 300,000,000 Labour 100,000,000 30,000,000 130,000,000 Variable overheads 20,000,000 10,000,000 30,000,000 Total marginal cost 320,000,000 140,000,000 460,000,000 ______________________________________________ Contribution 280,000,000 60,000,000 340,000,000 19
  • 20.
    Less: fixed overhead150,000,000 35,000,000 185,000,000 Net profit 130,000,000 25,000,000 155,000,000 Contribution ratio = C x 100 46.6% 30% 42.5% S Contribution ratio will decline. However total profit will increase. It would be better to increase the production of X product. Example 3.9 Accepting Special offer / Exploring new market. The Zenith Plastic is operating at 60% of it capacity. The cost position is as follows for producing 15000 units:- Material Shs 30,000 per unit Labour Shs. 15,000 per unit Variable overheads Shs. 5,000 per unit Fixed overheads Shs. 20,000 per unit or shs.300,000,000 Total FC 70,000 Profit 20,000 per unit Selling price Shs 90,000 per unit The import duty in the EA region has been abolished. A company in Kenya is willing to buy 10,000 units at a price of Shs. 60,000 each. However the extra production can not be sold in Tanzania. Would you recommend that the company should accept this offer? Solution: Statement of Marginal cost & contribution Existing Kenya order Total 15,000 unit 10,000 unit 25,000 unit Material 450,000,000 300,000,000 750,000,000 Labour 225,000,000 150,000,000 375,000,000 Variable overheads 75,000,000 50,000,000 125,000,000 Marginal cost 750,000,000 500,000,000 1,250,000,000 Sales 1,350,000,000 600,000,000 1,950,000,000 20
  • 21.
    Contribution 600,000,000 100,000,000700,000,000 Les: fixed cost 300,000,000 ---------- 300,000,000 Profit 300,000,000 100,000,000 400,000,000 Contribution ratio 44.44% 16.66% 35.89% Contribution ratio will decline after accepting the Kenya’s offer. However in absolute terms the profit margin will increase by Shs 100,000,000 so the Kenya’s offer should be taken on board, as this will help us to operate at full capacity. Operating Leverage Operating leverage influences the net operating income of the firm due to investing decision. The investments are made in fixed assets incurring fixed costs and incurring variable costs. In many cases due to investments in fixed assets, the variable costs are reduced considerably. So how much investment is to be made in each category is a planning function, which should be looked into carefully. Operating leverage is the extent to which a firms fixed costs contribute to total operating costs at different level of sales. The DOL measures the % change in NOI (%∆NOI) for a given % in change in sales (%∆S). The DOL is a Magnification factor. DOL exists because of fixed costs and fixed costs amplify changes in NOI for small changes in sales. DOL = Total Sales – Total Variable Costs or Total Sales – Total Variable Costs –Total Fixed Costs = Q (P-V) Q (P-V) – F DOL = %∆NOI %∆S Example 3.10 You have been provided with the following information concerning X Company and Y Company. X Company Shs Y Company Shs Sales 100,000 Sales 100,000 Fixed costs 50,000 per year Fixed costs 20,000 per year Variable costs 30% of sales Variable costs 60% of sales Compute 21
  • 22.
    i. The degreeof Operating Leverage ii. If the sales increase by 10% what would be the impact on NOI? X Company Y Company DOL = TS –TV DOL = TS –TV TS – TV– TF TS – TV– TF = 100,000 – 30,000 = 100,000 – 60,000 100,000 – 30,000 – 50,000 100,000 – 60,000 – 20,000 = 70,000 = 40,000 20,000 20,000 = 3.5 = 2.0 DOL = %∆NOI DOL = %∆NOI %∆S %∆S 3.5 = %∆NOI 2.0 = %∆NOI 10% 10% 35% = %∆NOI 20% = %∆NOI To Prove NOI of X C0. NOI=TS-VC-FC (before change in NOI) = 100,000-30,000-50,000 = 20,000 NOI= TS-VC-FC(new NOI) = 110,000-33,000-50,000 =27,000 ∆NOI =27,000-20,000 =7,000 %∆NOI=7,000 X 100 20,000 =35% Example 3.11 Light source makes bulbs and has F = shs.1, 000,000, V = shs.5 and P = shs.10 at a given Q = 250,000 units. Calculate the DOL and %∆NOI if the sales go up by 5%. DOL = Q (P-V) 22
  • 23.
    Q (P-V) –F = 250,000 (10 – 5) 250,000 (10 – 5) – 1,000,000 = 5.0 DOL = %∆NOI %∆S 5.0 = %∆NOI 5% 5 x 5% = %∆NOI 25% = %∆NOI The DOL is a Magnification factor. DOL exists because of fixed costs and fixed costs amplify changes in NOI for small changes in sales. Example 3.12 A small company in Morogoro has a current NOI of shs. 200,000. Next year NOI is expected to be shs. 300,000 as sales are expected to go up by 25%, what is its DOL. %∆NOI = New NOI- Old NOI Old NOI = 300,000 – 200,000 X 100 200,000 = 50% DOL = %∆NOI %∆S = 50% 25% = 2.0 Example 3.13 Chagga Bros. make seat covers for cars and sell at shs.20,000 each with a variable cost of shs.12,000 each. Next year he expects 20% drop in sales and 50% drop in NOI due to lack of demand. Current level of sales is 112 set of seat covers. What is the level of fixed cost? 23
  • 24.
    %∆S = -20%; %∆NOI = - 50% DOL = %∆NOI %∆S = -50% -20% = 2.5 DOL = Q (P – V) Q (P – V) – F 2.5 = 112(20,000 – 12,000) 112(20,000 – 12,000) – F 2.5 = 896,000 896,000 – F -2.5F + 2.5 x 896,000 = 896,000 -2.5F + 2,240,000 = 896,000 -2.5F = -2,240,000 + 896,000 -2.5F = -1,344,000 F = 537,600 24