Explain various types of costs incurred by an organization
Explain the nature of CVP analysis.
Calculate and interpret breakeven point and margin of safety.
Calculate the contribution to sales ratio, in single and multi-product situations, and demonstrate an understanding of its use.
Calculate target profit or revenue in single and multi-product situations, and demonstrate an understanding of its use.
Prepare break even charts and profit volume charts and interpret the information contained within each, including multi-product situations
Discuss the limitations of CVP analysis for planning and decision making.
CVP Analysis
Single Product
Multi Product
Further Aspects of CVP
Basic Breakeven Analysis
Major Assumption
Limitations
Graphical Approach
Breakeven Point
Advantages
C/S Ratio Margin of Safety Target Profit
Breakeven Charts
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1.
Costs
Costs are different from expenses. Costs are resources sacrificed to achieve an objective. Expenses are the costs charged against revenue in a particular accounting period. Hence, ―cost‖ is an economic concept, while ―expense‖ is a term that falls within the domain of accounting.
1.1
Direct Costs and Indirect Costs
1.1.1 Direct costs Direct costs can be defined as costs which can be actually traced to a cost object with little effort. Cost object may be a product, a department, a project etc. Direct costs typically benefit a single cost object therefore the classification of any cost either as direct or indirect is done by taking the cost object into perspective. A particular cost may be direct cost for one cost object but indirect cost for another cost object. Most direct costs are variable but this may not always be the case. For example, the salary of a supervisor for a month who has only supervised the construction of a single building is a direct fixed cost incurred on the building. Examples: Cost of gravel, sand, cement and wages incurred on production of concrete. 1.1.2 Indirect costs Costs which cannot be accurately attributed to specific cost objects are called indirect costs. These typically benefit multiple cost objects and it is impracticable to accurately trace them to individual products, activities or departments etc. Examples: Cost of depreciation, insurance, power, salaries of supervisors incurred in a concrete plant.
1.2
Fixed Costs and Variable Costs
1.2.1 Fixed Cost A cost that does not change with an increase or decrease in the amount of goods or services produced. Fixed costs are expenses that have to be paid by a company, independent of any business activity. It is one of the two components of the total cost of a good or service, along with variable cost. An example of a fixed cost would be a company's lease on a building. If a company has to pay $10,000 each month to cover the cost of the lease but does not manufacture anything during the month, the lease payment is still due in full. In economics, a business can achieve economies of scale when it produces enough goods to spread fixed costs. For example, the $100,000 lease spread out over 100,000 units means that each unit carries with it $1 in fixed costs. If the company produces 200,000 units, the fixed cost per unit drops to 50 cents.
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1.2.2 Variable Cost This is a corporate expense that varies with production output. Variable costs are those costs that vary depending on a company's production volume; they rise as production increases and fall as production decreases. Variable costs differ from fixed costs such as rent, advertising, insurance and office supplies, which tend to remain the same regardless of production output. Fixed costs and variable costs comprise total cost. Variable costs can include direct material costs or direct labor costs necessary to complete a certain project. For example, a company may have variable costs associated with the packaging of one of its products. As the company moves more of this product, the costs for packaging will increase. Conversely, when fewer of these products are sold the costs for packaging will consequently decrease.
1.3
Marginal Cost of Production
Marginal cost is the change in total cost that comes from making or producing one additional item. The purpose of analyzing marginal cost is to determine at what point an organization can achieve economies of scale. The calculation is most often used among manufacturers as a means of isolating an optimum production level. Manufacturing concerns often examine the cost of adding one more unit to their production schedules. This is because at some point, the benefit of producing one additional unit and generating revenue from that item will bring the overall cost of producing the product line down. The key to optimizing manufacturing costs is to find that point or level as quickly as possible.
1.4
Opportunity Cost
In microeconomic theory, the opportunity cost of a choice is the value of the best alternative forgone, in a situation in which a choice needs to be made between several mutually exclusive alternatives given limited resources. Assuming the best choice is made, it is the "cost" incurred by not enjoying the benefit that would be had by taking the second best choice available. The New Oxford American Dictionary defines it as "the loss of potential gain from other alternatives when one alternative is chosen". Opportunity cost is a key concept in economics, and has been described as expressing "the basic relationship between scarcity and choice"
1.5
Sunk Cost
This is a cost that has already been incurred and thus cannot be recovered. A sunk cost differs from other, future costs that a business may face, such as inventory costs or R&D expenses, because it has already happened. Sunk costs are independent of any event that may occur in the future. When making business or investment decisions, individuals and organizations typically look at the future costs that they may incur, by following a certain strategy. A company that has spent $5 million building a factory that is not yet complete, has to consider the Page | 4
$5 million sunk, since it cannot get the money back. It must decide whether continuing construction to complete the project will help the company regain the sunk cost, or whether it should walk away from the incomplete project. Money already spent and permanently lost. Sunk costs are past opportunity costs that are partially (as salvage, if any) or totally irretrievable and, therefore, should be considered irrelevant to future decision making. This term is from the oil industry where the decision to abandon or operate an oil well is made on the basis of its expected cash flows and not on how much money was spent in drilling it. Also called embedded cost, prior year cost, stranded cost, or sunk capital.
1.6 Differential cost Differential cost is the difference between the cost of two alternative decisions, or of a change in output levels. The concept is used when there are multiple possible options to pursue, and a choice must be made to select one option and drop the others. The concept can be particularly useful in step costing situations, where producing one additional unit of output may require a substantial additional cost. Here are two examples:
Example of alternative decisions. If you have a decision to run a fully automated operation that produces 100,000 units per year at a cost of $1,200,000, or of using direct labor to manually produce the same number of units for $1,400,000, then the differential cost between the two alternatives is $200,000.
Example of change in output. A work center can produce 10,000 units for $29,000 or 15,000 units for $40,000. The differential cost of the additional 5,000 units is $11,000.
In essence, you can line up the revenues and expenses from one decision next to similar information for the alternative decision, and the difference between all line items in the two columns is the differential cost. A differential cost can be a variable cost, a fixed cost, or a mix of the two – there is no differentiation between these types of costs, since the emphasis is on the gross difference between the costs of the alternatives or change in output. Since a differential cost is only used for management decision making, there is no accounting entry for it. There is also no accounting standard that mandates how the cost is to be calculated.
1.7 What is a Relevant cost? A relevant cost is a cost that only relates to a specific management decision, and which will change in the future as a result of that decision. The relevant cost concept is extremely useful for eliminating extraneous information from a particular decision-making process. Also, by eliminating irrelevant costs from a decision, management is prevented from focusing on information that might otherwise incorrectly affect its decision. Page | 5
The relevant cost concept is only applicable to management accounting activities; the concept is not used in financial accounting, since no spending decisions are involved in financial accounting. For example, the Archaic Book Company (ABC) is considering purchasing a printing press for its medieval book division. If ABC buys the press, it will eliminate 10 scribes who have been copying the books by hand. The wages of these scribes are relevant costs, since they will be eliminated in the future if management buys the printing press. However, the cost of corporate overhead is not a relevant cost, since it will not change as a result of this decision. The reverse of a relevant cost is a sunk cost. A sunk cost is an expenditure that has already been made, and so will not change on a go-forward basis as the result of a management decision.
2.
Cost-Volume-Profit Analysis
CVP analysis studies the relationship of cost-volume-profit at different levels of output. This analysis is an important tool for profit planning. The three factors of CVP analysis — costs, volume and profit — are interconnected and dependent on one another. For example, profits depend upon the selling price. Selling price, largely, depends upon cost of production. Cost of production, in turn, depends upon volume of production. It is only the variable costs that vary directly with production, whereas fixed costs remain constant, regardless of the volume of production, in the short-run. In some quarters, there is an opinion that business firms, rarely, operate at their breakeven point. Therefore, the break-even analysis is of very limited use to the management. This is incorrect. Reason is many people consider CVP analysis and Break-even point are one and the same. It is not so. The scope of CVP analysis is quite wide, while BEP is only a part of CVP analysis. Break-even analysis provides answer how much sales are to be made to avoid losses. CVP analysis provides not only this answer, as BEP is a part of it, but provides answers in many areas to the management. Understanding CVP relationship is important in financial decision making to a dynamic management. It provides right answers to the following questions such as:
How much sales are required to avoid losses? What level of sales is required to achieve a targeted amount of profit? What will be the effect of change in prices, costs and volume on profits? What will be the effect of change in sales mix on profits? What will be the new break-even point, if there is change in prices, costs, volume or sales mix? Should we buy or manufacture some products or components? What will be the impact of plant expansion on the relationship of cost-volumeprofit? Page | 6
Which product or product mix is most profitable and which one is least profitable? Should the sale of a product or operation of a plant be discontinued? Is it desirable to shut down the plant, temporarily?
These are some of the intricate questions for which management can find answers with the help of CVP analysis. All the above aspects have immense influence on the profitability of the firm. CVP analysis is concerned with entire profit planning, as management’s main thrust is to build a good level of profit, at all times. This analysis provides the necessary insight to the management to take suitable decisions for necessary and timely action. It is of great use for profit planning, cost control and decision-making.
CVP Analysis and Break-Even Analysis Many think break-even analysis and CVP analysis are one and the same. It is not so. The Break-even analysis is the most widely known form of CVP analysis. For this reason, many use both the terms interchangeably. The purpose of CVP analysis is to examine the effect of change in costs, volume and price on profits. This is a comprehensive study. Break-even analysis is a part of CVP analysis.
Break-Even Analysis Break-even analysis establishes the relationship between revenues and costs with respect to volume. It indicates the level of sales at which total costs are equal to total revenues. Breakeven analysis is a specific way of presenting information to management in a precise manner. Many a time, CVP analysis is popularly designated as break-even analysis. But, there is a narrow difference between the two. CVP analysis is concerned with the entire profit planning, while the break-even analysis is one of the techniques used in that process. Break-even point: Break-even point is the point at which the firm makes no profit or loss. At the break-even point, the firm is in the stage of equilibrium. The equilibrium point is commonly known as break-even point. Break-even point is that point, where the revenue is just equal to total costs. It is the point where the firm makes neither profit nor loss. This is a zero position. After this level, if the firm makes production and sells above the variable cost, it earns profit. If the sales fall below this level, firm sustains loss. There are two approaches to calculate the break-even point. They are: (A) Break-even Formulae Approach and (B) Break-even Chart or Graphic Method Break-even Analysis Page | 7
(A) Break-even Formulae Approach: The break-even point can be calculated in terms of units, in terms of money value of sales volume or as a percentage of estimated capacity.
Contribution When the selling price per unit is more than its variable cost, the excess is called contribution. Total contribution is calculated by multiplying the unit contribution with the number of units sold. Total contribution is the excess amount, after covering total fixed costs that is incurred by the firm. After covering fixed costs, the amount left out from total sales in the firm is gross margin. So, contribution covers total fixed costs and profit. If the contribution does not cover fixed costs, the difference is loss, sustained by the firm. Every firm looks to achieve break-even point, at the earliest. After the break-even level, whatever is sold that can leave in the form of contribution to the firm is a welcome decision. While making production and sales decisions, the firm chooses that product that gives the highest contribution. Contribution is vital in profit planning decision-making. Firm is always concerned to choose that product, where it can sell and achieve the highest amount of contribution. Contribution is important to the finance manager and, equally, to marketing manager to show impressive performance of the firm, in terms of profitability. The formulae for their calculation are
Contribution per unit = Selling price per unit – Variable cost per unit
Contribution per unit × Number of units sold = Total Contribution
Total Contribution = Total fixed costs + Profit
Profit = Total Contribution – Total fixed costs
Loss = Total fixed costs – Total contribution BEP in Terms of Units: The break-even point, in terms of units, can be computed by dividing fixed costs by contribution per unit. The formula for break-even point (BEP), in terms of units, is as follows:
The above formula is useful to find out break-even point, in terms of number of units of sales. Page | 8
From the above formula, it is evident that the selling price per unit should be higher than the variable cost per unit to have positive break-even point. Suppose, if the variable cost is higher than the selling price, a negative sales volume can be calculated, mathematically, to arrive at break-even point, but is of no help in the real life situation. No Fixed Costs Situation: In case, a firm has no fixed costs, what is the break-even point to that firm? If the firm does not produce anything, it does not incur any loss. So, no production level is the first break-even point. This is the safest situation for the firm. At each level, total contribution is equal to profit. So, every sales level will be the breakeven point to that firm, if there are no fixed costs to the firm.
2.1
Breakeven Analysis
2.1.1
Key Terms (a)
Contribution per unit = unit selling price – unit variable costs
(b)
Breakeven point = activity level at which there is neither profit nor loss =
(c)
Total fixed cos ts Contributi on per unit
Contribution/sales (C/S) ratio = profit/volume (P/V) ratio =
Contributi on 100% Sales
(d)
Sales revenue at breakeven point = fixed costs ÷ C/S ratio
(e)
Margin of safety (in units) = budgeted sales units – breakeven sales units
Budgeted sales – breakeven sales Budgeted sales
(f)
Margin of safety (as %)
(g)
Sales volume to achieve a target profit
× 100%
Fixed cost + target profit Contribution per unit
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2.1.2
Exercise 1 A company manufactures and sells a single product which has the following cost and selling price structure. £/Unit £/Unit Selling price 120 Direct material 22 Direct labour 36 Variable overhead 14 Fixed overhead 12 84 Profit per unit 36 The fixed overhead absorption rate is based on the normal capacity of 2,000 units per month. Assume that the same amount is spent each month on fixed overheads. Budgeted sales for next month are 2,200 units. You are required to calculate; (i) The break-even point in sales units per month. (ii) The margin of safety for next month (iii)The budgeted profit for next month (iv) The sales required to achieve a profit of £ 96,000 in a month.
2.1.3
Exercise 2 A company manufactures a single product which has the following cost structure based on a production budget of 10,000 units. Materials – 4 kg at $3/kg $12 Direct labour – 5 hours at $7/hour $35 Variable production overheads are recovered at the rate of $8 per direct labour hour. Other costs incurred by the company are: $ Factory fixed overheads 120,000 Selling and distribution overheads 160,000 Fixed administration overheads 80,000 The selling and distribution overheads include a variable element due to a distribution cost of $2 per unit. The fixed selling price of the unit is $129. You are required to; (a)
Calculate how many units have to be sold for the company to breakeven.
(b)
Calculate the sales revenue which would give a net profit of $40,000. Page | 10
(c) If the company could buy in the units instead of manufacturing them, calculate how much it would be prepared to pay if both: (i) estimated sales for next year are 9,500 units at $129 each; and (ii) $197,500 of fixed selling, distribution and administrative overheads would still be incurred even if there is no production (all other fixed overheads would be saved).
2.2
The Graphical Approach for Single Product
2.2.1 The second way to find the break-even is to use the graphical method. The graphical method is based on the break-even chart, a graphical representation of costvolume-profit relationships and the break-even point. It is an attempt to help management in their understanding of these relationships and so enable them to decide on the optimum level of output.
2.2.2
Exercise 3 A new product has the following sales and cost data. Selling price
$60 per unit
Variable costs
$40 per unit
Fixed costs
$25,000 per month
Forecast sales 1,800 units per month You are required to; Prepare a breakeven chart using the above data.
2.2.3
Exercise 4 A company manufactures a single product which incurs fixed costs of £ 30,000 per annum. Annual sales are budgeted to be 70,000 units at a sales price of £ 30 per unit. Variable costs are £ 28.50 per unit. (a) Draw a profit-volume graph, and use it to determine the break-even point. The company is now considering improving the quality of the product and increasing the selling price to £ 35 per unit. Sales volume will be unaffected, but fixed cost will increase to £ 45,000 per annum and variable costs to £ 33 per unit. (b) Draw, on the same graph as for part (a), a second profit-volume graph and comment on the results.
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2.2.4
Exercise 5 A summary of a manufacturing company’s budgeted profit statement for its next financial year, when it expects to be operating at 75% of capacity, is given below. £ Seles 9,000 units at £32 Less: Direct material Direct labour Production overhead - fixed - variable Gross Profit Less: admin, selling & distribution costs - fixed - variable Net profit
£ 288,000
54,000 72,000 42,000 18,000
36,000 27,000
186,000 102,000
63,000 39,000
It has been estimated that; (i) If the selling price per unit were reduced to £28, the increased demand would utilize 90% of the company’s capacity without any additional advertising expenditure. (ii) To attract sufficient demand to utilize full capacity would require a 15% reduction in the current selling price and a £5,000 special advertising campaign. You are required to; (a) Calculate the break-even point in units, based on the original budget. (b) Calculate the break-even points and profits which would result from each of the two alternatives and compare them with the original budget.
3.
Breakeven Analysis for Multiple Products
3.1
A major assumption
3.1.1 Organizations typically produce and sell a variety of products and services. To perform breakeven analysis in a multi-product organization, however, a constant product sales mix must be assumed. In other words, we have to assume that whenever x units of product A are sold, y units of product B and z units of product C are also sold.
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3.1.2
Exercise 6 PL produces and sells two products. The M sells for $7 per unit and has a total variable cost of $2.94 per unit, while the N sells for $15 per unit and has a total variable cost of $4.5 per unit. The marketing department has estimated that for every five units of M sold, one unit of N will be sold. The organization’s fixed costs total $36,000. You are required to; 1. Calculate contribution per unit 2. Calculate contribution per mix 3. Calculate the breakeven point in terms of the number of mixes 4. Calculate the breakeven point in terms of the number of units of products 5. Calculate the breakeven point in terms of revenue
3.1.3
Exercise 7 Alpha manufactures and sells three products, the beta, the gamma and the delta. Relevant information is as follows. Beta Gamma Delta $ per unit $ per unit $ per unit Selling price 135.00 165.00 220.00 Variable cost 73.50 58.90 146.20 Total fixed costs are $950,000. An analysis of past trading patterns indicates that the products are sold in the ratio 3:4:5 You are required to; Calculate the breakeven point for Alpha.
3.2
Contribution to sales (C/S) ratio for multiple products
3.2.1 The breakeven point in terms of sales revenue can be calculated as fixed costs / average C/S ratio. 3.2.2 Any change in the proportions of products in the mix will change the contribution per mix and the average C/S ratio and hence the breakeven point. 3.2.3 You should know that the C/S ratio is sometimes called the profit/volume ratio or P/V ratio. Page | 13
3.2.4
Exercise 8 As exercise 3 above, we can calculate the breakeven point of PL using the C/S ratio for multiple products. You are required to; 1. Calculate revenue per mix 2. Calculate contribution per mix (see example 2) 3. Calculate average C/S ratio 4. Calculate the breakeven point 5. Calculate revenue ratio of mix 6. Calculate breakeven sales
3.2.5
Exercise 9 Calculate the breakeven sales revenue of product Beta, Gamma and Delta (see Exercise 2 above) using the approach shown in Example 3.
3.2.6
Points to Bear in Mind Any change in the proportions of products in the mix will change the contribution per mix and the average C/S ratio and hence the breakeven point. (a) If the mix shifts towards products with lower contribution margins, the breakeven point (in units) will increase and profits will fall unless there is a corresponding increase in total revenue. (b) A shift towards products with higher contribution margins without a corresponding decrease in revenues will cause an increase in profits and a lower breakeven point. (c) If sales are at the specified level but not in the specified mix, there will be either a profit or a loss depending on whether the mix shifts towards products with higher or lower contribution margins.
3.3
Margin of safety for multiple products
3.3.1 The margin of safety for a multi-product organization is equal to the budgeted sales in the standard mix less the breakeven sales in the standard mix. It may be expressed as a percentage of the budgeted sales.
3.3.2
Exercise 10 BA produces and sells two products. The W sells for $8 per unit and has a total variable cost of $3.80 per unit, while the R sells for $14 per unit and has a total variable cost of $4.20. For every five units of W sold, six units of R are sold. BA's fixed costs are $43,890 per period. Page | 14
Budgeted sales revenue for next period is $74,400, in the standard mix. You are required to; Calculate the margin of safety in terms of sales revenue and also as a percentage of budgeted sales revenues. 1. 2. 3. 4. 5. 6.
3.4
Calculate contribution per unit Calculate contribution per mix Calculate the breakeven point in terms of the number of mixes Calculate the breakeven point in terms of the number of units of products Calculate the breakeven point in terms of revenue Calculate the margin of safety
Target profits for multiple products
3.4.1 The number of mixes of products required to be sold to achieve a target profit is calculated as: (fixed costs + required profit)/contribution per mix. 3.4.2
Exercise 11 An organisation makes and sells three products, F, G and H. The products are sold in the proportions F:G:H = 2:1:3. The organisation's fixed costs are $80,000 per month and details of the products are as follows. Selling price Product F G H
$ per unit 22 15 19
Variable cost $ per unit 16 19 13
The organisation wishes to earn a profit of $52,000 next month. Calculate the required sales value of each product in order to achieve this target profit. You are required to; 1. Calculate contribution per unit 2. Calculate contribution per mix 3. Calculate the required number of mixes 4. Calculate the required sales in terms of the number of units of the products and sales revenue of each product The sales revenue of $464,000 will generate a profit of $52,000 if the products are sold in the mix 2:1:3. Alternatively the C/S ratio could be used to determine the required sales revenue for a profit of $52,000. The method is again similar to that demonstrated earlier when calculating the breakeven point. Page | 15
3.4.3
Exercise 12 Using the information as Example 5, calculate the required sales of each products by using the C/S ratio. You are required to; 1. Calculate revenue per mix 2. Calculate contribution per mix 3. Calculate average C/S ratio 4. Calculate the required total revenue 5. Calculate revenue ratio of mix 6. Calculate required sales Which, allowing for roundings, is the same answer as calculated in the first example.
3.5
Multi-product breakeven charts
(A)
Breakeven charts
3.5.1 Breakeven charts for multiple products can be drawn if a constant product sales mix is assumed. 3.5.2 Here, there are three approaches to draw the multi-product breakeven charts. 3.5.3
Exercise 13 – Approach 1: Output in $ Sales and a Constant Product Mix Assume that budgeted sales are 2,000 units of X, 4,000 units of Y and 3,000 units of Z. A breakeven chart would make the assumption that output and sales of X, Y and Z are in the proportions 2,000: 4,000: 3,000 at all levels of activity, in other words that the sales mix is 'fixed' in these proportions. We begin by carrying out some calculations. Budgeted costs Costs $ Variable costs of X (2,000 x $3) 6,000 Variable costs of Y (4,000 x $4) 16,000 Variable costs of Z (3,000 x $5) 15,000 Total variable 37,000 costs Fixed costs Total budgeted costs
X (2,000 x $8) Y (4,000 x $6) Z (3,000 x $6) Budgeted revenue
Revenue $ 16,000 24,000 18,000 58,000
10,000 47,000
The breakeven chart can now be drawn.
Page | 16
The breakeven point is approximately $27,500 of sales revenue. This may either be read from the chart or computed mathematically. (a) The budgeted C/S ratio for all three products together contribution/sales = $(58,000 – 37,000)/$58,000 = 36.21%.
is
(b) The required contribution to break even is $10,000, the amount of fixed costs. The breakeven point is $10,000/36.21% = $27,500 (approx) in sales revenue. The margin of safety is approximately $(58,000 – 27,500) = $30,500.
3.5.4
Exercise 14 – Approach 2: Products in Sequence The products could be plotted in a particular sequence (say X first, then Y, then Z). Using the data from Approach 1, we can calculate cumulative costs and revenues as follows. Product
X (2,000 units) Y (4,000 units) Z (3,000 units)
Cumulative units Nil 2,000 6,000 9,000
Cumulative costs $ 10,000 16,000 32,000 47,000
Cumulative revenue $ Nil 16,000 40,000 58,000
The breakeven chart can now be drawn.
Page | 17
In this case the breakeven point occurs at 2,000 units of sales (2,000 units of product X). The margin of safety is roughly 4,000 units of Y and 3,000 units of Z.
3.5.5
Exercise 15 – Approach 3: Output in Terms of % of Forecast Sales and a Constant Product Mix The breakeven point can be read from the graph as approximately 48% of forecast sales ($30,000 of revenue). Alternatively, with contribution of $(58,000 – 37,000) = $21,000, one percent of forecast sales is associated with $21,000/100 = $210 contribution. Breakeven point (%) = fixed costs/contribution per 1% = $10,000/$210 = 47.62% ∴Margin of safety = (100 – 47.62) = 52.38%
Page | 18
(B)
Multi-product P/V charts
3.5.6
The same information could be shown on a P/V chart.
3.5.7
Exercise 16 Same information as Example 7, Product X Y Z Total
Contribution $ 10,000 8,000 3,000 21,000
Sales $ 16,000 24,000 18,000 58,000
C/S ratio % 62.50 33.33 16.67 36.21
By convention, the products are shown individually on a P/V chart from left to right, in order of the size of their C/S ratio. In this example, product X will be plotted first, then product Y and finally product Z. A dotted line is used to show the cumulative profit/loss and the cumulative sales as each product's sales and contribution in turn are added to the sales mix. Product X X and Y X, Y and Z
Cumulative sales $ 16,000 40,000 58,000
($16,000 – $16,000)
Cumulative profit $ 8,000 11,000
You will see on the graph which follows that these three pairs of data are used to plot the dotted line, to indicate the contribution from each product. The solid line which joins the two ends of this dotted line indicates the average profit which will be earned from sales of the three products in this mix.
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The diagram highlights the following points. (a) Since X is the most profitable in terms of C/S ratio, it might be worth considering an increase in the sales of X, even if there is a consequent fall in the sales of Z. (b) Alternatively, the pricing structure of the products should be reviewed and a decision made as to whether the price of product Z should be raised so as to increase its C/S ratio (although an increase is likely to result in some fall in sales volume). The multi-product P/V chart therefore helps to identify the following. (a) The overall company breakeven point. (b) Which products should be expanded in output and which, if any, should be discontinued. (c) What effect changes in selling price and sales volume will have on the company's breakeven point and profit?
3.5.8
Exercise 17 A company sells three products, X, Y and Z. Cost and sales data for one period are as follows. X Y Z Sales volume 2,000 units 2,000 units 5,000 units Sales price per unit $3 $4 $2 Variable cost per unit $2.25 $3.50 $1.25 Total fixed costs $3,250 Page | 20
Required: Construct a multi-product P/V chart based on the above information on the axes below.
4.
Further Aspects of CVP Analysis
4.1 The usefulness of CVP analysis is restricted by its unrealistic assumptions, such as constant sales price at all levels of activity. However CVP has the advantage of being more easily understood by non-financial managers due to its graphical depiction of cost and revenue data. 4.2
Limitations: (a) It is assumed that fixed costs are the same in total and variable costs are the same per unit at all levels of output. This assumption is a great simplification. (b) Fixed costs will change if output falls or increases substantially (most fixed costs are step costs). (c) The variable cost per unit will decrease where economies of scale are made at higher output volumes, but the variable cost per unit will also eventually rise when diseconomies of scale begin to appear at even higher volumes of output (for example the extra cost of labour in overtime working). Page | 21
(d) The assumption is only correct within a normal range or relevant range of output. It is generally assumed that both the budgeted output and the breakeven point lie within this relevant range. (e) It is assumed that sales prices will be constant at all levels of activity. This may not be true, especially at higher volumes of output, where the price may have to be reduced to win the extra sales. (f) Production and sales are assumed to be the same, so that the consequences of any increase in inventory levels or of 'de-stocking' are ignored. (g) Uncertainty in the estimates of fixed costs and unit variable costs is often ignored.
4.3
Advantages: (a) Graphical representation of cost and revenue data (breakeven charts) can be more easily understood by non-financial managers. (b) A breakeven model enables profit or loss at any level of activity within the range for which the model is valid to be determined, and the C/S ratio can indicate the relative profitability of different products. (c) Highlighting the breakeven point and the margin of safety gives managers some indication of the level of risk involved.
5.
Limiting factor decision making
A limiting factor is any factor which is in scare supply and which stops the organization from expanding its activities further, i.e. it limits the organization’s activities. The limiting factor for many trading organizations is sales volume because they cannot sell as much as they would like. However, other factors may also be limited, especially in the short term. For example, machine capacity or the supply of skilled labour may be limited for one or two periods until some actions can be taken to alleviate the shortage.
5.1 Decisions involving a single limiting factor If an organization is faced with a single limiting factor, for example machine capacity, then it must ensure that a production plan is established which maximizes the profit from the use of the available capacity. Assuming that fixed cost remain constant, this is the same as saying that the contribution must be maximized from the use of the Page | 22
available capacity. The machine capacity must be allocated to those products which earn the most contribution per machine hour. This decision rule can be stated as ―maximizing the contribution per unit of limiting factor‖. Exercise 18 LMN Limited manufactures three products L, M and N. The company which supplies the two raw materials which are used in all three products has informed LMN that their employees are refusing to work overtime. This means that supply of the materials is limited to the following quantities for the next period. Material A Material B
1,030 kg 1,220 kg
No other source of supply can be found for the next period. Information relating to the three products manufactured by LMN Limited is as follows.
Quantity of manufactured:
material
used
Material A (kg) Material B (kg) Maximum sales demand (units) Contribution per unit sold
per
L
M
N
2 5 120 £15
1 3 160 £12
4 7 110 £17.50
unit
Owing to the perishable nature of the products, no finished goods stocks are held. You are required to; (a) Recommend a production mix which will maximize the profits of LMN Limited for the forthcoming period. (b) LMN Limited has a valued customer to whom they wish to guarantee the supply of 50 units of each product next period. Would this alter your recommended production plan?
Exercise 19 Gill Limited manufactures three products E, F and G. The products are all finished on the same machine. This is the only mechanized part of the process. During the next period the production manager is planning an essential major maintenance overhaul of the machine. This will restrict the available machine hours to 1,400 hours for the next period. The data for the three products is as follows. Page | 23
Selling price Variable cost Fixed production cost Other fixed cost Profit Maximum demand (units/period)
E £/unit 30 13 10 2 5 250
F £/unit 17 6 8 1 2 140
G £/unit 21.00 9.00 6.00 3.50 2.50 130
No stocks are held. Fixed production costs are absorbed using a machine hour rate of £2 per machine hour. You are required to; Determine the production plan that will maximize profit for the forthcoming period.
References
Louderback J and Holmen JS, Managerial Accounting, Tenth Edition Ross SA, Westerfield RW and Jordan BD, Fundamentals of Corporate Finance, Ninth Edition CFA Level 2 Book 2; Financial Reporting and Analysis and Corporate Finance http://www.investopedia.com
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