Cost-volume-Profit Analysis Cost-volumesprot relationship: A primary function of accounting is the collection of cost and revenue data which may then be used to examine the existing relationships between cost behaviour and revenue behaviour. Any analysis, whether graphical or algebraic, makes certain assumptions about the behaviour of costs and revenue. In its simplest form. cost-volume-prot analysis makes the following assumptions: 1. Rovenue per unit of output is constant. Thus total rEvenue varies directly with volume [TR = P'CL Total Revenue is Price of each unit * the unit Else-Id]. 2. Costs can he classied to he either fixed or variable [FC. vc]. a. Fixed costs are those costs which remain constant over the time period considered for all levels of out-put. Examples of costs in this category are: depreciation, rent. property taxes. supervision and management salaries. Since fixed costs are constant in total. they vary per unit of output. They decrease per unit of output as volume increases and increase per unit of output as volume decreases. in. 1li'ariable costs are costs that are constant per unit of output regardless of volume and thus fluctuate in total amount as volume fluctuates. Examples of costs in this category antI direct matErial costs. a hoot labour costs and sales commissions. The above assumptions presenta simplied view of the real world. Fixed costs are not constant across all levels of output but tend to change in a step-like manner. Per unit variable costs are not always constant but are influenoed by economies of scale. There is no blaclr. and white classification of costs into fixed costs and variable costs; rather many costs are semi-variable. that is. they contain a xed component as well as a variable component. However, for purposes of an uncomplicated introductory analysis. the assumptions made serve a useful purpose. Using these simplifying assumptions, the behaviour of revenue and the behaviour of costs may be represented graphically by straight-line diagrams as shown in Figures 1 and 1. Figure 1. Revenue behaviour Figure 2. Cost behaviour Total Cost Total Revenue Sales S Total Variable Cost Fixed Cost Volume of output Volume of output The following components are basic to cost-volume-profit relationships and mathematical notation will be used for these components as indicated: X = Volume of output P = Selling price (revenue) per unit of output TR = Total revenue TC = Total cost FC = Fixed cost TVC = Total variable cost VC - Variable cost per unit of output O NI - Net income (profit). The Accounting Relationships (income statement equations) Formula 1 TOTAL REVENUE = TOTAL COST + NET INCOME (TR = TC + NI) is basic to cost-volume-profit analysis; the following relationships are also useful: Formula 2 TOTAL REVENUE = VOLUME x UNIT REVENUE ( TR = (X)(P) ) Formula 3 TOTAL COST = FIXED COST + TOTAL VARIABLE COST (TC = FC + TVC) 2Formula 4 TOTAL VARIABLE COST = VOLUME x VARIABLE COST PER UNIT ( TVC = (X)(VC) ) Formula 5 TOTAL REVENUE = FIXED COST + TOTAL VARIABLE COST + NET INCOME (TR = FC + TVC + NI) Break-even Analysis The most popular approach to cost-volume-profit analysis is referred to as break- even analysis. The break-even approach focuses on the profitability of the business and is specifically concerned with identifying the level of output at which the business neither makes a profit nor sustains a loss, that is the level of output at which NET INCOME = 0. This level of output, at which NI = 0, is referred to as the break-even point and is obtainable from Formula 1 (or Formula 5) above. Since NI = 0 the break-even point is the level of output at which TOTAL REVENUE = TOTAL COST The relationship between revenue and costs at different levels of output may be portrayed graphically by showing revenue behaviour (Figure 1, above) and cost behaviour (Figure 2, above) on the same graph. The resulting graph shows the break-even point and is known as a break-even chart (see Figure 3, below).Figure 3. Break-even Chart There are several linear lines involved: Total Revenue K Break-even Break-even Profit [TR], Y = m1. X sales point Total Cost [TC], Y = m2. X + b Total Variable Sales $ Cost [TVC], Y = m3. X Fixed Cost [FC], Y = b Loss X Break-even Volume of output [X] Volume (In units or as a % of capacity) Notes to the charts 1. The horizontal axis is used to represent volume of output either as a number of units or as a percent of capacity. The vertical axis represents dollar values (sales revenue). The origin is at zero-representing zero volume and zero dollars. 2. The total revenue line is drawn by plotting two or more total revenue points (one of which is always the origin) and joining them. 3. The fixed cost line is drawn parallel to the horizontal axis from a point on the vertical axis which represents total fixed cost dollars. 4. The total cost line is drawn by plotting two or more total cost points (one of which is always the point where the fixed cost line starts on the vertical axis) and joining them. 5. The point where the total revenue line and the total cost line intersect is the break-even point. 6. The point of intersection on the horizontal axis of the perpendicular drawn from the break- even point to the horizontal axis indicates the break-even volume in units or as a percent of capacity. 7. The point of intersection on the vertical axis of the perpendicular drawn from the break-even point to the vertical axis indicates the break-even volume in dollars ($Sales).8. The area between the horizontal axis and the fixed cost line represents the fixed cost in dollars. 9. The area between the fixed cost line and the total cost line represents the total variable cost in dollars for the various levels of operations. 10. The area between the total revenue line and the total cost line to the left of the break- even point represents the loss area where total revenue is less than total cost. 11. The area between the total cost line and the total revenue line to the right of the break- even point represents the profit area where total revenue is greater than total cost. The graphical approach resulting in a break-even chart is complemented by an algebraic approach which utilizes Formulae 1 and 2. The cases are the two distinct situations which may be encountered depending on the accounting data that is available. For the first situation, the accounting information is in terms of units. For the second situation, the accounting information is in terms of total dollars. The information on Excel Spread-Sheet programming techniques, mathematical built-in functions for common use, finance use, and for business use are described in Excel through the help feature.Historical Price Data Marketing Year Seed Oil Mash Average Price Index Average Price Index Average Price Index $/short ton $/short ton $/short ton 127.7 317.8 63 192.4 465 87 242 662.2 105 242 668.2 111 274 791.3 124 6 242 732 108 290 951 134 8 347.2 1123 153 436 1297.3 193 10 422.8 1312 187 11 466 1416 193 12 582 1664 247 13 508 1317.4 242 14 428 1182.4 197 15 434 1334.4 210Sunflower oil contains a number of fatty acids, some which are desirable in food products and others that are not. One desirable fatty acid is oleic acid. TourneSol produces high oleic oil for the wholesale market, and requires that the oleic acid content be a minimum of 77%. Sunflower oil also contains trace amounts of iodine. The market requires that that iodine content be a minimum of 0.78% and maximum of 0.88% The oleic acid and iodine content for the sunflower seeds from the three suppliers is given in the table below. Supplier Oleic Acid lodine A 72% 0.95% B 82% 0.85% C 65% 0.72% For all three suppliers, it is expected that the average yield of oil from the seeds is 30%. There is no net loss of material, so the yield of mash from the same supply is expected to be 70%. Because the oleic acid and iodine content varies across the three suppliers, so does the price. It is expected that the cost of supply from the suppliers will be a percentage of the market average price of seeds. Supplier Cost as % of Average Market Price of Seed A 85% B 100% C 90%% The company faces an additional variable production cost of $10/short ton and an estimated fixed cost of $1,750,000 over the upcoming production period. The company is asking you to provide a recommendation on the amount of raw material it should purchase from each supplier to minimize its cost of feedstock. Management is also looking for an analysis on the profitability of the company in the next production cycle