Cost-Volume-Profit Analysis: Understanding Revenue, Cost, Profit Relationship, Lecture notes of Management Theory

An in-depth analysis of cost-volume-profit (cvp) analysis, a financial management technique used to examine the behavior of total revenues, total costs, and operating profit as changes occur in output level, selling price, variable costs, or fixed costs. The concepts of revenues, cost drivers, breakeven point, and sensitivity analysis, among others.

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Management Accounting
Chapter 8:
Cost-Volume-Profit analysis (CVP: examines the behavior of total revenues, total costs and
operating profit as changes occur in the output level, selling price, variable costs or fixed costs;
provides a sweeping financial overview of the planning process
revenues: inflows of assets received in exchange for products or services provided to customers
revenue driver: a factor that affects revenue
General case: The most detailed way of predicting total revenues and total costs is to consider
multiple revenue drivers and multiple cost drivers. โ†’ extensive and time-consuming
The term CVP analysis is widely used as representing the special case where a single revenue and
cost driver are used.
Our restriction to units of output as the sole revenue or cost driver is important to keep in mind. It
means that in the CVP model, changes in the level of revenues and costs arise only because the
output level changes.
We assume that: Total costs=Variable costs+fixed costs
operating profit: total revenues from operations minus total costs from operations (excluding
income taxes)
Operating profit=Total revenues โ€“ Total costs
Net profit: operating profit plus non-operating revenues (such as interest revenue) minus non-
operating costs (such as interest cost) minus income taxes
Net profit=operating profit โ€“ income taxes
abbreviations:
USP=unit selling price; UVC=unit variable cost; UCM=unit contribution margin (USP-UVC);
FC=fixed costs; Q=quantity of output units sold (or manufactured); OP=operating profit;
TOP=target operating profit; NP=Net profit; QT=the number of units sold to earn the target profit
CVP assumptions:
1. Total costs can be divided into a fixed component and a component that is variable with
respect to the level of output
2. The behavior of total revenues and total costs is linear in relation to output units within the
relevant range
3. The unit selling price, unit variable costs and unit fixed costs are known and are constant
4. The analysis either covers a single product or assumes that the proportion of different
products when multiple products are sold will remain constant as the level of total units sold
changes
5. All revenues and costs can be added and compared without taking into account the time
value of money
6. Changes in the level of revenues and costs arise only because of changes in the number of
products (or service) units produced and sold. The number of output units is the only
revenue and cost driver
breakeven point: that quantity of output where total revenues and total costs are equal, that is,
where the operating profit is zero
Three methods for determining the breakeven point:
โ€“Equation method: the income statement can be expressed in equation form as follows:
Revenues โ€“ Variable costs โ€“ Fixed costs = Operating profit
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Management Accounting Chapter 8: Cost-Volume-Profit analysis (CVP: examines the behavior of total revenues, total costs and operating profit as changes occur in the output level, selling price, variable costs or fixed costs; provides a sweeping financial overview of the planning process revenues: inflows of assets received in exchange for products or services provided to customers revenue driver: a factor that affects revenue General case: The most detailed way of predicting total revenues and total costs is to consider multiple revenue drivers and multiple cost drivers. โ†’ extensive and time-consuming The term CVP analysis is widely used as representing the special case where a single revenue and cost driver are used. Our restriction to units of output as the sole revenue or cost driver is important to keep in mind. It means that in the CVP model, changes in the level of revenues and costs arise only because the output level changes. We assume that: Total costs=Variable costs+fixed costs operating profit: total revenues from operations minus total costs from operations (excluding income taxes) Operating profit=Total revenues โ€“ Total costs Net profit: operating profit plus non-operating revenues (such as interest revenue) minus non- operating costs (such as interest cost) minus income taxes Net profit=operating profit โ€“ income taxes abbreviations: USP=unit selling price; UVC=unit variable cost; UCM=unit contribution margin (USP-UVC); FC=fixed costs; Q=quantity of output units sold (or manufactured); OP=operating profit; TOP=target operating profit; NP=Net profit; QT=the number of units sold to earn the target profit CVP assumptions:

  1. Total costs can be divided into a fixed component and a component that is variable with respect to the level of output
  2. The behavior of total revenues and total costs is linear in relation to output units within the relevant range
  3. The unit selling price, unit variable costs and unit fixed costs are known and are constant
  4. The analysis either covers a single product or assumes that the proportion of different products when multiple products are sold will remain constant as the level of total units sold changes
  5. All revenues and costs can be added and compared without taking into account the time value of money
  6. Changes in the level of revenues and costs arise only because of changes in the number of products (or service) units produced and sold. The number of output units is the only revenue and cost driver breakeven point: that quantity of output where total revenues and total costs are equal, that is, where the operating profit is zero Three methods for determining the breakeven point:
  • Equation method: the income statement can be expressed in equation form as follows: Revenues โ€“ Variable costs โ€“ Fixed costs = Operating profit

(USPxQ) โ€“ (UVCxQ) โ€“ FC = OP โ†’ set operating profit equal to zero

  • contribution margin method: an algebraic manipulation of the equation method; contribution margin is equal to revenues minus costs of the output (a product or service) that vary with respect to the units of output (USPxQ) โ€“ (UVCxQ) โ€“ FC = OP โ†’ Q = (FC + OP)/UCM โ†’ at the breakeven point, OP= Breakeven number of units=(FC)/(UCM) contribution income statement: groups line items by cost behavior pattern to highlight the contribution margin
  • Graph method: we plot the total costs line and the total revenue line โ†’ point of intersection = breakeven point
    1. Total cost line: the sum of fixed costs and the variable costs
    2. Total revenues line: one convenient starting point is zero revenues at the zero output level, select a second point by choosing any other convenient output level and determine its total revenues Target operating profit: how many units must be sold to earn an operating profit of xEUR? Revenues โ€“ Variable costs โ€“ Fixed costs = Target profit QT=(FC+TOP)/UCM PV graph: shows the impact on operating profit of changes in the output level; the PV line can be drawn using two points, one convenient point X is the level of fixed costs at zero output, which is also the operating loss at this output level. A second convenient point Y is the breakeven point โ†’ line is drawn by connecting X and Y and draw line beyond Y Impact of income taxes: Target net profit = (Operating profit) โ€“ ((Operating profit)x(Tax rate)) Target net profit = (Operating profit) x (1 โ€“ Tax rate) Operating profit = (Target net profit)/(1 โ€“ Tax rate) The presence of income taxes will not change the breakeven point. Why? Because, by definition, operating profit at the breakeven point is zero, and thus no income taxes will be paid. However, other types of taxes may affect the breakeven point. Sensitivity analysis and uncertainty: Sensitivity analysis: what-if technique that examines how a result will change if the original predicted data are not achieved or if an underlying assumption changes In the context of CVP, sensitivity analysis will answer such questions as: What will operating profit be if the output level decreases from the original prediction? The sensitivity to various possible outcomes broadens managers' perspectives as to what might actually occur despite their well-laid plans Using spreadsheets, managers can easily conduct CVP-based sensitivity analyses to examine the effect and interaction of changes in selling prices, unit variable costs, fixed costs and target operating profits. One aspect of sensitivity analysis is the margin of safety: which is the excess of budgeted revenues over the breakeven revenues; the answer to the what-if question: if budgeted revenues are above breakeven and drop, how far can they fall below budget before the breakeven point is reached? Such a fall could be due to a competitor having a better product, poorly executed marketing and so on.

Contribution margin percentage: the total contribution margin divided by revenues variable-cost percentage: the total variable costs (with respect to units of output) divided by revenues gross margin percentage: gross margin divided by revenues