Introduction to Accounting IM51005B Lecture 7 Cost Volume Profit (CVP) Analysis Dr Sarah Lauwo

Types of Cost behaviour Patterns Recall the summary of our cost behaviour discussion from Previous lecture

Variable Costs and Activity Base Units produced Machine hours Units produced Machine hours A measure of the event causing the incurrence of a variable cost – a cost driver A measure of the event causing the incurrence of a variable cost – a cost driver Miles driven Labour hours Miles driven Labour hours

Cost- Volume Profit The accountant’s cost–volume–profit model Constant variable cost and selling price is assumed. Only one break-even point, and profit increases as volume increases. The objective is to provide an accurate representation of cost and revenue behaviour only within the relevant range of output.

The Break-Even Point (BEP) The break-even point is the point in the volume of activity where the organization’s revenues and expenses are equal.

B-E-P At this amount of sales, the organization has no profit or loss; it breaks even. To compute BEP, we need to shows the total contribution margin, which is total sales revenue minus total variable expenses. Total contribution margin is the amount of revenue that is available to contribute to covering fixed expenses after all variable expenses have been covered

Equation Approach (£500 × X) (£300 × X) – – £80,000 = 0 (£200X) – Sales revenue – Variable expenses – Fixed expenses = Profit At BEP : Profit = 0 Unit sales price Sales volume in units × Unit variable expense Sales volume in units × (£500 × X) (£300 × X) – The equation approach can be used to find the break-even point. This approach is based on the profit equation. Income (or profit) is equal to sales revenue minus expenses. Expenses can be separated in variable and fixed expenses. At the break-even point, income is $0. (LO1) – £80,000 = 0 (£200X) – £80,000 = 0 X = 400 Units

Contribution-Margin Approach Consider the following information developed by the accountant at Curl, Inc.: For each additional surf board sold, Curl generates $200 in contribution margin. Curl, Inc. manufactures surf boards. Each surf board sells for $500 and has variable costs of $300. (LO2) Therefore, the contribution margin per unit is $200. When enough surf boards are sold so that the total contribution margin is $80,000, Curl Inc. will break even for the period. (LO2)

Contribution-Margin Approach Fixed expenses Unit contribution margin Break-even point (in units) = To compute the break-even volume of surf boards, divide the total fixed expenses by the unit contribution margin. For Curl, Inc., $80,000 is divided by $200, which is 400 surf boards. That means that the break-even point is 400 surf boards. (LO2) $80,000 $200 = 400 surf boards

Contribution-Margin Approach Here is the proof! 400 × $500 = $200,000 400 × $300 = $120,000 The break-even point of 400 units can be proven by first calculating total sales: multiply $500 x 400 units for $200,000 in total sales. The variable expenses are $300 per unit x 400 units, which is $120,000. Total sales less total variable expenses is total contribution margin of $80,000. When fixed expenses of $80,000 are deducted from the total contribution margin, leaving $0 in net income. (LO2)

Contribution Margin Ratio Calculate the break-even point in sales dollars rather than units by using the contribution margin ratio. Contribution margin Sales = CM Ratio Sometimes management prefers that the break-even point be expressed in sales dollars rather than units. This can be accomplished by using the contribution margin ratio. The formula for the contribution margin ratio is contribution margin divided by sales. Then divide fixed expenses by the contribution margin ratio to determine the total sales dollars at the break-even point. (LO2) Fixed expense CM Ratio Break-even point (in sales dollars) =

Graphing Cost-Volume-Profit Relationships Viewing CVP relationships in a graph gives managers a perspective that can be obtained in no other way. Consider the following information for Curl, Inc.: While the break-even point conveys useful information to management, it does not show how profit changes as activity changes. Managers will often use a cost-volume-profit (CVP) graph to show the relationship between profit and volume of activity. Consider Curl, Inc. At sales of 300 unit, Curl Inc. incurs a net loss of $20,000. The break-even point occurs at 400 units and a $20,000 profit occurs when sales are at 500 units. (LO3)

Cost-Volume-Profit Graph Total expenses In step 4, the total expense line is drawn. Since the total expenses at zero units sold is only the fixed costs, the total expense line crosses the vertical axis at the amount of fixed costs. This line then passes through the point plotted in step 3. (LO3) Fixed expenses

Cost-Volume-Profit Graph Total expenses In step 5, compute the total sales revenue at any volume. Plot that point. For Curl, Inc., look at 500 units. Multiply the unit sales price of $500 per unit times 500 units for total sales revenue of $250,000. (LO3) Fixed expenses

Cost-Volume-Profit Graph Total sales Total expenses In Step 6, draw the total revenue line. This line passes through the point plotted in step 5 and the origin. (LO3) Fixed expenses

Cost-Volume-Profit Graph Total sales Profit area Break-even point Total expenses In step 7, the break-even point, the profit area, and the loss area are all labeled. The break-even point is the point at which total expenses and total sales are equal, which is where the two lines cross. The profit area is the area where the total sales line is above the total expenses line. This is where revenues exceed expenses. The loss area is the area where the total expenses line is above the total sales line. This is where expenses exceeds revenues. (LO3) Fixed expenses Loss area

Profit-Volume Graph Some managers like the profit-volume graph because it focuses on profits and volume. Break-even point Profit area Yet another approach to graphing cost-volume-profit relationships is called a profit-volume graph. It highlights the amount of profit or loss. The graph intercepts the vertical axis at the amount equal to fixed expenses at the zero activity level. The graph crosses the horizontal axis at the break-even point. The vertical distance between the horizontal axis and the profit line, at a particular level of sales volume, is the profit or loss at that volume. (LO3) Loss area

Target Net Profit We can determine the number of surfboards that Curl must sell to earn a profit of $100,000 using the contribution margin approach. Fixed expenses + Target profit Unit contribution margin = Units sold to earn the target profit When a company has a net profit they are trying to achieve, or a target net profit, the contribution margin approach can be used to determine the number of units that must be sold. This is very similar to finding the break-even point. The numerator is fixed expenses plus the target profit. The denominator is the contribution margin per unit. The result is the units that need to be sold to earn the targeted net profit. (LO4) $80,000 + $100,000 $200 = 900 surf boards

Equation Approach Sales revenue – Variable expenses – Fixed expenses = Profit ($500 × X) ($300 × X) – $80,000 = $100,000 The equation approach also can be used to find the units of sales required to earn a target net profit. Recall that in the profit equation, profit is equal to revenues minus variable and fixed expenses. Recall that profit was set to zero to determine the break-even point. When management has determined a target net profit greater than zero, that number becomes profit variable in the equation. (LO4) ($200X) = $180,000 X = 900 surf boards

Applying CVP Analysis Safety Margin The difference between budgeted sales revenue and break-even sales revenue. The amount by which sales can drop before losses occur. The safety margin of an enterprise is the difference between the budgeted sales revenue and the break-even sales revenue. This is the amount by which sales can drop before losses occur. (LO4)

Assumptions Underlying CVP Analysis Selling price and variable cost per unit remain constant throughout the entire relevant range. Costs are linear over the relevant range. Profits are calculated on a variable costing basis Costs can be accurately divided into their fixed and variable elements In manufacturing firms, inventories do not change (units produced = units sold). The analysis applies over the relevant range only For any cost-volume-profit analysis to be valid, the following important assumptions must be reasonably satisfied within the relevant range. 1. The behavior of total revenue is linear (straight-line). This implies that the price of the product or service will not change as sales volume varies within the relevant range. 2. The behavior of total expenses is linear (straight-line) over the relevant range. This implies the following more specific assumptions. a. Expenses can be categorized as fixed, variable, or semivariable. Total fixed expenses remain constant as activity changes, and the unit variable expense remains unchanged as activity varies. b. The efficiency and productivity of the production process and workers remain constant. 3. In multiproduct organizations, the sales mix remains constant over the relevant range. 4. In manufacturing firms, the inventory levels at the beginning and end of the period are the same. This implies that the number of units produced during the period equals the number of units sold. (LO6)

CVP Relationships and the Income Statement On a traditional income statement, cost of goods sold includes both variable and fixed manufacturing costs, as measured by the firm’s product-costing system. The gross margin is computed by subtracting cost of goods sold from sales. Selling and administrative expenses are then subtracted; each expense includes both variable and fixed costs. The traditional income statement does not disclose the breakdown of each expense into its variable and fixed components. (LO7)

CVP Relationships and the Income Statement Many operating managers find the traditional income-statement format difficult to use, because it does not separate variable and fixed expenses. Instead they prefer the contribution income statement. The contribution format highlights the distinction between variable and fixed expenses. On the contribution income statement, all variable expenses are subtracted from sales to obtain the contribution margin. All fixed costs are then subtracted from the contribution margin to obtain net income. Operating managers frequently prefer the contribution income statement, because its separation of fixed and variable expenses highlights cost-volume-profit relationships. It is readily apparent from the contribution-format statement how income will be affected when sales volume changes by a given percentage. (LO7)

Cost Structure and Operating Leverage The cost structure of an organization is the relative proportion of its fixed and variable costs. Operating leverage is: the extent to which an organization uses fixed costs in its cost structure. greatest in companies that have a high proportion of fixed costs in relation to variable costs. The cost structure of an organization is the relative proportion of its fixed and variable costs. Cost structures differ widely among industries and among firms within an industry. A company using a computer-integrated manufacturing system has a large investment in plant and equipment, which results in a cost structure dominated by fixed costs. In contrast, a home builder contractor’s cost structure has a much higher proportion of variable costs. The highly automated manufacturing firm is capital-intensive, whereas the home building contractor is labor-intensive. An organization’s cost structure has a significant effect on the sensitivity of its profit to changes in volume. The extent to which an organization uses fixed costs in its cost structure is called operating leverage. The operating leverage is greatest in firms with a large proportion of fixed costs, low proportion of variable costs, and the resulting high contribution margin ratio. (LO8) 7-24

Measuring Operating Leverage factor Contribution margin Net income = The managerial accountant can measure a firm’s operating leverage, at a particular sales volume, using the operating leverage factor. The formula is contribution margin divided by net income. At sales of 500 surfboards, Curl’s contribution margin is $100,000 and net income is $20,000; therefore, its operating leverage factor is 5. (LO8) $100,000 $20,000 = 5

Measuring Operating Leverage A measure of how a percentage change in sales will affect profits. If Curl increases its sales by 10%, what will be the percentage increase in net income? The operating leverage factor is a measure, at a particular level of sales, of the percentage impact on net income of a given percentage change in sales revenue. Multiplying the percentage change in sales revenue by the operating leverage factor yields the percentage change in net income. At Curl, Inc., a 10% increase in sales would be multiplied by the operating leverage of 5. Therefore, if Curl experiences a 10% increase in sales, it can expect a 50% increase in net income. (LO8)

CVP Analysis, Activity-Based Costing, and Advanced Manufacturing Systems An activity-based costing system provides a much more complete picture of cost-volume-profit relationships and, thus, it provides better information to managers. Break-even point = Fixed costs Unit contribution margin Traditional cost-volume-profit analysis focuses on the number of units sold as the only cost and revenue driver. Sales revenue is assumed to be linear in units sold. Moreover, costs are categorized as fixed or variable, with respect to the number of units sold, within the relevant range. This approach is consistent with traditional product-costing systems, in which cost assignment is based on a single, volume-related cost driver. In CVP analysis, as in product costing, the traditional approach can be misleading or provide less than adequate information for various management purposes. An activity based costing system provides a much more complete picture of cost-volume-profit relationships and, thus, it provides better information to managers. (LO9)

A Move Toward JIT and Flexible Manufacturing Overhead costs like setup, inspection, and material handling are fixed with respect to sales volume, but they are not fixed with respect to other cost drivers. This is the fundamental distinction between a traditional CVP analysis and an activity-based costing CVP analysis. The point of this section is that activity-based costing provides a richer description of a company’s cost behavior. Just as ABC can improve an organization’s product-costing system, it also can facilitate a deeper understanding of cost behavior and CVP relationships. (LO10)

Effect of Income Taxes Target after-tax net income 1 - t = Income taxes affect a company’s CVP relationships. To earn a particular after-tax net income, a greater before-tax income will be required. Target after-tax net income 1 - t = Before-tax net income The requirement that companies pay income taxes affects their cost-volume-profit relationships. To earn a particular after-tax net income, a greater before-tax income will be required. To determine what the before-tax net income is, the after-tax net income is divided by 1 minus the tax rate. The formulas presented in this chapter can now be used with the before-tax net income to provide for the effect of taxes. (LO11)