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Accounting Principles II: Cost-Volume-
Profit Relationships
Complete Study Guide
Cost Behavior
The way a specific cost reacts to changes in activity levels is called cost behavior. Costs may stay the same or may change proportionately in response to a change in activity. Knowing how a cost reacts to a change in the level of activity makes it easier to create a budget, prepare a forecast, determine how much profit a new product will generate, and determine which of two alternatives should be selected. Fixed costs Fixed costs are those that stay the same in total regardless of the number of units produced or sold. Although total fixed costs are the same, fixed costs per unit changes as fewer or more units are produced. Straight‐line depreciation is an example of a fixed cost. It does not matter whether the machine is used to produce 1,000 units or 10,000,000 units in a month, the depreciation expense is the same because it is based on the number of years the machine will be in service. Variable costs Variable costs are the costs that change in total each time an additional unit is produced or sold. With a variable cost, the per unit cost stays the same, but the more units produced or sold, the higher the total cost. Direct materials is a variable cost. If it takes one yard of fabric at a cost of $5 per yard to make one chair, the total materials cost for one chair is $5. The total cost for 10 chairs is $50 (10 chairs × $5 per chair) and the total cost for 100 chairs is $500 (100 chairs × $5 per chair). Graphically, the total fixed cost looks like a straight horizontal line while the total variable cost line slopes upward.
The graphs for the fixed cost per unit and variable cost per unit look exactly opposite the total fixed costs and total variable costs graphs. Although total fixed costs are constant, the fixed cost per unit changes with the number of units. The variable cost per unit is constant. When cost behavior is discussed, an assumption must be made about operating levels. At certain levels of activity, new machines might be needed, which results in more depreciation, or overtime may be required of existing employees, resulting in higher per hour direct labor costs. The definitions of fixed cost and variable cost assumes the company is operating or selling within the relevant range (the shaded area in the graphs) so additional costs will not be incurred.
at zero units of activity. To compute the variable cost per unit, the slope of the line is determined by choosing two points and dividing the change in their cost by the change in the units of activity for the two points selected. For example, using data from the following example, if 36,000 gallons of water and 60,000 gallons of water were selected, the change in cost is $6,000 ($20,000 – $14,000) and the change in activity is 24,000 (60,000 – 36,000). This makes the slope of the line, the variable cost, $0.25 ($6,000 ÷ 24,000), and the fixed costs $5,000. See the graph to illustrate the point. High ‐ low method. The high ‐ low method divides the change in costs for the highest and lowest levels of activity by the change in units for the highest and lowest levels of
activity to estimate variable costs. The high point of activity is 75,000 gallons and the low point is 32,000 gallons. The variable cost per unit is estimated to be $0.163. It was calculated by dividing $7,000 ($20,000 – $13,000) by 43,000 (75,000 – 32,000) gallons of water. Least ‐ squares regression analysis. The least ‐ squares regression analysis is a statistical method used to calculate variable costs. It requires a computer spreadsheet program (for example, Excel) or calculator and uses all points of data instead of just two points like the high‐low method.
Cost-Volume-Profit Analysis
Cost-volume-profit (CVP) analysis is used to determine how changes in costs and volume affect a company's operating income and net income. In performing this analysis, there are several assumptions made, including: Sales price per unit is constant. Variable costs per unit are constant. Total fixed costs are constant. Everything produced is sold. Costs are only affected because activity changes. If a company sells more than one product, they are sold in the same mix. CVP analysis requires that all the company's costs, including manufacturing, selling, and administrative costs, be identified as variable or fixed. Contribution margin and contribution margin ratio Key calculations when using CVP analysis are the contribution margin and the contribution margin ratio. The contribution margin represents the amount of income or profit the company made before deducting its fixed costs. Said another way, it is the amount of sales dollars available to cover (or contribute to) fixed costs. When calculated as a ratio, it is the percent of sales dollars available to cover fixed costs. Once fixed costs are covered, the next dollar of sales results in the company having income. The contribution margin is sales revenue minus all variable costs. It may be calculated using dollars or on a per unit basis. If The Three M's, Inc., has sales of $750,000 and total variable costs of $450,000, its contribution margin is $300,000. Assuming the company sold 250,000 units during the year, the per unit sales price is $3 and the total variable cost per unit is $1.80. The contribution margin per unit is $1.20. The contribution margin ratio is 40%. It can be calculated using either the contribution margin in dollars or the contribution
This income statement format is known as the contribution margin income statement and is used for internal reporting only. The $1.80 per unit or $450,000 of variable costs represent all variable costs including costs classified as manufacturing costs, selling expenses, and administrative expenses. Similarly, the fixed costs represent total manufacturing, selling, and administrative fixed costs. Break ‐ even point in dollars. The break‐even point in sales dollars of $750, is calculated by dividing total fixed costs of $300,000 by the contribution margin ratio of 40%. Another way to calculate break‐even sales dollars is to use the mathematical equation.
In this equation, the variable costs are stated as a percent of sales. If a unit has a $3.00 selling price and variable costs of $1.80, variable costs as a percent of sales is 60% ($1.80 ÷ $3.00). Using fixed costs of $300,000, the break‐even equation is shown below. The last calculation using the mathematical equation is the same as the break‐ even sales formula using the fixed costs and the contribution margin ratio previously discussed in this chapter. Break ‐ even point in units. The break‐even point in units of 250,000 is calculated by dividing fixed costs of $300,000 by contribution margin per unit of $1.20.
Targeted income CVP analysis is also used when a company is trying to determine what level of sales is necessary to reach a specific level of income, also called targeted income. To calculate the required sales level, the targeted income is added to fixed costs, and the total is divided by the contribution margin ratio to determine required sales dollars, or the total is divided by contribution margin per unit to determine the required sales level in units. Using the data from the previous example, what level of sales would be required if the company wanted $60,000 of income? The $60,000 of income required is
called the targeted income. The required sales level is $900,000 and the required number of units is 300,000. Why is the answer $900,000 instead of $810, ($750,000 [break‐even sales] plus $60,000)? Remember that there are additional variable costs incurred every time an additional unit is sold, and these costs reduce the extra revenues when calculating income. This calculation of targeted income assumes it is being calculated for a division as it ignores income taxes. If a targeted net income (income after taxes) is being calculated, then income taxes would also be added to fixed costs along with targeted net income. Assuming the company has a 40% income tax rate, its break‐even point in sales is $1,000,000 and break‐even point in units is 333,333. The amount of income taxes used in the calculation is $40,000 ([$60,000 net income ÷ (1 – .40 tax rate)]
by budgeted sales. If the Three M's, Inc., has budgeted sales of $800,000, its margin of safety is $50,000 ($800,000 budgeted sales – $750,000 break‐even sales) or 6.7% ($50,000 ÷ $750,000), a rather low margin of safety. If, however, its budgeted sales are $900,000, its margin of safety is $150,000 ($900,000 budgeted sales – $750,000 break‐even sales) or 20% ($150,000 ÷ $750,000). The competition, economy, and assumptions in the sales budget must be reviewed by management to assess whether 20% is a comfortable margin of safety.
Sensitivity Analysis
A business environment can change quickly, so a business should understand how sensitive its sales, costs, and income are to changes. CVP analysis using the break‐even formula is often used for this analysis. For example, marketing suggests a higher quality product would allow The Three M's, Inc., to raise its selling price 10%, from $3.00 to $3.30. To increase the quality would increase variable costs to $2.00 per unit and fixed costs to $350,000. If The Three M's, Inc., followed this scenario, its break‐even in units would be 269,231. These changes in variable costs and sales result in a higher break‐even point in units than the 250,000 break‐even units calculated with the original assumptions. The critical question is, “Will the customers continue to purchase, and are new or existing customers identified that will purchase the additional 19,231 units of the product required to break even at the higher sales price?”
