Cost Chapter 16
Concepts used to measure risk Margin of safety Operating leverage
margin of safety the units sold or expected to be sold or sales revenue earned or expected to be earned above the break-even volume. - If a firm's margin of safety is large given the expected sales for the coming year, the risk of suffering losses is less
Two frequently used approaches to finding the break-even point are
the operating income approach and the contribution margin approach.
The graph in Exhibit 16.2 can be used to assess Gordon's profit (or loss) at any level of sales activity. For example, the profit associated with the sale of 40 units can be read from the graph by
(1) drawing a vertical line from the horizontal axis to the profit line and (2) drawing a horizontal line from the profit line to the vertical axis. As we can see, the profit associated with sales of 40 units is $100. The profit-volume graph, while easy to interpret, fails to reveal how costs change as sales volume changes. A more comprehensive graph provides this detail.
Break-even units =
(Total fixed cost)/Price − Variable cost per unit)
Basic Concepts for CVP Analysis
- A useful tool for organizing the firm's costs into fixed and variable categories is the contribution-margin-based income statement. - Recall that operating income is income before income taxes - Operating income includes only revenues and expenses from the firm's normal operations.
Graphical Representation of CVP Relationships - Cost-Volume-Profit Graph
- Depicts relationships among cost, volume, and profits - To obtain more detailed relationships, it is necessary to graph the total revenue line and the total cost line
Cost-Volume-Profit (CVP) Analysis
- Emphasizes the interrelationships of costs, quantity sold, and price - Brings together all of the financial information of the firm
Common fixed expenses:
- Fixed costs that are not traceable to the segments - Would remain even if one of the segments was eliminated
Multiple-Product Analysis Direct fixed expenses
- Fixed costs that can be traced to each segment - Would be avoided if the segment did not exist
Sensitivity Analysis and CVP
- Sensitivity analysis: What-if technique that examines the impact of changes in underlying assumptions on an answer - One can input data and set up formulas to calculate break-even points and expected profits - Data can be varied as desired to see what impact changes have on the expected profit
Break-Even Point and Target Income in Sales Revenue
- Units-sold measure can be converted to a sales-revenue measure by multiplying the unit sales price by the units sold - Any answer expressed in units sold can be easily converted to an answer expressed in terms of sales revenue, if the break-even units can be easily computed. This is seldom the case, however, in a multiproduct firm.
Steps in implementing Units-sold approach to cvp Analysis
1: Determine what a unit is 2; separate costs into fixed and variable components - CVP focuses on the firm as a whole and all costs of the company are taken into account - Variable costs include all costs that increase as more units are sold, including direct materials, direct labor, variable overhead, and variable selling and administrative costs. Similarly, fixed costs are composed of all fixed overhead and fixed selling and administrative expenses.
Contribution margin ratio
= (Price − Variable cost per unit)/Price = (Sales − Total variable cost)/Sales
Variable product cost per unit
= Direct materials + Direct labor + Variable overhead
Variable cost per unit
= Direct materials + Direct labor + Variable overhead + Variable selling expense
Contribution margin per unit
= Price − Variable cost per unit
Contribution Margin Approach
A refinement of the equation approach is the contribution margin approach. It simply recognizes that at break-even, the total contribution margin equals the fixed expenses - The contribution margin is sales revenue minus total variable costs.
Operating income = Total revenue - [Fixed costs + (Unit variable cost × Number of units) + (Setup cost × Number of setups) + (Engineering cost × Number of engineering hours)]
Break-even units = [Fixed costs + (Setup cost × Number of setups) + (Engineering cost × Number of engineering hours)]/Price - Unit variable cost)
CVP Analysis in Nonprofit entities
CVP analysis is helpful in not-for-profit entities Managers should be aware of the different types of costs, the different drivers, and the underlying economic conditions that affect them
CVP Analysis and Non-Unit Cost Drivers
CVP can be modified to take in account costs that vary with non-unit cost drivers Modification helps provide accurate insights concerning cost behavior
Mix of costs that an organization chooses can have a considerable influence on its operating risk and profit level
Degree of operating leverage = Total contribution margin/Profit
Prices and Costs Known with Certainty
Finally, the fifth assumption is that prices and costs are known. Actually, firms seldom know variable costs and fixed costs with certainty. A change in one variable usually affects the value of others. Often, there is a probability distribution to consider. There are formal ways of explicitly building uncertainty into the CVP model. Exploration of these issues is introduced in the next section.
Number of units =
Fixed costs/Unit contribution margin
Comparison of the Two Approaches For a single-product setting, converting the break-even point in units answer to a sales-revenue answer is simply a matter of multiplying the unit sales price by the units sold. Then why bother with a separate formula for the sales-revenue approach?
For a single-product setting, neither approach has any real advantage over the other. Both offer much the same level of conceptual and computational difficulty.
Fortunately, break-even revenue can be computed directly by developing a separate formula based on total fixed costs, target profit, and the contribution margin ratio
In this case, the important variable is sales revenue, so both the revenue and the variable costs must be expressed in dollars instead of units.
A profit-volume graph portrays the relationship between profits and sales volume. The profit-volume graph is the graph of the operating income equation [Operating income = (Price × Units) − (Unit variable cost × Units) − Fixed costs].
In this graph, operating income (profit) is the dependent variable, and number of units is the independent variable. Usually, values of the independent variable are measured along the horizontal axis and values of the dependent variable along the vertical axis.
Break-Even Point in Units for the Multiple-Product Setting
Multiple-product analysis requires the expected sales mix - Sales mix: Relative combination of products being sold by a firm -Defining sales mix allows one to convert a multiple-product problem to a single-product CVP format
The first assumption, linear cost and revenue functions, deserves additional consideration.
Panel A, portrays the curvilinear revenue and cost functions. We see that as quantity sold increases, revenue also increases, but eventually revenue begins to rise less steeply than before. This is explained quite simply by the need to decrease price as many more units are sold. The total cost function is more complicated, rising steeply at first, then leveling off somewhat (as increasing returns to scale develop), and then rising steeply again (as decreasing returns to scale develop). How can we deal with these complicated relationships?
Cost equation for JIT Total cost = Fixed costs + (Unit variable cost × Units) + (Engineering cost × Number of engineering hours)
Results for the conventional and ABC computations will be the same as long as the levels of activity for the non-unit-based cost drivers remain the same - ABC equation for CVP analysis is a richer representation of the underlying cost behavior
Sales-revenue approach
Sales = (Total fixed costs + Operating income)/Contribution margin ratio At break even, operating income equals zero Break-even sales = Total fixed costs/Contribution margin ratio
Just as the variable cost ratio can be computed using total or unit figures, the contribution margin ratio (40 percent in our exhibit) can also be computed in these two ways.
That is, one can divide the total contribution margin by total sales ($40/$100), or one can use unit contribution margin divided by price ($4/$10). Naturally, if the variable cost ratio is known, it can be subtracted from 1 to yield the contribution margin ratio (1 − 0.60 = 0.40).
Assumptions of Cost-Volume-Profit Analysis
The analysis assumes a linear revenue function and a linear cost function. The analysis assumes that price, total fixed costs, and unit variable costs can be accurately identified and remain constant over the relevant range. The analysis assumes that what is produced is sold. For multiple-product analysis, the sales mix is assumed to be known. The selling prices and costs are assumed to be known with certainty.
Constant Sales Mix
The fourth assumption is a constant sales mix. In single-product analysis, the sales mix is obviously constant—100 percent of sales consists of the one product. Multiple-product break-even analysis requires a constant sales mix. However, it is virtually impossible to predict the sales mix with certainty. Typically, this constraint is handled in practice through sensitivity analysis. By using spreadsheet analysis, the sensitivity of variables to a variety of sales mixes can be readily assessed.
Relevant Range
The second assumption is linked to the definition of relevant range. Once a relevant range has been identified, then the cost and price relationships are assumed to be known and constant.
Production Equal to Sales
The third assumption is that what is produced is sold. There is no change in inventory over the period. The fact that inventory has no impact on break-even analysis makes sense. Break-even analysis is a short-run decision-making technique, so we are looking to cover all costs of a particular period of time. Inventory embodies costs of a previous period and is not considered.
As a result, when the income target is expressed as net income, we must add back the income taxes to get operating income.
Therefore, to use either the equation method or the contribution margin approach, the after-tax profit target must first be converted to a before-tax profit target.
In a multiple-product setting, however, CVP analysis is more complex and the sales-revenue approach is significantly easier.
This approach maintains essentially the same computational requirements found in the single-product setting, whereas the units-sold approach becomes more difficult. Even though the conceptual complexity of CVP analysis does increase with multiple products, the operation is reasonably straightforward.
In general, taxes are computed as a percentage of income. The after-tax profit, or net income, is computed by subtracting income taxes from the operating income (or before-tax profit).
Thus, to convert the after-tax profit to before-tax profit, simply divide the after-tax profit by the quantity (1 − Tax rate)
ABC equation for CVP analysis
Total cost = Fixed costs + (Unit variable cost × Number of units) + (Setup cost × Number of setups) + (Engineering cost × Number of engineering hours)
The Equation Method for Break-Even and Target Income
Units for a target profit = (Total fixed cost + Target income)/(Price − Variable cost per unit)
Operating Leverage
Use of fixed costs to extract higher percentage changes in profits as sales activity changes - Greater the degree of operating leverage, the more that changes in sales activity will affect profits
break-even point in sales revenue
Uses the assumed sales mix Avoids the requirement of building a package contribution margin Computational effort is similar to that used in the single-product setting
To express variable cost in terms of sales revenue, we compute the variable cost ratio,
Variable cost ratio: Proportion of each sales dollar that must be used to cover variable costs
Risk and Uncertainty in CVP Analysis
Ways in which managers deal with risk and uncertainty - Realize the uncertain nature of future prices, costs, and quantities - Consider a break-even band instead of a break-even point - Engage in sensitivity or what-if analyses
After-Tax Profit Targets Income taxes are generally calculated as a percentage of income. When calculating the break-even point, income taxes play no role because the taxes paid on zero income are zero
When the company needs to know how many units to sell to earn a particular net income, however, some additional consideration is needed.
The contribution margin ratio
is the proportion of each sales dollar available to cover fixed costs and provide for profit. - In Exhibit 16.1, if the variable cost ratio is 60 percent of sales, then the contribution margin must be the remaining 40 percent of sales. It makes sense that the complement of the variable cost ratio is the contribution margin ratio. After all, the proportion of the sales revenue left after variable costs are covered should be the contribution margin component.
