ACCT 3306: Chapter 5: Cost-Volume-Profit Relationships
Mixed Costs
A mixed cost contains both variable and fixed elements. Consider the example of utility cost.
Least-Squares Regression Method (Part 3)
A regression line of the form Y = a + bX is fitted to the data, where a (the intercept) represents the total fixed cost and b (the slope) represents the variable cost per unit of activity. In our Maintenance Cost example, The slope b is $6.02, and represents the estimated variable maintenance cost per hour of maintenance. The intercept a is $4,395.67, and represents the estimated fixed monthly maintenance cost. Note that the R 2 is approximately 0.92, which is quite good and indicates that 92% of the variation in maintenance cost is explained by the variation in maintenance hours.
Preparing the Profit Graph
An even simpler form of the CVP graph is called the profit graph. Profit = Unit CM ×Q -Fixed Costs
Cost Structure and Profit Stability
Cost structure refers to the relative proportion of fixed and variable costs in an organization. Managers often have some latitude in determining their organization's cost structure.
Break-Even Analysis: Dollar Sales Using CM Ratio
Dollar sales to break even = Fixed Expenses / CM Ratio
The Contribution Approach - Part 2
Each month, RBC must generate at least $80,000 in total contribution margin to break-even (which is the level of sales at which profit is zero).
CVP Relationships in Equation Form - Using Unit Contribution Margin
It is often useful to express the simple profit equation in terms of the unit contribution margin (Unit CM) as follows: Unit CM = Selling price per unit -Variable expenses per unit Unit CM = P -V Profit = (P ×Q -V ×Q) -Fixed expenses Profit = (P -V) ×Q -Fixed expenses Profit = Unit CM ×Q -Fixed expenses
Operating Leverage
Operating leverage is a measure of how sensitive net operating income is to percentage changes in sales. It is a measure, at any given level of sales, of how a percentage change in sales volume will affect profits. Degree of operating leverage = Contribution margin / Net operating income
Target Profit Analysis -Equation Method
Profit = Unit CM × Q -Fixed expenses Our goal is to solve for the unknown "Q"which represents the quantity of units that must be sold to attain the target profit.
Contribution Margin Ratio (CM Ratio) and the Variable Expense Ratio - Step 2
The CM ratio can also be calculated by dividing the contribution margin per unit by the selling price per unit.
The Margin of Safety in Dollars
The margin of safety is the excess of budgeted or actual sales dollars over the break-even volume of sales dollars. It is the amount by which sales can drop before losses are incurred. The higher the margin of safety, the lower the risk of not breaking even and incurring a loss. Margin of safety in dollars = Total sales -Break-even sales
The Contribution Approach - Part 5
We do not need to prepare an income statement to estimate profits at a particular sales volume. Simply multiply the number of units sold above break-even by the contribution margin per unit. If RBC sells 430 bikes, its net operating income will be $6,000 (30 units ×$200 per unit).
The Definition of Sales Mix
• Sales mix is the relative proportion in which a company's products are sold. • Different products have different selling prices, cost structures, and contribution margins. • When a company sells more than one product, break-even analysis becomes more complex as the following example illustrates.
Contribution Margin Ratio (CM Ratio) and the Variable Expense Ratio - Step 4
Having defined the two terms, it bears emphasizing that the contribution margin ratio and the variable expense ratio can be mathematically related to one another:
Analysis of Mixed Costs
In account analysis, each account is classified as either variable or fixed based on the analyst's knowledge of how the account behaves. The engineering approach classifies costs based upon an industrial engineer's evaluation of production methods, and material, labor, and overhead requirements.
Contribution Margin (CM)
the amount remaining from sales revenue after variable expenses have been deducted.Sales
Least-Squares Regression Method (Part 2)
Excel can be used to estimate the intercept (fixed cost) and slope (variable cost per unit) that minimize the sum of the squared errors. The cost analysis objective is the same: Y = a + bX Least-squares regression also provides a statistic, called the R2 , which is a measure of the goodness of fit of the regression line to the data points.
Least-Squares Regression Method
A method used to analyze mixed costs if a scattergraph plot reveals an approximately linear relationship between the X and Y variables. This method uses all of the data points to estimate the fixed and variable cost components of a mixed cost. The goal of this method is to fit a straight line to the data that minimizes the sum of the squared errors.
Structuring Sales Commissions
Companies generally compensate salespeople by paying them either a commission based on sales or a salary plus a sales commission. Commissions based on sales dollars can lead to lower profits in a company.
Additional Applications of CVP Concepts Example 2: Change in Variable Costs and Sales Volume. What is the profit impact if RBC can use higher quality raw materials, thus increasing variable costs per unit by $10, to generate an increase in unit sales from 500 to 580?
Sales increase by $40,000 and net operating income increases by $10,200.
Additional Applications of CVP Concepts Example 1: Change in Fixed Cost and Sales Volume. What is the profit impact if RBC can increase unit sales from 500 to 540 by increasing the monthly advertising budget by $10,000?
Sales increased by $20,000, but net operating income decreased by $2,000. A shortcut solution using incremental analysis: Increase in CM (40 units X $200) = 8,000 Increase in advertising expenses = 10,000 Decrease in net operating income(2,000)
The Contribution Approach - Part 1
Sales, variable expenses, and contribution margin can also be expressed on a per-unit basis. If Racing sells an additional bicycle, $200 additional CM will be generated to cover fixed expenses and profit.
CVP Relationships in Equation Form
The contribution format income statement can be expressed in the following equation: Profit = (Sales -Variable expenses) - Fixed expenses Profit = (Sales Price * Quantity) - Variable Expense per Unit x Quantity) - Fixed Expenses
Basics of Cost-Volume-Profit Analysis
The contribution income statement is helpful to managers in judging the impact on profits of changes in selling price, cost, or volume. The emphasis is on cost behavior. Contribution Margin (CM) is the amount remaining from sales revenue after variable expenses have been deducted CM is used first to cover fixed expenses. Any remaining CM contributes to net operating income.
Contribution Margin Ratio (CM Ratio) and the Variable Expense Ratio - Step 1
The contribution margin as a percentage of sales is referred to as the contribution margin ratio (CM ratio). This ratio is computed as follows: CM ratio = CM / Sales
Break-Even Analysis: Equation Method
The equation method relies on the basic profit equation introduced earlier in the chapter. Because Racing Bicycle has only one product, we'll use the contribution margin form of this equation to perform the break-even calculations. We calculate break-even by solving the equation below: Profit = Unit CM × Q -Fixed expenses
Break-Even Analysis: Formula Method
The formula method is a shortcut version of the equation method. It centers on the idea discussed earlier in the chapter that each unit sold provides a certain amount of contribution margin that goes toward covering fixed expenses. Unit sales to break even = Fixed expenses / Unit CM
Cost-Volume-Profit Analysis: Key Assumptions
To simplify CVP calculations, managers typically adopt the following assumptions with respect to these factors: 1.Selling price is constant. The price of a product or service will not change as volume changes. 2.Costs are linear and can be accurately divided into variable and fixed components. The variable costs are constant per unit and the fixed costs are constant in total over the entire relevant range. 3.In multi product companies, the mix of products sold remains constant.
Target Profit Analysis -Formula Method
Unit sales to attain the target profit = Target profit + Fixed expenses /CM per unit =
Target Profit Analysis -Formula Method Sales Dollars
We can also compute the target profit in terms of sales dollars using either the equation method or the formula method. Dollar sales to attain the target profit = Target profit + Fixed expenses / CM ratio
Applications of Contribution Ratio
If RBC increases sales from 400 to 500 bikes ($50,000), contribution margin will increase by $20,000 ($50,000 ×40%). Here is the proof: A $50,000 increase in sales revenue results in a $20,000 increase in CM ($50,000 ×40% = $20,000).
The Contribution Approach - Part 3
If RBC sells 400 units in a month, it will be operating at the break-even point.
The Contribution Approach - Part 4
If RBC sells one more bike (401 bikes), net operating income will increase by $200.
Preparing the CVP Graph
In a CVP graph, unit volume is usually represented on the horizontal (X) axis and dollars on the vertical (Y) axis. 1. UnitsDraw a line parallel to the volume axis to represent total fixed expenses. 2. Choose some sales volume, say 400 units, and plot the point representing total expenses (fixed and variable). Draw a line through the data point back to where the fixed expenses line intersects the dollar axis. 3. Choose some sales volume, say 400 units, and plot the point representing total sales. Draw a line through the data point back to the point of origin.
Target Profit Analysis
In target profit analysis, we estimate what sales volume is needed to achieve a specific target profit. We can compute the number of units that must be sold to attain a target profit using either: (1) Equation method, or (2) Formula method.
Break-Even Analysis
The equation and formula methods can be used to determine the unit sales and dollar sales needed to achieve a target profit of zero. Let's use the RBC information to complete the break-even analysis.
Applications of Contribution Ratio -Increase in Sales Volume
The relationship between profit and the CM ratio can be expressed using the following equation: Profit = (CM ratio ×Sales) -Fixed expenses
CVP Relationships in Graphic Form
The relationships among revenue, cost, profit, and volume can be expressed graphically by preparing a CVP graph. Racing Bicycle developed contribution margin income statements at 0, 200, 400, and 600 units sold. We will use this information to prepare the CVP graph.
Comparing Results from the Least-Squares Regression and the High-Low Method
The two methods just discussed provide different estimates of the fixed and variable cost components of a mixed cost. This is to be expected because each method uses differing amounts of the data points to provide estimates. Least-squares regression provides the most accurate estimate because it uses all the data points.
The High-Low Method - Select High and Low Values
The variable cost per hour of maintenance is equal to the change in cost divided by the change in hours.
Contribution Margin Ratio (CM Ratio) and the Variable Expense Ratio - Step 3
The variable expenses as a percentage of sales is referred to as the variable expense ratio. This ratio is computed as follows: Variable expense ratio = Variable Expenses / Sales
Cost Structure and Profit Stability -High and Low Fixed Cost Structures
There are advantages and disadvantages to high fixed cost (or low variable cost) and low fixed cost (or high variable cost) structures. An advantage of a high fixed cost structure is that income will be higher in good years compared to companies with lower proportion of fixed costs. A disadvantage of a high fixed cost structure is that income will be lower in bad years compared to companies with lower proportion of fixed costs. Companies with low fixed cost structures enjoy greater stability in income across good and bad years.