Now, we can use the contribution margin approach to calculate the even number of units. What about the contribution margin approach used in determining the unit break-even point.
Profit Targets
Based on the information in this income statement, how much sales revenue must More-Power earn to break even. Breakthrough Sales Fixed Costs (Price/Margin Contribution) Breakthrough Sales Fixed Costs/Margin Contribution Ratio.
Comparison of the Two Approaches
M ultiple-Product Analysis
Break-Even Point in Units
But the product margin at the rate covers only direct fixed costs; common fixed costs remain to be covered. Allocating fixed joint costs to each product line before calculating the breakeven point can solve this difficulty.
Sales M ix
Individual break-even points can be obtained if income is defined as product margin. Thus, 15,625 regular sanders and 15,000 mini sanders must be sold to break even on the product.
Sales M ix and CVP Analysis
Another way to manage the increased complexity is to move from the units sold approach to the sales revenue approach.
Sales Dollars Approach
It can also help managers quickly understand what impact an increase or decrease in sales will have on the break-even point.
The Profit-Volume Graph
The Cost-Volume-Profit Graph
Notice that the total revenue line starts at the origin and rises with a slope equal to the selling price per unit (slope of 10). When the total revenue line is below the total cost line, the loss zone is defined. Similarly, the profit margin is determined when the total revenue line is above the total cost line.
The point where the total revenue line and the total cost line intersect is the break-even point.
Assumptions of Cost-Volume-Profit Analysis
The total cost line intersects the vertical axis at a point equal to total fixed costs and rises with a slope equal to variable costs per unit (slope 5). In addition, total costs can be divided into fixed costs of $100 and variable costs of $200. Let's review the basic revenue and total cost functions defined in economics.
The total cost function is more complicated, at first it rises sharply, then levels off somewhat (as increasing returns to scale develop) and then rises sharply (as diminishing returns to scale develop).
Relevant Range
Production Equal to Sales
Constant Sales M ix
Prices and Costs Known with Certainty
Changes in the CVP Variables
This question can be answered without using equations, but using unit contributions. Note that to calculate the increase in total profit, we only need to consider the incremental increase in total contribution margin and fixed costs. So the question can only be answered by looking at the effect on the overall contribution margin.
As with the first alternative, the profit impact can be assessed by looking at the incremental effects on contribution margin and fixed costs.
Introducing Risk and Uncertainty
Of the three alternatives identified by the marketing study, the only one that promises profitability is the third. Next, managers move from considering a break-even point to what might be called a break-even point. In other words, given the uncertain nature of the data, perhaps a firm can break even when 1,800 to 2,000 units are sold.
In this regard, a spreadsheet is useful, as managers establish outcome (or target profit) relationships and then check to see the impact that different costs and prices have on quantity sold.
M argin of Safety
First, of course, management must be aware of the uncertain nature of future prices, costs, and quantities.
Operating Leverage
If fixed costs are used to reduce variable costs so that contribution increases and profits decrease, the level of operating leverage increases, signaling an increase in risk. An automated system has a higher percentage increase because it has a higher degree of operating leverage. When choosing between the two systems, the effect of operating leverage is a valuable piece of information.
Moreover, the increased operational leverage is available under the automated system due to the presence of increased fixed costs.
Sensitivity Analysis and CVP
CVP Analysis and Activity-Based Costing
At the break-even point, operating income is zero, and the number of units that must be sold to break even is as follows. Break Units [Fixed Cost (Setup Cost Number of Setups) (Engineering Cost Number of Engineering Hours)]/(Variable Cost Unit Price). Comparing the ABC breakpoint with the conventional breakpoint reveals two important differences.
Second, the numerator in the ABC break-even equation has two non-unit variable cost terms: one for batch-related activities and one for product-maintenance activities.
Strategic Implications: Conventional CVP Analysis versus ABC Analysis
They were probably aware of the increase in these two variables, but the conventional cost equation diverted attention from figuring out how much of an impact changes in those variables would have. The information conveyed to the engineers by the conventional equation gave the impression that any reduction in labor costs – without impact on direct materials or variable overhead costs – would reduce overall costs, as changes in the level of labor activity would have no impact on fixed costs. However, the ABC equation indicates that a reduction in labor input that negatively impacts installation activities or technical support may be undesirable.
Providing ABC cost information to designers would likely lead them down a different path—a path that would be more beneficial to the company.
CVP Analysis and JIT
The impact of decisions on batches and products can then be examined within CVP. The subject of cost, volume and profit analysis naturally lends itself to the use of many equations. Operating Income (Price Number of Units) (Variable Costs per Unit Number of Units) Total Fixed Costs.
ABC total cost Fixed costs (Variable costs per unit Number of units) (Costs at batch level Batch driver) (Costs at product level Product driver).
B REAK -E VEN P OINT , T ARGETED
ABC break-even units [fixed cost (lot-level cost, lot driver) (product-level cost, driver)]/(variable cost unit price).
P ROFIT , M ARGIN OF S AFETY
Required
CVP WITH A CTIVITY -B ASED C OSTING
LU TION
Break Units [Fixed Cost (Setup Cost) (Engineer Hour Cost)]/(Price Unit Cost). Explain why the contribution per unit becomes the profit per unit above the breakeven point. If the contribution increases from 30 to 35 percent of sales, what will happen to the break-even point and why will it occur.
Break-even point 737 General fixed expenses 745 Contribution margin 738 Contribution margin ratio 741 Cost-volume-profit graph 749 Degree of operating leverage 757 Direct fixed expenses 745 Margin of safety 756 Net income 738.
B REAK -E VEN IN U NITS
Explain how CVP analysis developed for single products can be used in a multi-product environment. Why might a multiproduct firm choose to calculate only the total revenue rate of return rather than the amount of the discount rate by product. Why the activity-based costing approach to CVP analysis provides more insight than the conventional approach.
B REAK -E VEN IN U NITS , T ARGET I NCOME
B REAK -E VEN FOR A S ERVICE F IRM
B REAK -E VEN IN S ALES D OLLARS
B REAK -E VEN IN S ALES D OLLARS , M ARGIN OF S AFETY
B REAK -E VEN IN U NITS , A FTER -T AX
T ARGET I NCOME , CVP A SSUMPTIONS
The sales organization anticipates that by significantly reducing the selling price, 2,700 units can be sold during the remainder of the year. Reduce unit variable costs by $25 through the use of less expensive materials and slightly modified production techniques. The selling price will also be reduced by $30, and sales of 2,200 units are expected for the remainder of the year.
Determine which of the alternatives Almo Company should choose to achieve its annual profit after tax.
CVP, B EFORE - AND A FTER -T AX T ARGETED I NCOME
Determine the number of units Alma must sell to break even, assuming that the selling price and cost structure do not change. Determine the number of units Alma must sell to reach its after-tax profit target.
B REAK -E VEN IN S ALES D OLLARS , C HANGES IN V ARIABLES
What is the breakeven point (rounded to the nearest dollar) for Lauterbach Corporation for the current year. For the coming year, Lauterbach Corporation's management anticipates a 10 percent increase in variable costs and a $45,000 increase in fixed costs.
C ONTRIBUTION M ARGIN , CVP, N ET I NCOME , M ARGIN OF S AFETY
O PERATING L EVERAGE
CVP A NALYSIS WITH M ULTIPLE P RODUCTS
A FTER -T AX T ARGET I NCOME , P ROFIT A NALYSIS
The hourly wages of the staff are projected to be $25 for the paralegal, $20 for the paralegal, $15 for the legal secretary and $10 for the clerk-receptionist. A total of 400 hours of overtime is expected for the year; it will be split equally between the legal secretary and the clerk-receptionist positions. This will require the group to purchase malpractice insurance, which is expected to cost $180,000 annually.
Determine how many new clients will need to visit the law firm that Don Masters and his colleagues are considering in order for the firm to break even during its first year of business.
U SING A C OMPUTER S PREADSHEET TO S OLVE M ULTIPLE - P RODUCT B REAK -E VEN , V ARYING S ALES M IX
C ONTRIBUTION M ARGIN , U NIT A MOUNTS
B REAK -E VEN IN S ALES D OLLARS , V ARIABLE - C OSTING R ATIO , C ONTRIBUTION M ARGIN
C HANGES IN B REAK -E VEN P OINTS WITH C HANGES IN U NIT P RICES
B REAK -E VEN , A FTER -T AX T ARGET I NCOME , M ARGIN OF S AFETY , O PERATING L EVERAGE
B ASIC CVP C ONCEPTS
CVP A NALYSIS : S ALES -R EVENUE A PPROACH , P RICING , A FTER -T AX T ARGET I NCOME
M ULTIPLE P RODUCTS , B REAK -E VEN A NALYSIS , O PERATING
L EVERAGE , S EGMENTED I NCOME S TATEMENTS
Assume that actual revenues will be 40 percent higher than projected. The Jay-rider is a cross between a rowing machine and an exercise bike (like the Nordic rider™). For the first year, Ironjay estimates that the jay-rider will cannibalize 600 units of jay-flex sales.
Calculate the number of jay-flex machines, sets of free weights, and jay-riders that must be sold for Ironjay to break even.
B REAK -E VEN IN U NITS AND S ALES D OLLARS , M ARGIN OF S AFETY
CVP A NALYSIS , I MPACT OF A CTIVITY -B ASED C OSTING
She was also informed by the engineer that if 20,000 radios were produced and sold (her projection based on her marketing research), they would have the same activity data as recorders (use the same direct labor hours, machine hours, setups, and soon). Convinced that 20,000 units could be sold, Betty was prepared to strongly recommend the new product line. How much additional profit would be expected under this scenario, assuming 20,000 radios are sold.
Using an activity-based costing method, calculate the break-even point and the incremental profit that would be earned by selling 20,000 units.
ABC AND CVP A NALYSIS : M ULTIPLE P RODUCTS
Betty was told that a factory-wide overhead rate was being used to allocate overhead costs based on direct labor hours. Explain why the CVP analysis in Requirement 2 is more accurate than the analysis in Requirement 1. Using the conventional approach, calculate the number of cases of Rose and the number of cases of Violet that must be sold before the company can break even.
Using an activity-based approach, calculate the number of cases of each product that must be sold in order for the company to break even.
C OLLABORATIVE L EARNING E XERCISE
Run three regressions using the following independent variables: (a) number of setups, (b) number of machine hours, and (c) a multiple regression using both number of setups and machine hours. Using the results of the multiple regression equation (from requirement 1), calculate the number of boxes of pasta that must be sold to break even. The production manager believes that with careful planning he can keep the total number of setups (for both pasta and sauce) at the same number as last year.
Using the data from Problems 17-27, Part I and the results of the multiple regression equation, calculate the break-even number of boxes of pasta and jars of sauce.
C YBER R ESEARCH C ASE
