9.1 Cost-Volume-Profit (CVP) Analysis Flashcards
A company uses cost-volume-profit analysis to evaluate a new project. The total fixed costs of production per year are $160,000. The unit variable cost is $50. Which one of the following combinations of unit selling price and breakeven number of units sold per year is correct?
A. $50 selling price and 3,200 breakeven number of units.
B. $25 selling price and 6,400 breakeven number of units.
C. $70 selling price and 8,000 breakeven number of units.
D. $100 selling price and 1,600 breakeven number of units.
C. $70 selling price and 8,000 breakeven number of units.
If the selling price is $70, the unit contribution margin is $20 ($70 - $50). The breakeven point in units equals 8,000 ($160,000 ÷ $20).
Formula for breakeven point in units
Fixed Costs / Unit contribution margin
Fixed Costs / UCM
Kim is thinking of organizing a fundraiser to support a local charity. She has planned to rent a banquet hall and provide the guests with food, entertainment, and various party favors. She has decided to charge $500 a person. After researching around town, Kim has discovered the following costs:
Fixed Costs
Rental fee of banquet hall $150,000
Advertising 50,000
Entertainment 4,000
Variable Costs Per Guest
Food $12
Other miscellaneous costs 8
How many guests must attend in order for Kim to break even?
A. 425
B. 443
C. 417
D. 408
A. 425
The breakeven point in units equals total fixed costs ($150,000 + $50,000 + $4,000 = $204,000) divided by the unit contribution margin ($500 selling price – $12 food – $8 other = $480). Kim’s breakeven number of guests is thus 425 ($204,000 ÷ $480).
Formula for Contribution margin, Contribution margin ratio
Contribution margin = selling price - total variable costs
Contribution margin ratio = contribution margin ÷ selling price
Donnelly Corporation manufactures and sells T-shirts imprinted with college names and slogans. Last year, the shirts sold for $7.50 each, and the variable cost to manufacture them was $2.25 per unit. The company needed to sell 20,000 shirts to break even. The net income last year was $5,040. Donnelly’s expectations for the coming year include the following:
* The sales price of the T-shirts will be $9.
* Variable cost to manufacture will increase by one-third.
* Fixed costs will increase by 10%.
* The income tax rate of 40% will be unchanged.
The selling price that would allow Donnelly to maintain the same contribution margin ratio as last year is
A. $9.75
B. $9.00
C. $10.00
D. $8.25
C. $10.00
Last year, unit variable cost was $2.25, so the unit contribution margin (UCM) was $5.25 ($7.50 price – $2.25), and the contribution margin ratio (CMR) was 70% ($5.25 ÷ $7.50). If variable costs increase by one-third, the new variable cost is $3 [$2.25 × (4 ÷ 3)]. If a 70% CMR is desired, the $3 variable cost is 30% of sales, and the unit sales price is $10 ($3 ÷ 30%).
One of the major assumptions limiting the reliability of breakeven analysis is that
A. Efficiency and productivity will continually increase.
B. Total variable costs will remain unchanged over the relevant range.
C. Total fixed costs will remain unchanged over the relevant range.
D. The cost of production factors varies with changes in technology.
C. Total fixed costs will remain unchanged over the relevant range.
One of the inherent simplifying assumptions used in CVP analysis is that fixed costs remain constant over the relevant range of activity.
Which one of the following is true regarding a relevant range?
A. Total variable costs will not change.
B. Total fixed costs will not change.
C. Actual fixed costs usually fall outside the relevant range.
D. The relevant range cannot be changed after being established.
B. Total fixed costs will not change.
The relevant range is the range of activity over which unit variable costs and total fixed costs are constant. The incremental cost of one additional unit of production will be equal to the variable cost.
Cost-volume-profit (CVP) analysis is a key factor in many decisions, including choice of product lines, pricing of products, marketing strategy, and use of productive facilities. A calculation used in a CVP analysis is the breakeven point. Once the breakeven point has been reached, operating income will increase by the
A. Gross margin per unit for each additional unit sold.
B. Contribution margin per unit for each additional unit sold.
C. Fixed costs per unit for each additional unit sold.
D. Variable costs per unit for each additional unit sold.
B. Contribution margin per unit for each additional unit sold.
At the breakeven point, total revenue equals total fixed costs plus the variable costs incurred at that level of production. Beyond the breakeven point, each unit sale will increase operating income by the unit contribution margin (Unit sales price – Unit variable cost) because fixed cost will already have been recovered.
Delphi Company has developed a new product that will be marketed for the first time during the next fiscal year. Although the Marketing Department estimates that 35,000 units could be sold at $36 per unit, Delphi’s management has allocated only enough manufacturing capacity to produce a maximum of 25,000 units of the new product annually. The fixed costs associated with the new product are budgeted at $450,000 for the year, which includes $60,000 for depreciation on new manufacturing equipment.
Data associated with each unit of product are presented as follows. Delphi is subject to a 40% income tax rate.
Direct material: $ 7.00
Direct labor: 3.50
Manufacturing overhead: 4.00
Variable manufacturing cost: $14.50
Selling expenses: 1.50
Total variable cost: $16.00
The number of units of the new product that Delphi Company must sell during the next fiscal year in order to break even is
A. 20,930
B. 18,140
C. 22,500
D. 25,500
C. 22,500
The breakeven point in units equals total fixed costs divided by the unit contribution margin. The unit contribution margin is $20 ($36 selling price - $16 unit variable cost). Hence, the breakeven point is 22,500 units ($450,000 ÷ $20).
A manufacturer contemplates a change in technology that would reduce fixed costs from $800,000 to $700,000. However, the ratio of variable costs to sales will increase from 68% to 80%. What will happen to the breakeven level of revenues?
A. Decrease by $301,470.50.
B. Decrease by $500,000.
C. Decrease by $1,812,500.
D. Increase by $1,000,000.
D. Increase by $1,000,000.
The original breakeven level was:
Breakeven point = Fixed costs ÷ Contribution margin ratio
= $800,000 ÷ (1.0 – .68)
= $2,500,000
The new level is:
Breakeven point = Fixed costs ÷ Contribution margin ratio
= $700,000 ÷ (1.0 – .80)
= $3,500,000
Thus, there is an increase of $1,000,000 ($3,500,000 – $2,500,000).
The breakeven point in units increases when unit costs
A. Increase and sales price remains unchanged.
B. Decrease and sales price remains unchanged.
C. Remain unchanged and sales price increases.
D. Decrease and sales price increases.
A. Increase and sales price remains unchanged.
A BEP ratio can be increased either by raising the numerator or lowering the denominator. The breakeven point in units is calculated by dividing fixed costs by the unit contribution margin. If selling price is constant and costs increase, the unit contribution margin decreases. The effect is to decrease the denominator and increase the ratio.
Which of the following would decrease unit contribution margin (UCM) the most?
A. A 15% decrease in selling price.
B. A 15% increase in variable expenses.
C. A 15% decrease in variable expenses.
D. A 15% decrease in fixed expenses.
A. A 15% decrease in selling price.
UCM equals unit selling price minus unit variable costs. It can be decreased by either lowering the price or raising the variable costs. As long as UCM is positive, a given percentage change in selling price must have a greater effect than an equal but opposite percentage change in variable cost. The example below demonstrates this point.
Original: UCM = SP – UVC
= $100 – $50
= $50
Lower Selling Price: UCM = (SP × .85) – UVC
= $85 – $50
= $35
Higher Variable Cost:
UCM = SP – (UVC × 1.15)
= $100 – $57.50
= $42.50
Since $35 < $42.50, the lower selling price has the greater effect.
The breakeven point in units sold for a corporation is 44,000. If fixed costs are equal to $880,000 annually and variable costs are $10 per unit, what is the contribution margin per unit?
A. $0.05
B. $20.00
C. $44.00
D. $88.00
B. $20.00
The breakeven point in units is equal to the fixed costs divided by the unit contribution margin (UCM).
Fixed costs ÷ UCM = Breakeven point in units
$880,000 ÷ UCM = 44,000 units
UCM = $20
Bruell Electronics Co. is developing a new product, surge protectors for high-voltage electrical flows. The cost information below relates to the product:
Unit Costs
Direct materials $3.25
Direct labor 4.00
Distribution .75
The company will also be absorbing $120,000 of additional fixed costs associated with this new product. A corporate fixed charge of $20,000 currently absorbed by other products will be allocated to this new product. If the selling price is $14 per unit, the breakeven point in units (rounded to the nearest hundred) for surge protectors is
A. 8,500 units.
B. 10,000 units.
C. 15,000 units.
D. 20,000 units.
D. 20,000 units.
The breakeven point in units for a new product equals total additional fixed costs divided by the unit contribution margin. Unit variable costs total $8 ($3.25 + $4.00 + $.75). Thus, UCM is $6 ($14 unit selling price – $8 unit variable cost), and the breakeven point is 20,000 units ($120,000 ÷ $6).
Barnes Corporation manufactures skateboards and is in the process of preparing next year’s budget. The pro forma income statement for the current year is presented below.
Sales $1,500,000
Cost of sales:
Direct materials $250,000
Direct labor 150,000
Variable overhead 75,000
Fixed overhead 100,000
= (575,000)
Gross profit $ 925,000
Selling and G&A:
Variable $200,000
Fixed 250,000
= (450,000)
Operating income
$ 475,000
The breakeven point (rounded to the nearest dollar) for Barnes Corporation for the current year is
A. $146,341
B. $636,364
C. $729,730
D. $181,818
B. $636,364
Fixed costs total $350,000 ($100,000 overhead + $250,000 SG&A). Variable costs total $675,000. Given sales of $1,500,000, the contribution margin is $825,000 ($1,500,000 – $675,000). Thus, the contribution margin percentage is 55% ($825,000 ÷ $1,500,000). Dividing the $350,000 of fixed costs by 55% produces a breakeven point of $636,363.64
Barnes Corporation manufactures skateboards and is in the process of preparing next year’s budget. The pro forma income statement for the current year is presented below.
Sales $1,500,000
Cost of sales:
Direct materials $250,000
Direct labor 150,000
Variable overhead 75,000
Fixed overhead 100,000
= (575,000)
Gross profit
$ 925,000
Selling and G&A:
Variable $200,000
Fixed 250,000
= (450,000)
Operating income
$ 475,000
For the coming year, the management of Barnes Corporation anticipates a 10% increase in sales, a 12% increase in variable costs, and a $45,000 increase in fixed expenses. The breakeven point for next year will be
A. $729,027
B. $862,103
C. $214,018
D. $474,000
A. $729,027
Sales are expected to be $1,650,000 ($1,500,000 × 1.10), variable costs $756,000 ($675,000 × 1.12), and fixed expenses $395,000 ($350,000 + $45,000). Thus, the contribution margin will be $894,000 ($1,650,000 – $756,000), and the contribution margin percentage is 54.1818%. The breakeven point is therefore $729,027 ($395,000 fixed expenses ÷ .541818).
All of the following are assumptions of cost-volume profit analysis except
A. Total fixed costs do not change with a change in volume.
B. Revenues change proportionately with volume.
C. Variable costs per unit change proportionately with volume.
D. Sales mix for multi-product situations do not vary with volume changes.
C. Variable costs per unit change proportionately with volume.
They remain constant within the relevant range
Formula for breakeven point in sales dollars
Fixed Costs / CM Ratio
The Company had the following operating results for the current period: 22,000 sales units, $924,000 sales, $594,000 variable expenses, and $324,000 fixed expenses. If the company expects variable expenses to increase by $2 per unit and fixed expenses to increase by $29,600 next year, what will be the increase in the number of units need to sell to break even?
A. 1,973 units
B. 3,323 units
C. 4,907 units
D. 5,600 units
D. 5,600 units
A company has a contribution margin of $4,000 and fixed costs of $1,000. If the total contribution margin increases by $1,000, operating profit would
A. Decrease by $1,000.
B. Increase by more than $1,000.
C. Increase by $1,000.
D. Remain unchanged.
C. Increase by $1,000.
Since fixed costs remain unchanged, a change in contribution margin results in an identical change in operating profit within the relevant range.
A company currently sells 46,000 units of its product annually at a sales price of $38 per unit. Variable costs per unit total $21 and the total fixed costs each year are $749,000. Fixed costs include the annual salary of three sales staff, which is $55,000 each. Management is considering changing the sales staff’s compensation. Under this proposal, sales staff salaries would decrease to $25,000, but sales staff would also receive a commission of $2 per unit for each unit sold. Management estimates this option will increase sales 10%. Should management change to the commission-based plan, and why?
A. No, because it will decrease net income by $23,000.
B. No, because it will decrease operating income by $23,000.
C. Yes, because it will increase operating income by $67,000.
D. Yes, because it will increase net income by $67,000.
C. Yes, because it will increase operating income by $67,000.
Currently, the company has a contribution margin of $782,000 [46,000 units × ($38 sales price – $21 variable cost per unit)]. If the company changes the staff’s compensation, the contribution margin will be $759,000 [(46,000 × 1.1) × ($38 sales price – $21 variable cost per unit – $2 commission per unit)]. Thus, the contribution margin will decrease by $23,000. The change will save $90,000 in staff salaries [($55,000 – $25,000) × 3 staff members]. Therefore, the change will increase operating income by $67,000 ($90,000 – $23,000) and the company should adopt the commission-based plan.
A company sells its single product for $30 per unit. The contribution margin ratio is 45%, and fixed costs are $10,000 per month. The company has an effective income tax rate of 40%. If the company sells 1,000 units in the current month, the company’s variable expenses would be
A. $12,000
B. $16,500
C. $9,900
D. $13,50
B. $16,500
The company’s contribution margin ratio reveals that 45% of the sales price of each product is contribution margin. Thus, 55% of the sales price goes to variable costs (100% – 45%), making the per-unit variable cost $16.50 ($30 × 55%). Since the company sold 1,000 units in the current month, total variable costs were $16,500 (1,000 × $16.50).
The following information pertains to Syl Co.:
Sales: $800,000
Variable costs: 160,000
Fixed costs: 40,000
What is Syl’s breakeven point in sales dollars?
A. $50,000
B. $40,000
C. $160,000
D. $200,000
A. $50,000
The breakeven point in sales dollars is the fixed costs divided by the contribution margin ratio. Variable costs equal 20% of sales ($160,000 ÷ $800,000). Thus, the contribution margin ratio is 80%, and the breakeven point in dollars is $50,000 ($40,000 FC ÷ 80%)
A company is contemplating marketing a new product. Fixed costs will be $800,000 for production of 75,000 units or less and $1,200,000 if production exceeds 75,000 units. The variable cost ratio is 60% for the first 75,000 units. Variable costs will decrease to 50% of sales for units in excess of 75,000. If the product is expected to sell for $25 per unit, how many units must the company sell to break even?
A. 80,000
B. 120,000
C. 111,000
D. 96,000
C. 111,000
The BEP in units is equal to fixed cost divided by the difference between unit selling price and unit variable cost (the unit contribution margin). At less than 75,000 units, fixed costs are $800,000 and UCM is $10 [$25 - ($25 x 60%)]. At this UCM, 80,000 units ($800,000 ÷ $10) must be sold, but this volume is not within the relevant range. At any production level greater than 75,000 units, total fixed costs are $1,200,000 but there are two UCM layers. The first 75,000 units sold will produce a contribution margin of $750,000 (75,000 x $10). Hence, another $450,000 ($1,200,000 - $750,000) must be contributed. The UCM is $12.50 [$25 - ($25 x 50%)] for units in excess of 75,000 and 36,000 ($450,000 ÷ $12.50) additional units must be sold. Total unit sales at BEP are 111,000 (75,000 + 36,000).
