ACG6308 - Chapter 9
Cotton Company produces and sells socks. Variable costs are budgeted at $4 per pair, and fixed costs for the year are expected to total $90,000. The selling price is expected to be $6 per pair. The sales dollars required for Cotton Company to make a before-tax profit (πB) of $10,000 are:
$10,000 = $6Q − [$4Q + $90,000] Q = $100,000 / $2/unit = 50,000 units Required sales dollars = Q × selling price per unit Required sales dollars = 50,000 units × $6 per unit = $300,000
Tom's Sports Wear is a retailer of sports hats located in Atlanta, Georgia. Although Tom's carries numerous styles of sports hats, each hat has Sales price$ 36.00Per-unit variable costs: Invoice cost18.60Sales commissions5.40Total per-unit variable costs$ 24.00Total annual fixed costs: Advertising$ 24,000Rent30,000Salaries126,000Total fixed costs$ 180,000 The annual breakeven point in unit sales is calculated to be:
$180,000/($36.00 − $24.00) = 15,000 units
Sleepy Time is a retailer of luxury bed frames located in Los Angeles, California. Due to a recent industry-wide financial crisis, the CFO of Sleepy Time fears a significant drop in the firm's upcoming income stream. The CFO asked you to use the company financial information provided below. Sales price per unit$ 3,000.00Per-unit variable costs: Invoice cost2,218.80Sales commissions281.20Total per-unit variable costs$ 2,500.00Total annual fixed costs: Advertising$ 236,000Rent178,000Salaries386,000Total fixed costs$ 800,000 The annual breakeven point in dollars is:
$800,000 / [($3,000 − $2,500)/unit / $3,000)/unit] = $800,000/0.166666667 = $4,800,000
Required unit sales =
(F + πB)/contribution margin per unit
Weighted-average contribution margin per unit =
(Sales Mix/Total sales mix) / Contribution Margin
Which type of firm would choose a high-fixed-costs structure to exploit an advantage?
A firm with a dominant position in its market.
Cost-volume-profit (CVP) relationships that are curvilinear may be analyzed linearly by considering only:
A relevant range of volume.
Shock Company manufactures computer monitors. The following is a summary of its basic cost and revenue data: Per UnitPercentSales price$ 480100Variable costs31265Unit contribution margin$ 16835 Assume that Shock Company is currently selling 600 computer monitors per month and monthly fixed costs are $80,000.What is Shock Company's degree of operating leverage (DOL) at this sales volume (i.e., at 600 units)? (Round your answer to three decimal places.)
At Q = 600 units, total contribution margin (CM) = $168/unit × 600 units = $100,800 At Q = 600 units, operating income = CM − FC = $100,800 − $80,000 = $20,800 At Q = 600 units, degree of operating leverage (DOL) = CM/operating income = $100,800/$20,800 = 4.846
Lamp Company has the following cost-volume-profit (CVP) data: Breakeven point, in units2,000Selling price per unit$ 625Total fixed costs$ 125,000 What is the variable cost per unit (rounded to two decimal places)?
At breakeven, total CM = total fixed costs, F Given the above data, we have (at the breakeven point): 2,000 units × ($625 − v)/unit = $125,000, where v = variable cost per unit. Therefore, variable cost per unit, v = ((2,000 units × $625/unit) − $125,000)/2,000 units = $1,125,000/2,000 units = $562.50
The cost-volume-profit (CVP) profit-planning model assumes that over the relevant range of activity:
Both revenues and total costs are linear.
In the current year, Comfy Couch Company expected to sell 12,000 leather sofas. Fixed costs for the year were expected to be $8,400,000; unit sales price was budgeted at $4,600; and unit variable costs were expected to be $2,200. Comfy Couch Company's margin of safety ratio (MOS %) is (rounded to two decimal places)
Break-even point, in sales dollars = Fixed costs/contribution margin ratio = $8,400,000 / [($4,600 − $2,200)/unit / $4,600/unit)] = $8,400,000/0.5217391 = $16,100,000 Margin of Safety (MOS) = Budgeted (planned) sales dollars − Breakeven sales dollars = (12,000 units × $4,600/unit) − $16,100,000 = $39,100,000. MOS % = MOS (in dollars)/Budgeted sales (in dollars) = $39,100,000/($4,600/unit × 12,000 units) = $39,100,000/$55,200,000 = 70.83%.
Shock Company manufactures computer monitors. The following is a summary of its basic cost and revenue data: Per UnitPercentSales price$ 480100Variable costs31265Unit contribution margin$ 16835 Assume that Shock Company is currently selling 600 computer monitors per month and monthly fixed costs are $80,000. Shock Company's margin of safety ratio (MOS%) if 600 units are sold would be (Round up your intermediate calculations to the nearest whole unit.)
Break-even point, in units = Fixed costs/contribution margin per unit = $80,000 (given) / $168/unit (given) = 477 units (rounded up) MOS% = MOS (in units)/Actual (or budgeted) sales, in units = (600 − 477) units/600 units = 123 units/600 units = 20.5%
Shock Company manufactures computer monitors. The following is a summary of its basic cost and revenue data: Per UnitPercentSales price$ 480100Variable costs31265Unit contribution margin$ 16835 Assume that Shock Company is currently selling 600 computer monitors per month and monthly fixed costs are $80,000. What is Shock Company's margin of safety (MOS), in units, if 600 units are sold and all costs and revenues are as budgeted? (Round intermediate calculation up to nearest whole number of units.)
Break-even point, in units = Fixed costs/contribution margin per unit = $80,000 (given) / $168/unit (given) = 477units (rounded up) Margin of Safety (MOS) = Budgeted sales (units) − Breakeven sales (units) = 600 − 477 = 123 units
For the current year, Electric Corporation expected to sell 42,000 industrial power cords. Fixed costs were expected to total $1,650,000; unit sales price was expected to be $3,750; and unit variable costs were budgeted at $2,250. Electric Corporation's margin of safety (MOS) in units is:
Break-even point, in units = Fixed costs/contribution margin/unit = $1,650,000 / ($3,750 − $2,250)/unit = $1,650,000 / $1,500/unit = 1,100 units Margin of Safety (MOS) = Budgeted units − Breakeven sales, in units = 42,000 units (given) − 1,100 units = 40,900 units.
During the current year, Mute Corporation expected to sell 24,000 telephone switches. Fixed costs for the year were expected to be $12,144,000, the unit sales price was budgeted at $3,200, and unit variable costs were budgeted at $1,440. Mute's margin of safety ratio (MOS %) is:
Break-even, in dollars = 6,900 units × $3,200/unit = $22,080,000 (or, $12,144,000 / [($3,200 − $1,440)/unit / $3,200/unit] = $12,144,000/0.55 = $22,080,000). Therefore, margin of safety (MOS) in dollars = (24,000 units × $3,200/unit) − $22,080,000 = $54,720,000. MOS % = MOS/Budgeted sales dollars = $54,720,000/(24,000 budgeted units × $3,200 budgeted selling price per unit) = $54,720,000/$76,800,000 = 71.25%
During the current year, Mute Corporation expected to sell 24,000 telephone switches. Fixed costs for the year were expected to be $12,144,000, the unit sales price was budgeted at $3,200, and unit variable costs were budgeted at $1,440. Mute's margin of safety (MOS) in units is
Break-even, in units = $12,144,000/($3,200 − $1,440) per unit = 6,900 units Therefore, margin of safety (MOS) = 24,000 units − 6,900 units = 17,100 units
What can the weighted average contribution margin ratio be used for?
Breakeven and profit planning for sales volume expressed in dollars (Y) rather than units (Q).
Breakdown of total breakeven units =
Breakeven in units (total) * (Sales Mix/Total Sales Mix)
Wet Mop Incorporated expects to sell 10,000 mops. Fixed costs (for the year) are expected to be $10,000, unit sales price is expected to be $12, and unit variable costs are budgeted at $7. Wet Mop's margin of safety ratio (MOS %) is:
Breakeven point in units = Fixed costs/contribution margin/unit = $10,000 / $5/unit = 2,000 units Margin of safety ratio (MOS %) = (Budgeted sales, in units − Breakeven sales, in units)/Breakeven sales, in units MOS% = (10,000 − 2,000) units/10, 000 units = 8,000 units/10,000 units = 80%
Wet Mop's margin of safety (MOS) in sales dollars is:
Breakeven point in units = Fixed costs/contribution margin/unit = $10,000 / ($12 − $7)/unit = 2,000 units Breakeven point in dollars = selling price per unit × breakeven point in units = $12/unit × 2,000 units = $24,000 Expected (budgeted) sales level, in dollars = $12/unit × 10,000 units = $120,000 Margin of safety (MOS) = Budgeted sales dollars − breakeven sales dollars = $120,000 − $24,000 = $96,000Also: MOS = excess of budgeted over breakeven sales (in units) × budgeted selling price/unit = 8,000 units × $12/unit = $96,000
Wet Mop Incorporated expects to sell 10,000 mops. Fixed costs (for the year) are expected to be $10,000, unit sales price is expected to be $12, and unit variable costs are budgeted at $7. Wet Mop's margin of safety (MOS) in units is:
Breakeven point in units = Fixed costs/contribution margin/unit = $10,000 / ($12 − $7)/unit = 2,000 units Therefore, margin of safety (MOS) = Budgeted (planned) sales volume − Breakeven sales volume = 10,000 units (given) − 2,000 units = 8,000 units
The sales and cost data for two companies in the transportation industry are as follows: X CompanyY CompanyAmountPercentAmountPercentSales$ 120,000100$ 120,000100Variable costs72,0006036,00030Contribution margin48,0004084,00070Fixed costs36,000 72,000 Operating income (πB)$ 12,000 $ 12,000 X Company's margin of safety ratio (MOS%) (rounded) is:
Breakeven point, in sales dollars = Fixed costs/contribution margin ratio = $36,000/0.40 = $90,000 Margin of Safety (MOS) = Budgeted (or actual) sales dollars − Breakeven sales, in dollars = $120,000 − $90,000 = $30,000 Margin of Safety Ratio (MOS%) = MOS/Budgeted (or actual) sales = $30,000/$120,000 = 25.00%
The sales and cost data for two companies in the transportation industry are as follows: X CompanyY CompanyAmountPercentAmountPercentSales$ 120,000100$ 120,000100Variable costs72,0006036,00030Contribution margin48,0004084,00070Fixed costs36,000 72,000 Operating income (πB)$ 12,000 $ 12,000 Y Company's margin of safety (MOS) in sales dollars (rounded) is:
Breakeven point, in sales dollars = Fixed costs/contribution margin ratio = $72,000/0.70 = $102,857.14 MOS = Budgeted (or actual) sales − Breakeven sales = $120,000 − $102,857.14 = $17,143 (rounded)
MOS =
Budgeted (or actual) sales − Breakeven sales
(MOS) in units =
Budgeted (planned) sales volume − Breakeven sales volume
X Company's degree of operating leverage (DOL) at the current sales volume level is calculated to be
Contribution margin (CM)/Operating income (πB)
The sales and cost data for two companies in the transportation industry are as follows: X CompanyY CompanyAmountPercentAmountPercentSales$ 120,000100$ 120,000100Variable costs72,0006036,00030Contribution margin48,0004084,00070Fixed costs36,000 72,000 Operating income (πB)$ 12,000 $ 12,000 XCompany'sdegree of operating leverage (DOL) at the current sales volume level is calculated to be:
Contribution margin (CM)/Operating income (πB) = $48,000/$12,000 = 4.00
The difference between sales price per unit and variable cost per unit is the:
Contribution margin per unit (cm).
Birdie Corporation is the maker of high-quality golf bags. The company currently has three different lines of bags, which it sells to sporting goods stores and golf shops throughout the world. Birdie sells a constant mix of 4 small bags for each medium-sized bag and 5 medium bags for each large-sized bag. Total fixed costs for the year are expected to be $2,027,562. (Note: round all decimals to three places; round final answers up to nearest whole number.) SmallMediumLargeSelling price per bag$ 100$ 150$ 250Variable cost per bag$ 60$ 95$ 160 The breakeven point in units (for the year) would be:
Contribution margin per unit for small, medium, large bags (respectively) = $40, $55, $90 Sales mix (based on physical units): small, medium, large: 20, 5, 1 (that is, 4 × 5, 5, 1) Weighted-average contribution margin per unit = [(20/26) × $40/unit] + [(5/26) × $55/unit] + [(1/26) × $90/unit] = [0.769231 × $40/unit] + [0.192308 × $55/unit] + [0.038462 × $90/unit] = $30.769 + $10.577 + $3.462 = $44.808/unit. Breakeven in units (total) = Fixed costs/weighted-average contribution margin per unit = $2,027,562 / $44.808/unit = 45,250. Breakdown of total breakeven units: Small = [45,250 units × (20/26)] = 34,808 units; Medium = [45,250 units × (5/26)] = 8,702; Large = [45,250 units × (1/26)] = 1,741 units.
What tool can you use to incorporate probabilities into the What-If analysis?
Decision Tables
Which one of the following is defined, at any given sales volume, as the ratio of the total contribution margin to operating profit at that sales volume?
Degree of operating leverage (DOL).
Cotton Company produces and sells socks. Variable costs are budgeted at $4 per pair, and fixed costs for the year are expected to total $90,000. The selling price is expected to be $6 per pair. The sales units required for Cotton Company to make an after-tax profit (πA) of $15,000, given an income tax rate of 40%, are:
Desired after-tax profit (πA) = $15,000 Desired pre-tax profit (πB) = (πA)/(1 − t) Desired pre-tax profit (πB) = $15,000/(1 − 0.40) = $25,000 $25,000 = $6Q − [$4Q + $90,000] Required sales, in units, Q = $115,000 / $2/unit = 57,500 units
At the breakeven point, total fixed cost (F) is:
Equal to the total contribution margin (CM).
Super Sports plans to market a new product for the upcoming college season. Costs associated with the new product, at two different volume ranges, are as follows: ≤ 200,000 units> 200,000 unitsFixed costs (total)$ 300,000$ 425,000Selling price per unit$ 20$ 20Contribution margin ratio15%15% How many units must be sold in order to reach a before-tax income (πB) of $400,000?
First try Q < 200,000 units: ($300,000 + $400,000)/0.15 = $4,666,667 $4,666,667 / $20/unit = 233,333 units; this is > 200,000 units, so Try fixed costs for Q > 200,000 units, as follows: ($425,000 + $400,000)/0.15 = $5,500,000 $5,500,000 / $20/unit = 275,000 units
Break-even point, in dollars =
Fixed Cost/(CM/Sales)
annual breakeven point, in unit sales =
Fixed Cost/Contribution Margin (per unit)
Break-even point, in sales dollars =
Fixed costs/contribution margin ratio
Breakeven in units (total) =
Fixed costs/weighted-average contribution margin per unit
What excel tool can be used in cost planning to determine the most cost-effective trade-off between different types of costs?
Goal Seek.
A cost-volume-profit (CVP) analysis models short-term profit (πB) as a function of all of the following variables except:
Gross margin.
High operating leverage represents increased risk associated with relatively:
High fixed cost in the firm's cost structure.
Net change in operating income =
Increase in contribution margin − Increase in fixed costs
A relatively low margin of safety ratio (MOS%) for a product is usually an indication that the product:
Is riskier than a product with a higher margin of safety ratio.
Which of the following statements regarding CVP (cost-volume-profit) analysis is true?
It is a short-term profit-planning tool.
MOS %
MOS (in dollars)/Budgeted sales (in dollars)
Many cost functions are __________ in nature when considered over the entire range of possible output levels.
Nonlinear.
Cotton Company produces and sells socks. Variable costs are budgeted at $4 per pair, and fixed costs for the year are expected to total $90,000. The selling price is expected to be $6 per pair. The sales dollars required to make an after-tax profit (πA) for Cotton Company of $15,000, given an income tax rate of 40%, are calculated to be:
Required unit sales = (F + πB)/contribution margin per unit = ($90,000 + ($15,000 / (1 − 0.40)) / ($6 − $4)/unit = ($90,000 + $25,000) / $2/unit = 57,500 units Required sales, in dollars = 57,500 units × $6/unit = $345,000
Increase in contribution margin =
contribution margin ratio × increase in sales dollars
New level of operating income (πB) =
existing level of operating income + net change in operating income
Photo Finish, Incorporated produces and sells picture frames. Variable costs are expected to be $17 per frame; fixed costs for the year are expected to total $130,000. The budgeted selling price is $25 per frame. The sales units required by Photo Finish to make a before-tax profit (πB) of $15,000 would be:
πB = TR − TC = pQ − (vQ + F), where p = selling price/unit, v = variable cost/unit, Q = sales volume (in units), and F = total fixed costs (per year). $15,000 = $25Q − ($17Q + $130,000) Q = 18,125 units
The following information pertains to Cans Corporation: Sales (22,500 units)$ 900,000Fixed costs$ 350,000Breakeven sales point, in dollars$ 700,000 If the sales price per unit were to decrease by 5% and variable expenses were to increase by $2.00 per unit, which of the following is true?
Selling price per unit, p = $900,000 / 22,500 units = $40/unit. Per-unit variable cost, v, is determined from the formula to calculate the contribution margin ratio: contribution margin ratio = 0.5 (i.e., $350,000/$700,000); ($40 − v)/$40 = 0.5; therefore, v = $20/unit New selling price per unit = $40 × 0.95 (given) = $38; new variable cost per unit = $20 + $2 (given) = $22/unit. New cm/unit = New selling price/unit − New variable cost/unit = $38/unit − $22/unit = $16/unit. Breakeven, in units = Fixed costs/new cm/unit = $350,000 (given) / $16/unit = 21,875 units. Therefore, breakeven point, in dollars = breakeven point, in units × new selling price per unit = 21,875 units × $38/unit = $831,250.
What are the two broad methods for dealing with uncertainty as applied to the cost-volume-profit (CVP) modeling process?
Sensitivity analysis and measures of operating risk
Which of the following is a technique most suited to dealing with uncertainty regarding the inputs to a cost-volume-profit (CVP) (short-term profit-planning) model?
Sensitivity analysis.
The contribution income statement would require a firm to:
Separate costs into fixed and variable categories.
What cost behavior could make an approximation via relevant range unworkable?
Step-costs.
The following information pertains to Corn Corporation: Selling price per unit $ 670Variable cost per unit$ 250Total fixed costs$ 327,600Income tax rate35% How many total units must be sold to obtain an after-tax profit (πA) of $47,775?
Targeted after-tax profit, πA = $47,775 (given) Targeted pre-tax profit, πB = πA/(1 − t) = $47,775/(1 − 0.35) = $73,500 Required sales, in units, Q = [(F + πB)/contribution margin per unit] = [($327,600 + $73,500) / ($670 − $250)/unit] = $401,100 / $420/unit = 955 units
The breakeven point is:
The sales volume at which revenues equal total cost plus an operating profit of zero.
Cost-volume-profit (CVP) analysis with multiple products assumes that sales will continue at the same mix of products, expressed in either sales units or sales dollars. This assumption is essential, because a change in the product mix will probably change:
The weighted-average contribution margin (per unit or ratio).
Income taxes have the following effect on the breakeven point calculation:
They have no effect on the breakeven point.
Index Corporation compares two products' margin of safety ratios (MOS%). Product A has a ratio of 0.13 and product B has a ratio of 0.31. Everything else held constant, what should the managers at Index Corporation do and why?
They should choose Product B because it is less risky and might require less management attention than Product A.
Effective use of the cost-volume-profit (CVP) model requires an understanding of all of the following concepts, except:
Total cost of goods sold (CGS).
Kevin Company sold 5,000 units for a price of $50 per unit and had the following information: Variable expenses$ 160,000Fixed expenses$ 125,000Breakeven sales point $ 347,222 If the sales price per unit were to increase by 10%, variable expenses were to increase by 12.5%, and fixed expenses were to increase by 20%, what would be the new contribution margin per unit?
Variable cost per unit = $160,000/5,000 units = $32 per unit New contribution margin per unit = new selling price per unit − new variable cost per unit = ($50/unit × 1.1) − ($32/unit × 1.125) = ($55.00 − $36.00)/unit = $19.00/unit
Genie Company can produce two types of lamps, the Enlightner and Foglighter. The data on the two lamp models are as follows: EnlightnerFoglighterSales volume in units500400Unit sales price$ 300$ 400Unit variable cost200240Unit contribution margin$ 100$ 160 It takes one machine hour to produce each product. Total fixed costs for the manufacture of both products are $90,000. Demand is high enough for either product to keep the plant operating at maximum capacity. Assuming that sales mix in terms of units remains constant, what is the breakeven point in total units?
Weighted-average contribution margin per unit = [(5 / 9) × $100/unit] + [(4 / 9) × $160/unit] = $126.67/unit Breakeven sales (in units) = Fixed costs/weighted-average contribution margin per unit = $90,000 / $126.67/unit = 711 units (rounded up)
Genie Company can produce two types of lamps, the Enlightner and Foglighter. The data on the two lamp models are as follows: EnlightnerFoglighterSales volume in units500400Unit sales price$ 300$ 400Unit variable cost200240Unit contribution margin$ 100$ 160 It takes one machine hour to produce each product. Total fixed costs for the manufacture of both products are $90,000. Demand is high enough for either product to keep the plant operating at maximum capacity. Assuming that sales mix in terms of dollars remains constant, what is the breakeven point in dollars?
Weighted-average contribution margin ratio = [($150/$310) × (1/3)] + [($160/$310) × 0.4] = 0.3677 Where: Sales value of Enlightner = $300/unit × 500 units = $150,000; Sales value of Foglighter = $400/unit × 400 units = $160,000 Where contribution margin ratio for Enlightner = 0.33333 (i.e., $100/unit / $300/unit) and the contribution margin ratio for Foglighter = 0.4 (i.e., $160/unit / $400/unit) Thus, the breakeven point in terms of sales dollars = Fixed costs/weighted-average contribution margin ratio = $90,000/0.3677 = $244,737 [rounded up].
