CVP: EXERCISES AND PROBLEMS 1.
Gilley, Inc., sells a single product. The company's most recent income statement is given below. Sales (4,000 units) Less variable expenses Contribution margin Less fixed expenses Net income
$120,000 (68,000) 52,000 (40,000) $ 12,000
Required: a.
Contribution margin per unit is
b.
If sales are doubled to $240,000, total variable costs will equal
$ _______________
If sales are doubled to $240,000, total fixed costs will equal
$ _______________
d.
If 10 more units are sold, profits will increase by
$ _______________
e.
Compute how many units must be sold to break even.
# _______________
f.
Compute how many units must be sold to achieve profits of $20,000.
# _______________
c.
$ _______________ per unit
Answer: a. b. c. d. e. f.
Contribution margin per unit is $30 – $17 = $13 $68,000 x 2 = $136,000 $40,000 Contribution margin of $13 x 10 units = $130 Fixed costs of $40,000 / Contribution margin per unit $13 = 3,077 units (Fixed costs of $40,000 + Profits $20,000) / CM per unit $13 = 4,616 units
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2.
Blankinship, Inc., sells a single product. The company's most recent income statement is given below. Sales Less variable expenses Contribution margin Less fixed expenses Net income
$200,000 (120,000) 80,000 (50,000) $ 30,000
Required: a.
Contribution margin ratio is
__________ %
b.
Breakeven point in total sales dollars is
$ _______________
c.
To achieve $40,000 in net income, sales must total
$ _______________
d.
If sales increase by $50,000, net income will increase by
$ _______________
Answer: a. b. c. d.
3.
Contribution margin ratio is $80,000 / $200,000 = 40% Fixed costs $50,000 / 0.40 CM% = $125,000 in sales [Fixed costs $50,000 + Net income $40,000] / 0.40 CM% = $225,000 in sales $50,000 x 0.40 CM% = $20,000 increase in net income
In 2004, Grant Company has sales of $800,000, variable costs of $200,000, and fixed costs of $300,000. In 2005, the company expects annual property taxes to decrease by $15,000. Required: a. Calculate operating income and the breakeven point for 2004. b. Calculate the breakeven point for 2005.
Answer: a.
In 2004, operating income is $800,000 sales revenue – $200,000 variable costs – $300,000 fixed costs = $300,000. The breakeven point for 2004 is $400,000 in total sales dollars. $600,000 CM / $800,000 sales revenue = 0.75 CM ratio. $300,000 total fixed costs / 0.75 CM ratio = $400,000 in total sales to break even.
b.
The breakeven point for 2005 is $380,000 in total sales dollars. $300,000 fixed costs – $15,000 reduction in property taxes = $285,000 estimated fixed costs for 2005. $285,000 total fixed costs / 75% CM ratio = $380,000 in total sales to break even. 2
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4.
Berhannan’s Cellular sells phones for $100. The unit variable cost per phone is $50 plus a selling commission of 10%. Fixed manufacturing costs total $1,250 per month, while fixed selling and administrative costs total $2,500. Required: a. What is the contribution margin per phone? b. What is the breakeven point in phones? c. How many phones must be sold to earn pretax income of $7,500?
Answer: a. CM per phone = $100 – $50 – 0.1($100) = $40 b. N = Breakeven in phones $100N – $50N – $10N – $1,250 – $2,500 = 0 $40N – $3,750 = 0 N = $3,750 / $40 = 93.75 phones Breakeven is 94 phones c. N = Phones to be sold $100N – $50N – $10N – $1,250 – $2,500 = $7,500 $40N = $11,250 N = $11,250 / $40 = 281.25 phones 282 phones must be sold
5
Alex Miller, Inc., sells car batteries to service stations for an average of $30 each. The variable cost of each battery is $20 and monthly fixed manufacturing costs total $10,000. Other monthly fixed costs of the company total $8,000. Required: a. b. c. d.
What is the breakeven point in batteries? What is the margin of safety, assuming sales total $60,000? What is the breakeven level in batteries, assuming variable costs increase by 20%? What is the breakeven level in batteries, assuming the selling price goes up by 10%, fixed manufacturing costs decline by 10%, and other fixed costs decline by $100?
Answer: a. N = Breakeven units $30N – $20N – $10,000 – $8,000 = 0 $10N – $18,000 = 0 N = $18,000/$10 = 1,800 batteries b. Margin of safety = $60,000 – ($30 x 1,800) = $6,000 3 Create PDF files without this message by purchasing novaPDF printer (http://www.novapdf.com)
c. N = Breakeven units $30N – $24N – $10,000 – $8,000 = 0 $6N – $18,000 = 0 N = $18,000/$6 = 3,000 batteries d. N = Breakeven units $33N – $20N – $9,000 – $7,900 = 0 $13N – $16,900 = 0 N = $16,900/$13 = 1,300 batteries
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6.
Furniture, Inc., sells lamps for $30. The unit variable cost per lamp is $22. Fixed costs total $9,600. Required: a. What is the contribution margin per lamp? b. What is the breakeven point in lamps? c. How many lamps must be sold to earn a pretax income of $8,000? d. What is the margin of safety, assuming 1,500 lamps are sold? Answer: a. Contribution margin per lamp = $30 – $22 = $8 b. N = Breakeven point in lamps $30N – $22N - $9,600 = 0 $8N – $9,600 = 0 N = $9,600/$8 = 1,200 lamps c. N = Target sales in lamps $30N – $22N – $9,600 – $8,000 = 0 $8N – $17,600 = 0 N = $17,600/$8 = 2,200 lamps d. Margin of safety = Sales – Breakeven sales = ($30.00 x 1,500) – $36,000 = $9,000
7.
Yurus Manufacturing Company produces two products, X and Y. The following information is presented for both products: X Y Selling price per unit $36 $24 Variable cost per unit 28 12 Total fixed costs are $234,000. Required: a. b. c.
Calculate the contribution margin for each product. Calculate breakeven point in units of both X and Y if the sales mix is 3 units of X for every unit of Y. Calculate breakeven volume in total dollars if the sales mix is 2 units of X for every 3 units of Y.
Answer: a. X: $36 – $28 = $8 Y: $24 – $12 = $12 b. (3 x $8) + (1 x $12) = $36 $234,000/$36 = 6,500 units 5 Create PDF files without this message by purchasing novaPDF printer (http://www.novapdf.com)
X: 6,500 x 3 = 19,500 units Y: 6,500 x 1 = 6,500 units c. (2 x $8) + (3 x $12) = $52 $234,000/$52 = 4,500 units X: 4,500 x 2 = 9,000 x $36 = $324,000 Y: 4,500 x 3 = 13,500 x $24 = $324,000 Total dollar sales = $648,000
8.
Bob’s Textile Company sells shirts for men and boys. The average selling price and variable cost for each product are as follows: Men’s Selling Price Variable Cost
Boys' Selling Price Variable Cost
$28.80 $20.40
$24.00 $16.80
Fixed costs are $38,400. Required: a. What is the breakeven point in units for each type of shirt, assuming the sales mix is 2:1 in favor of men's shirts? b. What is the operating income, assuming the sales mix is 2:1 in favor of men's shirts, and sales total 9,000 shirts? Answer: a. N = breakeven in boys' shirts 2N = breakeven in men's shirts $24N + $28.80(2N) – $16.80N – $20.40(2N) – $38,400 = 0 $81.6N – $57.6N – $38,400 = 0 $24N – $38,400 = 0 N = $38,400/$24 = 1,600 shirts Therefore, to break even, 1,600 boys' shirts and 3,200 men’s shirts need to be sold. b. Sales in units Revenue Variable costs Contribution margin Fixed costs Operating income
Boys' 3,000
Men's 6,000
Total 9,000
$72,000 50,400 $21,600
$172,800 122,400 $50,400
$244,800 172,800 $72,000 38,400 $33,600
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9.
Mount Carmel Company sells only two products, Product A and Product B.
Selling price Variable cost per unit Total fixed costs
Product A $40 $24
Product B $50 $40
Total
$840,000
Mount Carmel sells two units of Product A for each unit it sells of Product B. Mount Carmel faces a tax rate of 30%. Required: a. What is the breakeven point in units for each product assuming the sales mix is 2 units of Product A for each unit of Product B? b. What is the breakeven point if Mount Carmel’s tax rate is reduced to 25%, assuming the sales mix is 2 units of Product A for each unit of Product B? c. How many units of each product would be sold if Mount Carmel desired an after-tax net income of $73,500, facing a tax rate of 30%? Answer: a. N = breakeven in product B 2N = breakeven in product A ($40 x 2N) + ($50 x N) – ($24 x 2N) – ($40 x N) – $840,000 = 0 ($130 x N) – ($88 x N) – $840,000 = 0 $42N – $840,000 = 0 N = $840,000 / $42 = 20,000 Therefore, to break even, 40,000 units of Product A and 20,000 units of Product B need to be sold. b. The breakeven point would be the same. At the breakeven point there is no pre-tax income, so the tax rate change is irrelevant in this situation. c. N = number of units of product B 2N = number of units of product A ($40 x 2N) + ($50 x N) – ($24 x 2N) – ($40 x N) – $840,000 = $73,500 / (1 – .3) ($130 x N) – ($88 x N) – $840,000 = $105,000 $42N – $945,000 = 0 N = $945,000 / $42 =22,500 Therefore, to meet the profit goal, 2 x N = 45,000 units of Product A and N = 22,500 units of Product B need to be sold.
10.
Stephanie’s Stuffed Animals reported the following: Revenues $1,000 Variable manufacturing costs $ 200 Variable nonmanufacturing costs $ 230 Fixed manufacturing costs $ 150 7
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Fixed nonmanufacturing costs
$ 140
Required: a. Compute contribution margin. b. Compute gross margin. c. Compute operating income. Answer: a. Contribution margin $1,000 – $200 – $230 = $570 b. Gross margin $1,000 – $200 – $150 = $650 c. Operating income $1000 – $200 – $230 – $150 – $140 = $280
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