What is the breakeven point in units for a product that sells for $10 if fixed costs are $4,000 and variable costs are 20% of sales?
Detailed Answer
Answer (B) is correct. The breakeven point is where profit is zero and sales = fixed costs + variable costs, so 10x = 4,000 + 2x. Thus, 8x = 4,000, or x = 500 units. Alternatively, dividing the $4,000 of fixed costs by the $8 per unit contribution margin gives the same result.
2
Madengrad Company manufactures a single electronic product called Precisionmix. This unit is a batch-density monitoring device attached to large industrial mixing machines used in flour, rubber, petroleum, and chemical manufacturing. Precisionmix sells for $900 per unit. The following variable costs are incurred to produce each Precisionmix device:
Direct labor
$180
Direct materials
240
Factory overhead
105
Variable production costs
252
Marketing costs
75
Total variable costs
$600
Madengrad’s income tax rate is 40%, and annual fixed costs are $6,600,000. Except for an operating loss incurred in the year of incorporation, the firm has been profitable over the last 5 years.
If Madengrad Company achieves a sales and production volume of 8,000 units, the annual before-tax income (loss) will be
Detailed Answer
Answer (A) is correct. At a volume of 8,000 units, sales will be $7,200,000 (8,000 units × $900), and variable costs will be $4,800,000 (8,000 units × $600). Thus, the contribution margin is $2,400,000. Deducting the $6,600,000 of fixed costs from the contribution margin leaves a net loss of $4,200,000.
3
Madengrad Company manufactures a single electronic product called Precisionmix. This unit is a batch-density monitoring device attached to large industrial mixing machines used in flour, rubber, petroleum, and chemical manufacturing. Precisionmix sells for $900 per unit. The following variable costs are incurred to produce each Precisionmix device:
Direct labor
$180
Direct materials
240
Factory overhead
105
Variable production costs
252
Marketing costs
75
Total variable costs
$600
Madengrad’s income tax rate is 40%, and annual fixed costs are $6,600,000. Except for an operating loss incurred in the year of incorporation, the firm has been profitable over the last 5 years.
The annual sales volume required for Madengrad Company to break even is
Detailed Answer
Answer (A) is correct. The formula for the breakeven point in units divides the fixed costs by the unit contribution margin ($900 selling price – $600 unit variable cost = $300). Hence, the breakeven point is 22,000 units ($6,600,000 ÷ 300).
4
Madengrad Company manufactures a single electronic product called Precisionmix. This unit is a batch-density monitoring device attached to large industrial mixing machines used in flour, rubber, petroleum, and chemical manufacturing. Precisionmix sells for $900 per unit. The following variable costs are incurred to produce each Precisionmix device:
Direct labor
$180
Direct materials
240
Factory overhead
105
Variable production costs
252
Marketing costs
75
Total variable costs
$600
Madengrad’s income tax rate is 40%, and annual fixed costs are $6,600,000. Except for an operating loss incurred in the year of incorporation, the firm has been profitable over the last 5 years.
Assume a 10% increase in annual fixed costs, a 20% unit cost increase for direct labor, and a reduction in unit material costs of 25%, with no change in selling price. After incorporating these changes, Madengrad Company’s contribution margin would be
Detailed Answer
Answer (C) is correct. The original unit contribution margin (UCM) was $300 ($900 selling price – $600 unit variable cost). Unit direct labor cost is now 20% higher ($180 × 20% = $36), and unit direct materials cost is reduced by 25% ($240 × 25% = $60). Thus, the net result is that unit variable cost is reduced by $24 ($60 – $36), and the UCM will be $324 ($300 + $24). The new contribution margin percentage is therefore 36% ($324 ÷ $900).
5
Madengrad Company manufactures a single electronic product called Precisionmix. This unit is a batch-density monitoring device attached to large industrial mixing machines used in flour, rubber, petroleum, and chemical manufacturing. Precisionmix sells for $900 per unit. The following variable costs are incurred to produce each Precisionmix device:
Direct labor
$180
Direct materials
240
Factory overhead
105
Variable production costs
252
Marketing costs
75
Total variable costs
$600
Madengrad’s income tax rate is 40%, and annual fixed costs are $6,600,000. Except for an operating loss incurred in the year of incorporation, the firm has been profitable over the last 5 years.
Assume a 10% increase in annual fixed costs, a 20% unit cost increase for direct labor, and a reduction in unit material costs of 25%, with no change in selling price. Madengrad Company’s breakeven point would increase (decrease) (rounded to the nearest whole unit) by
Detailed Answer
Answer (D) is correct. The new contribution margin is $324. Dividing this amount into the fixed costs will determine the new unit breakeven point. Fixed costs have increased by 10% to $7,260,000 ($6,600,000 × 1.1), and the new breakeven point is 22,407 units ($7,260,000 ÷ $324). The original unit breakeven point was 22,000 units. Hence, the production changes increased the breakeven point by 407 units (22,407 – 22,000).
6
A company has sales of $500,000, variable costs of $300,000, and operating income of $150,000. If the company increased the sales price per unit by 10%, reduced fixed costs by 20%, and left variable cost per unit unchanged, what would be the new breakeven point in sales dollars?
Detailed Answer
Answer (A) is correct. The breakeven point in sales dollars is equal to total fixed costs divided by the
contribution margin ratio. Fixed costs are $50,000 ($500,000 sales – $300,000 variable costs – $150,000 operating income). If sales increase by 10% ($500,000 × 1.10 = $550,000) and fixed costs decrease by 20% ($50,000 × .80 = $40,000), the new contribution margin is 45.45% [($550,000 – $300,000) ÷ $550,000]. The new breakeven point can be calculated as follows: BEP in dollars = Fixed costs ÷ CMR = $40,000 ÷ .4545 =$88,000
7
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
Detailed Answer
Answer (B) is correct. 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.
8
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
Detailed Answer
Answer (A) is correct. 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).
9
Romashka, Inc., plans to introduce a new product. The marketing manager forecasts a unit selling price of $500. The variable cost per unit is estimated to be $100. In addition, there is a total of $110,000 fixed indirect manufacturing costs, and $150,000 in fixed operating costs associated with these units. What quantity will the company have to sell to break even?
Detailed Answer
Answer (D) is correct. The breakeven point in units equals total fixed costs divided by the unit contribution margin. Romashka’s breakeven quantity can therefore be derived thusly: Breakeven point = ($110,000 + $150,000) ÷ ($500 –$100 ) = $260,000 ÷ $400 = 650 units
10
A company makes a product that sells for $30. During the coming year, fixed costs are expected to be $180,000, and variable costs are estimated at $26 per unit. How many units must the company sell to break even?
Detailed Answer
Answer (C) is correct. The contribution margin per unit is $4 ($30 selling price – $26 unit variable cost). Fixed costs of $180,000 divided by the contribution of $4 per unit gives breakeven sales volume of 45,000 units.