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.
How many surge protectors (rounded to the nearest hundred) must Bruell Electronics sell at a selling price of $14 per unit to gain $30,000 additional income before taxes?
Detailed Answer
Answer (D) is correct. The number of units to be sold to generate a specified pre-tax income equals the sum of total fixed costs and the targeted pre-tax income, divided by the unit contribution margin. Unit variable costs total $8 ($3.25 + $4.00 + $.75), and UCM is $6 ($14 unit selling price – $8). Thus, the desired unit sales level equals 25,000 units [($120,000 + $30,000) ÷ $6].
2
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.
How many surge protectors (rounded to the nearest hundred) must Bruell Electronics sell at a selling price of $14 per unit to increase after-tax income by $30,000? Bruell Electronics’ effective income tax rate is 40%.
Detailed Answer
Answer (D) is correct. The number of units to be sold to generate a specified pre-tax income equals the sum of total fixed costs and the targeted pre-tax income, divided by the unit contribution margin. Given a desired after-tax income of $30,000 and a tax rate of 40%, the targeted pre-tax income must be $50,000 [$30,000 ÷ (1.0 – .40)]. Unit variable costs total $8 ($3.25 + $4.00 + $.75), and UCM is $6 ($14 unit selling price – $8). Hence, the desired unit sales level is 28,333 [($120,000 + $50,000) ÷ $6]. Rounded to the nearest hundred, the answer is 28,300 units.
3
Austin Manufacturing, which is subject to a 40% income tax rate, had the following operating data for the period just ended:
Selling price per unit $60
Variable cost per unit $22
Fixed costs 504,000
Management plans to improve the quality of its sole product by (1) replacing a component that costs $3.50 with a higher-grade unit that costs $5.50 and (2) acquiring a $180,000 packing machine. Austin will depreciate the machine over a 10-year life with no estimated salvage value by the straight-line method of depreciation. If the company wants to earn after-tax income of $172,800 in the upcoming period, it must sell
Detailed Answer
Answer (C) is correct. The units to be sold equal fixed costs plus the desired pretax profit, divided by the unit contribution margin. In the preceding year, the unit contribution margin is $38 ($60 selling price – $22 unit variable cost). That amount will decrease by $2 to $36 in the upcoming year because of use of a higher-grade component. Fixed costs will increase from $504,000 to $522,000 as a result of the $18,000 ($180,000 ÷ 10 years) increase in fixed costs attributable to depreciation on the new machine. Dividing the $172,800 of desired after-tax income by 60% (the complement of the tax rate) produces a desired before-tax income of $288,000. Hence, the breakeven point in units is 22,500 [($522,000 + $288,000) ÷ $36].
4
A company has just completed the final development of its only product, general recombinant bacteria, which can be programmed to kill most insects before dying themselves. The product has taken 3 years and $6,000,000 to develop. The following costs are expected to be incurred on a monthly basis for the normal production level of 1,000,000 pounds of the new product:
Direct materials
300,000
Direct labor
1,250,000
Variable factory overhead
450,000
Fixed factory overhead
2,000,000
Variable selling, general and administrative expenses
900,000
Fixed selling, general and administrative expenses
1,500,000
Total
6,400,000
At a sales price of $5.90 per pound, the sales in pounds necessary to ensure a $3,000,000 profit the first year would be (to the nearest thousand pounds)
Detailed Answer
Answer (C) is correct. In breakeven analysis, total revenue equals fixed costs plus variable costs. If a given profit is desired, it is treated as a fixed cost. Exclusive of profit, the annual fixed cost is $42,000,000 ($3,500,000 per month of fixed factory overhead and SG&A expense × 12 months). The variable cost per pound is $2.90 [($300,000 + $1,250,000 + $450,000 + $900,000) ÷ 1,000,000 lbs.]. If X equals sales in pounds, the level of sales needed to earn a $3,000,000 profit is
$5.90X = $3,000,000 + $42,000,000 + $2.90X
$3X = $45,000,000
X = 15,000,000 pounds
This analysis assumes that no additional costs are incurred when production exceeds the normal level of 1,000,000 pounds per month.
5
A company that sells its single product for $40 per unit had after-tax net income for the past year of $1,188,000 after applying an effective tax rate of 40%. The projected costs for manufacturing and selling its single product in the coming year are listed below.
Variable costs per unit
$
Direct material
5
Direct labor
4
Manufacturing overhead
6
Selling and administrative costs
3
Total variable cost per unit
18
Annual fixed operating costs
Manufacturing overhead
6,200,000
Selling and administrative costs
3,700,000
Total annual fixed cost
9,900,000
The dollar sales volume required in the coming year to earn the same after-tax net income as the past year is
Detailed Answer
Answer (B) is correct. The desired after-tax net income is $1,188,000 (the past year’s amount). Given a 40% tax rate, the pretax equivalent is $1,980,000 [$1,188,000 ÷ (1.0 – .40)]. Pretax net income equals dollar sales (unit sales × $40), minus total fixed costs, minus total variable costs (unit sales × unit variable cost). Hence, the contribution margin (sales – variable costs) is equated with the sum of fixed costs and the targeted pretax net income. Unit sales (S) equal 540,000, and sales dollars equal $21,600,000 (540,000 units × $40).
$40 S – $9,900,000 – $18 S = 1,980,000
$22 S = $11,880,000
S = 540,000 units
6
A company that sells its single product for $40 per unit had after-tax net income for the past year of $1,188,000 after applying an effective tax rate of 40%. The
projected costs for manufacturing and selling its single product in the coming year are listed below.
Variable costs per unit
$
Direct material
5
Direct labor
4
Manufacturing overhead
6
Selling and administrative costs
3
Total variable cost per unit
18
Annual fixed operating costs
Manufacturing overhead
6,200,000
Selling and administrative costs
3,700,000
Total annual fixed cost
9,900,000
The company has learned that a new direct material is available that will increase the quality of its product. The new material will increase the direct material costs by $3 per unit. The company will increase the selling price of the product to $50 per unit and increase its marketing costs by $1,575,000 to advertise the higher-quality product. The number of units the company has to sell in order to earn a 10% before-tax return on sales would be
Detailed Answer
Answer (D) is correct. Pretax net income (10% of dollar sales) equals dollar sales (unit sales × $50), minus total fixed costs (increased by $1,575,000 of marketing costs), minus total variable costs (increased by $3 per unit). Unit sales (S) therefore equal 478,125 units.
.10($50 S) = $50 S – ($9,900,000 + $1,575,000) – ($18 + $3)S
$24 S = $11,475,000
S = 478,125 units
7
A manufacturer produces a product that sells for $10 per unit. Variable costs per unit are $6 and total fixed costs are $12,000. At this selling price, the company earns a profit equal to 10% of total dollar sales. By reducing its selling price to $9 per unit, the manufacturer can increase its unit sales volume by 25%. Assume that there are no taxes and that total fixed costs and variable costs per unit remain unchanged. If the selling price were reduced to $9 per unit, the profit would be
Detailed Answer
Answer (A) is correct. To determine the profit under the new pricing policy, the sales volume under the old policy must be calculated. $10X – $6X – 12,000 = 0.1($10X)
X = 4,000 units
The expected volume at the new price of $9 is 5,000 units (4,000 × 125%), and the new profit is $3,000 [(5,000 × $9) – (5,000 × $6) – $12,000.
8
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
Sales for the coming year are expected to exceed last year’s by 1,000 units. If this occurs, Donnelly’s sales volume in the coming year will be
Detailed Answer
Answer (A) is correct.
Because last year’s after-tax profit was $5,040, pretax net income must have been $8,400 [$5,040 ÷ (1.0 – .40)]. Because fixed costs have been fully recovered at the BEP, all of the UCM beyond that sales level is included in pretax operating income. The UCM was $5.25, so the units sold in excess of the 20,000-unit BEP equaled 1,600 ($8,400 ÷ $5.25). If 21,600 total units were sold last year, an increase of 1,000 units results in sales of 22,600 units.
9
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
If Donnelly Corporation wishes to earn $22,500 in net income for the coming year, the company’s sales volume in dollars must be
Detailed Answer
Answer (D) is correct. An after-tax net income of $22,500 equals a pretax income of $37,500 [$22,500 ÷ (1.0 – .40)]. With a UCM of $6 contributing toward the $153,000 total of fixed cost ($115,500) and desired profit ($37,500), 25,500 units ($153,000 ÷ $6) must be sold. At $9 per unit, sales revenue is $229,500.
10
For one of its divisions, Buona Fortuna Company has fixed costs of $300,000 and a variable-cost percentage equal to 60% of its $10 per unit selling price. It would like to earn a pre-tax income of $90,000 per year from the division.
How many units will Buona Fortuna have to sell to earn a pre-tax income of $90,000 per year?
Detailed Answer
Answer (D) is correct. Buona Fortuna’s unit contribution margin is 4 ( $10 unit price – $6 unit variable cost). By treating desired profit as an additional fixed cost, the target unit sales can be calculated as follows:
Target unit sales = (Fixed costs + Target operating income) ÷ UCM
= ($300,000 + $90,000) ÷ $4
97,500
