9.2 CVP Analysis - Target Income Calculations Flashcards
Total production costs of prior periods for a company are listed as follows. Assume that the same cost behavior patterns can be extended linearly over the range of 3,000 to 35,000 units and that the cost driver for each cost is the number of units produced.
The company is concerned about its current operating performance that is summarized as follows.
Sales ($12.50 per unit) $300,000
Variable costs 180,000
Net operating loss (40,000)
How many additional units should have been sold in order for the company to break even?
A. 16,000 units.
B. 12,800 units.
C. 8,000 units.
D. 32,000 units.
C. 8,000 units.
The breakeven point in units equals fixed costs divided by the difference between unit price and unit variable cost. Fixed costs were $160,000 [($300,000 sales – $180,000 VC) + $40,000 NOL], units sold equaled 24,000 ($300,000 sales ÷ $12.50 SP), and unit variable cost was $7.50 ($180,000 VC ÷ 24,000 units sold). Accordingly, the breakeven point in units was 32,000 [$160,000 FC ÷ ($12.50 SP – $7.50 unit VC)], and the additional units that should have been sold to break even equaled 8,000 (32,000 – 24,000).
A company, 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. The company 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
A. 19,300 units.
B. 21,316 units.
C. 22,500 units.
D. 23,800 units.
C. 22,500 units.
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].
A manufacturer is considering introducing a new product that will require a $250,000 investment of capital. The necessary funds would be raised through a bank loan at an interest rate of 8%. The fixed operating costs associated with the product would be $122,500, while the contribution margin percentage would be 42%. Assuming a selling price of $15 per unit, determine the number of units (rounded to the nearest whole unit) the manufacturer would have to sell to generate earnings before interest and taxes (EBIT) of 32% of the amount of capital invested in the new product.
A. 35,318 units.
B. 32,143 units.
C. 25,575 units.
D. 23,276 units.
B. 32,143 units.
The manufacturer has determined it must generate EBIT equal to 32% of the capital invested in this project, or $80,000 ($250,000 × 32%). The number of units it must produce to achieve this level of EBIT can be derived as follows:
Breakeven point = (Fixed costs + EBIT) ÷ Unit contribution margin
= ($122,500 + $80,000) ÷ ($15 × 42%)
= $202,500 ÷ $6.30
= 32,142.86 units
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 maximum after-tax profit that can be earned by Delphi Company from sales of the new product during the next fiscal year is
A. $30,000
B. $50,000
C. $110,000
D. $66,000
A. $30,000
Delphi’s breakeven point is 22,500 units ($450,000 fixed costs ÷ $20 UCM). The unit contribution margin (UCM) is $20 ($36 selling price – $16 unit variable costs). At the breakeven point, all fixed costs have been recovered. Hence, pretax profit equals the unit contribution margin times unit sales in excess of the breakeven point, or $50,000 [(25,000 unit sales – 22,500 BEP) × $20 UCM]. After-tax profit is $30,000 [$50,000 × (1.0 – .40)].
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
Delphi Company’s management has stipulated that it will not approve the continued manufacture of the new product after the next fiscal year unless the after-tax profit is at least $75,000 the first year. The unit selling price to achieve this target profit must be at least
A. $37.00
B. $36.60
C. $34.60
D. $39.00
D. $39.00
If X represents the necessary selling price, 25,000 equals maximum sales volume, $16 is the variable cost per unit, $450,000 is the total fixed cost, and $125,000 [$75,000 target after-tax profit ÷ (1.0 – .40)] is the desired pre-tax profit, the following formula may be solved to determine the requisite unit price:
25,000 (X – $16) – $450,000 = $125,000
25,000X – $400,000 – $450,000 = $125,000
25,000X = $975,000
X = $39
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?
A. 10,700 units.
B. 12,100 units.
C. 20,000 units.
D. 25,000 units.
D. 25,000 units.
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].
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%.
A. 10,700 units.
B. 12,100 units.
C. 20,000 units.
D. 28,300 units.
D. 28,300 units.
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.
Starlight Theater stages a number of summer musicals at its theater in northern Ohio. Preliminary planning has just begun for the upcoming season, and Starlight has developed the following estimated data:
Mr. Wonderful
Average Attendance per Performance: 3,500
Ticket price: $18
Variable Costs: $3
Fixed Costs: $165,000
That’s Life
# of performances: 20
Average Attendance per Performance: 3,000
Ticket price: 15
Variable Costs: 1
Fixed Costs: 249,000
All That Jazz
# of performances: 12
Average Attendance per Performance: 4,000
Ticket price: 20
Variable Costs: 0
Fixed Costs: 316,000
Starlight will also incur $565,000 of common fixed operating charges (administrative overhead, facility costs, and advertising) for the entire season and is subject to a 30% income tax rate.
If Starlight’s management desires “Mr. Wonderful” to produce an after-tax contribution of $210,000 toward the firm’s overall operating income for the year, total attendance for the production would have to be
A. 25,833
B. 20,800
C. 31,000
D. 25,000
C. 31,000
The unit contribution margin on “Mr. Wonderful” is $15 ($18 selling price – $3 unit variable cost). Treating desired after-tax profit as an additional fixed cost allows the target unit sales to be calculated as follows:
Target unit sales
= {Fixed costs + [Target net income ÷ (1.0 – .30)]} ÷ UCM
= [$165,000 + ($210,000 ÷ .70)] ÷ $15
= ($165,000 + $300,000) ÷ $15
= 31,000
A company wants to earn a 6% return on sales after taxes. The company’s effective income tax rate is 40%, and its contribution margin is 30%. If the company has fixed costs of $240,000, the amount of sales required to earn the desired return is
A. $1,000,000
B. $1,200,000
C. $400,000
D. $375,000
B. $1,200,000
The company can calculate its target sales figure as follows:
Net income = Operating income – (Operating income × Tax rate)
.06Sales = .3Sales – $240,000 – [(.3Sales – $240,000) × .40]
.06Sales = .3Sales – $240,000 – .12Sales + $96,000
–.12Sales = –$144,000
Sales = $1,200,000
