CHAPTER 20 COST-VOLUME-PRO COST-VOLUME-PROFIT FIT ANAL A NALYSIS YSIS
SOLUTIONS TO BRIEF EXERCISES B. Ex. Ex. 20.1 20.1
a. Total Total vari variabl ablee costs costs increa increase se appro approxim ximate ately ly in in propo proporti rtion on to to an increa increase se in in the the volume of activity. b. Variable costs per unit remain remain relatively constant at all levels of activity; this is the reason that total variable costs vary in proportion to changes in the th e volume of activity. c. Total fixed fixed costs remain remain relativel relatively y constant constant despite increase increasess in the volume of activity. d. Because Because total fixed fixed costs tend to remain remain constant constant as the volume volume of activity activity increases, fixed costs per unit decline with increases in the volume of activity. e. Semivariabl Semivariablee costs include include both fixed fixed and variable variable cost elements. elements. Because Because of the variable cost element, total semivariable costs tend to rise as the volume of activity increases. Due to the fixed element of the semivariable cost, however, this increase is less than proportionate to the increase in the volume of activity. f. On a per-unit per-unit basis, the the fixed elements elements of of a semivariabl semivariablee cost decline decline as the volume of activity increases, but the variable elements tend to remain constant. Thus, semivariable costs per unit decline as the volume of activity rises, but not as rapidly as if the entire cost were fixed.
B. Ex. 20.2
a. Variable. The cost of goods sold normally rises and falls in almost direct proportion to changes in net sales. Although fixed manufacturing overhead is a component of cost of goods sold, it is applied on a per unit basis and, therefore, acts like a variable cost. b. As described described in this exercise, exercise, the salaries salaries to salespeople salespeople are semivariabl semivariablee with respect to net sales. The monthly minimum amount represents a fixed cost that does not vary with fluctuations in net sales. However, the commissions on sales transactions represent a variable element of sales salaries that does fluctuate in approximate proportion to fluctuations in net sales.
SOLUTIONS TO BRIEF EXERCISES B. Ex. Ex. 20.1 20.1
a. Total Total vari variabl ablee costs costs increa increase se appro approxim ximate ately ly in in propo proporti rtion on to to an increa increase se in in the the volume of activity. b. Variable costs per unit remain remain relatively constant at all levels of activity; this is the reason that total variable costs vary in proportion to changes in the th e volume of activity. c. Total fixed fixed costs remain remain relativel relatively y constant constant despite increase increasess in the volume of activity. d. Because Because total fixed fixed costs tend to remain remain constant constant as the volume volume of activity activity increases, fixed costs per unit decline with increases in the volume of activity. e. Semivariabl Semivariablee costs include include both fixed fixed and variable variable cost elements. elements. Because Because of the variable cost element, total semivariable costs tend to rise as the volume of activity increases. Due to the fixed element of the semivariable cost, however, this increase is less than proportionate to the increase in the volume of activity. f. On a per-unit per-unit basis, the the fixed elements elements of of a semivariabl semivariablee cost decline decline as the volume of activity increases, but the variable elements tend to remain constant. Thus, semivariable costs per unit decline as the volume of activity rises, but not as rapidly as if the entire cost were fixed.
B. Ex. 20.2
a. Variable. The cost of goods sold normally rises and falls in almost direct proportion to changes in net sales. Although fixed manufacturing overhead is a component of cost of goods sold, it is applied on a per unit basis and, therefore, acts like a variable cost. b. As described described in this exercise, exercise, the salaries salaries to salespeople salespeople are semivariabl semivariablee with respect to net sales. The monthly minimum amount represents a fixed cost that does not vary with fluctuations in net sales. However, the commissions on sales transactions represent a variable element of sales salaries that does fluctuate in approximate proportion to fluctuations in net sales.
B. Ex. 20.2 (continued)
c. Income taxes are not a fixed, variable, or semivariable cost with respect to net sales. Income taxes may be viewed as a variable cost, but the relevant activity base is taxable income, not net sales. (Different tax brackets complicate the analysis of income taxes expense, even given taxable income as the activity base. Therefore, cost-volume-profit analysis usually focuses upon operating income—that is, income before income tax expense and other items that resist classification as costs that are fixed, variable, or semivariable with respect to net sales.) d. Fixed. Property tax expense is known for each period and is not affected by fluctuations in sales volume. e. Fixed. Depreciation expense on a sales showroom is independent of the level of net sales. Fluctuations in net sales have no effect upon the amount of depreciation applicable during the period to the sales showroom. (Depreciation can become a variable cost only when it is treated as a product cost, or when depreciation is computed using the units-of-output method. Neither of these situations applies to the depreciation on a sales showroom, which is a period cost.) f. Fixed. Use of an accelerated method causes depreciation expense to change from one period to the next, but the expense for each period still remains “fixed” with respect to fluctuations in net sales. The key idea is that fluctuations in net sales have no effect upon the amount of depreciation expense applicable to the period.
B. Ex. 20.3
a. (1) Estimated cost of responding to 150 emergency calls in one month: Fixed element of monthly emergency response cost cost ……………………………………………….. Variable cost of responding to 150 calls (150 calls × $200 per call) ……………………… Estimated total cost of responding to emergency calls ……………………………………………….. (2) Average cost per call (150 calls per month): Estimated total cost of responding to 150 emergency calls per month [part a (1) ] ……… Number of calls …………………………………… Average cost per call ($45,000 ÷ 150 calls) …….
$ 15,000 30,000 $ 45,000
$ 45,000 150 $ 300
B. Ex. 20.3 (continued)
b.
The overall cost of responding to emergency calls is semivariable—that is, it includes both fixed and variable elements. Therefore, when the volume of emergency calls is unusually low, the average cost of responding to each call will rise, because the fixed cost elements must be spread over fewer calls.
B. Ex. 20.4
a.
Contribution margin ratio 60% (100%, minus variable costs of 40%)
b.
Break-Even Sales Volume
Fixed Costs + Target Profit Contribution Margin Ratio $6,000 + $0 60% $10,000
c.
B. Ex. 20.5
a.
Fixed element of room service costs ………………………… Variable element of room service costs ($20,000 × 40%) … Estimated total room service costs in a month generating $20,000 room service revenue ………………
$
6,000 8,000
$ 14,000
If contribution margin ratio is 25%, variable costs must be 75% of sales Unit sales price = $45 variable costs ÷ 75% = $60 Unit Contribution Margin
Unit Sales Price
Variable Cost per Unit
$60 (above) - $45 = $15 b.
Fixed Costs + Target Operating Income
Sales Volume (in units)
Unit Contribution Margin =
$800,000 + $400,000 $15
= 80,000 units c.
Sales Volume (in dollars)
=
= =
Fixed Costs + Target Operating Income Contribution Margin Ratio $800,000 + $400,000 25% $4,800,000
[or 80,000 units (part b ) x ($60 unit sales price (part a ) = $4,800,000]
B. Ex. 20.6
a. If variable costs are 60% of sales revenue, the contribution margin ratio must be (100% - 60%) = 40% b.
Break-Even Sales Volume =
Fixed Costs CM ratio
$24,000 =
Fixed Costs 40%
c.
Sales Volume = =
; Fixed Costs = $9,600
Fixed Costs + Target Operating Income Contribution Margin Ratio $9,600 + $36,000 40%
= $ 114,000 B. Ex. 20.7
a. Break-even sales volume ($60 × 75,000 units) ………… Contribution margin ratio ………………………………. Fixed costs ($4,500,000 × 30%) …………………………….
$ 4,500,000 30% $ 1,350,000
b. Break-even sales volume ($60 × 75,000 units) …………… Less: Fixed costs (part a ) ………………………………… Variable cost at 75,000 units ……………………………… Variable cost per unit ($3,150,000 ÷ 75,000 units) ………
$ 4,500,000 1,350,000 $ 3,150,000 $ 42
Alternatively, if the contribution margin ratio is 30%, variable costs must amount to 70% of the unit sales price. Thus, $60 sales price × 70% = $42. c. Total costs = fixed costs + (variable cost per unit × number of units) = $1,350,000 + ($42 × number of units)
B. Ex. 20.8
a.
$6,000
b.
$9,000
($2,400 additional monthly fixed cost, divided by 40% contribution margin) [($2,400 additional cost + $1,200 target operating income) ÷ 40%]
B. Ex. 20.9
The following activity bases could be suggested to each of your clients:
Client Freeman’s Retail Floral Shop Susquehanna Trails Bus Wilson Pump Manufacturers
McCauley & Pratt, Attorneys at Law
B. Ex. 20.10
a.
Contribution Margin Ratio Flashlights 60% Batteries 25% Average contribution margin ratio
Possible Activity Bases Sales dollars Passenger miles driven Number of pumps produced Sales dollars Machine hours Direct labor hours Billable client hours Number of cases
Percentage of × Total Sales 20% 80%
Fixed Costs/Average Contribution Margin Ratio
Average = Contribution 12% 20% 32%
=
Break-Even Sales Revenue
$1,600,000 ÷ 32% = $5,000,000 b.
Fixed Costs + Target Operating Income Average Contribution Margin Ratio
= Target Revenue
($1,600,000 + $3,000,000) ÷ 32% = $14,375,000
SOLUTIONS TO EXERCISES Ex. 20.1
a. b. c. d. e. f. g. h.
Break-even point Fixed costs Relevant range Contribution margin Unit contribution margin Economies of scale Semivariable costs None (This is not a meaningful measurement; variable costs have already been deducted in arriving at operating income.)
Ex. 20.2
a. (1) High point Low point Changes
Machine Hours 6,000 2,500 3,500
Manufacturing Overhead $320,000 180,000 $140,000
Thus, the estimated variable element of Bursa Mfg. Co.’s manufacturing overhead is $40 per machine hour. [$140,000 change in cost divided by 3,500 unit change in the activity base (machine hours)]. (2) Total manufacturing overhead at 6,000 machine-hour level ………………………. Variable element of manufacturing overhead at 6,000 machine-hour level (6,000 machine hours × $40 per machine hour) ………..………………… Fixed element of manufacturing overhead …...…. b. Estimated manufacturing overhead at activity level of 4,500 machine hours: Fixed element [part a (2) ] ………………………….. Variable cost element ($40 per machine hour × 4,500 machine hours) …...…………………… Total estimated manufacturing overhead ……. c. Estimated manufacturing overhead: February: $80,000 + ($40 per MH × 3,200 MH) ….... March: $80,000 + ($40 per MH × 4,900 MH) ..... Actual manufacturing overhead ….....…… Amount over (under) estimated …..…..…
$ 320,000
$
240,000 80,000
$
80,000
$
180,000 260,000
February $
March
208,000 $
$
224,000 (16,000)
$
276,000 264,000 12,000
Ex. 20.3
a. Unit contribution margin: $90 $38 = $52 b. Sales required to break-even: $650,000 ÷ $52 = 12,500 units c. ($650,000 + $234,000) ÷ $52 = 17,000 units
Ex. 20.4
a. Contribution margin ratio Relative sales mix ………
Break-Even in Sales =
Product 1 60% × 30% 18%
+
Product 2 20% × 70% 14% = 32%
Fixed Costs Contribution Margin Ratio
Break-Even in Sales = $96,000 ÷ 32% = $300,000 b. Contribution margin ratio Relative sales mix ………
Break-Even in Sales =
Product 1 60% × 20% 12%
+
Product 2 20% × 80% 16% = 28%
Fixed Costs + Target Operating Income Contribution Margin Ratio
Break-Even in Sales = ($96,000 + $16,000) ÷ 28% = $400,000 Ex. 20.5
a.
(1) (2) (3)
Sales $200,000 180,000 600,000
b. (1) (2) (3)
Sales $900,000 600,000 500,000
Variable Costs $120,000 105,000 360,000
Contribution Margin Ratio per Unit $20 15 30
Fixed Operating Costs Income $55,000 $25,000 45,000 30,000 150,000 90,000
Variable Costs $720,000 360,000 350,000
Contribution Margin Ratio Ratio (%) 20% 40% 30%
Fixed Operating Costs Income $85,000 $95,000 165,000 75,000 90,000 60,000
Units Sold 4,000 5,000 8,000
Ex. 20.6
Ex. 20.7
It is never ethical to lie to one’s employees. This type of behavior will only serve to promote an atmosphere of distrust throughout the company. Rather than attempting to motivate the sales force by lying about sales quotas, the company should consider rewarding regional sales managers using commissions and bonuses.
a. Contribution Margin Ratio
b.
Break-Even Dollar Sales Volume
=
Unit Sales Price - Variable Cost per Unit Unit Sales Price
=
$30 $6 = 80% $30
=
=
c.
Dollar Sales Volume
=
=
Fixed Costs + $0 Contribution Margin Ratio $360,000 = $450,000 80%
Fixed Costs + Target Operating Income Contribution Margin Ratio $360,000 + $440,000 80%
= $1,000,000
d. Sales volume (60,000 unit s x $30) Less: Break-even sales volume (per part b ) Margin of safety at 60,000 units
$
$
1,800,000 450,000 1,350,000
e. Operating Income = Margin of Safety × Contribution Margin Ratio = $1,350,000 × 80% = $1,080,000
Ex. 20.8
a. Projected operating Income with out either in vestment: ($1,200,000 × 0.25) - $80,000
$
Ad Campaign Projected sales revenue × CM ratio Total contribu tion margin minus fixed costs Operating inco me
$1,260,000 (1) $ 0.25 $ 315,000 $ (100,000) $ 215,000 $
220,000
Ordering System 1,200,000 0.30 360,000 (100,000) 260,000
Thus projected operating income will decrease by $5,000 if the ad campaign is chosen ($215,000 - $220,000), and increase by $40,000 ($260,000 - $220,000) if the ordering system is chosen. (1)
($1,200,000 x 1.05)
b.
For the ad campaign to result in an equal increase in operating income, the total contribution margin produced must equal that of the ordering system ($360,000). Sales Revenue x 25% = $360,000 Sales Revenue = $1,440,000 Percentage Increase =
$1,440,000 - $1,200,000 $1,200,000
= 20%
Ex. 20.9
a. Contribution margin per unit: Unit sale price Less: Variable cost per un it ($50,000 ÷ $40,000 units ) Contribution margin per unit
$
1.75 1.25 0.50
$
78,750
$
70,000 8,750
$
66,500
$
67,500 (1,000)
b. Margin of safety at sales of 45,000 unit s: Sales revenue ($1.75 × $45,000 units) Less: Sales revenue at break-even point ($1.75 × $40,000 uni ts) Margin of safety
c. Estimated operating loss at sales level of 38,000 units: Sales revenue ($1.75 × 38,000 units) Less: Variable cos ts ($1.25 × 38,000 units ) Fixed cos ts (given) Operating Income (loss) d. (1) Unit cost at production level of 40,000 units: Variable cost per unit Fixed cost per unit ( 20,000 ÷ 40,000 units) Total unit cost (2) Unit cost at production level of 50,000 units: Variable cost per u nit Fixed cost per unit ( 20,000 ÷ 50,000 units) Total unit cos t
$
47,500 20,000
$
1.25 0.50 1.75
$
1.25 0.40 1.65
$
Total cost per unit declines at higher production levels because the fixed manufacturing costs are allocated over a greater number of units.
Ex. 20.10
a.
Contribution Margin Unit Sales Price - Variable Costs = Ratio Sales Price = Break-Even Sales = Volume =
Ex. 20.11
$45 - $27 = 40% $45 Fixed Costs Contribution Margin Ratio $300,000 = $750,000 40%
b. Sale volume at 20,000 units (20,000 × $45) …………………. Less: Break-even sales volume (part a ) ……………………… Margin of safety sales volume …………………………………
$
a. Selling price per unit …………………………………………… Variable manufacturing costs per unit…………………………. Variable selling and administrative costs per unit …………… Contribution margin per unit……………………………………
$
Fixed manufacturing costs …………………………………….. Fixed selling and administrative costs ……………………….. Total fixed costs ………………………………………………..
$
Total fixed costs ………………………………………………… Divided by contribution margin per unit ……………………… Monthly break-even in units ……………………………………
$
$
$
$
b. Contribution margin ratio (CM ÷ SP) ………………………….. Total fixed costs ………………………………………………… Target monthly income …………………………………………
c. Total fixed costs ………………………………………………… Contribution margin ratio ……………………………………… Monthly break-even sales revenue …………………………… Current monthly sales level …………………………………… Monthly break-even sales revenue …………………………… Margin of safety …………………………………………………
20 (6) (2) 12 300,000 600,000 900,000 900,000 ÷ $12 75,000 60%
$ $
Divided by contribution margin ratio …………………………. Sales revenue required …………………………………………
900,000 750,000 150,000
$ $ $ $ $
900,000 1,200,000 2,100,000 ÷ 60% 3,500,000 900,000 ÷ 60% 1,500,000 2,500,000 (1,500,000) 1,000,000
Ex. 20.11 (continued)
Ex. 20.12
d. Anticipated increase in sales revenue ………………………. Contribution margin ratio …………………………………… Estimated increase in operating income …………………….
$ $
100,000 x 60% 60,000
20,000 units x $7 per unit = $140,000 total fixed costs xe
os s ÷ on r u on
arg n = rea - ven n n s
$140,000 ÷ (SP - $26) = 10,000 units 10,000 SP - $260,000 = $140,000 10,000 SP = $400,000 SP = Selling Price = $40 per unit Ex. 20.13
a. The lowest bid price required to maintain the current level of operating income equals total variable cost per unit: Direct materials ……………………………………………….. Direct labor ……………………………………………………. Variable manufacturing overhead ………………………….. Lowest bid price to maintain current income level …………
$
$
9 8 7 24
b. Contribution Margin Ratio (CM%) = Contribution Margin (CM) ÷ Selling Price (SP) 36% = (SP - $9 - $8 - $7 - .04 SP) ÷ SP 0.36 SP = 0.96 SP - $24 $24 = 0.60 SP SP = Bid Price = $40
Ex. 20.14
Vests $120 (60)
a. Unit selling prices Unit variable costs
Skis $300 (210)
Ropes $50 (10)
Unit contribution margins Divided by unit selling prices
$60 120
$90 300
$40 50
Unit contribution margin ratios
50%
30%
80%
Mix % 20% 70% 10%
Average = CM 10% 21% 8% 39%
Vests Skis Ropes Average contribution margin ratio
CM% 50% 30% 80%
x
Fixed Costs ÷ Average Contribution Ratio (CM%) = Break-Even Sales Revenue $741,000 ÷ 39% = $1,900,000 b. (Fixed Costs + Operating Income)/CM% = Sales Revenue Required ($741,000 + $234,000) ÷ 39% = $2,500,000 c. To maximize operating income, the marketing manager should pursue a strategy that shifts the sales mix away from the products with the lowest contribution margin ratios (vests and skis) to the product with the highest contribution margin ratio (ropes).
Ex. 20.15
($975,000 - $700,000) ÷ (19,250 DLH - $12,375 DLH) = $40 per DLH a. b. $975,000 = Monthly Fixed Costs
($40 × 19,250 DLH)
Monthly Fixed Costs = $975,000 - $770,000 = $205,000 Total 3-Month Cost = ($205,000 × 3 months)
($40 × 40,000 DLH)
c. Total 3-Month Cost = $615,000
$1,600,000 = $2,215,000
SOLUTIONS TO PROBL EMS SET A PROBLEM 20.1A IONIC CHARGE
25 Minutes, Easy
a. Required contribution margin per unit Budgeted operating Income Fixed costs Total required contrib ution margin Number of units to be produced and sold Required contribu tion margin per unit ($1,500,000 ÷ 60,000 un its )
$ $
Required sales price per un it: Required contribu tion margin per unit Variable costs and expenses per unit Total required unit sales price
b.
$
25
$
25 50 75
$
Break-Even Sales Volume (in units) =
=
700,000 800,000 1,500,000 60,000
Fixed Costs Contribution Margin per Unit $800,000 $25
= 32,000 units
c. Margin of safety at 60,000 units: Sales volu me at 60,000 uni ts ($75 × 60,000 unit s) Less: Break-even sales vo lume ($75 × $32,000 units) Margin of safety
$ $
4,500,000 2,400,000 2,100,000
PROBLEM 20.1A IONIC CHARGE (concluded) d. No. With a unit sales price of $60, the break-even sales volume is 80,000 units: Unit contribution margin = $60 - $50 variable costs = $10 Break-even sales volume (in units) =
$800,000 $10
= 80,000 units Unless Ionic Charge has the ability to manufacture 80,000 units (or lower fixed and/or variable costs), setting the unit sales price at $60 will not enable the company to break-even. Of course, even if it is able to lower its costs, there must be sufficient demand to support a sales level of 80,000 units, or more.
25 Minutes, Medium
PROBLEM 20.2A BLASTER CORPORATION
a. Sales price per unit: Budgeted costs Ad d: Bu dgeted op erat ing inc ome Budgeted sales revenue Sales price per pair ($3,150,000 ÷ 30,000 pairs) b. (1) Total fixed costs: Manufacturi ng overh ead ($720,000 × 75%) Selling and adminst rative exp enses ($600,000 × 80%) Total fixed costs (2) Variable costs and expenses per pair of boots: Direct materials Direct labor Manufacturi ng o verhead ($24 × 25%) Selling and admi nist rative expens e ($20 × 20%) Total variable costs per p air (3) Contribution margin per pair of boots: Sales pr ice per pair Less: Variable costs per pair [fro m (2) ] Contribution margin per pair (4) Number of pairs required to break even: Fixed costs [fro m (1) ] Contribution margin per pair [from (3) ] Number o f pair s r equired to b reak even ($1,020,000 ÷ $80)
$ $ $
$ $
$
$
$ $
$ $
2,250,000 900,000 3,150,000 105
540,000 480,000 1,020,000
21 10 6 4 41
121 41 80
1,020,000 80 12,750
30 Minutes, Medium
a.
PROBLEM 20.3A STOP-N-SHOP
PROBLEM 20.3A STOP-N-SHOP (continued) The following information is used for parts b. and c. of this problem. Operating data: Revenue per parking-space hour Variable costs per parking-space hour Fixed costs per year: Supervisor’ s salary Wages ($300 × 52 × 5) Rent on lot ($7,250 × 12) Fixed maintenance and other expenses ($3,000 × 12) Total fixed costs
50 cents 5 cents $
24,000 78,000 87,000 36,000 $ 225,000
Capacity = 800 spaces × 2,500 hours per year = 2,000,000 parking-space hours per year Revenue at full capacity = 2,000,000 × $0.50 = $1,000,000 per year
PROBLEM 20.3A STOP-N-SHOP (concluded)
b. Contribution margin ratio: Parking charge per hour Less: Variable costs per unit Contribution margin per unit Contribution margin ratio ($0.45 ÷ $0.50) Break-even sales volume: Fixed costs: Rent on lot ($7,250 × 12) Supervisor's salary Wages ($300 × 52 × 5) Fixed maintenance and other costs ($3,000 × 12) Total annual fixed costs Contribution margin ratio (above) Break-even sales volume ($225,000 ÷ 0.90) c. (1) New contribution margin ratio per parking-space hour: Parking charge per hour Less: Variable costs ($0.05 + $0.15) Contribution margin per unit New contribution margin ratio ($0.30 ÷ $0.50) New level of fix ed costs: Rent on lot ($7,250 × 12) Supervisor’s salary Vacation pay ($300 × 2 × 5) Fixed maintenance and other costs ($3,000 × 12) Total fixed costs under new arrangement
(2) Required sales revenue to produce desired operating income: Total fixed costs under new arrangement (above) Ad d: Targ et p ro fi t Total contribution margin required New contribution margin ratio (above) Sales volume ($450,000 ÷ 0.60)
$ $
$
$ $
$ $
$
$
$ $ $
0.50 0.05 0.45 90%
87,000 24,000 78,000 36,000 225,000 90% 250,000
0.50 0.20 0.30 60%
87,000 24,000 3,000 36,000 150,000
150,000 300,000 450,000 60% 750,000
30 Minutes, Medium
PROBLEM 20.4A RAINBOW PAINTS
a. Contribution margin ratio: Unit sales price Less: Variable costs per unit Contribution margin per gallon Contribution margin ratio ($4 ÷ 10, the unit sales price)
$ $
Break-even sales volu me in d ollars: Fixed costs ($3,160 + $3,640 + $1,200) Contribution margin ratio (above) Break-even sales volume in dollars ($8,000 ÷ 0.4)
$ $
Break-even s ales v olume in gallons: Break-even sales volume in dollars (above) Unit sales price Break-even sales volume in gal. ($20,000 ÷ $10 per gal.)
$
10 6 4 40%
8,000 40% 20,000
20,000 10 2,000
b. On the following page.
c. Projected operating income at various levels: Contribution margin per gallon ($10 - $6) Total contribution margin at indicated volume Less: Fixed costs Projected monthly operating income
2,200 Gal lo ns $ 4 $ 8,800 8,000 $ 800
2,600 Gal lo ns $ $ $
4 10,400 8,000 2,400
PROBLEM 20.4A RAINBOW PAINTS (concluded) b.
PROBLEM 20.5A SIMON TEGUH
40 Minutes, Strong
a.
Unit contribution margin: Sales price per unit Less: Variable costs per unit: Merchandise Rental commission Unit contribution margin
$
c.
Sales volume to produce operating income equal to 30% return on investment: Total monthly fixed costs (part a ) Desired operating income ($45,000 × 30% × 1/12) Total desired contribution margin Contribution margin per unit (part a ) Sales volume in units ($3,825 ÷ $0.45 per unit)
d.
$
0.30 0.45
$
$ $
Break-even volume in dollars: Break-even volume in units (above) Unit sales price Break-even volume in dollars (6,000 units × $0.75)
See following page.
0.75
0.25 0.05
Break-even volume in units: Monthly fixed costs: Depreciation ($36,000 × 0.20 × 1/12) Wages Other Total monthly fixed costs Contribution margin per unit (above) Break-even volume in units ($2,700 ÷ $0.45)
b.
$
$ $
$ $ $
600 1,500 600 2,700 0.45 6,000
6,000 0.75 4,500
2,700 1,125 3,825 0.45 8,500
Sales volu me in doll ars (8,500 unit s × $0.75 per unit )
$
6,375
New monthly fixed costs [$2,700 + (20 × $30)] New contrib ution margin per unit: Unit sales price Less: Variable costs per unit (only merchandise cost) New break-even volume in units ($3,300 ÷ $0.50 per unit)
$
3,300
$
0.50 6,600
$
0.75 0.25
PROBLEM 20.5A SIMON TEGUH (concluded) b.
PROBLEM 20.6A PRECISION SYSTEMS
30 Minutes, Strong
a.
Variable costs per unit before 15% increase in the cost of direct labor Increase in cost of direct labor, 15% of $20 Variable costs and expenses per unit after 15% increase in the cost of direct labor
$
60 3
$
63
$ $
105 100 5
$
100
$
63 37
Because the contribu tion margin r atio of 40% is required, the variable costs of $63 per unit must equal 60% of sales price after the wage increase. New sales price, $63 ÷ 0.60 Sales price before increase Required increase in sales price per unit
b.
Un it c on tr ib ut io n m ar gi n: Sales price per unit Less: Variable costs per unit following 15% increase in direct labor cos t (part a ) Unit contribution margin
Sales volume required to maintain current operating income: Sales Volume
Fixed Costs + Target Operating Income Unit Contribution Margin
$390,000 + $350,000 $37
c.
= 20,000 units Current Capacity (20,000 Units)
Total contribution margin ($37 per unit) Less: Fixed costs Operating income at full capacity *$390,000 + addition al depreciatio n per y ear on new mach iner y, $140,000 (20% of $700,000).
$ $
740,000 390,000 350,000
After Expansion (25,000 Units) $ $
925,000 530,000* 395,000
35 Minutes, Strong
a.
PROBLEM 20.7A PERCULA FARMS
Raising clownfish will result in the highest operating income. Clownfish
b.
Number of salable fish × sale price Total revenue
$ $
100,000 4 400,000
Variable costs: Eggs Feedings Water changes Heating and lighting Total variable costs Total contribution margin Fixed costs: Operating income
$ $ $ $
5,500 78,750 35,000 14,000 133,250 266,750 80,000 186,750
Angelfish
$ $
$
$ $ $
50,000 10 500,000
9,500 150,000 100,000 20,000 279,500 220,500 80,000 140,500
The most important factors in determining operating income are survival rates, and the costs of feeding and water changes.
c. and d. Operating inc ome with new filter material: Clownfish Number of salable fish × sale price Total revenue
$ $
120,000 4 480,000
Variable costs: Eggs Feedings Water changes Heating and lighting Total variable costs Total contribution margin Fixed costs: Operating income
$ $ $ $
5,500 84,000 35,000 14,000 138,500 341,500 88,000 253,500
Angelfish
$ $
$
$ $ $
60,000 10 600,000
9,500 160,000 50,000 20,000 239,500 360,500 88,000 272,500
Percula will earn the highest operating income by purchasing the new filter material and raising angelfish.
PROBLEM 20.7A PERCULA FARMS (concluded) c. and d. Operating income with new heating and ligh ting equipment: Number of salable fish × sale price Total revenue Variable costs: Eggs Feedings Water changes Heating and lighting Total variable costs Total contribution margin Fixed costs: Operating income
Clownfish 105,000 $ 4 $ 420,000
Angelfish 55,000 $ 10 $ 550,000
$ $ $ $
$
5,500 78,750 35,000 10,500 129,750 290,250 88,000 202,250
$ $ $
9,500 150,000 100,000 15,000 274,500 275,500 88,000 187,500
PROBLEM 20.8A
35 Minutes, Strong
LIFEFIT PRODUCTS
a.
b.
Contribution margins of product lines: Shoes ($15 contribution margin ÷ $50 sales price) Shorts ($4 contribution margin ÷ $5 sales price)
(1)
(2)
(3)
c.
30% 80%
Average contribution mar gin ratio: From shoes (30% contribution margin × 80% of sales mix) From shorts (80% contribution margin × 20% of sales mix) Av erag e co ntri buti on mar gin r ati o Mo nt hl y o per at in g i nc om e: Total sales Av erag e co ntri buti on mar gin r ati o Total contribution margin ($1,000,000 × 40%) Less: Fixed costs and expenses Operating income Monthly break-even sales volume (in dollars): Fixed costs and expenses Av erag e co ntri buti on mar gin r ati o Break-even sales volume ($378,000 ÷ 40%)
24% 16% 40%
$ $ $
$ $
Assuming new sales mix (shoes, 70%; shorts, 30%) (1) Average contribution margin ratio: From shoes (30% contribution margin × 70% of sales) From shorts (80% contribution margin × 30% of sales) Av erag e co ntri buti on mar gin r ati o (2)
(3)
Mo nt hl y o per at in g i nc om e: Total sales Av erag e co ntri buti on mar gin r ati o Total contribution margin ($1,000,000 × 45%) Less: Fixed costs and expenses Operating income Monthly break-even sales volume (in dollars): Fixed costs and expenses Av erag e co ntri buti on mar gin r ati o Break-even sales volume ($378,000 ÷ 45%)
1,000,000 × 40% 400,000 378,000 22,000
378,000 ÷ 40% 945,000
21% 24% 45%
$ $ $
$ $
1,000,000 × 45% 450,000 378,000 72,000
378,000 ÷ 45% 840,000
PROBLEM 20.8A LIFELIFT PRODUCTS (con cluded) d.
In the new sales mix, increased sales of shorts have replaced some sales of shoes. Shorts have a much higher contribution margin than shoes. Thus, at a given sales volume, selling shorts instead of shoes provides more contribution margin, contributes more toward operating income, and lowers the sales volume required to break even.
