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CHAPTER 4COST-VOLUME-PROFIT ANALYSIS: A MANAGERIAL PLANNING TOOL
DISCUSSION QUESTIONS
1. CVP analysis allows managers to focus on selling prices, volume, costs, profits, and sales mix. Many different “what-if” questions can be asked to assess the effect of changes in key variables on profits.
2. The units sold approach defines sales vol-ume in terms of units of product and gives answers in these same terms. The unit con-tribution margin is needed to solve for the break-even units. The sales revenue ap-proach defines sales volume in terms of rev-enues and provides answers in these same terms. The overall contribution margin ratio can be used to solve for the break-even sales dollars.
3. Break-even point is the level of sales activity where total revenues equal total costs, or where zero profits are earned.
4. At the break-even point, all fixed costs are covered. Above the break-even point, only variable costs need to be covered. Thus, contribution margin per unit is profit per unit, provided that the unit selling price is greater than the unit variable cost (which it must be for break even to be achieved).
5. Variable cost ratio = Variable costs/Sales
Contribution margin ratio = Contribution margin/Sales
Contribution margin ratio = 1 – Variable cost ratio
6. No. The increase in contribution is $9,000 (0.3 × $30,000), and the increase in advertis-ing is $10,000. If the contribution margin ratio is 0.40, then the increased contribution mar-gin is $12,000 (0.4 × $30,000). This is $2,000 above the increased advertising expense, so the increased advertising would be a good decision.
7. Sales mix is the relative proportion sold of each product. For example, a sales mix of 3:2 means that three units of one product are sold for every two of the second product.
8. Packages of products, based on the ex-pected sales mix, are defined as a single product. Selling price and cost information for this package can then be used to carry out CVP analysis.
9. This statement is wrong; break-even analy-sis can be easily adjusted to focus on tar-geted profit.
10. The basic break-even equation is adjusted for targeted profit by adding the desired tar-geted profit to the total fixed costs in the nu-merator. The denominator remains the con-tribution margin per unit.
11. A change in sales mix will change the contri-bution margin of the package (defined by the sales mix), and thus will change the units needed to break even.
12. Margin of safety is the sales activity in excess of that needed to break even. The higher the margin of safety, the lower the risk.
13. Operating leverage is the use of fixed costs to extract higher percentage changes in prof-its as sales activity changes. It is achieved by increasing fixed costs while lowering variable costs. Therefore, increased leverage implies increased risk, and vice versa.
14. Sensitivity analysis is a “what-if” technique that examines the impact of changes in un-derlying assumptions on an answer. A com-pany can input data on selling prices, vari-able costs, fixed costs, and sales mix and set up formulas to calculate break-even points and expected profits. Then, the data can be varied as desired to see what impact changes have on the expected profit.
15. A declining margin of safety means that sales are moving closer to the break-even point. Profit is going down, and the possibility of loss is greater. Managers should analyze the reasons for the decreasing margin of safety and look for ways to increase revenue and/or decrease costs.
4-4-11
4-24-2
MULTIPLE-CHOICE EXERCISES
4–1 d
4–2 c
4–3 a
4–4 d
4–5 e
4–6 b
4–7 b
4–8 d
4–9 d Break-even units = = 3,000
4–10 d Variable cost ratio = = 0.80, or 80%
Contribution margin ratio = = 0.20, or 20%
4–11 e
4–12 a Units to be sold = = 6,200
4-4-11
CORNERSTONE EXERCISES
Cornerstone Exercise 4–13
1. Variable cost per unit = Direct materials + Direct labor
+ Variable factory overhead + Variable selling expense
= $30 + $5 + $12 + $2
= $49
2. Total fixed expense = $14,000 + $15,400 = $29,400
3. Head-First CompanyContribution Margin Income Statement
For the Coming Year
Total Per Unit
Sales ($70 × 5,000 helmets).................................. $350,000 $70Total variable expense ($49 × 5,000)................... 245,000 49 Total contribution margin..................................... $105,000 $21Total fixed expense............................................... 29,400 Operating income ................................................. $ 75,600
Cornerstone Exercise 4–14
1. Break-even units =
=
= 1,400 helmets
2. Head-First CompanyContribution Margin Income Statement
At Break-Even Total
Sales ($70 × 1,400 helmets)....................................................... $98,000Total variable expense ($49 × 1,400)......................................... 68,600 Total contribution margin.......................................................... $29,400Total fixed expense.................................................................... 29,400 Operating income....................................................................... $ 0
4-4-22
Cornerstone Exercise 4–15
1. Variable cost ratio =
=
= 0.70, or 70%
2. Contribution margin ratio =
=
=
= 0.30, or 30%
3. Head-First CompanyContribution Margin Income Statement
For the Coming YearPercentof Sales
Sales ($70 × 5,000 helmets).................................. $350,000 100%Total variable expense ($49 × 5,000)................... 245,000 70 Total contribution margin..................................... $105,000 30Total fixed expense............................................... 29,400 Operating income ................................................. $ 75,600
Cornerstone Exercise 4–16
1. Break-even sales dollars =
=
= $98,000
4-4-33
Cornerstone Exercise 4–16 (Concluded)
2. Head-First CompanyContribution Margin Income Statement
At Break-Even Total
Sales............................................................................................ $98,000Total variable expense ($98,000 × 0.70).................................... 68,600 Total contribution margin.......................................................... $29,400Total fixed expense.................................................................... 29,400 Operating income....................................................................... $ 0
Cornerstone Exercise 4–17
1. Break-even units =
=
= 5,300 helmets
2. Head-First CompanyContribution Margin Income Statement
At 5,300 Helmets Sold Total
Sales ($70 × 5,300 helmets)....................................................... $371,000Total variable expense ($49 × 5,300)......................................... 259,700 Total contribution margin.......................................................... $111,300Total fixed expense.................................................................... 29,400 Operating income....................................................................... $ 81,900
Cornerstone Exercise 4–18
1. Sales for target income =
=
= $371,000
4-4-44
Cornerstone Exercise 4–18 (Concluded)
2. Head-First CompanyContribution Margin Income Statement
At 5,300 Helmets Sold Total
Sales............................................................................................ $371,000Total variable expense ($371,000 × 0.70).................................. 259,700 Total contribution margin.......................................................... $111,300Total fixed expense.................................................................... 29,400 Operating income....................................................................... $ 81,900
Cornerstone Exercise 4–19
1. Any package with 5 bicycle helmets for every 1 motorcycle helmet is fine. For example, 5:1, or 10:2, or 30:6. Throughout the rest of this exercise, we will use 5:1.
Unit Unit Package UnitVariable Contribution Sales Contribution
Product Price Cost Margin Mix Margin
Bicycle helmet $ 70 $ 49 $21 5 $105Motorcycle helmet 220 143 77 1 77 Package total $182
2. Break-even packages =
=
= 300 packages
Break-even bicycle helmets = Number of packages × Sales mix amount
= 300 × 5
= 1,500
Break-even motorcycle helmets = Number of packages × Sales mix amount
= 300 × 1
= 300
4-4-55
Cornerstone Exercise 4–19 (Concluded)
3. Head-First CompanyContribution Margin Income Statement
At Break-Even Total
Sales [($70 × 1,500) + ($220 × 300)]........................................... $171,000Total variable expense [($49 × 1,500) + ($143 × 300)].............. 116,400 Total contribution margin.......................................................... $ 54,600Total fixed expense.................................................................... 54,600 Operating income....................................................................... $ 0
Cornerstone Exercise 4–20
1. Contribution margin ratio =
= 0.3193
Break-even sales dollars =
=
= $170,999
2. Head-First CompanyContribution Margin Income Statement
At Break-Even Sales Dollars
Total Sales............................................................................................ $170,999Total variable expense ($170,999 × 0.6807).............................. 116,399 Total contribution margin.......................................................... $ 54,600Total fixed expense.................................................................... 54,600 Operating income....................................................................... $ 0
4-4-66
Cornerstone Exercise 4–21
1. Margin of safety in units = Budgeted units – Break-even units
= 5,000 – 1,400
= 3,600
2. Margin of safety in sales revenue = Budgeted sales – Break-even sales
= $350,000 – $98,000
= $252,000
Cornerstone Exercise 4–22
Degree of operating leverage =
=
= 1.4
Cornerstone Exercise 4–23
1. Percent change in operating income = DOL × % Change in sales
= 1.4 × 15%
= 21%
2. Expected operating income = Original income + (% Change × Original income)
= $75,600 + (0.21 × $75,600)
= $91,476
4-4-77
EXERCISES
Exercise 4–24
1. Direct materials........................................................................... $3.90Direct labor.................................................................................. 1.40Variable overhead....................................................................... 2.10Variable selling and administrative expense........................... 1 .60 Unit variable cost........................................................................ $9 .00
Unit contribution margin = Price – Unit variable cost
= $16 – $9
= $7
2. Contribution margin ratio = = 0.4375, or 43.75%
Variable cost ratio = = 0.5625, or 56.25%
3. Break-even units = = 12,850
4. Sales ($16 × 12,850).................................................................... $205,600Variable cost ($9 × 12,850)......................................................... 115,650
Total contribution margin..................................................... $ 89,950Less: Fixed expenses ($52,000 + $37,950)............................... 89,950
Operating income.................................................................. $ 0
Exercise 4–25
1. Unit variable cost = $7.60 × 0.60 = $4.56
Unit contribution margin = $7.60 – $4.56 = $3.04
2. Break-even units = = 115,000
4-4-88
Exercise 4–25 (Concluded)
3. Break-even sales revenue = $7.60 × 115,000 = $874,000
OR
Break-even sales revenue = = $874,000
4. Sales............................................................................................ $874,000Less: Variable costs................................................................... 524,400 Contribution margin................................................................... $349,600Less: Fixed costs........................................................................ 349,600 Operating income....................................................................... $ 0
Exercise 4–26
1. Contribution margin ratio =
= = 0.20, or 20%
2. Variable cost ratio = = 0.80, or 80%
OR
Variable cost ratio = 1 – Contribution margin ratio = 1.00 – 0.20 = 0.80
3. Break-even revenue =
= = $34,500
4-4-99
Exercise 4–27
1. Sales ($14 × 27,000).................................................................... $378,000Variable cost ($9.50 × 27,000).................................................... 256,500
Total contribution margin..................................................... $121,500Less: Fixed expenses................................................................. 126,000 Operating income....................................................................... $ (4,500 )
2. Break-even units = = 28,000
3. Units to earn target income = = 30,200
Exercise 4–28
1. Break-even units =
=
= 187,500
2. Unit variable cost includes all variable costs on a unit basis:
Direct materials..................................................................... $0.27Direct labor............................................................................ 0.58Variable overhead................................................................. 0.63Variable selling...................................................................... 0 .17 Unit variable cost.................................................................. $1 .65
Unit variable manufacturing cost includes the variable costs of production on a unit basis:
Direct materials..................................................................... $0.27Direct labor............................................................................ 0.58Variable overhead................................................................. 0 .63 Unit variable manufacturing cost........................................ $1 .48
Unit variable cost is used in CVP because it includes all variable costs, not just manufacturing costs.
4-4-1010
Exercise 4–28 (Concluded)
3. Units to earn $12,600 =
= 203,250
4. Sales revenue to earn $12,600 = 203,250 × $2.45 = $497,962.50
Exercise 4–29
1. Break-even units = = 208,000
2. Expected sales in units.............................................................. 380,000Break-even units......................................................................... (208,000)Margin of safety (in units).......................................................... 172,000
3. Expected sales revenue ($6.28 × 380,000)................................ $2,386,400Break-even sales revenue*........................................................ 1,306,240 Margin of safety (in dollars)....................................................... $1,080,160
*Break-even revenue = Price × Break-even units = $6.28 × 208,000 units
Exercise 4–30
A B C D Sales $15,000 $15,600* $16,250* $10,600Total variable costs 5,000 11,700 9,750 5,300 *
Total contribution margin $10,000 $ 3,900 $ 6,500* $ 5,300*Total fixed costs 9,500 * 4,000 6,136 * 4,452
Operating income (loss) $ 500 $ (100 )* $ 364 $ 848
Units sold 3,000* 1,300 125 1,000Price per unit $5.00 $12* $130 $10.60*Variable cost per unit $1.67* $9 $78* $5.30*Contribution margin per unit $3.33* $3 $52* $5.30*Contribution margin ratio 67%* 25%* 40% 50%*Break even in units 2,853* 1,333* 118* 840*
*Designates calculated amount.
(Note: Calculated break-even units that include a fractional amount have been rounded to the nearest whole unit.)
4-4-1111
Exercise 4–31
1. Variable cost ratio = = 0.45, or 45%
Contribution margin ratio = = 0.55, or 55%
2. Because all fixed costs are covered by break even, any revenue above break even contributes directly to operating income.
Sales Contribution margin ratio = Increased operating income
$30,000 × 0.55 = $16,500
Therefore, operating income will be $16,500 higher.
3. Break-even sales revenue = = $114,545 (rounded to the nearest
dollar)
Sales............................................................................................ $114,545Less: Variable cost ($114,545 × 0.45)........................................ 51,545
Contribution margin.............................................................. $ 63,000Less: Fixed cost.......................................................................... 63,000
Operating income.................................................................. $ 0
4. Expected sales............................................................................ $315,000Break-even sales........................................................................ 114,545
Margin of safety..................................................................... $200,455
5. Sales revenue............................................................................. $280,000Break-even sales........................................................................ 114,545
Margin of safety..................................................................... $165,455
4-4-1212
Exercise 4–32
1. Sales mix is 2:1 (twice as many DVDs are sold as equipment sets).
2. Variable Sales TotalProduct Price – Cost = CM × Mix = CM
DVDs $12 $4 $8 2 $16Equipment sets 15 6 9 1 9
Total $25
Break-even packages = = 2,800
Break-even DVDs = 2 × 2,800 = 5,600
Break-even equipment sets = 1 × 2,800 = 2,800
Exercise 4–33
1. Sales mix is 2:1:4 (twice as many DVDs will be sold as equipment sets, and four times as many yoga mats will be sold as equipment sets).
2. Variable Sales TotalProduct Price – Cost = CM × Mix = CM
DVDs $12 $ 4 $8 2 $16Equipment sets 15 6 9 1 9Yoga mats 18 13 5 4 20
Total $45
Break-even packages = = 2,630
Break-even DVDs = 2 × 2,630 = 5,260
Break-even equipment sets = 1 × 2,630 = 2,630
Break-even yoga mats = 4 × 2,630 = 10,520
4-4-1313
Exercise 4–33 (Concluded)
3. Switzer CompanyIncome Statement
For the Coming Year
Sales............................................................................................ $555,000Less: Total variable costs.......................................................... 330,000
Contribution margin.............................................................. $225,000Less: Total fixed costs............................................................... 118,350
Operating income.................................................................. $106,650
Contribution margin ratio = = 0.405, or 40.5%
Break-even revenue = = $292,222
4. Margin of safety = $555,000 – $292,222 = $262,778
Exercise 4–34
1. Sales mix is 3:5:1 (three times as many small basics will be sold as carved models, and five times as many large basics will be sold as carved models).
2. Variable Sales TotalProduct Price – Cost = CM × Mix = CM
Small basic $120 $ 70 $50 3 $150Large basic 200 150 50 5 250Carved model 350 275 75 1 75
Total $475
Break-even packages = = 940
Break-even small basic models = 3 × 940 = 2,820
Break-even large basic models = 5 × 940 = 4,700
Break-even carved models = 1 × 940 = 940
4-4-1414
Exercise 4–34 (Concluded)
3. Sonora CompanyIncome Statement
For the Coming Year
Sales............................................................................................ $17,100,000Less: Total variable costs.......................................................... 12,350,000
Contribution margin.............................................................. $ 4,750,000Less: Total fixed costs............................................................... 446,500
Operating income.................................................................. $ 4,303,500
Contribution margin ratio = = 0.2778, or 27.78%
Break-even revenue = = $1,607,271
4. Margin of safety = $17,100,000 – $1,607,271 = $15,492,729
Exercise 4–35
Break-even point = 2,500 units; + line is total revenue, and x line is total cost.
4-4-1515
X
X
Exercise 4–35 (Continued)
2. a. Fixed costs increase by $5,000:
Break-even point = 3,750 units
4-4-1616
X
X
Exercise 4–35 (Continued)
2. b. Unit variable cost increases to $7:
Break-even point = 3,333 units
4-4-1717
X
X
Exercise 4–35 (Continued)
2. c. Selling price increases to $12:
Break-even point = 1,667 units
4-4-1818
X
X
Exercise 4–35 (Concluded)
2. d. Both fixed costs and unit variable cost increase:
Break-even point = 5,000 units
Exercise 4–36
1. Unit contribution margin = = $27
Break-even units = = 20,000 units
2. Operating income = 30,000 × $27 = $810,000
3. Contribution margin ratio = = 0.45, or 45%
Break-even sales revenue = = $1,200,000
Profit = ($200,000 × 0.45) – $54,000 = $36,000
4-4-1919
X
X
Exercise 4–37
1. Break-even sales dollars = = $1,580,431
*Contribution margin ratio = = 0.58, or 58%
2. Margin of safety = $2,250,000 – $1,580,431 = $669,569
3. Degree of operating leverage =
=
= 3.36
4. Percent change in operating income = 3.36 × 0.20 = 0.67
New operating income = $388,350 + (0.67 × $388,350) = $648,545
4-4-2020
Exercise 4–38
1. Variable Sales PackageProduct Price – Cost = CM × Mix = CM
Vases $40 $30 $10 2 $20Figurines 70 42 28 1 28
Total $48
Break-even packages = = 625
Break-even vases = 2 × 625 = 1,250
Break-even figurines = 1 × 625 = 625
2. The new sales mix is 3 vases to 2 figurines.
Variable Sales PackageProduct Price – Cost = CM × Mix = CM
Vases $40 $30 $10 3 $30Figurines 70 42 28 2 56
Total $86
Break-even packages = = 410
Break-even vases = 3 × 410 = 1,230
Break-even figurines = 2 × 410 = 820
4-4-2121
Exercise 4–39
1. a. Variable cost per unit = = $19.20
b. Contribution margin per unit = = $4.80
c. Contribution margin ratio = = 0.20, or 20%
d. Break-even units = = 315,000
e. Break-even sales dollars = = $7,560,000
OR
Break-even sales dollars = 315,000 × $24 = $7,560,000
2. Units for target income = = 377,500
3. Additional operating income = $50,000 × 0.20 = $10,000
4. Margin of safety in units = 350,000 – 315,000 = 35,000 units
Margin of safety in sales dollars = $8,400,000 – $7,560,000 = $840,000
5. Degree of operating leverage = = 10.0
6. New operating income = $168,000 + [(10 × 0.10) ($168,000)] = $336,000
4-4-2222
PROBLEMS
Problem 4–40
1. Break-even units =
=
=
= 89,600 units
2. Units for target profit =
=
= 169,600 units
3. Contribution margin ratio = = 0.40
With additional sales of $50,000, the additional profit would be 0.40 × $50,000 = $20,000.
4. Current units = $2,480,000
= 124,000 units$20
Margin of safety in units = 124,000 – 89,600 = 34,400 units
4-4-2323
Problem 4–41
1. Break-even units =
=
= 19,200 units
2. Break-even units =
= 16,500 units
3. The reduction in fixed costs reduces the break-even point because less contri-bution margin is needed to cover the new, lower fixed costs. Operating income goes up, and the margin of safety also goes up.
Problem 4–42
1. Unit contribution margin = = $15
Break-even point = = 66,667 units
Contribution margin ratio = = 0.3
Break-even sales = = $3,333,333
OR
= $50 × 66,667 = $3,333,350 (rounded)
Note: Difference in break-even sales due to rounding.
2. Increased contribution margin ($1,000,000 × 0.3).................... $300,000Less: Increased advertising expense....................................... 100,000
Increased profit..................................................................... $200,000
4-4-2424
Problem 4–42 (Concluded)
3. $315,000 × 0.3 = $94,500
4. Margin of safety = $6,400,000 – $3,333,333 = $3,066,667
Or
= $6,400,000 – $3,333,350 = $3,066,650 (rounded)
Note: Difference in margin of safety due to rounding in break-even sales.
5. = 2.09 (operating leverage)
20% × 2.09 = 41.8% (profit increase)
Problem 4–43
1. Sales mix:
Squares: = 10,000 units
Circles: = 50,000 units
Variable Contribution Sales TotalProduct Price – Cost* = Margin × Mix = CM
Squares $30 $10 $20 1 $ 20Circles 50 10 40 5 200
Package $220
* = $10
= $10
Break-even packages = = 7,400 packages
Break-even squares = 7,400 × 1 = 7,400
Break-even circles = 7,400 × 5 = 37,000
4-4-2525
Problem 4–43 (Concluded)
2. New mix:Variable Contribution Sales Total
Product Price – Cost* = Margin × Mix = CM
Squares $30 $10 $20 3 $ 60Circles 50 10 40 5 200
Package $260
Break-even packages = = 6,262 packages
Break-even squares = 6,262 × 3 = 18,786
Break-even circles = 6,262 × 5 = 31,310
3. Increase in contribution margin for squares (25,000 × $20).. . $ 500,000Decrease in contribution margin for circles (5,000 × $40)...... (200,000 )
Increase in total contribution margin.................................. $ 300,000Less: Additional fixed expenses............................................... 245,000
Increase in income................................................................ $ 55,000
Gosnell would gain $55,000 by increasing advertising for the squares. This is a good strategy.
Problem 4–44
1. Break-even units = = 650,000
Margin of safety in units = 830,000 – 650,000 = 180,000
2. Sales revenue ($0.36 × 830,000)................................................ $298,800Total variable cost ($0.27 × 830,000)......................................... 224,100
Total contribution margin..................................................... $ 74,700Total fixed expense.................................................................... 58,500
Operating income.................................................................. $ 16,200
3. Units for target profit =
= 1,050,000
4-4-2626
Problem 4–44 (Concluded)
4. Operating income = Sales – (Variable cost ratio × Sales) – Fixed cost
0.20 Sales = Sales – (0.75 × Sales) – $58,500
0.20 Sales = 0.25 Sales – $58,500
$58,500 = (0.25 Sales – 0.20 Sales)
$58,500 = 0.05 Sales
Sales = $1,170,000
Problem 4–45
1. Contribution margin ratio = = 0.54, or 54%
2. Revenue = = $277,778
3. $560,400 × 110% = $616,440
$257,784 × 110% = 283,562
$332,878
Contribution Margin Ratio = = 0.54
The contribution margin ratio remains at 0.54.
4. Additional variable expense: $560,400 × 0.03 = $16,812
New contribution margin = $302,616 – $16,812 = $285,804
New contribution margin ratio = = 0.51
Break-even point = = $294,118
The effect is to increase the break-even point.
4-4-2727
Problem 4–45 (Concluded)
5. Present contribution margin...................................................... $302,616Projected contribution margin*................................................. 326,604 Increase in contribution margin/profit...................................... $ 23,988
*($560,400 + $80,000) × 0.51 = $326,604
Operating leverage will decrease because the increase in variable costs (the sales commission) causes a decrease in the contribution margin.
Doerhing should pay the commission because profit would increase by $23,988.
Problem 4–46
1. Revenue =
=
= $450,000
2. Of total sales revenue, 60 percent is produced by floor lamps and 40 percent by desk lamps.
= 12,000 units
= 12,000 units
Thus, the sales mix is 1:1.
4-4-2828
Problem 4–46 (Concluded)
Variable Contribution Sales TotalProduct Price – Cost = Margin × Mix = CM
Floor lamps $30 $20.00 $10.00 1 $10.00Desk lamps 20 13.33 6.67 1 6.67 Package $16.67
Number of packages =
=
= 8,998 packages
Floor lamps: 1 × 8,998 = 8,998
Desk lamps: 1 × 8,998 = 8,998
3. Operating leverage =
=
= 4.0
Percentage change in profits = 4.0 × 40% = 160%
Problem 4–47
1. Door Handles Trim Kits
CM $12 – $9 = $3 $8 – $5 = $3CM ratio $3/$12 = 0.25 $3/$8 = 0.375
2. Contribution margin:
($3 × 20,000) + ($3 × 40,000) $180,000
Less: Fixed costs 146,000
Operating income $ 34,000
4-4-2929
Problem 4–47 (Concluded)
3. Sales mix (from Requirement 2): 1 door handle to 2 trim kits
Price – V = CM × Sales Mix = Total CM
Door handle $12 $9 $3 1 $3.00Trim kit 8 5 3 2 6.00
Package $9.00
Break-even packages = = 16,222
Door handles = 1 × 16,222 = 16,222Trim kits = 2 × 16,222 = 32,444
4. Revenue (70,000 × $8)................................................................ $560,000Variable cost (70,000 × $5)......................................................... 350,000
Contribution margin.............................................................. $210,000Fixed cost.................................................................................... 111,000
Operating income.................................................................. $ 99,000
Yes, operating income is $65,000 higher than when both door handles and trim kits are sold.
Problem 4–48
1. Break-even units = = 21,429
* = $14
Break-even in dollars = 21,429 × $42** = $900,018
OR
= = $900,000
The difference is due to rounding.
** = $42
4-4-3030
Problem 4–48 (Concluded)
2. Margin of safety = $1,218,000 – $900,000 = $318,000
3. Sales............................................................................................ $1,218,000Variable cost (0.45 × $1,218,000)............................................... 548,100
Contribution margin.............................................................. $ 669,900Fixed costs.................................................................................. 550,000
Operating income.................................................................. $ 119,900
Break-even in units = = 23,810
Break-even in sales dollars = = $1,000,000
* = $23.10
** = 55%
Problem 4–49
1. Variable cost ratio =
= = 0.38, or 38%
Contribution margin ratio =
=
= 0.62, or 62%
2. Break-even sales revenue = = $500,000
3. Margin of safety = Sales – Break-even sales= $930,000 – $500,000 = $430,000
4-4-3131
Problem 4–49 (Concluded)
4. Contribution margin from increased sales = ($7,500)(0.62) = $4,650
Cost of advertising = $5,000
No, the advertising campaign is not a good idea, because the company’s oper-ating income will decrease by $350 ($4,650 – $5,000).
Problem 4–50
1. Income = Revenue – Variable cost – Fixed cost
$0 = 1,500P – $300(1,500) – $120,000
$0 = 1,500P – $450,000 – $120,000
$570,000 = 1,500P
P = $380
2. = 128,000
Unit variable cost = $2.25
Problem 4–51
1. Contribution margin per unit = $5.60 – $4.20*= $1.40
*Variable costs per unit:
$0.70 + $0.35 + $1.85 + $0.34 + $0.76 + $0.20 = $4.20
Contribution margin ratio = = 0.25
2. Break-even in units = = 32,000 boxes
Break-even in sales = 32,000 × $5.60 = $179,200
OR
= = $179,200
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Problem 4–51 (Concluded)
3. Sales ($5.60 × 35,000)................................................................. $196,000Variable cost ($4.20 × 35,000).................................................... 147,000
Contribution margin.............................................................. $ 49,000Fixed cost.................................................................................... 44,800
Operating income.................................................................. $ 4,200
4. Margin of safety = $196,000 – $179,200 = $16,800
5. Break-even in units = = 22,400 boxes
New operating income = $6.20(31,500) – $4.20(31,500) – $44,800= $195,300 – $132,300 – $44,800 = $18,200
Yes, operating income will increase by $14,000 ($18,200 – $4,200).
Problem 4–52
1. Company A: = 2
Company B: = 6
2. Company A Company B
X = X =
X = X =
X = $250,000 X = $416,667
Company B must sell more than Company A to break even because it must cover $200,000 more in fixed costs (it is more highly leveraged).
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Problem 4–52 (Concluded)
3. Company A: 2 × 50% = 100%
Company B: 6 × 50% = 300%
The percentage increase in profits for Company B is much higher than Com-pany A’s increase because Company B has a higher degree of operating lever-age (i.e., it has a larger amount of fixed costs in proportion to variable costs as compared to Company A). Once fixed costs are covered, additional revenue must cover only variable costs, and 60 percent of Company B’s revenue above break even is profit, whereas only 20 percent of Company A’s revenue above break even is profit.
Problem 4–53
1. Contribution margin ratios:
May of current year = = 0.549, or 54.9%
May of prior year = = 0.561, or 56.1%
2. Break-even point in sales dollars:
May of current year = = $37,031
May of prior year = = $24,599
3. Margin of safety:
May of current year = $43,560 – $37,031 = $6,529May of prior year = $41,700 – $24,599 = $17,101
4. Clearly, the sharp rise in fixed costs from the prior year to the current year has had a strong impact on the break-even point and the margin of safety. Kicker will need to ensure that tight cost control is exercised since the margin of safety is much slimmer. Still, the decision to go with the OEM investment pro-gram could pay large dividends in the future. Note that the margin of safety and break-even point give the company important information on the potential risk of the venture but do not tell it the upside potential.
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CASES
Case 4–54
1. Let X be a package of 3 Grade I cabinets and 7 Grade II cabinets.
0.3X($3,400) + 0.7X($1,600) = $1,600,000
X = 748 packages
Grade I: 0.3 × 748 = 224 unitsGrade II: 0.7 × 748 = 524 units
2. Variable Contribution Sales TotalProduct Price – Cost = Margin × Mix = CM
I $ 3,400 $ 2,686 $714 3 $2,142II 1,600 1,328 272 7 1,904
Package 21,400 17,354 $4,046
Direct fixed costs — I $ 95,000Direct fixed costs — II 95,000Common fixed costs 35,000
Total fixed costs $225,000
= 56 packages
Grade I: 3 × 56 = 168Grade II: 7 × 56 = 392
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Case 4–54 (Continued)
3. Variable Contribution Sales TotalProduct Price – Cost = Margin × Mix = CM
I $ 3,400 $ 2,444 $956 3 $2,868II 1,600 1,208 392 7 2,744
Package 21,400 15,788 $5,612
$21,400X = $1,600,000 – $600,000X = 47 packages remaining
Grade I: 3 × 47 = 141Grade II: 7 × 47 = 329
Additional contribution margin:141($956 – $714) + 329($392 – $272) $73,602Increase in fixed expenses 44,000
Increase in income $29,602
Break-even: = 48 packages
Grade I: 3 × 48 = 144Grade II: 7 × 48 = 336
If the new break-even point is interpreted as a revised break-even point for the current year, then total fixed costs must be reduced by the contribution mar-gin already earned (through the first five months) to obtain the units that must be sold for the last seven months. These units would then be added to those sold during the first five months:
Contribution margin earned = $600,000 – (83* × $2,686) – (195* × $1,328) = $118,102
*224 – 141 = 83; 524 – 329 = 195
X = = 27 packages
From the first five months, 28 packages were sold (83/3 or 195/7). Thus, the re-vised break-even point is 55 packages (27 + 28)—in units, 165 of I and 385 of II.
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Case 4–54 (Concluded)
4. Variable Contribution Sales TotalProduct Price – Cost = Margin × Mix = CM
I $3,400 $2,686 $714 1 $714II 1,600 1,328 272 1 272
Package $986
New sales revenue $1,000,000 × 130% = $1,300,000
$5,000X = $1,300,000X = 260 packages
Thus, 260 units of each cabinet will be sold during the rest of the year.
Effect on profits:
Change in contribution margin:$714(260 – 141) – $272(329 – 260) $66,198
Increase in fixed costs:$70,000(7/12) 40,833
Increase in operating income $25,365
X =
=
= 299 packages (or 299 of each cabinet)
The break-even point is computed as follows:
X =
=
= 179 packages (179 of each)
To this, add the units already sold, yielding the revised break-even point:I: 83 + 179 = 262II: 195 + 179 = 374
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Case 4–55
1. Break-even point =
First process: = 5,000 cases
Second process: = 8,333 cases
2. Income = X(Price – Variable cost) – Fixed costX($30 – $10) – $100,000 = X($30 – $6) – $200,000
$20X – $100,000 = $24X – $200,000$100,000 = $4X
X = 25,000 cases
The manual process is more profitable if sales are less than 25,000 cases; the automated process is more profitable at a level greater than 25,000 cases. It is important for the manager to have a sales forecast to help in deciding which process should be chosen.
3. The right to decide which process should be chosen belongs to the divisional manager. Danna has an ethical obligation to report the correct information to her superior. By altering the sales forecast, Danna unfairly and unethically in-fluenced the decision-making process. Managers certainly have a moral obli-gation to assess the impact of their decisions on employees, and every effort should be taken to be fair and honest with employees. Danna’s behavior, how-ever, is not justified by the fact that it helped a number of employees retain their employment. First, Danna had no right to make that decision. Danna cer-tainly has the right to voice her concerns about the impact of automation on the employees’ well-being. In so doing, perhaps the divisional manager would come to the same conclusion even though the automated system appears to be more profitable. Second, the choice to select the manual system may not be the best for the employees anyway. The divisional manager may possess more information, making the selection of the automated system the best al-ternative for all concerned, provided the sales volume justifies its selection. For example, if the automated system is viable, the divisional manager may have plans to retrain and relocate the displaced workers in better jobs within the company. Third, her motivation for altering the forecast seems more driven by her friendship with Jerry Johnson than any legitimate concerns for the layoff of other employees. Danna should examine her reasoning carefully to assess the real reasons for her behavior. Perhaps in so doing, the conflict of interest that underlies her decision will become apparent.
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