CHAPTER 4 COST-VOLUME-PROFIT ANALYSIS: A … 3e sm04.pdf · COST-VOLUME-PROFIT ANALYSIS: A MANAGERIAL PLANNING TOOL DISCUSSION QUESTIONS 1. CVP analysis allows managers to focus on
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CHAPTER 4 COST-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 volume in terms of units of product and gives answers in these same terms. The unit contribution margin is needed to solve for the break-even units. The sales revenue approach defines sales volume in terms of revenues 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 advertising is $10,000. If the contribution margin ratio is 0.40, then the increased contribution 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 expected 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 analysis can be easily adjusted to focus on target profit.
10. The basic break-even equation is adjusted for target profit by adding the desired target profit to the total fixed costs in the numerator. The denominator remains the contribution margin per unit.
11. A change in sales mix will change the contribution 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 profits 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 underlying assumptions on an answer. A company can input data on selling prices, variable 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.
2. Head-First Company Contribution Margin Income Statement
At Break-Even Total Sales ........................................................................................... $98,000 Total variable expense ($98,000 × 0.70) ................................... 68,600 Total contribution margin ......................................................... 29,400 Total fixed expense .................................................................... 29,400 Operating income ...................................................................... $ 0
Cornerstone Exercise 4–5
1. Break-even units = (Total fixed cost + Target income)
(Price Unit variable cost)-
= ($29,400 + $81,900)
($70 $49)-
= 5,300 helmets
2. Head-First Company
Contribution Margin Income Statement At 5,300 Helmets Sold
Total Sales ($70 × 5,300 helmets) ....................................................... $371,000 Total variable expense ($49 × 5,300) ........................................ 259,700 Total contribution margin ......................................................... 111,300 Total fixed expense .................................................................... 29,400 Operating income ...................................................................... $ 81,900
Cornerstone Exercise 4–6
1. Sales for target income = (Total fixed cost + Target income)
2. Head-First Company Contribution Margin Income Statement
At Sales Revenue of $371,000 Total Sales ........................................................................................... $371,000 Total variable expense ($371,000 × 0.70) ................................. 259,700 Total contribution margin ......................................................... 111,300 Total fixed expense .................................................................... 29,400 Operating income ...................................................................... $ 81,900
3. A contribution margin income statement helps managers make better decisions in that it focuses their attention on those areas that are easiest to control. Variable costs are usually more easily controlled than fixed costs.
Cornerstone Exercise 4–7
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 Unit Variable Contribution Sales Contribution Product Price Cost Margin Mix Margin
1. Contribution Margin Income Statement Starfirst Company
Contribution Margin Income Statement Sales $1,575,000 Variable costs 1,222,500 Contribution margin 352,500 Fixed costs 183,300 Operating income $ 169,200
2. Break-even point in units
Contribution margin per unit: $42 - $32.60 = $9.40 Break-even point in units: $183,300/$9.40 = 19,500 units
3. Units needed to generate $200,000 in operating income
Fixed costs + Target profit = $183,300 + $200,000 = $383,300 Units required = $383,300/$9.40 = 40,777 units (rounded)
Exercise 4–16
1. Unit variable cost includes all variable costs on a unit basis:
Direct materials ..................................................................... $0.27 Direct labour ......................................................................... 0.58 Variable overhead ................................................................. 0.63 Variable selling ..................................................................... 0.17 Unit variable cost .................................................................. $1.65
Unit variable manufacturing cost includes the variable costs of production on a unit basis:
Direct materials ..................................................................... $0.27 Direct labour ......................................................................... 0.58 Variable 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.
A B C D Sales $15,000 $15,600* $16,250* $10,600 Total 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 1,000 Price 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.)
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 Total Product Price – Cost = CM × Mix = CM
Small basic $180 $ 105 $75 3 $225 Large basic 300 225 75 5 375 Carved 525 412 113 1 113 Total $713
Break-even packages = $713
$669,750 = 940 (rounded up)
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
3. Sonora Company
Income Statement For the Coming Year
Sales ........................................................................................... $25,650,000 Less: Total variable costs ......................................................... 18,520,000 Contribution margin ............................................................. 7,130,000 Less: Total fixed costs .............................................................. 669,750 Operating income ................................................................. $ 6,460,250
Contribution margin ratio = $7,130,000
$25,650,000 = 0.2780, or 27.80%
Break-even revenue = 0.2780
$669,750 = $2,409,173
4. Margin of safety = $25,650,000 – $2,409,173 = $23,240,827
2. d. Both fixed costs and unit variable cost increase:
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
0 1,000 2,000 3,000 4,000 5,000 6,000 7,000
Units Sold
Rev
enu
e a
nd
Co
st (
$)
Break-even point = 5,000 units
Exercise 4–24
1. Unit contribution margin: $75 - $24.75 = $50.25 per unit
Break-even units: Fixed costs
Contribution margin =
$984,025
$50.25 = 19,583 units
2. Sell 30,000 units above break-even
Operating income increases by the contribution margin. Contribution margin for 30,000 units = 30,000 x $50.25= $1,507,500
3. Contribution margin ratio = Contribution margin
Sales =
$50.25
$75 = 67%
Break-even in dollars = Fixed costs
CM ratio =
$984,025
.67 = $1,468,694 *
Revenues up by $500,000 to $2,300,000, then CM at new level = $2,300,000 x .67 = $1,541,000 New operating income = CM – fixed costs = $1,541,000 - $984,025 = $556,975 *rounded up
3. It is better to use contribution margin ratio in determining break-even for a multi-product company because it makes the calculations easier when dealing with sales mix.
1. Break-even point in units = Fixed costs/Contribution margin per unit
= $3,213,924/$21 = 153,044 units
2. Units to sell to earn $2,700,000 = (Fixed costs + Target profit)/CM per unit
= ($3,213,924 + $2,700,000)/$21 = 281,616*
3. Contribution margin ratio = CM/Sales = $21/$60 = 35% Sales increase by $300,000; Additional operating income = Increased sales * CM ratio = $300,000 x .35 = $105,000
4. Margin of safety = Sales – Break-even sales Sales in units = $13,800,000/$60 = 230,000 units Break-even sales in units = Fixed costs/CM per unit = $3,213,924/$21 = 153,044 units Margin of safety = 230,000 units – 153,044 units = 76,956 units
Operating leverage will decrease from 1.98 ($302,616/$152,616) to 1.85 ($326,604/$176,604) because the increase in the contribution margin of $23,988 is exactly equal to the increase in the operating income, which results in a decrease in the operating leverage.
Alonzo should pay the commission because profit would increase by $23,988.
Problem 4–34
1. Revenue = Fixed cost
(1 Variable rate)-
= (1/3)
$150,000
= $450,000
2. Of total sales revenue, 60 percent is produced by floor lamps and 40 percent
4. The theory behind the operating leverage concept is that a company will increase its profits in direct relationship to the relationship between its fixed costs and its variable costs. The more fixed costs a company has the more impact an increase in revenues will have on profit because its fixed costs have been covered.
Steven Kissick, Lawyer Contribution Income Statement
Revenue $180,000 Variable costs Direct 66,000 Indirect 17,500 Contribution margin 96,500 Fixed costs Direct 88,000 Indirect 110,000 Operating income/(Loss) (101,500) Income tax (27.5%) 0 Net loss $(101,500)
1. Break-even revenue = Fixed costs
Contribution margin ratio
Contribution margin ratio = Contribution margin
Revenue
$96,500
$180,000 = 53.61%
($88,000 + $110,000)
0.5361 = $369,334 *rounded
2. To generate $150,000 after tax income, the pre-tax income
must be = $150,000
(1 - Tax rate)
Pre-tax income is = $206,897
Target revenue = (Fixed cost + Target profit)
CM%
($198,000 + $206,897)
0.5361 = $755,264 *rounded up
3. At $350 per hour, it would appear that this target is not reasonable. Based
on a 40-hour week and 50 working weeks of the year, there are 2,000 hours in a normal work year. Kissick would have to bill 2,158 hours per year to achieve his objective. If he raised his rate to $380, his goal would be realized.
Company B must sell much more than Company A to break even because it must cover $200,000 more in fixed costs (it is more highly leveraged).
3. Company A: 2 × 50% = 100%
Company B: 6 × 50% = 300%
The percentage increase in profits for Company B is much higher than Company A’s increase because Company B has a much higher degree of operating leverage (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.
4. After-tax profit of $1,300,000 is pre-tax profit of $2,000,000.
Target units are calculated by taking the fixed costs plus the target pre-tax profit divided by the contribution margin per package and then calculating the number of each unit in a package.
Fixed costs ($1,429,200) plus target profit ($2,000,000) = $3,429,200
2. Break-even point in sales dollars (in thousands):
May of current year = 0.549
$20,330 = $37,031
May of prior year = 0.561
$13,800 = $24,599
3. Margin of safety (in thousands):
May of current year = $43,560 – $37,031 = $6,529 May 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 large impact on the break-even point and the margin of safety. Bissonette 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 program 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.
3. Variable Contribution Sales Total Product Price – Cost = Margin × Mix = CM
I $ 3,400 $ 2,444 $956 3 $2,868 II 1,600 1,208 392 7 2,744 Package 21,400 15,788 $5,612
$21,400X = $1,600,000 – $600,000 X = 47 packages remaining
Grade I: 3 × 47 = 141 Grade II: 7 × 47 = 329
Additional contribution margin: 141($956 – $714) + 329($392 – $272) = $73,602 Increase in fixed expenses 44,000 Increase in operating income $29,602
Break-even point for the year: ($225,000 + $75,430)
$5,612 = 54 packages
Grade I: 3 × 54 = 162 Grade II: 7 × 54 = 378
If the new break-even point is the revised break-even point for the current year, therefore total fixed costs must be reduced by the contribution margin 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:
From the first five months, 28 packages were sold (83/3 or 195/7). Thus, the revised break-even point is 55 packages (27 + 28)—in units, 165 of I and 385 of II.
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. Donna has an ethical obligation to report the correct information to her superior. By altering the sales forecast, Donna would unfairly and unethically influence the decision-making process. Managers certainly have a moral obligation to assess the impact of their decisions on employees, and every effort should be taken to be fair and honest with employees. Donna’s behaviour, however, is not justified by the fact that it would help a number of employees retain their employment. First, Donna has no right to make that decision. Donna certainly 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 alternative 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 Hussan Khalil than any legitimate concerns for the layoff of other employees. Donna should examine her reasoning carefully to assess the real reasons for her behaviour. Perhaps in so doing, the conflict of interest that underlies her decision will become apparent.