18.2(a)The break-even point in sales units is calculated using the following formula:
18.2(a)The break-even point in sales units is calculated using the following formula:
=
(b)The break-even point is calculated in sales dollars using the following formula:
=
(c)In the graphical approach, sales revenue and total costs are graphed. The break-even point occurs at the intersection of the total revenue and total cost lines.
EXERCISE 18.25 (25 minutes) Cost volume profit analysis and decisions: manufacturer
1Break-even point (in units)=
= = 4000 TVs
2New break-even point (in units)=
= = 4400 TVs
3Sales revenue (5000 3000)= $15 000 000
Variable costs (5000 2000) 10 000 000
Contribution margin 5 000 000
Fixed costs 4 000 000
Net profit $1 000 000
4New break-even point (in units) =
= 8000 TVs
5Analysis of price change decision:
Price
$3 000 $2 500
Sales revenue: (5000 3000) 15 000 000 (6200 2500) 15 500 000
Variable costs: (5000 2000) 10 000 000 (6200 2000) ________ 12 400 000
Contribution margin 5 000 000 3 100 000
Fixed expenses 4 000 000 4 000 000
Net profit (loss) $1 000 000 ($900 000)
The price cut should not be made, since instead of $1 000 000 profit, a loss of $900 000 will incur.
Additional question
1 Bicycle type Sales price Unit variable cost Unit contribution margin
Road bikes $2000 $800 ($750 + $50) $1200
Mountain bikes 1500 600 ($575 + $25 900
2 Sales mix: Road bicycles 25%
Mountain bicycles 75%
3 Weighted-average unit contribution margin = ($1200 25%) + ($900 75%) = $975
4 Break even point (units) = $390 000/975 = 400 bicycles
Bicycle type Break-even sales volume Sales price Sales revenue
Road bikes 100 (400 0.25) $2000 $200 000
Track bikes 300 (400 0.75) 1500 450 000
Total $650 000
5
Sales volume required to ear target net profit of $409500
= (390 000 + 409 500) / 975 = 820
This means that the shop will need to sell the following volume of each type of bicycle to earn the target net profit:
Road bikes205 (820 0.25)
Mountain bikes615 (820 0.75)
EXERCISE 18.27(20 minutes) CVP analysis with income taxes: service firm
1
2
3 Service revenue required to earn target after-tax profit of $260 000
4 A change in the tax rate will have no effect on the firms break-even point. At the break-even point, the firm has no profit and does not have to pay any income taxes.
EXERCISE 18.28 (25 minutes) (appendix) Contribution margin statement; operating leverage: manufacturer
1(a)Traditional income statement:
East Asian Publications
Income Statement
for the year ended 31 December
Sales $2 000 000
Less: Cost of goods sold 1 500 000
Gross margin 500 000
Less: Operating expenses: Selling expenses $150 000 Administrative expenses $150 000 300 000
Net profit $200 000
(b)Contribution income statement:
East Asian Publications
Income Statement
for the year ended 31 December
Sales $2 000 000
Less: Variable expenses: Variable manufacturing $1 000 000 Variable selling 100 000 Variable administrative 30 000 1 130 000
Contribution margin 870 000
Less: Fixed expenses: Fixed manufacturing 500 000 Fixed selling 50 000 Fixed administrative $120 000 670 000
Net profit $200 000
2
3
= 10% 4.35
= 43.5%
4Most operating managers prefer the contribution income statement for answering this type of question. The contribution format highlights the contribution margin and separates fixed and variable expenses.
EXERCISE 18.29 (25 minutes) (appendix) Cost structure and operating leverage: service firm
1The following income statement, often called a common-size income statement, provides a convenient way to show the cost structure.
Amount Percent
Revenue $1 500 000 100
Variable costs 900 000 60
Contribution margin 600 000 40
Fixed costs 450 000 30
Net profit $ 150 000 10
2
Decrease in revenue Contribution margin percentage Decrease innet profit
$300 000* 40% = $120 000
* $300 000 = $1 500 000 20%
The key to understanding this answer is to realise that the change in net profit will be the same as the change in contribution margin, since fixed costs will not change.
3
4
EXERCISE 18.30 (10 minutes) (appendix) Cost structure and operating leverage: service firm
Requirement 1 Requirement 2
Revenue $1 875 000 $1 500 000
Less:Variable expenses 1 125 000 1 800 000
Contribution margin 750 000 (300 000)
Less:Fixed expenses 630 000 350 000
Net profit (loss) $ 120 000 $(650 000)
SOLUTIONS TO PROBLEMS
PROBLEM 18.31 (30 minutes) Cost volume profit calculations; multiple break-even points; CVP graph: manufacturer
1Break-even point in sales dollars, using the contribution margin ratio:
2Target net profit, using contribution-margin approach:
3 New unit variable manufacturing cost = $12 120%
= $14.40
Break-even point in sales dollars:
4Let P denote the selling price that will yield the same contribution-margin ratio:
$(30 - 12 6) / $30=(P - $14.40 - $6.00) / P
0.4=(P - $20.40) / P
0.4P=P - $20.40
$20.40=0.6P
P=$20.40 / 0.6
P=$34
Check: New contribution-margin ratio is:
$(34 - $14.40 - $6.00) / $34=0.4
5The new break-even point can be calculated as follows:
Break-even point= fixed costs / contribution margin per unit
=
Or= $1 290 000 revenue
6
PROBLEM 18.32 (30 minutes) Cost volume profit relationships; indifference point: manufacturer
1Unit contribution margin:
Sales price $32.00
Less variable costs: Sales commissions ($32 5%) $ 1.60 Variable component costs 8.00 9.60
Unit contribution margin $22.40
Break-even point= fixed costs unit contribution margin
= $1 971 200 $22.40
= 88 000 units
2Model A is more profitable when sales and production average 184 000 units.
Model A Model B
Sales revenue (184 000 units $32.00) $5 888 000 $5 888 000
Less variable costs: Sales commissions ($5 888 000 5%) 294 400 294 400
Variable component costs: 184 000 units $8.00 1 472 000 184 000 units $6.40 1 177 600
Total variable costs 1 766 400 1 472 000
Contribution margin 4 121 600 4 416 000
Less: Annual fixed costs 1 971 200 2 227 200
Net profit $2 150 400 $2 188 800
3Annual fixed costs will increase by $180 000 ($900 000 5 years) because of straight-line depreciation associated with the new equipment, to $2 407 200 ($2 227 200 + $180 000). The unit contribution margin is ($4 416 000 184 000 units) i.e. $24. Thus:
Required sales=(fixed costs + target net profit) unit contribution margin
=($2 407 200 + $1 912 800) $24
= 180 000 units
4Let X = volume level at which annual total costs are equal
$8.00X + $1 971 200=$6.40X + $2 227 200
$1.60X=$256 000
X=160 000 units
PROBLEM 18.33 (30 minutes) Basic CVP relationships: manufacturer
1
2
3 Number of sales units required to earn target net profit
4 Margin of safety = budgeted sales revenue break-even sales revenue
= (140 000)($25) $3 375 000 = $125 000
5Break-even point if direct labour costs increase by 10 per cent:
New unit contribution margin = $25.00 $8.20 ($4.00)(1.10) $6.00 $1.60
= $4.80
Break-even point
6 Contribution margin ratio
Old contribution margin ratio
Let P denote sales price required to maintain a contribution-margin ratio of .208. Then P is determined as follows:
Check: New contribution margin ratio
PROBLEM 18.34 (30 minutes) Basic CVP relationships; income taxes: manufacturer
1
2
3 Number of sales units required to earn target net profit after tax
4 Margin of safety = budgeted sales revenue break-even sales revenue
= (140 000)($25) $3 375 000 = $125 000
5Break-even point if direct labour costs increase by 10 percent:
New unit contribution margin = $25.00 $8.20 ($4.00)(1.10) $6.00 $1.60
= $4.80
Break-even point
PROBLEM 18.35 (40 minutes) Cost volume profit equation; sensitivity analysis: manufacturer
1 & 2
Costs per unit
Direct material $8.20
Direct labour 4.00
Manufacturing overhead 6.00
Selling expenses 1.60
Fixed manufacturing costs $288 000
Fixed selling and admin costs $414 000
Sales 140 000 110 000 120 000 130 000 140 000 150 000 160 000 170 000
Selling price 25 33 31 28 25 22 19 16
Sales revenue 3 500 000 3 630 000 3 720 000 3 640 000 3 500 000 3 300 000 3 040 000 2 720 000
Direct material 1 148 000 902 000 984 000 1 066 000 1 148 000 1 230 000 1 312 000 1 394 000
Direct labour 560 000 440 000 480 000 520 000 560 000 600 000 640 000 680 000
Manufacturing overhead 840 000 660 000 720 000 780 000 840 000 900 000 960 000 1 020 000
Selling expenses 224 000 176 000 192 000 208 000 224 000 240 000 256 000 272 000
Total variable costs 2 772 000 2 178 000 2 376 000 2 574 000 2 772 000 2 970 000 3 168 000 3 366 000
Less fixed costs
Manufacturing fixed costs 288 000 288 000 288 000 288 000 288 000 288 000 288 000 288 000
Selling and admin fixed costs 414 000 414 000 414 000 414 000 414 000 414 000 414 000 414 000
Total fixed costs 702 000 702 000 702 000 702 000 702 000 702 000 702 000 702 000
Total costs 3 474 000 2 880 000 3 078 000 3 276 000 3 474 000 3 672 000 3 870 000 4 068 000
Profit before taxes 26 000 750 000 642 000 364 000 26 000 -372 000 -830 000 -1 348 000
Income taxes @ 30% 7 800 225 000 192 600 109 200 7 800 -111 600 -249 000 -404 400
Profit after taxes 18 200 525 000 449 400 254 800 18 200 -260 400 -581 000 -943 600
3The use of electronic spreadsheets to conduct a sensitivity analysis is very useful to management. It enables managers to determine the effect on profit of changing certain key variables, such as changing selling prices and sales volumes.
PROBLEM 18.36 (35 minutes) Cost volume profit relationships; automation: manufacturer
1
2The companys net profit would increase from this years $157 500 to next years net profit of $225 500, if the sales volume is increased to 2100 tonnes next year. The revised contribution margin statement is as follows:
Salesa $1 050 000
Variable costs: Manufacturingb 367 500 Selling costsc 210 000 Total variable costs 577 500
Contribution margin 472 500
Fixed costs: Manufacturing $ 100 000 Selling costs 107 500 Administrative 40 000 Total fixed costs 247 500
Net profit $225 000
a $900 000 x 2 100 / 1 800 b $315 000 x 2 100 / 1 800 c $180 000 x 2 100 / 1 800 3The firm would earn net profit of $ 352 500 under its full manufacturing capacity, as shown below.
Salesa $1 425 000
Variable costs: Manufacturingb $525 000 Selling costsc 300 000 Total variable costs 825 000
Contribution margin 600 000
Fixed costs: Manufacturing 100 000 Selling costs 107 500 Administrative 40 000 Total fixed costs 247 500
Net profit $352 500
a 1 500 x $500 + 1 500 x $450 b $315 000 x 3 000 / 1 800 c $180 000 x 3 000 / 1 800 4If the firms current net profit of $157 500 is to be maintained, the firm will need to break even on its sales in the new territory. The breakeven point on the new territory activity is 308 tonnes, as shown in the following workings:
Contribution margin in new territory = $225 $25 = $200
BE units in new territory = $61 500 / $200
= 308 units (rounded)
5The new break-even volume is 1224 tonnes and $612 000 in sales dollars, should the firm adopt automation for its manufacturing process. The workings are shown below:
Contribution margin with automated process = $225 + $25 = $250
BE units with automated process = ($247 500 + $58 500) / $250 per tonne
= 1224 tonnes
BE sales dollars with automated process
= 1224 tonnes x $500 = $612 000
6The new break-even sales dollars is $1 140 000, as shown below:
Contribution margin = $225 ($500 x 0.10) $40 = $135
Contribution margin ratio = $135/$450 = 0.30
Sales dollars to earning a net profit of $94 500
= $(247 500 + 94 500 )/ 0.30
= $1 140 000
PROBLEM 18.37 (35 minutes) Basic CVP relationships; impact of operating changes; target profit: manufacturer
1Current profit:
Sales revenue ... $4 032 000
Less: Variable costs . $1 008 000 Fixed costs 2 736 000 3 744 000
Net profit.. $288 000
AudioFriend has a contribution margin of $72 [($4 032 000 $1 008 000) 42 000 units] and desires to increase profit to $576 000 (i.e. $288 000 2). In addition, the current selling price is $96 ($4 032 000 42 000 units). Thus:
Required sales= (fixed costs + target net profit) unit contribution margin
= ($2 736 000 + $576 000) $72
= 46 000 sets or $4 416 000 (46 000 sets @ $96)
2If operations are shifted to China, the new unit contribution margin will be $74.40 ($96.00 $21.60). Thus:
Break-even point = fixed costs unit contribution margin
= $2 380 800 $74.40
= 32 000 units
3(a)AudioFriend desires a 32 000-unit break-even point with a $72 unit contribution margin. Fixed costs must therefore drop by $432 000, from $2 736 000 to $2 304 000, as follows:
Let X= fixed costs
X $72= 32 000 units
X= $2 304 000
(b)As the following calculations show, AudioFriend will have to generate a contribution margin of $85.50 to produce a 32 000-unit break-even point. Based on a $96.00 selling price, this means that the company can incur variable costs of only $10.50 per unit. Given the current variable cost of $24.00 ($96.00 $72.00), a decrease of $13.50 per unit ($24.00 $10.50) is needed.
Let X= unit contribution margin
$2 736 000 X= 32 000 units
X= $85.50
4(a)Increase
(b)No effect
(c)Increase
(d)No effect
PROBLEM 18.38 (45 minutes) Cost volume profit; multiple products; changes in costs and sales mix: manufacturer
1 Greenfingers Gardening Tools Ltd (GGT)
Budgeted income statement
for the year ended 31 December
Weeders Hedge clippers Leaf blowers Total
Unit selling price $84 $108 $144 Variable manufacturing cost 39 36 75 Variable selling cost 15 12 18 Total variable cost 54 48 93 Contribution margin per unit 30 60 51 Unit sales 50 000 50 000 100 000 Total contribution margin $1 500 000 $3 000 000 $5 100 000 $9 600 000
Fixed manufacturing overhead $6 000 000
Fixed selling and administrative costs 1 800 000
Total fixed costs 7 800 000
Profit before taxes 1 800 000
Income taxes (40%) 720 000
Budgeted net profit $1 080 000
2
(a) Unit contribution (b) Sales proportion (a) (b)
Weeders $30 0.25 $7.50
Hedge clippers 60 0.25 15.00
Leaf blowers 51 0.50 25.50
Weighted-average unit contribution margin $48.00
Sales proportions:
Sales proportion Total unit sales Product line sales
Weeders 0.25 162 500 40 625
Hedge clippers 0.25 162 500 40 625
Leaf blowers 0.50 162 500 81 250
Total 162 500
3
(a) Unit contribution (b) Sales proportion (a) (b)
Weeders $30 0.20 $6.00
*Hedge clippers 57 0.20 11.40
Leaf blowers 36 0.60 21.60
Weighted-average unit contribution margin $39.00
* Variable selling cost increases. Thus, the unit contribution decreases to $57 [$108 ($36 + $12 + $3)].
The variable manufacturing cost increases 20 per cent. Thus, the unit contribution decreases to $36 [$144 (1.2 $75) $18].
Sales proportions:
Sales proportions Total unit sales Product line sales
Weeders 0.20 200 000 40 000
Hedge clippers 0.20 200 000 40 000
Leaf blowers 0.60 200 000 120 000
Total 200 000
PROBLEM 18.39 (40 minutes) Cost volume profit analysis; sales mix and employee incentive systems: manufacturer
1Sales mix refers to the relative proportion of each product sold when a company sells more than one type of product.
2(a)Yes. Plan A sales are expected to total 65 000 units (19 500 + 45 500), which compares favourably with current sales of 60 000 units.
(b)The sales staff would be likely to promote Standard because it has a higher selling price than Deluxe ($86 versus $74) and sales staff earn a commission based on gross dollar sales under plan A. As the following figures show, Deluxe sales will comprise a greater proportion of total sales under Plan A.
Current Plan A
Units Sales mix Units Sales mix
Deluxe 21 000 35% 45 500 70%
Standard 39 000 65% 19 500 30%
Total 60 000 100% 65 000 100%
(c)Yes. Commissions will total $535 600 ($5 356 000 10 per cent), which compares favourably against the current flat salaries of $400 000.
Deluxe sales: 45 500 units $86 $3 913 000
Cold King sales: 19 500 units $74 1 443 000
Total $5 356 000
(d)No. The company would be less profitable under the new plan.
Current Plan A
Sales revenue: Deluxe: 21 000 units $86; 45 500 units $86 $1 806 000 $3 913 000
Standard: 39 000 units $74; 19 500 units $74 2 886 000 1 443 000
Total revenue $4 692 000 $5 356 000
Less variable cost: Deluxe: 21 000 units $65.00; 45 500 units $65.00 $1 365 000 $2 957 500
Standard: 39 000 units $41.00; 19 500 units $41.00 1 599 000 799 500
Sales commissions (10% of sales revenue) 535 600
Total variable cost $2 964 000 $4 292 600
Contribution margin $1 728 000 $1 063 400
Less fixed cost (salaries) 400 000 __
Net profit $1 328 000 $1 063 400
3 (a)The total units sold under both plans are the same; however, the sales mix has shifted under Plan B in favour of the more profitable product as judged by the contribution margin. Deluxe has a contribution margin of $21.00 ($86.00 $65.00), and Standard has a contribution margin of $33.00 ($74.00 $41.00).
Plan A Plan B
Units Sales mix Units Sales mix
Standard 19 500 30% 39 000 60%
Deluxe 45 500 70% 26 000 40%
Total 65 000 100% 65 000 100%
(b)Plan B is more attractive than Plan A, both to the sales force and to the company. Salespeople also earn more money under Plan B than the current flat salary ($549 900 vs. $400 000). However, the company is more profitable in the current situation ($1 328 000) than under either plan ($1 283 100 for Plan B and $1 063 400 for plan A).
Current Plan B
Sales revenue: Deluxe: 21 000 units $86; 26 000 units $86 $1 806 000 $2 236 000
Standard: 39 000 units $74; 39 000 units $74 2 886 000 2 886 000
Total revenue $4 692 000 $5 122 000
Less variable cost: Deluxe: 21 000 units $65.00; 26 000 units $65.00 $1 365 000 $1 690 000
Standard: 39 000 units $41.00; 39 000 units $41.00 1 599 000 1 599 000
Total variable cost $2 964 000 $3 289 000
Contribution margin $1 728 000 $1 833 000
Less: Sales force compensation: Flat salaries 400 000 Commissions ($1 833 000 30%) 549 900
Net profit $1 328 000 $1 283 100
PROBLEM 18.40 (50 minutes) Cost volume profit and activity-based analysis; product mix: manufacturer
1 Timber Polystyrene Unit-related costs: Unit costs Total costs Unit costs Total costs Assembling $36 $36 Packaging 6 4 Materials 70 52 112 $11 200.000a 92 $4 600 000b Batch-related costs: Setting-up 80 90 Inspection 60 50 Moving material 60 50 $200 50 000c $190 95 000d Product-related costs: Advertising 30 000 50 000 Total product, batch and unit related costs $11 280 000 $4 745 000 $16 025 000
Facility costs e 360 000
$16 385 000
a - $112 x 100 000 units b - $92 x 50 000 units c - $200 x 250 batches d - $190 x 500 batches e - Facility level costs are not allocated to products as they have no identifiable cost driver. Alternatively these costs could be allocated by number of units produced in which case the product costs would be $11 520 000 for the Timber Crates and $4 865 000 for the Polystyrene Crates
2The sales mix for Timber crates is2/3 (=100 000 units / 15 000 units),
and for Polystyrene crates is1/3 (=50 000 units),
and so the weighted average contribution margin is2/3 x ($138 - $112) + 1/3 x ($100 - $92)
= $20
Made up of 19 500 Timber crates and 9 750 Polystyrene crates
3Assuming that the batch size for the Polystyrene crates is changed to 2000 units, then the batch related cost for polystyrene crates is $4750 (= $190 x 25 batches) and the total batch related cost for the two products is $54 750. The new break-even point is calculated as follows:
4While the increase in batch size has caused a reduction in the break-even point, reducing batch sizes may not be the best solution for the company.
Larger batch sizes might actually cause costs (facility costs) to increase. This is due to the costs associated with inventory build-ups, including increased storage, insurance, spoilage and obsolescence costs, and the opportunity costs associated with tying up funds in excessive levels of inventories.
PROBLEM 18.41 (35 minutes) (appendix) Basic CVP relationships; incentive systems; cost structure; operating leverage: wholesaler
1Plan A break-even point= fixed costs unit contribution margin
= $49 500 $49.50*
= 1000 units
Plan B break-even point= fixed costs unit contribution margin
= $148 500 $67.50**
= 2200 units
* $180 [($180 10%) + $112.50]
** $180 $112.50
2Operating leverage refers to the proportion of fixed costs in an organisations overall cost structure. An organisation that has a relatively high proportion of fixed costs and low proportion of variable cost has a high operating leverage.
3Calculation of contribution margin and profit at 6000 units of sales:
Plan A Plan B
Sales revenue: 6000 units $180 $1 080 000 $1 080 000
Less variable costs: Cost of purchasing product:
6000 units $112.50 $675 000 $675 000
Sales commissions: $1 080 000 0.10 108 000
Total variable cost 783 000 675 000
Contribution margin 297 000 405 000
Fixed costs 49 500 148 500
Net profit $247 500 $256 500
Plan A has a higher percentage of variable costs to sales (72.5 per cent) compared to Plan B (62.5 per cent). Plan Bs fixed costs are 13.75 per cent of sales, compared to Plan As 4.58 per cent.
Operating leverage factor = contribution margin net profit
Plan A: $297 000 $247 500 = 1.2
Plan B: $405 000 $256 500 = 1.58 (rounded)
Plan B has the higher operating leverage, as it has a higher reliance on fixed costs.
4 & 5Calculation of profit at 5000 units:
Plan A Plan B
Sales revenue: 5000 units $180 $900 000 $900 000
Less variable costs: Cost of purchasing product:
5000 units $112.50 562 500 562 500
Sales commissions: $900 000 0.10 90 000 Total variable cost 652 500 562 500
Contribution margin 247 500 337 500
Fixed costs 49 500 148 500
Net profit $198 000 $189 000
Plan A profitability decrease:
$247 500 $198 000 = $49 500; $49 500 $247 500 = 20%
Plan B profitability decrease:
$256 500 $189 000 = $67 500; $67 500 $171 000 = 26.3% (rounded)
ATA will experience a larger percentage decrease in profit if it adopts Plan B, because Plan B has a higher operating leverage. Stated differently, Plan Bs decrease in sales revenue leads to a higher percentage decline in profitability due to the high proportion of fixed costs in the cost structure.
Note: The percentage decreases in profitability can be calculated by multiplying the percentage decrease in sales revenue by the operating leverage factor. Sales dropped from 6000 units to 5000 units, or 16.67 per cent. Thus:
Plan A: 16.67% 1.2 = 20.0%
Plan B: 16.67% 1.58 = 26.3% (rounded)
6Heavily automated manufacturers have sizable investments in plant and equipment, so have a high percentage of fixed costs in their cost structures. As a result, there is a high degree of operating leverage.
In a severe economic downturn, when sales volume decreases, these firms suffer a significant decrease in profitability. Such firms would be a more risky investment compared with firms that have a low degree of operating leverage. Of course, when times are good, the increase in sales volume would have a favourable impact on profitability in a company with high operating leverage.
PROBLEM 18.42 (45 minutes) (appendix) Basic CVP relationships; cost structure; operating leverage
1Break-even point in units:
Calculation of contribution margins:
Labour-intensive production system Computer-assisted manufacturing system
Selling price $45.00 $45.00
Variable costs: Direct material $8.40 $7.50 Direct labour 10.80 9.00 Variable overhead 7.20 4.50 Variable selling cost 3.00 29.40 3.00 24.00
Contribution margin per unit $15.60 $21.00
(a)Labour-intensive production system:
(b)Computer-assisted manufacturing system:
2Zodiacs management would be indifferent between the two manufacturing methods at the volume (X) where total costs are equal.
$29.40X + $2 730 000 = $24X + $4 410 000
$5.40X = $1 680 000
X = 311 111 units*
* Rounded 3Operating leverage is the extent to which a firms operations employ fixed operating costs. The greater the proportion of fixed costs used to produce a product, the higher the operating leverage. Thus, the computer-assisted manufacturing method utilises a higher level of operating leverage.
The higher the operating leverage, the greater the change in operating profit (loss) relative to a small fluctuation in sales volume. Thus, there is a higher degree of variability in operating profit if operating leverage is high.
4Management should employ the computer-assisted manufacturing method if annual sales are expected to exceed 311111 units, and the labour-intensive manufacturing method if annual sales are not expected to exceed 311111 units.
5Zodiacs management should consider many other business factors before selecting a manufacturing method. These include:
the variability or uncertainty with respect to demand quantity and selling price
the ability to produce and market the new product quickly
the ability to discontinue production and marketing of the new product while incurring the least amount of loss.
SOLUTIONS TO CASES
CASE 18.43 (50 minutes) Break-even analysis; safety margin: service firm
1In order to break even, during the first year of operations, 10 220 clients must visit the law office being considered by Steven Clark and his colleagues, as the following calculations show.
Fixed expenses:
Advertising$1 960 000
Rent (6000 $112)672 000
Council rates108 000
Utilities148 000
Professional indemnity insurance720 000
Depreciation ($240 000/4)60 000
Wages and on costs:
Regular wages: ($100 + $80 + $60 + $40) 16 360 $1 612 800
Overtime wages: (200 $60 1.5) + (200 $40 1.5)30 000
Total wages1 642 800
On costs at 40%$657 1202 299 920
Total fixed expenses $5 967 920
Break-even point:
0= revenue variable cost fixed cost
0= $120X + ($8000 0.2X 0.3)* $16X $5 967 920
0= $120X + $480X $16X $5 967 920
$584X= $5 967 920
X= 10 220 clients (rounded)
* Revenue calculation: $120X represents the $60 consultation fee per client. ($8 000 .2X .30) represents the predicted average settlement of $8 000, multiplied by the 20% of the clients whose judgments are expected to be favourable, multiplied by the 30% of the judgment that goes to the firm.
2Safety margin:
Safety margin = budgeted sales revenue break-even sales revenue
Budgeted (expected) number of clients = 50 360 = 18 000
Break-even number of clients = 10 220 (rounded)
Safety margin = [($120 18 000) + ($8 000 18 000 0.20 0.30)] [($120 10 220) + ($8 000 10 220 0.20 0.30)]
= [$120 + ($8 000 .20 .30)] (18 000 10 220)
= $600 7 780
= $4 668 000
3The assumptions underlying the break-even analysis of this law office include that the variable costs of serving each client are the same and the total fixed cost remains constant irrespective of the actual number of clients served. For example, the staffs wages and advertising expenses are allocated equally to each of 10,220 clients. The analysis ignores the possibility of cost drivers other than the number of clients. It also makes a number of untested assumptions about the number of clients and the number of favourable settlements or judgements. Where these assumptions are not met, the outcomes estimated from the CVP analysis will not be achieved. Given the uncertainty surrounding some of these assumptions it may be a good idea to use sensitivity analysis to assess how sensitive the estimated breakeven point is to changes in key variables.
CASE 18.44 (50 minutes) Break-even analysis; CVP relationships: hospital
1The break-even point is 16 900 patient-days, calculated as follows:
Narooma Medical Centre
Calculation of break-even point in patient-days:
Paediatrics for the year ended 30 June
Total fixed costs:
Medical centre charges $6 960 000
Supervising nurses ($60 000 4)* 240 000
Nurses ($48 000 10)* 480 000
Aides ($21 600 20)* 432 000
Total fixed costs $8 112 000
Contribution margin per patient-day: Revenue per patient-day $720
Variable cost per patient-day: ($4 800 000 20 000* patient-days) 240
Contribution margin per patient-day $480
*($14 400 000 $720 = 20 000 patient days) Break-even point in patient-days
2Net earnings would decrease by $1 456 000, calculated as follows:
Narooma Medical Centre
Calculation of loss from rental of additional 20 beds: Paediatrics
for the year ended 30 June
Increase in revenue
(20 additional beds 90 days $720 charge per day) $1 296 000
Increase in expenses: Variable charges by medical centre (20 additional beds 90 days $240 per day) $432 000
Fixed charges by medical centre ($6 960 000 60 beds = $116 000 per bed) ($116 000 20 beds) 2 320 000
Salaries (20 000 patient-days (before additional 20 beds) + 20 additional beds 90 days = 21 800, which does not exceed 22 000, therefore, no additional personnel are required.) 0
Total increase in expenses $2 752 000
Net change in earnings from rental of additional 20 beds $(1 456 000)
CASE 18.45 (50 minutes) Contribution margin statement; sales mix; advantages and disadvantages of CVP analysis: manufacturer
1 Delphina Products Ltd
Income Statement for the year ended June 30
(in thousands)
Dog food Cereal Breakfast bars Total
Sales (in kgs) 2 000 500 500 3 000
Sales revenue $1 000 $400 $200 $1 600
Variable manufacturing costs: Direct material 330 160 100 590
Direct labour 90 40 20 150
Manufacturing overhead* 27 12 6 45
Total variable manufacturing costs 447 212 126 785
Manufacturing contribution margin 553 188 74 815
Other variable costs: Commissions 50 40 20 110
Contribution margin 503 148 54 705
Direct operating costs: Advertising 50 30 20 100
Licenses 50 20 15 85
Total direct operating costs 100 50 35 185
Product profit contribution $403 $98 $19 $520
Fixed costs: Manufacturing overhead* 135
Sales salaries and benefits 60
General and administrative salaries and benefits 100
Total fixed costs 295
Operating profit before taxes $225
* Manufacturing overhead is 25 per cent variable and 75 per cent fixed. The variable portion includes the indirect labour and supplies ($15 000) and the employee benefits on indirect labour ($30 000). Therefore, $45 000/$180 000 = 25%.
2(a)
Dog food Cereal Breakfast bars Total
Sales (in kgs)
Sales mix 2 000
66.67% 500
16.67% 500
16.67% 3 000
100%
Sales revenue $1 000 $400 $200 $1 600
Contribution margin
Contribution margin per unit 503
$0.2515 148
$0.296 54
$0.108 705
Total direct operating costs 100 50 35 185
Break-even point (in kgs)
Contribution margin ratio
Break even point in sales dollars 397.6
50.3%
$198.8 169.92
37%
$135.94 324.07
27%
129.63 (b) Weighted-average unit contribution margin:
= $0.2515 x .66.67% + $0.296 x 16.67% + $0.108 x 16.67%
= $0.235
For the products to break-even on their direct costs:
Product related fixed costs = $185 000
Product related break-even in current product mix= 185 000/0.235= 787 000
In the ratio 66.7:16.7:16.7 the product mix in kg would be
525 000 kg of dog food; 131 000 kg of cereal and 131 000 kg of breakfast bars
Sales would need to exceed this to cover costs that cannot be related to any particular product.
Therefore, we can look at the break-even point for the whole company when we include the other fixed costs:
Total fixed costs to be covered for the company to break even = $185 000 +$295 000 = $480 000
Weighted-average unit contribution margin= $0.235 per kg
Break-even point for this sales mix = 2 043 000 kg (rounded)
In the current sales mix this represents 1 362 000 kg of dog food; 340 000 kg of cereal; 340 000 kg of breakfast bars.
(c) The answer in part (a) and the first calculation in part (b) do not allow for the non-product related costs and to ignore these costs could lead to inaccurate decisions. The analyst would need to allow a margin to cover these other fixed costs.
The last break-even point (1 362 000 kg of dog food; 340 000 kg of cereal; 340 000 kg of breakfast bars) takes into account all fixed costs. In sales revenues this break-even point is $681 000 of dog food, $272 000 of cereal and $136 000 of breakfast bars. It should be noted that the calculation does make an assumption that the sales mix will be constant, i.e. sales levels would rise and fall proportionately.
3(a)Advantages that CVP analysis can provide include:
determining the marginal contribution of products, which can assist management in planning sales volume and profitability including the calculation of a break-even point
identifying products that can support heavy sales promotion expenditures
assisting in decisions related to eliminating a product
accepting a special order at a discounted price.
(b)Difficulties that Delphina Products could expect to have in the CVP calculations include:
separating semi-variable costs into their fixed and variable components
determining how to treat joint or common costs
determining efficiency and productivity within the relevant range
determining a constant sales mix within the relevant range.
(c)Delphinas management should be aware of the following dangers when using CVP analysis:
the use of inaccurate assumptions for the calculations
CVP analysis focuses on the short term.
CASE 18.46 (45 minutes) Cost volume profit and comprehensive activity-based analysis; financial planning model: manufacturer
Cool Camping Company Initial data Unit level costs Batch level costs Direct material 70 Move materials to cutting 100
Cutting pattern 15 Set up cutting machines 250
Stitching 45 Move materials to sewing 120
Waterproofing 10 Set up sewing machines 180
Inspection 11 $650
Packaging 4 $155 Product level costs Order level costs Production/process design $50 000 Processing order 70
Delivery 140
$210
Customer level costs Market level costs Sales calls 150 Advertising $24 000
Handling complaints 75 $225 Facility level costs Administration $220 000
Sales units 75 000 Unit selling price $205 Sales revenue 15 375 000 Unit contribution margin $50
1 Profit model Sales revenue $205 75 000 $15 375 000
Less costs: Driver cost Number Total Unit level costs $155 75 000 $11 625 000 Other activity level costs: Batch level $650 1 875 1 218 750 Product level 50 000 Order level $210 3 750 787 500 Customer level $225 185 41 625 Market level 24 000 Facility level 220 000 Profit 13 966 875
$1 408 125
2 Break-even point Total other activity costs/Unit CM Total activity costs $2 341 875 Unit CM 50 Units required 46 838 3 Profit target Profit target $950 000 Other activity costs 2 341 875 Total CM required $3 291 875 Unit CM 50 Units required 65 838 4 Margin of safety Budgeted sales 75 000 Less break even sales 46 838 28 162 The margin of safety is the excess of forecast sales over break-even sales and indicates the amount by which sales may fall before the firm starts to incur losses.
5 (a) Sensitivity analysis Sales revenue $190 85 000 $16 150 000
Less costs: Cost Number Total Unit level costs $155 85 000 $13 175 000 Other activity level costs: Batch level $650 2 125* 1 381 250 Product level 50 000 Order level $210 4 250* 892 500 Customer level $225 185 41 625 Market level 24 000 Facility level 220 000 $15 784 375
Profit $365 625
* This solution assumes the batch size and order size do not change, and therefore the number of batches and customers increases proportionately.
(b) Sensitivity analysis Sales revenue $185 95 000 $17 575 000
Less costs: Cost Number Total Unit level costs $155 95 000 $14 725 000 Other activity level costs: Batch level $650 2 375* 1 543 750 Product level 50 000 Order level $210 4 450* 997 500 Customer level $225 185 41 625 Market level 24 000 Facility level 220 000 $17 601 875
Profit $26 875
* This solution assumes the batch size and order size do not change, and therefore the number of batches and customers increases proportionately
6 New marketing strategy Sales revenue $205 60 000 $12 300 000
Less costs: Cost Number Total Unit level costs $155 60 000 $9 300 000 Other activity level costs: Batch level $650 1500* 975 000 Product level 50 000 Order level $210 1 050 220 500 Customer level $225 75 16 875 Market level 24 000 Facility level 220 000 $10 806 375
Profit $1 493 625
* This solution assumes same batch size as currently used.
7The impact of the proposed changes to the original budget can be seen in the table below.
Original budget Option 5 (a) Option 5 (b) Option ( 6)
$ $ $ $
Profit (loss) $1 408 125
$365 625 ($26 875) $1 493 625
Increase (decrease) over original --------- ($1 042 500) ($1 435 000) 85 500
Total contribution margin $3 750 000 $2 975 000 $2 850 000 $3 000 000
Other activity costs $2 341 875 $2 609 375 $2 876 875 $1 506 375
Increase (decrease) in contribution margin over original ------ ($775 000) ($900 000) ($750 000)
Increase (decrease) in other activity costs over original ------ $267 500 $535 000 ($835 500)
Decreasing the selling price is not an effective strategy at either level, since the new profit is lower than the original forecast. This is due to the loss of contribution margin and increase in other activity costs. If management wishes to pursue a price sensitivity strategy, it needs to seek cost reductions in the activities associated with batch level and order level costs. To be profitable, the firm should consider increasing both average batch size and average order sizes.
By changing the marketing strategy, which involves ceasing trading with camping equipment suppliers, the firm loses $750 000 in contribution margin but saves $835 500 in activity costs above unit level. As a result, profit increases by $85 500.
Cool Camping Company can use the information generated by the financial model to investigate the outcomes of various strategies as the model indicates the factors which management should consider when evaluating a particular strategy.
