Chapter 18 (Cost Volume Profit)

Chapter 18 Solutions Manual t/a Management Accounting: Information for Creating and Managing Value 5e by Langfield-Smith, Thorne and Hilton 1

CHAPTER 18

COST VOLUME PROFIT ANALYSIS

ANSWERS TO QUESTIONS 18.1 The term unit contribution margin refers to the contribution that each unit of sales makes toward

covering fixed costs and earning a profit. The unit contribution margin is defined as the sales price minus unit variable cost.

18.2 (a) The break-even point in sales units is calculated using the following formula:

Break - even point(in units) =

fixed costs

unit contribution margin

(b) The break-even point is calculated in sales dollars using the following formula:

Break - even point(in sales dollars) =

fixed costs

contribution margin ratio

(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.

18.3 In addition to the break-even point, a CVP graph shows the impact on total costs, total revenue and profit when sales volume changes. The graph shows the sales volume required to earn a particular target net profit, by identifying the difference between revenue and total costs equal to the target net profit. The firm’s profit and loss areas are also indicated on a CVP graph.

18.4 The fixed costs of a travel agency may be the salaries of travel consultants, line rentals included in the phone bills, and rent of the agency premise or depreciation of office equipment. The increases in these fixed costs would mean a higher break even point in number of sales to clients, because more sales are required to cover higher fixed costs.

18.5 A profit-volume graph shows the profit to be earned at each level of sales volume.

18.6 It is true that fixed costs do not affect the contribution margin ratio and are therefore irrelevant. It is also true that the contribution margin ratio can be calculated by subtracting the variable cost per unit from the sales price per unit, then dividing the result by the sales price per unit. However, it can also be calculated by subtracting the total variable cost from the total sales revenue and then dividing the result by the total sales revenue.

18.7 The firm’s break even sales volume would decrease as the unit variable cost reduces. The unit contribution margin which is the denominator of the break even (sales volume) equation increases when the unit variable cost reduces.

18.8 The safety margin is the amount by which budgeted sales revenue exceeds break-even sales revenue. It is the amount by which actual sales can fall below budgeted sales before losses are incurred. Managers may use this information to highlight how close a project or enterprise is to the break-even point and hence focus on maintaining activities so that revenue does not fall below the break-even point. In this way managers can focus on keeping operations profitable, which adds to shareholder value.

18.9 The manufacturing director is correct. A price increase results in a higher unit contribution margin. An increase in the unit contribution margin causes the break-even point to decline.

The financial director’s reasoning is flawed. Even though the break-even point will be lower, the price increase will not necessarily reduce the likelihood of a loss. Customers will probably be less likely to buy the product at a higher price. Thus, the firm may be less likely to meet the lower break-even point (at a high price) than the higher break-even point (at a low price).

18.10 The safety margin referred to in the ‘Real life’ beef industry case is the difference between the current production and the break even production or the difference between the current price and break even price. In contrast, the safety margin referred to in other parts of this chapter is defined as the budgeted sales revenue minus the break even sales revenue. The concept of safety margin based on production indicates that Northern Territory appears to be most at risk in terms of achieving profitability, as the current production is well below the level of production required to break even and the current price is


the lowest of all regions,

18.11 The annual donation will partially offset the museum’s fixed costs. The reduction in net fixed costs will reduce the museum’s break-even point.

18.12 The sales mix of a multi-service organisation such as the veterinary practice is the relative proportion of the different types of services provided by the practice. The weighted-average unit contribution margin is the average of the unit contribution margins for the veterinary practice’s range of services (e.g. surgical procedures, laboratory tests, animal hospital services, examinations and vaccinations, and animal care) with each service’s contribution margin weighted by the relative proportion of the total number of services.

18.13 When CVP analysis is used in a multi-product firm a weighted average contribution margin is calculated, which is based on the relative sales mix of the products. Thus, the break-even point is only valid for that particular sales mix. This does not mean that using CVP analysis in multi-product firms is of little value, it simply means that we must be conscious that the firm will have a variety of break-even points depending on the particular forecast sales mixes.

18.14 When a company is liable for income taxes, then this may be taken into account when determining the target sales volume. When a target profit is stated as an after-tax amount, then the break-even formula must be modified to account for the amount of taxation payable. However, income taxes make no difference to determining the break-even point, as there is no tax payable on zero profit.

18.15 CVP analysis does not give details of how demand and supply influence sales price. It gives details of how many units need to be sold to break even or to achieve a target profit. CVP analysis does ignore the effect that sales price has on sales volume because it is not designed to predict sales.

18.16 Cost-volume-profit analysis can be used in budgeting by projecting the profit that will be achieved at the budgeted sales volume. Budgeting in a catering business begins with a sales forecast of number of dinners or meals provided. A CVP analysis also shows how pricing would contribute to the profitability, as changes in menu prices would change the contribution margin and affecting the break even sales volume. However, it is important to understand that CVP analysis does ignore the effect that sales price has on sales volume because it is not designed to predict sales.

18.17 A company’s gross margin is calculated by subtracting cost of goods sold from sales revenue, while the total contribution margin is calculated from subtracting variable costs from sales revenue. The cost of goods sold includes both variable and fixed manufacturing overhead. In calculating the contribution margin the variable cost of goods sold and variable selling and administrative costs are subtracted from sales revenue. Operating managers frequently prefer the contribution income statement because it separates fixed and variable costs. This format makes cost-volume-profit relationships more readily discernible, which is useful for planning as well as analysing cost behaviour.

18.18 CVP analysis is based on estimates of a number of variables, and whenever estimates are used, a degree of uncertainty exists. Sensitivity analysis is an approach that examines how a result or outcome may change if there are variations in the predicted data or underlying assumptions. Using simple spreadsheet models, the sensitivity to changes in certain variables can be determined, such as the sensitivity of profit to changes in fixed or variable costs.

18.19 The low-selling-price company may have a larger sales volume than the high-selling-price company. By spreading its fixed costs across a larger sales volume, the low-price firm can afford to charge a lower price and still earn the same profit as the high-price company. Suppose, for example, that Companies A and B have the following costs, sales prices, sales volumes, and profits.

Company A Company B Sales revenue:

350 units at $10 $3 500 100 units at $20 $2 000

Variable costs: 350 units at $6 2 100 100 units at $6 600

Contribution margin 1 400 1 400 Fixed costs 1 000 1 000 Profit $400 $400


18.20 Under activity-based costing we recognise a range of cost drivers, including non-volume-based drivers. However, under conventional CVP analysis it is assumed that product costs are driven by the volume of production and selling costs are driven by the volume of sales. The classification of fixed and variable costs of both production and sales is no longer considered relevant under an ABC system, therefore, under ABC we cannot satisfy some of the conventional assumptions of CVP analysis. Instead, we need to consider how to calculate the break-even point, or target sales volume, by considering complex relationships between a range of cost drivers and costs which can be considered as unit, batch or product-level costs for production, and order, customer, and market -level costs for customer-related matters, as well as facility level costs.

18.21 A business which uses an activity-based approach to analyse its production and customer-related costs will include the following variables in its profit equation:

Revenue (sales price × number of units sold) $xxxxx

Less expenses:

(activity costs per unit × number units produced and sold) $xx (activity costs per batch × number of batches) $xx (activity costs per product × number of product lines) $xx (activity costs per customer order × number of orders) $xx (activity costs per customer × number of customers) $xx (activity costs per market × number of markets) $xx (facility level costs) $xx $xxx

Profit $xx

Since this approach to determining profit is more complex than the conventional model, firms may utilise sophisticated computerised spreadsheets or financial planning software to manipulate the data.

18.22 CVP analysis assumes that costs are fixed or vary with the sales/production volume. As we have explained for Question 18.21 computer modelling can be used to move from CVP analysis to an activity-based costing model which recognises a much broader range of cost drivers, such as the number of batches, products, customers, orders and markets. Also a business can use computer modelling to perform sensitivity analysis to assess the effects of changes in the variables underlying the CVP model. The sensitivity analysis, therefore, can identifythe effect on profits of varying assumptions about the cost structure and cost drivers underlying CVP analysis.

18.23 East Ltd, which is highly automated, will have a cost structure dominated by fixed costs. West Ltd’s cost structure will include a larger proportion of variable costs than East Ltd’s cost structure.

A firm’s operating leverage factor, at a particular sales volume, is defined as its total contribution margin divided by its net profit. Since East Ltd has proportionately higher fixed costs, it will have a proportionately higher total contribution margin. Therefore, East Ltd’s operating leverage factor will be higher.

18.24 False. The statement is only partly true. A company with capital intensive processes is likely to have higher fixed costs and higher operating leverage (which is equal to contribution margin/net profit). The higher fixed costs often result in a higher break-even point and therefore a smaller safety margin.

18.25 When sales volume increases, Company X will have a higher percentage increase in profit than

Company Y. Company X’s higher proportion of fixed costs gives the firm a higher operating leverage factor. The company’s percentage increase in profit can be found by multiplying the percentage increase in sales volume by the firm’s operating leverage factor. Another way of understanding the ‘operating leverage’ effect is to compare the implications of both rising and falling sales on firms with different cost structures and contribution margins. When sales are rising, firms with a high contribution margin (such as X) benefit more than firms with a low contribution margin (such as Y) because each incremental dollar of sales provides a higher incremental contribution margin. Conversely, when there is a downturn in sales, each increment of lost sales has a higher impact in terms of lost contribution margin for ‘X’ firms than for ‘Y’ firms.

18.26 Firms with high fixed costs tend to have high operating leverage. The advantage of having high operating leverage is that a small increase in sales revenue will have a large increase on net profit. However, having high operating leverage can also be risky because the break-even point is very high.


SOLUTIONS TO EXERCISES EXERCISE 18.27 (20 minutes) Basic CVP analysis: retailer

1 Break-even point (in units) =

fixed costsunit contribution margin

= $40 000

$10 $5− = 8 000 pizzas

2 Contribution margin ratio = unit contribution marginunit sales price

= $10 $5

$10

− = 0.5

3 Break - even point(in sales dollars)

=

fixed costs contribution margin ratio

= $40 000

0.5 = $80 000

4 Target net profit = fixed costs + target profitunit contribution margin

= $40 000 + $60 000

$10 $5−

= $20 000 pizzas

EXERCISE 18.28 (25 minutes) Cost volume profit analysis and decisions: manufacturer

1 Break-even point (in units) = marginon contributiunit

costs fixed

=

4 000 000

3000 2000− = 4000 TVs

2 New break-even point (in units) = (4 000 000) (1.10)

3000 2000−

= 4 400 000

1 000 = 4400 TVs

3 Sales 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

4 New break-even point (in units) = 4 000 000

2500 2000−

= 8000 TVs


5 Analysis of price change decision: Price $3 000 $2 500 Sales revenue: (5 000 × 3 000) 15 000 000 (6 200 × 2 500) 15 500 000 Variable costs: (5 000 × 2 000) 10 000 000 (6 200 × 2 000) ________ 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.

EXERCISE 18.29 (25 minutes) Missing data; basic CVP relationships

Total sales

revenue Variable

costs

Total Contribution

margin Fixed costs Net profit

Break-even Sales

revenue 1 $160 000a $40 000 $120 000 $30 000 $90 000 $40 000 2 80 000 65 000 15 000 15 000b 0 80 000 3 120 000 40 000 80 000 30 000 50 000 45 000c 4 $110 000 $22 000 $88 000 $50 000 $38 000 $62 500d

Explanatory notes for selected items:

(a) Break-even revenue $40 000 Fixed costs 30 000 Variable costs $10 000

Therefore, variable costs are 25 per cent of sales revenue. When variable costs amount to $40 000, sales revenue is $160 000. (b) $80 000 is the break-even sales revenue which is identical with total sales revenue, so fixed costs

must be equal to the contribution margin of $15 000 and profit must be zero. (c) The contribution margin ratio is 0.667 (total contribution margin ÷ total sales revenue), so break-

even sales revenue is fixed cost ÷ contribution margin ratio = $30 000 ÷ 0.66666 = $45 000 (rounded)

(d) $62 500 = $50 000 ÷ 0.8, where 0.8 is the contribution margin ratio (88 000 / 110 000).

EXERCISE 18.30 (25 minutes) Cost volume profit graph: sports team

1 Cost-volume-profit graph: (see over)


Fixed cost line

Tickets sold per

year

Dollars per year

100 000

15 000 30 000

200 000

300 000

5 000 10 000 20 000 25 000

Profit area

Loss area

Total revenue

Break-even point:20 000 tickets

Total costs line

Total fixed costs

Total variable costs


2 Stadium capacity 10 000 Attendance rate × 2/3

Attendance per game 6 667 (rounded)

)rounded(3667600020

gameper Attendance

(tickets)point even -Break==

The team must play three games to break even.

EXERCISE 18.31 (25 minutes) Profit volume graph; safety margin: sports team

1 Profit-volume graph:

Tickets sold per

year

Dollars per year

15 000

100 000

200 000

5 000 10 000 20 000 25 000

Profit area

Loss area

Break-even point:20 000 tickets

Total profit/loss (100 000)

(200 000)

Total fixed costs $180 000

Profit line

Loss


2 Safety margin:

Budgeted sales revenue (12 games ×10 000 seats × 0.30 full × $10) .............................................................. $360 000 Break-even sales revenue (20 000 tickets × $10) ................................................................................................ 200 000 Safety margin .................................................................................................................... $160 000

3 Let P denote the break-even ticket price, assuming a 12-game season and 50 percent attendance:

(12)(10 000)(0.50)P – (12)(10 000)(0.50)($1) – $180 000 = 0

60 000P = $240 000

P = $4 per ticket

EXERCISE 18.32 (30 minutes) Cost volume profit analysis with multiple products: retailer

1 Bicycle type Sales price

Unit variable cost

Unit contribution margin

Road bikes $500 $300 ($275 + $25) $200 Track bikes 300 150 ($135 + $15) 150 2 Sales mix: Road bicycles 25% Track bicycles 75%

3 Weighted-average unit contribution margin = ($200 × 25%) + ($150 × 75%)

= $162.50

4 fixed expensesBreak - even point (in units)

weighted - average unit contribution margin

$65 000 400 bicycles

$162.5

=

= =

Bicycle type Break-even

sales volume Sales price Sales revenue Road bikes 100 (400 × .25) $500 $50 000 Track bikes 300 (400 × .75) 300 90 000 Total $140 000

5 Target net profit:

$65 000 $48 750

Sales volume required to earn target net profit of $48 750 $162.5

700 bicycles

+=

=

This means that the shop will need to sell the following volume of each type of bicycle to earn the target net profit:

Road bikes 175 (700 × 0.25) Medium-quality 525 (700 × 0.75)


EXERCISE 18.33 (20 minutes) Cost volume profit analysis with income taxes: service firm

1

Break - even volume of service revenue = fixed expenses


= $200 000

.25 = $800 000

2

Target before - tax profit = target after - tax net profit

1 − tax rate=

$120 0001 − .40

= $200 000

3 Service revenue required to earn target after-tax profit of $120 000

000 600 $1 0.25

0.40 1

000 $120 000 $200

ratiomargin on contributi

) (1

profitnet tax -aftertarget expenses fixed

=−+

=

−+

=t

4 A change in the tax rate will have no effect on the firm’s break-even point. At the break-even point, the

firm has no profit and does not have to pay any income taxes.

EXERCISE 18.34 (25 minutes) (appendix) Contribution margin statement; operating leverage: manufacturer

1 (a) Traditional income statement:

East Asian Publications Income Statement

for the year ended December 31 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 December 31 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

contribution marginOperating leverage factor (at $2 000 000 sales level)

net profit

$870 000 4.35$200 000

=

= =

3

Percentage increase in net profit = percentage increase

in sales revenue⎛ ⎝ ⎜ ⎞

⎠ ⎟ × operating

leverage factor⎛ ⎝ ⎜ ⎞

⎠ ⎟

= 10% × 4.35 = 43.5%

4 Most 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 18.35 (25 minutes) (appendix) Cost structure and operating leverage: service firm

1 The 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 expenses 900 000 60 Contribution margin 600 000 40 Fixed expenses 450 000 30 Net profit $150 000 10

2 Decrease in revenue

Contribution margin percentage

Decrease in net profit

$300 000* × 40%† = $120 000 * $300 000 = $1 500 000 × 20% † 40% = $600 000/$1 500 000

3

Operating leverage factor (at revenue of $1 500 000) = contribution margin

net profit

= $600 000$150 000

= 4

4

100%

4 %25

factor

leverage operating

revenuein

increase percentage profit net in change Percentage

=

× =

×= ⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛

EXERCISE 18.36 (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 675 000 350 000 Net profit (loss) $75 000 $(650 000)


SOLUTIONS TO PROBLEMS PROBLEM 18.37 (30 minutes) Cost volume profit calculations; multiple break-even points; CVP graph: manufacturer

1 Break-even point in sales dollars, using the contribution-margin ratio: fixed expenses

Break - even point contribution - margin ratio

$180 000 $72 000 $252 000

$20 $8 $4 .4$20

$630 000

=

+= =

− −

=

2 Target net profit, using contribution-margin approach: fixed expenses target net profit

Sales units required to earn profit of $180 000 unit contribution margin

$252 000 $180 000 $432 000

$20 $8 $4 $8 54 000 units

+=

+= =

− −

=

3 New unit variable manufacturing cost = $8 × 110% = $8.80

Break-even point in sales dollars:

$252 000 $252 000Break - even point

$20.00 $8.80 $4.00 .36$20

$700 000

= =− −

=

4 Let P denote the selling price that will yield the same contribution-margin ratio: $20 000 - $8.00 - $4.00 / $20.00 = P - $8.80 - $4.00 / P

0.4 = P - $12.80 / P 0.4P = P - $12.80 $12.80 = 0.6P P = $12.80 / 0.6 P = $21.33

Check: New contribution-margin ratio is: $21.33 $8.80 $4.00

.4$21.33

− −=

5. The new break-even point can be calculated as follows: Break-even point = fixed costs / contribution margin per unit

= $100 000 + $72 000

$20 - 12 =

$172 000

$8

= 21500 units

Or = $430 000


6

PROBLEM 18.38 (30 minutes) Basic CVP relationships; manufacturer

1 fixed costsBreak - even point (in units)


$468 000 90 000 units

$25.00 $19.80

=

= =−

2 fixed cost

Break - even point (in sales dollars) contribution - margin ratio

$468 000 $2 250 000

$25.00 $19.80

$25.00

=

= =−

3 Number of sales units

required to earn target net profit

fixed costs target net profit


$468 000 $260 000 140 000 units

$25.00 $19.80

+=

+= =

−

4 Margin of safety = budgeted sales revenue – break-even sales revenue = (120 000)($25) – $2 250 000 = $750 000 5 Break-even point if direct-labour costs increase by 10 percent:


New unit contribution margin = $25.00 – $10.50 – ($5.00)(1.08) – $3.00 – $1.30 = $4.80 Break-even point fixed costs

new unit contribution margin

$468 000 97 500 units

$4.80

=

= =

6 Contribution margin ratio

=

unit contribution marginsales price

Old contribution-margin ratio

=

$25.00 − $19.80$25.00

= .208

Let P denote sales price required to maintain a contribution-margin ratio of .208. Then P is determined as follows:

$10.50 ($5.00)(1.08) $3.00 $1.30 .208

$20.20 .208

.792 $20.20

$25.51 (rounded)

P

PP P

P

P

− − − −=

− =

=

=

Check: New contribution- margin ratio

(rounded) .208 $25.51

$1.30$3.0008)($5.00)(1.$10.50$25.51

=

−−−−=

PROBLEM 18.39 (30 minutes) Basic CVP relationships; income taxes: manufacturer

1 fixed costsBreak - even point (in units)


$468 000 90 000 units$25.00 $19.80

=

= =−

2 fixed cost

Break - even point (in sales dollars) contribution - margin ratio

$468 000 $2 250 000

$25.00 $19.80

$25.00

=

= =−

3 Number of sales units required

to earn target net profit after tax

(rounded) units 4180 172 $15.60

0007300.7)2 / 000 ($300 000 $468

marginon contributiunit

t))-(1profit / after tax net (target costs fixed

=

+=

+=

total batch, product and facility costsBreak - even point (Timber & Polysterene) =

weighted average contribution margin

($360000 $80000 $54750) / $20

$494750 / $20

24 738 units (rounded)

= + +

=

=

4. Margin of safety = budgeted sales revenue – break-even sales revenue


= (120 000)($25) – $2 250 000 = $750 000 5 Break-even point if direct-labour costs increase by 8 percent: New unit contribution margin = $25.00 – $10.50 – ($5.00)(1.08) – $3.00 – $1.30 = $4.80

Break-even point fixed costs new unit contribution margin

$468 000 97 500 units

$4.80

=

= =

PROBLEM 18.40 (30 minutes) Cost volume profit equation; sensitivity analysis: manufacturer

1 & 2

Cost per unit

Direct material $10.50

Direct labour 5.00

Manufacturing overhead 3.00

Selling expenses 1.30

Fixed manufacturing costs 192 000 Fixed selling and admin costs 276 000

Sales volumes (in units) 120 000 90 000 100 000 110 000 120 000 130 000 140 000 150,000

Selling price $25.00 $33.00 $31.00 $28.00 $25.00 $22.00 $19.00 $16.00

Sales revenue 3 000 000 2 970 000 3 100 000 3 080 000 3 000 000 2 860 000 2 660 000 2 400 000

Direct material 1 260 000 945 000 1 050 000 1 155 000 1 260 000 1 365 000 1 470 000 1 575 000

Direct labour 600 000 450 000 500 000 550 000 600 000 650 000 700 000 750,000

Manufacturing overhead 360 000 270 000 300 000 330 000 360 000 390 000 420 000 450,000

Selling expenses 156 000 117 000 130 000 143 000 156 000 169 000 182 000 195 000

Total variable costs 2 376 000 1 782 000 1 980 000 2 178 000 2 376 000 2 574 000 2 772 000 2 970 000

Less Fixed costs

Manufacturing costs 192 000 192 000 192 000 192 000 192 000 192 000 192 000 192 000

Selling and admin costs 276 000 276 000 276 000 276 000 276 000 276 000 276 000 276 000

Total fixed costs 468 000 468 000 468 000 468 000 468 000 468 000 468 000 468 000

Total costs 2 844 000 2 250 000 2 448 000 2 646 000 2 844 000 3 042 000 3 240 000 $3 438 000

Profit before taxes $156 000 $720 000 $652 000 $434 000 $156 000 ($182 000) ($580 000)($1 038

000)

3 The 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.

PROBLEM 18.41 (35 minutes) Basic CVP relationships; impact of operating changes: manufacturer

1 Current profit:

Sales revenue ………………………... $4 032 000 Less: Variable costs .………………… $1 008 000 Fixed costs…………………… 2 736 000 3 744 000 Net profit.……………………………. $288 000

Comp Tronics has a contribution margin of $72 [($4 032 000 – $1 008 000) ÷ 42 000 sets] and desires to increase profit to $576 000 ($288 000 × 2). In addition, the current selling price is $96 ($4 032 000 ÷


42 000 sets). 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) 2 If 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) Comp Tronics desires to have a 32 000-unit break-even point with a $72 unit contribution margin. Fixed costs must therefore drop by $432 000 ($2 736 000 – $2 304 000), as follows:

Let X = fixed costs X ÷ $72 = 32 000 units X = $2 304 000

(b) As the following calculations show, Comp Tronics will have to generate a contribution margin of $85.50 to produce a 32 000-unit break-even point. Based on an $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 18.42 Break-even point; income taxes; PV graph: manufacturer

1

($1000000 $700000)100000

fixed costsBreak - even point (in units)


$210 000 70 000 units−

=

= =

Break – even point in sales dollars = 70 000 units x $10 = $ 700,000 2 Number of sales units

required to earn target net profit

units000120

000120/000 $700 - 0000 000 (1

0.4)-(1 /000 $90 - 000 $210

marginon contributi unit

t))-(1/ profit afternet (target costs fixed

=

=

+=

3

)(50080

000100/000 $700 - 0000 000 (1

500 $31 - 000 $210

marginon contributiunit

costs fixed new units)(in pointseven -Break

roundedunits=

=

=


4

5 Number of sales units required to earn target net profit after tax rate @ 50% $90 000 (1-0.5)

$1000000 $700000100000

fixed costs (target net after profit/(1- t))


$210 000 130 000 units

−

+=

+= =

PROBLEM 18.43 (45 minutes) Cost volume profit relationships; evaluating alternatives: manufacturer

1 If the changes are made to the selling price or cost structure, the break even sales volume would vary according to the Cook’s Canopy company’s pricing policy and cost reduction scheme. Alternative (1):

Contribution margin = ($800 - $80) – $400 = $320 Breakeven point = Fixed costs_____

Unit contribution margin = $200 000/$320 = 625 units Alternative (2): Contribution margin = ($800 - $60) – ($400 - $50) = $390

Breakeven point = Fixed costs_____ Unit contribution margin = $200 000/$390 = 513 units (rounded)

Alternative (3): Contribution margin = ($800 - $40) – $400 = $360

Breakeven point = Fixed costs_____ Unit contribution margin = ($200 000 - $20 000)/$360 = 500 units

2 To achieve its annual after-tax profit objective of $480 000, management should select the first alternative, where the sales price is reduced by $80 and 2700 units are sold during the remainder of the


year. This alternative results in the highest profit and is the only alternative that equals or exceeds the company’s profit objective. Calculations for the three alternatives follow. Alternative (1):

400 482

40 1 000 $804profittax -After

000 $804

000 $200 000 220 $1 000 224 $2profittax -Before

000 220 $1

0503 $400cost Variable

000 224 2$

)7002)(720($ )350)(800($Revenue

$

).(

=

−×=

=

−−=

=

×=

=

+=

Alternative (2):

800 478


000 $798

000 $200 000 $910 000 908 $1profittax -Before

000 $910

200)2)(350($ $400)(350)(cost Variable

000 908 1$

)2002)(740($ )350)(800($Revenue

$

).(

=

−×=

=

−−=

=

×=

=

+=

Alternative (3):

000 408


000 $680

000 $180 000 $940 000 800 $1profittax -Before

000 $940

3502 $400cost Variable

000 800 1$

)0002)(760($ )350)(800($Revenue

$

).(

=

−×=

=

−−=

=

×=

=

+=

PROBLEM 18.44 (30 minutes) Cost volume profit relationships; indifference point; manufacturer

1 Unit contribution margin:

Sales price………………………………………… $32.00 Less variable costs:

Sales commissions ($32 × 5%)……………… $ 1.60 System variable 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

2 Model 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 System variable 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

3 Annual 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 $24 ($4 416 000 ÷ 184 000 units). Thus:

Required sales = (fixed costs + target net profit) ÷ unit contribution margin = ($2 407 200 + $1 912 800) ÷ $24 = 180 000 units

4 Let 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 18.45 (45 minutes) Break-even analysis; PV graph: service firm

1 Break-even sales volume for each model:

Break - even volume =

annual rental cost unit contribution margin

(a) Economy model:

$8 000

Break - even volume 25 000 boxes$1.75 $1.43

= =−

(b) Regular model:

$11 000

Break - even volume 27 500 boxes$1.75 $1.35

= =−

(c) Super model:

$20 000

Break - even volume 40 816 boxes (rounded)$1.75 $1.26

= =−

2 Profit-volume graph:


3 The sales price per box is the same regardless of the type of machine selected. Therefore, the same

profit (or loss) will be achieved with the Economy and Regular models at the sales volume, X, where the total costs are the same.

Model Variable cost

per box Total fixed

cost Economy $1.43 $8 000 Regular 1.35 11 000

This reasoning leads to the following equation: 8 000 + 1.43X = 11 000 + 1.35X Rearranging terms yields the following: (1.43 – 1.35)X = 11 000 – 8 000 0.08X = 3 000 X = 3 000/0.08 X = 37 500 boxes Or, stated slightly differently:

Volume at which both machines produce the same profit

fixed cost differential variable cost differential$3000

$.08

37 500 boxes

=

=

=

Check: the total cost is the same with either model if 37 500 boxes are sold.

Standard Super Variable cost: Economy, 37 500 × $1.43 $53 625 Regular, 37 500 × $1.35 $50 625 Fixed cost: Economy, $8 000 8 000 Regular, $11 000 11 000 Total cost $61625 $61 625

Since the sales price for popcorn does not depend on the popper model, the sales revenue will be the same under either alternative.


PROBLEM 18.46 (50 minutes) Cost volume profit and activity-based analysis; product mix: manufacturer

1 Timber Polystyrene

Unit-related 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 000a- $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

2 The sales mix for Timber crates is 2/3 (=100 000 units / 15 000 units), and for Polystyrene crates is 1/3 (=50 000 units), and so the weighted average contribution margin is 2/3 x ($138 - $112) + 1/3 x ($100 - $92) = $20

units25029

20/000585$

000 $700 - 0000 000 (1

$20 / 000)$360 000 $80 000 ($145

marginononcontributiaverageweighted

costsfacilityandproductbatch,total e)Polystyren&(Timber pointseven -Break

=

=

++=

=

Made up of 19 500 Timber crates and 9 750 Polystyrene crates

3 Assuming that the batch size for the Polystyrene crates is changed to 2 000 units, then the batch related cost for polystyrene crates is $4 750 (= $190 x 25 batches) and the total batch related cost for two products are $54 750. The new break-even point is calculated as follows:


units25029

20/000585$

000 $700 - 0000 000 (1

$20 / 000)$360 000 $80 750 ($54

marginononcontributiaverageweighted

costsfacilityandproductbatch,total e)Polystyren&(Timber pointseven -Break

=

=

++=

=

4 While 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 18.47 (45 minutes) Cost volume profit analysis and special projects; sales mix: professional service organisation

1 Contribution margin = $50 – $10 = $40 per film Fixed costs = $380 000 + 180 000 + 20 000 + 80 000 + 60 000 + 30

000 = $750 000

Break - even point = $750 000

$40= 18 750 films

Profit = (25 000 × $40) – $750 000 = $250 000 2 New fixed costs = $750 000 + 250 000* + 80 000 + 90 000 = $1 170 000 * Depreciation on the new machine = $750 000/3 = $250 000 Contribution margin of films produced on new machine:

= $60 – 16 = $44 per film

(rounded) filmper $42.667 =

75

25 $40

75

50 $44 =margin on contributi average-Weighted ⎟

⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛

×+×

(rounded) films 42222$42.667

000170$11=point even -break New

=

Break-up: Films on existing machine (1/3) 9 141 Films on new machine (2/3) 18 281 27 422 films 3 The new budgeted profit = ($40 × 25 000) + ($44 × 50 000) – $1 170 000 = $2 030 000 4 The budgeted profit has increased by $1 780 000 with the addition of the new machine. This is due to

the new machine having a high contribution of $44 per film, and a much larger capacity than the existing machine. Also, only an additional $420 000 in fixed costs is required to run the new machine.

Only 9545 films per year are required to break even on this new machine:


(rounded) films 5459 =$44

000$420 = machine newon point even -break lIncrementa

It should also be noted that the budgeted profit has been calculated assuming that the new machine will be operating at full capacity.

5 If the machine operates at 20 or 30 per cent capacity, the additional profit will be as follows:

[ ]( )

[ ]( )000$240 =

000$420 $44 0.3 00050 =capacity 30%At

000$20 =

000$420 - $44 0.2 00050 =capacity 20%At

−××

××

These two sales volumes are above the incremental break-even point of 9545; however, the margin of safety is a little slim: 455 (i.e. 9545 – [50 000x 0.2]) and 5455 (i.e. 9545 – [50 000 x 0.3]) respectively.

Dr Monte needs to consider whether or not 20–30 per cent of capacity is a likely estimate of sales in the first year, and whether that level of sales is likely to increase in the second or third years. If the utilisation of the machine is low, Dr Monte might consider investing in a machine with a smaller capacity and, hence, lower costs.

PROBLEM 18.48 (40 minutes) Cost volume profit analysis; sales mix and employee reward systems: manufacturer

1 Sales mix refers to the relative proportion of each product sold when a company sells more than one product.

2 (a) Yes. Plan A sales are expected to total 65 000 units (19 500 + 45 500), which compares favourably against current sales of 60 000 units.

(b) The sales staff would likely to promote Deluxe because it has a higher selling price than Standard ($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 $1063 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 Deluxe.............................................. 19 500 30% 39 000 60% Standard ........................................... 45 500 70% 26 000 40%

Total .......................................... 65 000 100% 65 000 100%

(b) Plan B is more attractive both to the sales force and to the company. Salespeople earn more money under this arrangement than the current situation ($503 100 vs. $400 000). The company is more profitable than the current situation and in terms of two plans ($1 173 900 vs. $1 063 400).

Current Plan B Sales revenue:

Deluxe: 21 000 units × $86; 39 000 units × $86........................ $1 806 000 $3 354 000 Standard: 39 000 units × $74; 26 000 units × $74 ..................... 2 886 000 1 924 000

Total revenue ....................................................................... $4 692 000 $5 278 000 Less variable cost:

Deluxe: 21 000 units × $65.00; 39 000 units × $65.00.............. $1 365 000 $2 535 000 Standard: 39 000 units × $41.00; 26 000 units × $41.00........... 1 599 000 1 066 000

Total variable cost ............................................................... $2 964 000 $3 601 000 Contribution margin .......................................................................... $1 728 000 $1 677 000 Less: Sales force compensation:

Flat salaries ................................................................................. 400 000 Commissions ($1 677 000 × 30%)............................................. 503 100

Net profit........................................................................................... $1 328 000 $1 173 900

PROBLEM 18.49 (35 minutes) Cost volume profit analysis; changes in sales prices and costs: manufacturer

1 $625 000 $375 000Unit contribution margin

25 000 units

$10 per unit

fixed costs Break - even point (in units)


$150 000 15 000 units

$10

−=

=

=

= =

2 Number of sales units required to earn target net profit

fixed costs target net profit


$150 000 $140 000 29 000 units

$10

+=

+= =


3 new fixed costsNew break - even point (in units)


$150 000 ($18 000 / 6) * 19125 units

$10 $2

=

+= =

−

* Annual straight-line depreciation on new machine † $2.00 = $4.50 – $2.50 increase in the unit cost of the new part

4 Number of sales units required to earn target net profit, given manufacturing changes

new fixed costs target net profit


$153 000 $100 000 *

$8

31625 units

+=

+=

=

* Last year’s profit: ($25)(25 000) – $525 000 = $100 000

5 unit contribution marginContribution - margin ratio

sales price

$10Old contribution - margin ratio .40

$25*

=

= =

* Sales price, given in problem. Let P denote the price required to cover increased direct-material cost and maintain the same contribution

margin ratio: * $15 $2

.40

$17 .40

.60 $17

$28.33 (rounded)

P

PP P

P

P

θ− −=

− =

=

=

* Old unit variable cost = $15 = $375 000 ÷ 25 000 units θ Increase in direct-material cost = $2

Check: $28.33 $15 $2

New contribution - margin ratio $28.33

.40 (rounded)

− −=

=

PROBLEM 18.50 (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 December 31 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

Total unit sales to break even = total fixed costs


= $7 800 000

$48 = 162 500 units

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 percent. Thus, the unit contribution

decreases to $36 [$144 – (1.2 × $75) – $18].

Total unit sales to break even = total fixed costs


= $7 800 000

$39 = 200 000 units

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 18.51 (35 minutes) Cost volume profit relationships; automation: manufacturer

1

tonnes

tonneper

1001225$/500247$

marginon contributi0.45unit

costs fixed )(in tonnespoint even -Break

225$ tonnes800 1

000 800 0008 $405 retiomargin on contributiUnit

==

=

=

=

2 The company’s net profit would increase from this year’s $ 157 500 to next year’s net profit of $ 225 500, should the sales volume is increased to 2 100 tonnes next year. The revised contribution margin statement is as follows,

Salesa $1 050 000Variable costs: Manufacturingb 367 500 Selling costsc 210 000 Total variable costs $577 500Contribution margin 472 500Fixed costs: Manufacturing 100 000 Selling costs 107 500 Administrative $40,000 Total fixed costs 247 500Net profit $225 000a - $900 000 x 2 100 / 1 800 b - $315 000 x 2 100 / 1 800 c - $180 000 x 2 100 / 1 800

3 The firm would earn net profit of $ 352 500 under its full manufacturing capacity, as shown below.

Salesa $1 425 000Variable costs: Manufacturingb $525 000 Selling costsc 300 000 Total variable costs 825 000Contribution margin 600 000Fixed costs: Manufacturing 100 000 Selling costs 107 500 Administrative 40 000 Total fixed costs 247 500Net profit $352 500a – 1 500 x $500 + 1 500 x $450 b - $315 000 x 3 000 / 1 800 c - $180 000 x 3 000 / 1 800

4 If the firm’s 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)

5 The 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

= 1 224 tonnes BE sales dollars with automated process

= 1 224 tonnes x $500 = $612 000

6 The 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 18.52 (45 minutes) Cost volume profit analysis; income taxes; marketing decisions: manufacturer

Summary of expenses: Expenses per year (in thousands) Variable Fixed Manufacturing $7 200 $2 340 Selling and administrative 2 400 1 920 Interest ______ 540

Costs from budgeted profit statement $9 600 $4 800 If the company employs its own sales force: Additional sales force costs 2 400 Reduced commissions [(.15 – .10) × $16 000] (800) _____ Costs with own sales force $8 800 $7 200 If the company sells through agents: Deduct cost of sales force (2 400) Increased commissions [(.225 – .10) × $16 000] _2 000 _____ Costs with agents paid increased commissions $10 800 $4 800

1

Break - even sales dollars = total fixed expenses


Contribution - margin ratio = 1 − total variable expenses

sales revenue

(a)

00000012$0.40

000 800 $4 dollars saleseven -Break

40.0

60.01000 000 $16

000 600 $9 - 1 retiomargin on Contributi

=

=

=

−=

=


(b)

00000016$0.45

000 200 $7 dollars saleseven -Break

45.0

55.01000 000 $16


=

=

=

−=

=

2

Required sales dollars =

total fixed costs + target income before income taxescontribution margin ratio

)(30869219$0.325

000 600 $1 000 800 $4 dollars saleseven -Break

325.0

675.01000 000 $16


rounded=

+=

=

−=

=

3 The volume in sales dollars (X) that would result in equal net profit is the volume of sales dollars where total expenses are equal.

Total expenses with agents paid increased commission = total expenses with own sales force

$10 800 000 $8 800 000 $4 800 000 $7 200 000

$16 000 000 $16 000 000

.675 $4 800 000 .55 $7 200 000

.125 $2 400 000

$19 200 000

X X

X X

X

X

+ = +

+ = +

=

=

Therefore, at a sales volume of $19 200 000, the company will earn equal before-tax profit under either alternative. Since before-tax income is the same, so is after-tax net profit.

PROBLEM 18.53 (35 minutes) (appendix) Basic CVP relationships; reward systems; cost structure; operating leverage: wholesaler

1 Plan A break-even point = fixed costs ÷ unit contribution margin = $22 000 ÷ $22* = 1 000 units

Plan B break-even point = fixed costs ÷ unit contribution margin

= $66 000 ÷ $30** = 2 200 units

* $80 – [($80 × 10%) + $50] ** $80 – $50

2 Operating leverage refers to the use of fixed costs in an organisation’s overall cost structure. An organisation that has a relatively high proportion of fixed costs and low proportion of variable costs has a high degree of operating leverage.

3 Calculation of contribution margin and profit at 6 000 units of sales:

Plan A Plan B


Sales revenue: 6000 units × $80………………………… $480 000 $480 000 Less variable costs:

Cost of purchasing product: 6000 units × $50 …………………………………

$300 000

$300 000

Sales commissions: $480 000 × 10% ..……………… 48 000 Total variable cost ..………………………..…… 348 000 300 000

Contribution margin……………………………………… 132 000 180 000 Fixed costs .………………………………………….…… 22 000 66 000 Net profit ………………………………………….……… $110 000 $114 000

Plan A has a higher percentage of variable costs to sales (72.5 per cent) compared to Plan B (62.5 per cent). Plan B’s fixed costs are 13.75 per cent of sales, compared to Plan A’s 4.58 per cent.

Operating leverage factor = contribution margin ÷ net profit Plan A: $132 000 ÷ $110 000 = 1.2 Plan B: $180 000 ÷ $114 000 = 1.58 (rounded) Plan B has the higher degree of operating leverage. 4 & 5 Calculation of profit at 5000 units:

Plan A Plan B Sales revenue: 5 000 units × $80 $400 000 $400 000 Less variable costs:

Cost of purchasing product: 5 000 units × $50

250 000

$250 000

Sales commissions: $400 000 × 10% .……………… 40 000 Total variable cost……………………….……… 290 000 250 000

Contribution margin……………………………………… 110 000 150 000 Fixed costs .……………………………………………… 22 000 66 000 Net profit.………………………………………………… $88 000 $84 000

Plan A profitability decrease: $110 000 – $88 000 = $22 000; $22 000 ÷ $110 000 = 20% Plan B profitability decrease: $114 000 – $84 000 = $30 000; $30 000 ÷ $114 000 = 26.3% (rounded) PneumoTech will experience a larger percentage decrease in profit if it adopts Plan B, because Plan B

has a higher degree of operating leverage. Stated differently, Plan B’s cost structure produces a greater percentage decline in profitability from the drop-off in sales revenue.

Note: The percentage decreases in profitability can be calcualted 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)

6 Heavily automated manufacturers have sizable investments in plant and equipment, along with 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, these firms typically suffer a significant decrease in profitability. Such firms would be a more risky investment when compared with firms that have a low degree of operating leverage. Of course, when times are good, increases in sales would tend to have a very favourable effect on earnings in a company with high operating leverage.

PROBLEM 18.54 (45 minutes) (appendix) Basic CVP relationships; cost structure; operating leverage

1 Break-even point in units:


Break - even point =

fixed costsunit contribution margin

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:

Break - even point in units = $1 980 000 + $750 000

$15.60

= $2 730 000

$15.60= 175 000 units

(b) Computer-assisted manufacturing system:

Break - even point in units = $3 660 000 + $750 000

$21

= $4 410 000

$21= 210 000 units

2 Zodiac’s 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

3 Operating leverage is the extent to which a firm’s operations employ fixed operating costs. The greater the proportion of fixed costs used to produce a product, the greater the degree of operating leverage. Thus, the computer-assisted manufacturing method utilises a greater degree of operating leverage.

The greater the degree of 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.

4 Management should employ the computer-assisted manufacturing method if annual sales are expected to exceed 311 111 units and the labour-intensive manufacturing method if annual sales are not expected to exceed 311 111 units.

5 Zodiac’s management should consider many business factors other than operating leverage before selecting a manufacturing method. Among these are:

• 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 18.55 (40 minutes) Activity-based costing; ethical issues: manufacturer

1 Date: Today To: Manufacturing Director, Saturn Games Ltd From: I. M. Student, Financial Controller Subject: Activity-based costing The $150 000 cost that has been characterised as fixed, is fixed with respect to production volume.

Under a conventional costing system, it is assumed that this cost will not increase with increases in volume. However, as the activity-based costing analysis demonstrates, these costs are not fixed with respect to other important cost drivers. This is the difference between a conventional costing system and an ABC system. The latter recognises that costs vary with respect to a variety of cost drivers, not just production volume. This is usually a more accurate representation of cost behaviour.

2 (a) New break-even point if automated manufacturing equipment is installed: Selling price $26 Costs that are variable (with respect to sales volume): Unit variable cost (80% × $375 000 ÷ 25 000) 12 Unit contribution margin $14 Total non-volume activity costs to be covered: Setup (300 set-ups at $50 per setup) $ 15 000 Engineering (800 hours at $28 per hour) 22 400 Inspection (100 inspections at $45 per inspection) 4 500 General factory overhead $166 100 Total 208 000 Fixed selling and administrative costs 30 000 Total non-volume activity costs that need to be covered $238 000

Break-even point (in units) = total non - volume activity costs


= $238 000

$14

= 17 000 units

(b) Sales (in units) required to show a profit of $140 000:

Number of sales required to

earn target net profit = total non - volume activity costs + target net profit


= $238 000 + $140 000

$14

= 27 000 units

3 If Saturn Games Ltd adopts the new manufacturing technology: (a) Its break-even point will be higher (17 000 units instead of 15 000 units*). (b) The number of sales units required to show a profit of $140 000 will be lower

(27 000 units instead of 29 000 units**). * Breakeven point with existing technology = $150 000/($25 - $15) = 15 000 units ** Number of units to earn a profit of $140 000, with existing technology = ($150 000 + $140 000) /($25 - $15) = 29000 units

These results are typical of situations where firms adopt advanced manufacturing equipment and practices. The break-even point increases because of the increased fixed costs due to the large investment in equipment. However, at higher levels of sales after fixed costs have been covered, the


larger unit contribution margin ($14 instead of $10) earns a profit at a faster rate. This results in the firm needing to sell fewer units to reach a given target profit level.

4 The financial controller should include the break-even analysis in the report. The Board of Directors needs a complete picture of the financial implications of the proposed equipment acquisition. The break-even point is a relevant piece of information. The controller should accompany the break-even analysis with an explanation as to why the break-even point will increase. It would also be appropriate to point out in the report that the advanced manufacturing equipment would require fewer sales units at higher volumes in order to achieve a given target profit, as in requirement (3) of this problem.

To withhold the break-even analysis from the report would be a violation of the Code of Ethics for Professional Accountants, issued by the Accounting Professional and Ethical Standards Board (APESB): • Integrity: The financial controller must act with honesty and integrity.

Not revealing the correct information breaches the trust of the Board of Directors and shows a lack of honesty and integrity.

• Objectivity: The financial controller must be impartial, objective and free of conflicts of interest in performance of his duties. Not disclosing all relevant information violates this.

• Independence: The financial controller must free of any interest which is, or is regarded as incompatible with integrity and objectivity.

5 The difficulties of using activity-based costs in CVP analysis can arise from the recognition that not all costs vary or are fixed with respect to volume. For example, with ABC in order to undertake accurate CVP analysis we need to estimate a certain number of batches that will be produced during the period. This is required to allow us to calculate a total of non-volume activity costs that need to be covered. However, once we use CVP analysis to calculate a break-even volume or target volume, this may lead to a change in batch size and the number of batches to be produced and, hence, a change in the total activity costs, which will mean the break-even or target volume is no longer accurate.

In this case, certain assumptions were made about the number of set-ups, engineering hours and inspections. Although not stated, these are probably batch-related costs. A certain production volume must have underlay these activity estimates and it may be that if 27 000 units are produced to meet the target profit of $140 000 that the activities and, hence, total costs will change. The target profit may not be achieved as predicted!

CASE 18.56 (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.

7 The impact of the proposed changes to the original budget can be seen in the table below. Original

budget Option 5a Option 5b 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 ------ $267 500 $535 000 ($835 500)


costs over original 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.

CASE 18.57 (50 minutes) Break-even analysis; safety margin: service firm

(Author’s note. Requirement 3 of Case 18.57 is missing (since previous edition), and new materials added.) 1 In 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 $980 000 Rent (6000 × $56) 336 000 Council rates 54 000 Utilities 74 000 Professional indemnity insurance 360 000 Depreciation ($120 000/4) 30 000 Wages and on costs:

Regular wages: ($50 + $40 + $30 + $20) × 16 × 360 $806 400 Overtime wages: (200 × $30 × 1.5) + (200 × $20 × 1.5) 15 000

Total wages 821 400 On costs at 40% $328 560 1 149 960

Total fixed expenses $2 983 960

Break-even point: 0 = revenue – variable cost – fixed cost 0 = $60X + ($4000 × 0.2X × .3)* – $8X – $2 983 960 0 = $60X + $240X – $8X – $2 983 960 $292X = $2 983 960 X = 10 220 clients (rounded)

* Revenue calculation: $60X represents the $60 consultation fee per client. ($4 000 × .2X × .30) represents the predicted average settlement of $4 000, 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.

2 Safety 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 = [($60 × 18 000) + ($4 000 × 18 000 × 0.20 × 0.30)] – [($60 × 10 220) + ($4 000 × 10 220 × 0.20 × 0.30)]

= [$60 + ($4 000 × .20 × .30)] × (18 000 – 10 220) = $300 × 7 780 = $2 334 000

3 The assumptions underlying the break-even analysis of this law office are the 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 staff’s wages and advertising expenses are allocated equally to each of 10,220 clients.


CASE 18.58 (50 minutes) Contribution margin statement; 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) 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

• ddentifying 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 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) Delphina Products Ltd’s 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 18.59 (50 minutes) Break-even analysis; CVP relationships: hospital

1 The 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 June 30

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

total fixed costs $8112 000 contribution margin per patient - day $480

16 900 patient days

= =

=

2 Net earnings would decrease by $728 000, calculated as follows:

Narooma Medical Centre Calculation of loss from rental of additional 20 beds: Paediatrics

for the year ended June 30 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)

Documents

Chapter 18 (Cost Volume Profit)