**Chapter 23 Cost-Volume-Profit Analysis**

QUESTION 1

The following information relates to Bonds Ltd for the year ended 31 December 2012:

$

Budgeted sales 1,000,000

Budgeted costs:

Direct materials 500,000

Direct labour (per unit)15

Other variable costs (per unit)2

Annual fixed costs150,000

Budgeted unit selling price50

Required:

(a)Calculate the break-even point in sales units for Bonds Ltd for the year ended 31 December 2012.

(6 marks)

(b)How many units would Bonds Ltd need to sell in 2012 if the company wanted to achieve a target profit of $225,500? (2 marks)

(Calculations to the nearest unit or dollar)

Answer

(a) / Total / Per unit$ / $

Variable costs:

Direct materials (Workings) / 500,000 / 25 / 2

Direct labour (20,000 $15) / 300,000 / 15 / 1

Other variable costs (20,000 $2) / 40,000 / 2 / 1

840,000 / 42 / 0.5

Workings:Budgeted production and sales units= $1,000,000 $50= 20,000 units

Direct materials per unit= $500,000 20,000 = $25

Contribution margin per unit = $50 $42 = $8(0.5 marks)

Break-even point in sales units = $150,000 $8 = 18,750 units(1 mark)

(b)Required sales units

= (Fixed costs + Target profit) Contribution margin per unit

= ($150,000 + $225,500) $8

= 46,938 units(2 marks)

QUESTION 2

Ivan Cheung runs a business making and selling three products: A, B and C.Their unit costs and selling prices are as follows:

Product AProduct BProduct C

$$$

Selling price100200400

Variable costs5090160

Fixed costs are $150,000 per month.

Required:

(a)Calculate the contribution margin ratio for each product.(4 marks)

(b)Assuming that expected annual sales for Product A and Product B are 10,000 units and 8,000 units respectively, calculate the number of Product C units that need to be sold

(i)to achieve break-even;

(ii)to achieve a target profit of $500,000.(5 marks)

(c)What is the use of cost-volume-profit analysis?(2 marks)

(Rounded up to the next unit or dollar)

Answer

(a)Contribution margin per unit:

Product A / Product B / Product C$ / $ / $

Selling price / 100 / 200 / 400

Variable costs / (50) / (90) / (160)

Contribution margin / 50 / 110 / 240 / 1

Contribution margin ratio:

Product A: $50 $100= 50%(1 mark)

Product B: $110 $200 = 55%(1 mark)

Product C: $240 $400= 60%(1 mark)

(b)Required contribution from Product C:

$Total fixed costs ($150,000 12) / 1,800,000 / 0.5

LessProduct A’s contribution (10,000 $50) / (500,000) / 0.5

Product B’s contribution (8,000 $110) / (880,000) / 0.5

Product C’s required contribution / 420,000 / 0.5

Required sales units of Product C to cover the fixed costs

= $420,000 $240

= 1,750 units(1 mark)

Required sales units to achieve the target profit

= ($420,000 + $500,000) $240

= $3,834 units(2 marks)

(c) Cost-volume-profit analysis helps management find out how total costs and total sales revenue change

with different levels of production or sales. It allows management to know how many units of output have to be produced and sold in order to break-even (i.e., cover fixed costs). (2 marks)

QUESTION 3

Ace Ltd manufactures and sells the three products below:

Grade AGrade BGrade C

Annual sales units1,000,0005,000,0003,000,000

Unit selling price$500$600$700

Unit variable costs$300$350$380

Fixed costs amount to $8,000,000 per year.

Required:

(a)Compute the break-even point in sales units for each product using the:

(i)Equation approach(7 marks)

(ii)Weightedaverage approach(6 marks)

(b)What is theunit contribution margin?(1 mark)

(Rounded up to the next unit or dollar)

Answer

(a)Workings:

Grade A / Grade B / Grade C$ / $ / $

Unit selling price / 500 / 600 / 700

Unit variable costs / (300) / (350) / (380)

Unit contribution margin / 200 / 250 / 320 / 1

Sales mix / 1 / 5 / 3 / 1

(i)Equation approach:

Let Q be the sales volume of Grade A

Sales volume of Grade B = 5Q

Sales volume of Grade C = 3Q

At the break-even point, total contribution margin = total fixed costs

($200 Q) + ($250 5Q) + ($320 3Q)= $8,000,000(1 mark)

$2,410Q= $8,000,000

Q= 3,319.5(1 mark)

Units of Grade A to be soldto break even = 3,319.5 1 = 3,320 units(1 mark)

Units of Grade B to be sold to break even = 3,319.5 5 = 16,598 units (1 mark)

Units of Grade C to be sold to break even = 3,319.5 3 = 9,959 units(1 mark)

(ii)Weighted average approach:

Weighted-average unit contribution= ($200 1/9) + ($250 5/9) + ($320 3/9)

= $267.78(2 marks)

Break-even point in sales units= Fixed costs Weighted-average unit contribution

= $8,000,000 $267.78 = 29,875.27 units(1 mark)

Units of Grade A to be sold to break even= 29,875.27 1/ 9 = 3,320 units(1 mark)

Units of Grade B to be sold to break even= 29,875.27 5/9 = 16,598 units(1 mark)

Units of Grade C to be sold to break even= 29,875.27 3/9 = 9,959 units(1 mark)

(b)The unit contribution margin is the difference between the unit selling price and unit variable costs of a product. (1 mark)

QUESTION 4

Eggplant Ltdproduces and sells a single product. The costs per unit are as follows:

Direct materials $100

Direct labour $60

Variable manufacturing overheads$10

Fixed manufacturing overheads$8.5

Variable non-manufacturing overheads$20

Fixed non-manufacturing overheads$4

Fixed costs for the year amountto $1,000,000. The budgeted sales volume is 80,000 units and the selling price is $280 per unit.

Required:

(a)Calculate:

(i)Contribution margin ratio(2 marks)

(ii)Break-even sales revenue(2 marks)

(iii)Margin of safety ratio(2 marks)

(b)Explain the term ‘margin of safety’.(2 marks)

(Calculations to two decimal places)

Answer

(a)(i)Unit contribution margin:

$ / $Sales / 280

Less / Variable costs:

Direct materials / 100

Direct labour / 60

Variable manufacturing overheads / 10

Variable non-manufacturing overheads / 20 / (190)

Unit contribution margin / 90 / 1

Contribution margin ratio = $90 $280= 32.14%(1 mark)

(ii)Break-even sales revenue

= Fixed costs Contribution margin ratio

= $1,000,000 32.14%

= $3,111,387.68(2 marks)

(iii)Margin of safety ratio

= {[(80,000 $280) $3,111,387.68] (80,000 $280)}

= 86.11%(2 marks)

(b)Margin of safety is the difference between actual or budgeted sales and break-even sales. It can be measured in dollars, units and percentages. It tells how far the sales volume or sales revenue has to fall before a loss occurs. The higher the margin of safety, the lower the probability of sales fallingbelow the break-even point. (2 marks)

QUESTION 5

Classics Ltd manufactures and sells two products: X and Y. Fixed costs total $1,500,000 per year. The revenue and cost information is as follows:

Product XProduct Y

Sales in units200,000300,000

Selling price per unit$30$15

Variable costs per unit$10$6

Required:

(a)Find the break-even sales units for each product, using the weighted average approach.(6 marks)

(b)If the company can sella total 550,000 units during the year, how many units of Product Y would be sold, assuming that the sales mix remains unchanged? (1 mark)

(c)If the unit selling prices are to increase by 20%, calculate the break-even sales units forProduct Y.

(5 marks)

(Rounded up to the next unit or dollar)

Answer

(a)Unit contribution margin:

Product X / Product Y$ / $

Unit selling price / 30 / 15

Unit variable costs / (10) / (6)

Unit contribution margin / 20 / 9 / 1

Sales mix / 2 / 3 / 1

Weighted-average unit contribution = ($20 2/5) + ($9 3/5) = $13.4(1 mark)

Break-even sales units = Fixed costs Weighted-average unit contribution

= $1,500,000 $13.4 = 111,940.30units(1 mark)

Units of Product X to be sold to break even = 111,940.3 2/5 = 44,777 units(1 mark)

Units of Product Y to be sold to break even = 111,940.3 3/5= 67,165 units(1 mark)

(b)Sales units of Product Y = 3/5 of total sales units

= 550,000 3/5

= 330,000 units(1 mark)

(c)Unit contribution margin:

Product X / Product Y$ / $

Unit selling price (X: $30 120%; Y: $15 120%) / 36 / 18 / 1

Unit variable costs / (10) / (6)

Unit contribution margin / 26 / 12 / 1

Sales mix / 2 / 3

Weighted-average unit contribution = ($26 2/5) + ($12 3/5) = $17.6(1 mark)

Break-even sales volume= Fixed costs Weighted-average unit contribution

= $1,500,000 $17.6 = 85,227.27 units(1 mark)

Units of Product Y to be sold to break even = 85,227.27 3/5 = 51,137 units(1 mark)

QUESTION 6

Datum Ltd produces a single product and has the following budgeted costinformation:

$

Direct labour 1,000,000

Direct materials 5,000,000

Administrative overheads (100% fixed)1,200,000

Production overheads (30% fixed; 70% variable)2,500,000

Selling and distribution overheads (50% fixed; 50% variable)1,600,000

The above budgetfigures are based on the budgeted production and sales of 50,000 units. The budgeted selling price is $500 per unit.

Required:

(a)Separate the above costs into fixed and variable components and then calculate the unit contribution margin. (6 marks)

(b)Calculate the break-even point in units and in dollars.(4 marks)

(c)Owing to inflation, variable selling and distribution overheads have increased by 20% and fixed production overheads have increased by 10%. Calculate the new break-even point in units. (5 marks)

(Rounded up to the next unit or dollar)

Answer

(a)Separation of costs into fixed and variable components:

Total costs / Fixed costs / Variable costs$ / $ / $

Direct labour / 1,000,000 / — / 1,000,000

Direct materials / 5,000,000 / — / 5,000,000

Administrative overheads / 1,200,000 / 1,200,000 / —

Production overheads (W1) / 2,500,000 / 750,000 / 1,750,000

Selling and distribution overheads (W2) / 1,600,000 / 800,000 / 800,000

11,300,000 / 2,750,000 / 8,550,000 / 3

Workings:

(W1)Fixed production overheads = $2,500,000 30% = $750,000

Variable production overheads = $2,500,000 70% = $1,750,000

(W2)Fixed selling and distribution overheads = $1,600,000 50% = $800,000

Variable selling and distribution overheads = $1,600,000 50% = $800,000

Variable costs per unit = $8,550,000 50,000 = $171(2 marks)

Unit contribution margin = $500 $171 = $329(1 mark)

(b)Break-even point in units= Fixed costs Unit contribution margin

= $2,750,000 $329

= 8,359 units(2 marks)

Break-even point in dollars= 8,359 $500

= $4,179,500(2 marks)

(c)Separation of costs into fixed and variablecomponents:

Total costs / Fixed costs / Variable costs$ / $ / $

Direct labour / 1,000,000 / — / 1,000,000

Direct materials / 5,000,000 / — / 5,000,000

Administrative overheads / 1,200,000 / 1,200,000 / —

Production overheads (W1) / 2,575,000 / 825,000 / 1,750,000

Selling and distribution overheads (W2) / 1,760,000 / 800,000 / 960,000

11,535,000 / 2,825,000 / 8,710,000 / 3

Workings:

(W1)Fixed production overheads = $750,000 110%= $825,000

Total production overheads = $825,000 + $1,750,000= $2,575,000

(W2)Variable selling and distribution overheads = $800,000 120%= $960,000

Total selling and distribution overheads = $800,000 + $960,000= $1,760,000

Variable costs per unit = $8,710,000 50,000 = $174.2(2 marks)

Unit contribution margin = $500 $174.2 = $325.8(1 mark)

Break-even point in units= Fixed costs Unit contribution margin

= $2,825,000 $325.8

= 8,671 units(2 marks)

QUESTION 7

Joy Manufacturing Ltd produces and sells a popular board game. This product sells for $250 each and has a contribution margin of 40%. The company’s fixed costs total $2,500,000 per year. The projected sales volume for the year is 50,000 units.

Required:

(a)Calculate the unit variable costs.(1 mark)

(b)Using the equation method:

(i)Calculate the break-even point in units and in dollars.(3 marks)

(ii)The number of units required to achieve a target profit of $1,250,000.(2 marks)

(iii)Calculate the break-even point in units and in dollars, assuming that the company is able to reduce the unit variable costs by $10. (3 marks)

(c)Using the contribution margin method:

(i)Calculate the break-even point in units and in dollars.(3 marks)

(ii)The number of units and revenue required to achieve a target profit of $3,125,000.(3 marks)

(iii)Calculate the break-even point in units and in dollars, assuming that the company is able to reduce unit variable costs by $20. (3 marks)

(Rounded up to the next unit or dollar)

Answer

(a)Unit variable costs = $250 (1 40%) = $150(1 mark)

(b)(i)Let Q be the number of units to be sold in order to break even

Sales revenue = $250Q

Variable costs = $150Q

Fixed costs = $2,500,000

Sales revenue= Fixed costs + Variable costs

$250Q = $2,500,000 + $150Q(1 mark)

$100Q= $2,500,000

Q= 25,000

Break-even point in units = 25,000 units(1 mark)

Break-even point in dollars = 25,000 $250 = $6,250,000(1 mark)

(ii)Let X be the number of units to be sold in order to achieve a target profit of $1,250,000

Sales revenue = $250X

Variable costs = $150X

Fixed costs = $2,500,000

Target profit = $1,250,000

Sales revenue= Fixed costs + Variable costs + Target profit

$250X = $2,500,000 + $150X + $1,250,000(1 mark)

$100X= $3,750,000

X= 37,500

Required sales units = 37,500 units (1 mark)

(iii)Let Q be the number of units to be sold in order to break even

Sales revenue = $250Q

Variable costs = $140Q

Fixed costs = $2,500,000

Sales revenue= Fixed costs + Variable costs

$250Q = $2,500,000 + $140Q(1 mark)

$110Q= $2,500,000

Q= 22,728

Break-even point in units = 22,728 units(1 mark)

Break-even point in dollars = 22,728 $250 = $5,682,000(1 mark)

(c)(i)Break-even point in units= Fixed costs Unit contribution margin

= $2,500,000 ($250 40%)

= 25,000 units(2 marks)

Break-even point in dollars= 25,000 $250

= $6,250,000(1 mark)

or

Break-even point in dollars= Fixed costs Contribution margin ratio

= $2,500,000 40%

= $6,250,000

(ii)Required sales units= ($2,500,000 + $3,125,000) $100

= 56,250 units(2 marks)

Required sales revenue= 56,250 $250

= $14,062,500(1 mark)

(iii)Unit variable costs = $150 $20 = $130

Unit contribution margin = $250 $130 = $120

Break-even point in units= Fixed costs Unit contribution margin

= $2,500,000 $120

= 20,834 units(2 marks)

Break-even point in dollars= 20,834 $250

= $5,208,500(1 mark)

QUESTION 8

Hill Ltd produces 12,000 units per month. The costs per unit are as follows:

$

Direct materials160

Direct labour100

Variable production overheads60

Variable sales overheads50

The projected selling price is $600 per unit. Fixed overheads are $910,800 per annum.

Required:

(a)Calculate the break-even point in units and in dollars.(3 marks)

(b)Calculate the break-even point in units if direct materials incur carriage inwards of 20% on cost.

(2 marks)

(c)Taking into account the information in (b), calculate:

(i)the margin of safety in revenue;(2 marks)

(ii)the number of units required to achieve a target profit of $990,000.(2 marks)

(d)State threeof the assumptions used in break-even analysis.(3 marks)

Answer

(a)Break-even sales in units= Fixed costs Unit contribution margin

= $910,800 ($600 $160 $100 $60 $50)

= $910,800$230

= 3,960 units (2 marks)

Break-even sales in dollars= 3,960 $600

= $2,376,000(1 mark)

(b)Break-even sales in units= Fixed costs Unit contribution margin

= $910,800 [$600 ($160 120%) $100 $60 $50]

= $910,800 $198

= 4,600 units(2 marks)

(c)(i)Margin of safety in revenue

= Actual revenue Break-even sales revenue

= (12,000 $600) (4,600 $600)

= $7,200,000 $2,760,000

= $4,440,000(2 marks)

(ii)Required sales units

= (Fixed costs + Target profit) Contribution margin per unit

= ($910,800 + $990,000) $198

= 9,600 units(2 marks)

(d)Assumptions used in break-even analysis:

Average or marginal variable costs remain constant when the level of activity changes.

Changes in revenue and costs are only caused by changes in sales volume.

The selling price remains constant.

The number of units produced is equal to the number of units sold.

The sales mix is constant when multiple products are involved.

The time value of money is ignored.

(Any three of the above, 1 mark each)

QUESTION 9

Kimmy Ltd anticipates selling 50,000 units in the current year at a price of $200 each. The cost information is as follows:

Direct labour at $10 per hour4 hours per unit

Direct materials at $12 per kg2 kg per unit

Variable manufacturing overheads$5 per direct labour hour

Variable administrative and selling overheads$18 per unit

Fixed overheads$60 per unit

Required:

(a)Calculate the following:

(i)Contribution margin per unit(3 marks)

(ii)Net profit for the year(2 marks)

(iii)Break-even point in units and in dollars(2 marks)

(iv)Margin of safety as a percentage of sales(1 mark)

The management is considering installinga computerised system to improve productivity. This will reduce direct labour time by one hour per unit. However, extra fixed overheadsof $50,000 per month will be incurred.

Required:

(b)Recalculate the net profit for the year, break-even point in units and margin of safety as a percentage

of sales.(8 marks)

(c)Calculate the number of sales units that would generate the same amountof net profit under (a) and (b). (4 marks)

(Calculations to two decimal places)

Answer

(a)(i)Contribution margin per unit:

$ / $Per unit:

Sales / 200

Less Variable costs:

Direct labour (4$10) / 40

Direct materials (2 $12) / 24

Variable manufacturing overheads (4 $5) / 20

Variable administrative and selling overheads / 18 / (102)

Contribution margin per unit / 98 / 3

(ii)Net profit for the year

= Total contribution margin Total fixed costs

= (50,000 $98) (50,000 $60)

= $4,900,000 $3,000,000

= $1,900,000(2 marks)

(iii)Break-even point in units= $3,000,000 $98

= 30,612.24

= 30,613 units (rounded up)(1 mark)

Break-even point in dollars= 30,613 $200

= $6,122,600(1 mark)

(iv)Margin of safety as a percentage of sales

= (50,000 30,613) 50,000

= 38.77%(1 mark)

(b)Contribution margin per unit:

$ / $Per unit:

Sales / 200

Less Variable costs:

Direct labour (3$10) / 30

Direct materials (2 $12) / 24

Variable manufacturing overheads (3$5) / 15

Variable administrative and selling overheads / 18 / (87)

Contribution margin per unit / 113 / 2

Net profit for the year

= (50,000 $113) [$3,000,000 + ($50,00012)]

= $2,050,000(2 marks)

Break-even point in units

= [$3,000,000 + ($50,00012)] $113

= 31,858.41

= 31,859 units (rounded up)(2 marks)

Margin of safety as a percentage of sales

= (50,000 31,859) 50,000

= 36.28%(2 marks)

(c)Let Q be the number of sales units that would generate the same amount of net profit under (a) and (b)

Let P be the net profit

Profit = Sales Variable costs Fixed costs

In (a), P = $200Q $102Q $3,000,000(1 mark)

In (b), P = $200Q $87Q $3,600,000 (1 mark)

$200Q $87Q $3,600,000= $200Q $102Q $3,000,000

$15Q= $600,000

Q= 40,000

Required number of sales units = 40,000 units(2 marks)

QUESTION 10

Faye Products Ltd manufactures and sells a single product. During the current year, the unit selling price of the product is $450, while the unit variable costs are $300. Fixed costs amount to $152,000 per month.

The company’s annual costs areanalysed as follows:

$

Direct materials3,000,000

Direct labour 2,000,000

Variable overheads1,000,000

Required:

(a)Calculate the break-even point in units and in revenue.(3 marks)

(b)Calculate the number of units to be sold to increase the net profit for the year by 50%.(5 marks)

The following changes will take place in the coming year:

(i)The company will increase the sales volume by 25% and the unit selling price to $460.

(ii)Fixed costs will increase to $156,000 per month.

(iii)All production workers will receive a 10% pay increase.

(iv)Variable overheads will increase by $50 per unit.

(v)Prices of direct material will increase by 20%.

Required:

Taking into consideration items (i) to (v), calculate for the coming year:

(c)Net profit (6 marks)

(d)Break-even point in units and in revenue(2 marks)

(e)The number of units required to achieve a net profit of $1,500,000(2 marks)

(Rounded up to the next unit or dollar)

Answer

(a)Break-even point in units= Fixed costs Unit contribution margin

= ($152,000 12) ($450 $300)

= 12,160 units(2 marks)

Break-even point in revenue= 12,160 $450

= $5,472,000(1 mark)

(b)Units sold in the current year

= Total variable costs Unit variable costs

= ($3,000,000 + $2,000,000 + $1,000,000) $300

= 20,000 units(1 mark)

Net profit for the year:

$Sales (20,000 $450) / 9,000,000

Less Variable costs (20,000 $300) / (6,000,000)

Contribution margin / 3,000,000

Less Fixed costs ($152,000 12) / (1,824,000)

Net profit / 1,176,000 / 2

Target net profit= $1,176,000 150%= $1,764,000 (1 mark)

Required number of units to be sold

= (Fixed costs + Target net profit) Unit contribution margin

= ($1,824,000 + $1,764,000) $150

= 23,920 units(1 mark)

(c)Net loss:

Total / Per unit$ / $

Sales [(20,000 125%) $460] / 11,500,000 / 460 / 1

Less Variable costs:

Direct materials ($3,000,000 125% 120%) / (4,500,000) / (180) / 1

Direct labour ($2,000,000 125% 110%) / (2,750,000) / (110) / 1

Variable overheads (Workings) / (2,500,000) / (100) / 1

Contribution margin / 1,750,000 / 70

Less Fixed costs ($156,00012) / (1,872,000) / 1

Net loss / (122,000) / 1

Workings:

Variable overheads per unit= ($1,000,000 20,000) + $50

= $100

Total variable overheads= 20,000125%$100

= $2,500,000

(d)Break-even point in units= $1,872,000 $70

= 26,743 units(1 mark)

Break-even point in revenue= 26,743 $460

= $12,301,780(1 mark)

(e)Required number of units

= (Fixed costs + Target net profit) Unit contribution margin

= ($1,872,000 + $1,500,000) $70

= 48,172 units(2 marks)

*NSS BAFS: Frank Wood’s Cost Accounting*1© Pearson Education Asia Limited 2011

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