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Cost volume analysis lesson 1 and lesson 2 for viewing accounting managerial accounting,
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Lesson 1 and 2: Cost-Volume-Profit Analysis and Other Related Topics For those who are not familiar with my types of exercises, they are broken down into theoretical, simple solving, and moderate solving / case type questions. The answer keys are at the end. Warm-Up
1) Explain why the break-even point changes when there is a change in sales mix.
2) Define the term ‘operating leverage’ and explain how the degree of operating leverage can influence future profits.
3) How can sensitivity analysis be used in conjunction with cost–volume–profit analysis?
4) A company has established a budgeted sales revenue for the forthcoming period of £500 000 with
an associated contribution of £275 000. Fixed production costs are £137 500 and fixed selling costs are £27 500.
What is the break-even sales revenue? (a) £75,625 (b) £90,750 (c) £250,000 (d) £300,000
5) Z plc currently sells products Aye, Bee and Cee in equal quantities and at the same selling price
per unit. The contribution to sales ratio for product Aye is 40 per cent; for product Bee it is 50 per cent and the total is 48 per cent. If fixed costs are unaffected by mix and are currently 20 per cent of sales, the effect of changing the product mix to: Aye 40%, Bee 25%, Cee 35% s that the total contribution/total sales ratio changes to: (a) 27.4% (b) 45.3% (c) 47.4% (d) 48.4% (e) 68.4%
6) The following information is required for sub-questions (a) and (b). W Ltd makes leather purses. It has drawn up the following budget for its next financial period:
6a) The margin of safety represents:
(i) 5.6% of budgeted sales (ii) 8.3% of budgeted sales (iii) 11.6% of budgeted sales (iv) 14.8% of budgeted sales
6b) The marketing manager has indicated that an increase in the selling price to $12.25 per unit would not affect the number of units sold, provided that the sales commission is increased to 8 per cent of the selling price.
ASSESSMENT MATERIAL
The review questions are short questions that enable you to assess your understanding of the maintopics included in the chapter. The numbers in parentheses provide you with the page numbers to
refer to if you cannot answer a specific question.The review problems are more complex and require you to relate and apply the content to various
business problems. The problems are graded by their level of difficulty. Solutions to review problems thatare not preceded by the term ‘IM’ are provided in a separate section at the end of the book. Solutions toproblems preceded by the term ‘IM’ are provided in the Instructor’s Manual accompanying this book thatcan be downloaded from the lecturer’s digital support resources. Additional review problems with fullyworked solutions are provided in the Student Manual that accompanies this book.
The digital support resources also includes over 30 case study problems. Several cases arerelevant to the content of this chapter. Examples include Dumbellow Ltd, Hardhat Ltd and MerrionProducts Ltd.
REVIEW QUESTIONS
8.1 Provide examples of how cost–volume–profit analysis can
be used for decision-making. (p. 168)
8.2 Explain what is meant by the term ‘relevant range’.
(pp. 170–71)
8.3 Define the term ‘contribution margin’. (p. 172)
8.4 Define the term ‘profit–volume ratio’ and explain how it can
be used for cost–volume–profit analysis. (pp. 173–74)
8.5 Describe and distinguish between the three different
approaches to presenting cost–volume–profit relationships
in graphical format. (pp. 175–78)
8.6 How can a company with multiple products use
cost–volume–profit analysis? (pp. 178–80)
8.7 Explain why the break-even point changes when there is a
change in sales mix. (pp. 179–80)
8.8 Describe the assumptions underlying cost–volume–profit
analysis. (pp. 183–84)
8.9 Define the term ‘operating leverage’ and explain how
the degree of operating leverage can influence future
profits. (pp. 180–81)
8.10 How can sensitivity analysis be used in conjunction with
cost–volume–profit analysis? (p. 184)
REVIEW PROBLEMS
8.11 Basic. A company has established a budgeted sales revenue
for the forthcoming period of £500000 with an associated
contribution of £275000. Fixed production costs are £137500 and
fixed selling costs are £27500.
What is the break-even sales revenue?
(a) £75625
(b) £90750
(c) £250000
(d) £300000
ACCA Paper 1.2 – Financial Information for Management
8.12 Basic. Z plc currently sells products Aye, Bee and Cee in equal
quantities and at the same selling price per unit. The contribution
to sales ratio for product Aye is 40 per cent; for product Bee it is
50 per cent and the total is 48 per cent. If fixed costs are unaffected
by mix and are currently 20 per cent of sales, the effect of
changing the product mix to:
Aye 40%
Bee 25%
Cee 35%
is that the total contribution/total sales ratio changes to:
(a) 27.4%
(b) 45.3%
(c) 47.4%
(d) 48.4%
(e) 68.4% CIMA Stage 2
8.13 Basic. The following information is required for sub-questions
(a) and (b).
W Ltd makes leather purses. It has drawn up the following
budget for its next financial period:
Selling price per unit $11.60
Variable production cost per unit $3.40
Sales commission 5% of selling price
Fixed production costs $430500
Fixed selling and administration costs $198150
Sales 90000 units
(a) The margin of safety represents:
(i) 5.6% of budgeted sales
(ii) 8.3% of budgeted sales
(iii) 11.6% of budgeted sales
(iv) 14.8% of budgeted sales
(b) The marketing manager has indicated that an increase in the
selling price to $12.25 per unit would not affect the number
of units sold, provided that the sales commission is
increased to 8 per cent of the selling price.
These changes will cause the break-even point (to the
nearest whole number) to be:
(i) 71033 units
(ii) 76016 units
(iii) 79879 units
(iv) 87070 units
CIMA – Management Accounting Fundamentals
ASSESSMENT MATERIAL 187
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These changes will cause the break-even point (to the nearest whole number) to be:
(i) 71,033 units (ii) 76,016 units (iii) 79,879 units (iv) 87,070 units
7) RT plc sells three products. Product R has a contribution margin of $30. Product S has a contribution margin of $20. Product T has a contribution margin of $25. Assume they all sell for $100 each. Monthly fixed costs are $100,000. If the products are sold in the ratio: R:2 S:5 T:3 The monthly break-even sales revenue, to the nearest $1, is: a) £400 000 (b) £411 107 (c) £425 532 (d) impossible to calculate without further
8) S plc produces and sells three products, X, Y and Z. It has contracts to supply products X and Y, which will utilize all of the specific materials that are available to make these two products during the next period. The revenue these contracts will generate and the information of products X and Y are as follows:
Product X = $10,000,000 in revenue, 85% of revenue are variable costs Product Y = $20,000,000 in revenue, 10% of revenue are variable costs
Product Z’s variable costs are 75% of total revenues. The total fixed costs of S plc are £5.5 million during the next period and management have budgeted to earn a profit of £1 million. Calculate the revenue that needs to be generated by Product Z for S plc to achieve the budgeted profit.
9) XYZ Ltd produces two products and the following budget applies:
You are required to calculate the break-even points for each product and the company as a whole and comment on your findings.
10) Toowomba manufactures various products and uses CVP analysis to establish the minimum level
of production to ensure profitability. Fixed costs of £50 000 have been allocated to a specific product but are expected to increase to £100 000 once production exceeds 30 000 units, as a new factory will need to be rented in order to produce the extra units. Variable costs per unit are stable at £5 per unit over all levels of activity. Revenue from this product will be £7.50 per unit.
(c) Assuming a margin of safety equal to 30 per cent of the
break-even value, calculate Z plc’s annual profit. (2 marks)
(d) Z plc is now considering opening another retail outlet
selling the same products. Z plc plans to use the same
profit margins in both outlets and has estimated that the
specific fixed costs of the second outlet will be £100 000
per annum.
Z plc also expects that 10 per cent of its annual sales
from its existing outlet would transfer to this second outlet if
it were to be opened.
Calculate the annual value of sales required from the
new outlet in order to achieve the same annual profit as
previously obtained from the single outlet. (5 marks)
(e) Briefly describe the cost accounting requirements of
organizations of this type. (4 marks)
Chartered Institute of Management Accountants Operational
Cost Accounting Stage 2
8.20 Intermediate: Preparation of a break-even chart with step
fixed costs. Toowomba manufactures various products and uses
CVP analysis to establish the minimum level of production to ensure
profitability.
Fixed costs of £50000 have been allocated to a specific product
but are expected to increase to £100000 once production exceeds
30000 units, as a new factory will need to be rented in order to
produce the extra units. Variable costs per unit are stable at £5 per
unit over all levels of activity. Revenue from this product will be
£7.50 per unit.
Required:
(a) Formulate the equations for the total cost at:
(i) less than or equal to 30000 units;
(ii) more than 30000 units. (2 marks)
(b) Prepare a break-even chart and clearly identify the break-
even point or points. (6 marks)
(c) Discuss the implications of the results from your graph in (b)
with regard to Toowomba’s production plans. (2 marks)
ACCA Paper 1.2 – Financial Information for Management
8.21 Intermediate: Changes in sales mix. XYZ Ltd produces two
products and the following budget applies for 20 × 2:
Product X Product Y
(£) (£)
Selling price 6 12
Variable costs 2 4
Contribution margin 4 8
Fixed costs apportioned 100000 200000
Units sold 70000 30000
You are required to calculate the break-even points for each product
and the company as a whole and comment on your findings.
8.22 Advanced: Non-graphical CVP behaviour. Tweed Ltd is a
company engaged solely in the manufacture of sweaters, which are
bought mainly for sporting activities. Present sales are direct to
retailers, but in recent years there has been a steady decline in
output because of increased foreign competition. In the last trading
year (2011) the accounting report indicated that the company
produced the lowest profit for 10 years. The forecast for 2012
indicates that the present deterioration in profits is likely to
continue. The company considers that a profit of £80000 should be
achieved to provide an adequate return on capital. The managing
director has asked that a review be made of the present pricing and
marketing policies. The marketing director has completed this
review, and passes the proposals on to you for evaluation and
recommendation, together with the profit and loss account for year
ending 31 December 2011.
Tweed Ltd profit and loss account for year ending 31 December 2011
(£) (£) (£)
Sales revenue
(100000 sweaters at
£10)
1 000000
Factory cost of goods sold:
Direct materials 100000
Direct labour 350000
Variable factory overheads 60000
Fixed factory overheads 220000 730000
Administration overhead 140000
Selling and distribution
overhead
Sales commission (2% of
sales)
20000
Delivery costs (variable
per unit sold)
50000
Fixed costs 40000 110000 980000
Profit 20 000
The information to be submitted to the managing director includes
the following three proposals:
(i) To proceed on the basis of analyses of market research
studies which indicate that the demand for the sweaters is
such that a 10 per cent reduction in selling price would
increase demand by 40 per cent.
(ii) To proceed with an enquiry that the marketing director has
had from a mail order company about the possibility of
purchasing 50000 units annually if the selling price is right.
The mail order company would transport the sweaters from
Tweed Ltd to its own warehouse, and no sales commission
would be paid on these sales by Tweed Ltd. However, if an
acceptable price can be negotiated, Tweed Ltd would be
expected to contribute £60000 per annum towards the cost
of producing the mail order catalogue. It would also be
necessary for Tweed Ltd to provide special additional
packaging at a cost of £0.50 per sweater. The marketing
director considers that in 2012 the sales from existing
business would remain unchanged at 100000 units, based
on a selling price of £10 if the mail order contract is
undertaken.
(iii) To proceed on the basis of a view by the marketing director
that a 10 per cent price reduction, together with a national
advertising campaign costing £30000 may increase sales
to the maximum capacity of 160000 sweaters.
Required:
(a) The calculation of break-even sales value based on the 2011
accounts.
(b) A financial evaluation of proposal (i) and a calculation of the
number of units Tweed Ltd would require to sell at £9 each to
earn the target profit of £80000.
(c) A calculation of the minimum prices that would have to be
quoted to the mail order company, first, to ensure that Tweed
Ltd would, at least, break-even on the mail order contract,
second, to ensure that the same overall profit is earned as
proposal (i) and, third, to ensure that the overall target profit
is earned.
(d) A financial evaluation of proposal (iii).
ASSESSMENT MATERIAL 189
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a) Formulate the equations for the total cost at: (i) less than or equal to 30 000 units; (ii) more than 30 000 units.
b) Prepare a break-even chart and clearly identify the break- even point or points. (c) Discuss the implications of the results from your graph in (b) with regard to Toowomba’s production plans.
Getting Serious:
11) Tweed Ltd is a company engaged solely in the manufacture of sweaters, which are bought mainly for sporting activities. Present sales are direct to retailers, but in recent years there has been a steady decline in output because of increased foreign competition. In the last trading year (2011) the accounting report indicated that the company produced the lowest profit for 10 years. The forecast for 2012 indicates that the present deterioration in profits is likely to continue. The company considers that a profit of £80 000 should be achieved to provide an adequate return on capital. The managing director has asked that a review be made of the present pricing and marketing policies. The marketing director has completed this review, and passes the proposals on to you for evaluation and recommendation, together with the profit and loss account for year ending 31 December 2011.
The information to be submitted to the managing director includes the following three proposals:
(i) To proceed on the basis of analyses of market research studies which indicate that the demand for the sweaters is such that a 10 per cent reduction in selling price would increase demand by 40 per cent.
(ii) To proceed with an enquiry that the marketing director has had from a mail order company about the possibility of purchasing 50 000 units annually if the selling price is right. The mail order company would transport the sweaters from Tweed Ltd to its own warehouse, and no sales commission would be paid on these sales by Tweed Ltd. However, if an acceptable price can be negotiated, Tweed Ltd would be expected to contribute £60 000 per annum towards the cost of
(c) Assuming a margin of safety equal to 30 per cent of the
break-even value, calculate Z plc’s annual profit. (2 marks)
(d) Z plc is now considering opening another retail outlet
selling the same products. Z plc plans to use the same
profit margins in both outlets and has estimated that the
specific fixed costs of the second outlet will be £100 000
per annum.
Z plc also expects that 10 per cent of its annual sales
from its existing outlet would transfer to this second outlet if
it were to be opened.
Calculate the annual value of sales required from the
new outlet in order to achieve the same annual profit as
previously obtained from the single outlet. (5 marks)
(e) Briefly describe the cost accounting requirements of
organizations of this type. (4 marks)
Chartered Institute of Management Accountants Operational
Cost Accounting Stage 2
8.20 Intermediate: Preparation of a break-even chart with step
fixed costs. Toowomba manufactures various products and uses
CVP analysis to establish the minimum level of production to ensure
profitability.
Fixed costs of £50000 have been allocated to a specific product
but are expected to increase to £100000 once production exceeds
30000 units, as a new factory will need to be rented in order to
produce the extra units. Variable costs per unit are stable at £5 per
unit over all levels of activity. Revenue from this product will be
£7.50 per unit.
Required:
(a) Formulate the equations for the total cost at:
(i) less than or equal to 30000 units;
(ii) more than 30000 units. (2 marks)
(b) Prepare a break-even chart and clearly identify the break-
even point or points. (6 marks)
(c) Discuss the implications of the results from your graph in (b)
with regard to Toowomba’s production plans. (2 marks)
ACCA Paper 1.2 – Financial Information for Management
8.21 Intermediate: Changes in sales mix. XYZ Ltd produces two
products and the following budget applies for 20 × 2:
Product X Product Y
(£) (£)
Selling price 6 12
Variable costs 2 4
Contribution margin 4 8
Fixed costs apportioned 100000 200000
Units sold 70000 30000
You are required to calculate the break-even points for each product
and the company as a whole and comment on your findings.
8.22 Advanced: Non-graphical CVP behaviour. Tweed Ltd is a
company engaged solely in the manufacture of sweaters, which are
bought mainly for sporting activities. Present sales are direct to
retailers, but in recent years there has been a steady decline in
output because of increased foreign competition. In the last trading
year (2011) the accounting report indicated that the company
produced the lowest profit for 10 years. The forecast for 2012
indicates that the present deterioration in profits is likely to
continue. The company considers that a profit of £80000 should be
achieved to provide an adequate return on capital. The managing
director has asked that a review be made of the present pricing and
marketing policies. The marketing director has completed this
review, and passes the proposals on to you for evaluation and
recommendation, together with the profit and loss account for year
ending 31 December 2011.
Tweed Ltd profit and loss account for year ending 31 December 2011
(£) (£) (£)
Sales revenue
(100000 sweaters at
£10)
1 000000
Factory cost of goods sold:
Direct materials 100000
Direct labour 350000
Variable factory overheads 60000
Fixed factory overheads 220000 730000
Administration overhead 140000
Selling and distribution
overhead
Sales commission (2% of
sales)
20000
Delivery costs (variable
per unit sold)
50000
Fixed costs 40000 110000 980000
Profit 20 000
The information to be submitted to the managing director includes
the following three proposals:
(i) To proceed on the basis of analyses of market research
studies which indicate that the demand for the sweaters is
such that a 10 per cent reduction in selling price would
increase demand by 40 per cent.
(ii) To proceed with an enquiry that the marketing director has
had from a mail order company about the possibility of
purchasing 50000 units annually if the selling price is right.
The mail order company would transport the sweaters from
Tweed Ltd to its own warehouse, and no sales commission
would be paid on these sales by Tweed Ltd. However, if an
acceptable price can be negotiated, Tweed Ltd would be
expected to contribute £60000 per annum towards the cost
of producing the mail order catalogue. It would also be
necessary for Tweed Ltd to provide special additional
packaging at a cost of £0.50 per sweater. The marketing
director considers that in 2012 the sales from existing
business would remain unchanged at 100000 units, based
on a selling price of £10 if the mail order contract is
undertaken.
(iii) To proceed on the basis of a view by the marketing director
that a 10 per cent price reduction, together with a national
advertising campaign costing £30000 may increase sales
to the maximum capacity of 160000 sweaters.
Required:
(a) The calculation of break-even sales value based on the 2011
accounts.
(b) A financial evaluation of proposal (i) and a calculation of the
number of units Tweed Ltd would require to sell at £9 each to
earn the target profit of £80000.
(c) A calculation of the minimum prices that would have to be
quoted to the mail order company, first, to ensure that Tweed
Ltd would, at least, break-even on the mail order contract,
second, to ensure that the same overall profit is earned as
proposal (i) and, third, to ensure that the overall target profit
is earned.
(d) A financial evaluation of proposal (iii).
ASSESSMENT MATERIAL 189
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producing the mail order catalogue. It would also be necessary for Tweed Ltd to provide special additional packaging at a cost of £0.50 per sweater. The marketing director considers that in 2012 the sales from existing business would remain unchanged at 100 000 units, based on a selling price of £10 if the mail order contract is undertaken.
(iii) To proceed on the basis of a view by the marketing director that a 10 per cent price reduction, together with a national advertising campaign costing £30 000 may increase sales to the maximum capacity of 160 000 sweaters.
Required: (a) The calculation of break-even sales value based on the 2011 accounts. (b) A financial evaluation of proposal (i) and a calculation of the number of units Tweed Ltd would require to sell at £9 each to earn the target profit of £80 000. (c) A calculation of the minimum prices that would have to be quoted to the mail order company, first, to ensure that Tweed Ltd would, at least, break-even on the mail order contract, second, to ensure that the same overall profit is earned as proposal (i) and, third, to ensure that the overall target profit is earned. (d) A financial evaluation of proposal (iii).
12) A local government authority owns and operates a leisure centre with numerous sporting
facilities, residential accommodation, a cafeteria and a sports shop. The summer season lasts for 20 weeks including a peak period of six weeks corresponding to the school holidays. The following budgets have been prepared for the next summer season:
Accommodation 60 single rooms let on a daily basis. 35 double rooms let on a daily basis at 160 per cent of the single room rate. Fixed costs £29 900. Variable costs £4 per single room per day and £6.40 per double room per day.
Sports Centre Residential guests each pay £2 per day and casual visitors £3 per day for the use of facilities. Fixed costs £15 500 Sports Shop Estimated contribution £1 per person per day. Fixed costs £8250 Cafeteria Estimated contribution £1.50 per person per day. Fixed costs £12 750 During the summer season the centre is open seven days a week and the following activity levels are anticipated: Double rooms fully booked for the whole season. Single rooms fully booked for the peak period but at only 80 per cent of capacity during the rest of the season. 30 casual visitors per day on average. You are required to: (a) calculate the charges for single and double rooms assuming that the authority wishes to make a £10 000 profit on accommodation; (b) calculate the anticipated total profit for the leisure centre as a whole for the season; (c) advise the authority whether an offer of £250 000 from a private leisure company to operate the centre for five years is worthwhile, assuming that the authority uses a 10 per cent cost of capital and operations continue as outlined above.
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13) Walt’s Woodwork Company makes and sells wooden shelves. Walt’s carpenters make the shelves in the company’s rented building. Walt has a separate office at another location that also includes a showroom where customers can view sample shelves and ask questions of salespeople. The company sells all the shelves it produces each year and keeps no inventories. The following information pertains to Walt’s Woodwork Company for the past year:
Make appropriate assumptions about cost behavior and assume that direct labor costs vary directly with the number of units produced. How many units must the company sell in order to earn a pre- tax profit of $500,000?
14) Johnson Company and Smith Company are competing firms that offer limousine service from the Charlesburg airport. While Johnson pays most of its employees on a per-ride basis, Smith prefers to pay its employees fixed salaries. Information about the selling prices per ride and cost structures of the two firms is given below.
(a) Calculate the breakeven point in the number of rides for both firms. (b) Draw two graphs plotting profit as a function of the number of rides for the two firms. (c) Explain which firm’s cost structure is more profitable. (d) Explain which firm’s cost structure is riskier. (e) What is the indifference point?
Answer Key:
1) The break-even point changes when the sales mix changes because there is a change in the weighted average contribution margin. You may be able to sell products with higher or lower contribution margins, which lessens/ increases the units needed to breakeven.
2) Operating leverage is the sensitivity of profits relative to growth in sales, and can be measured via the proportion of fixed costs relative to variable costs. It enhances profits significantly like a multiplier because high operating leverage has high fixed costs, so profits go up faster relative to revenues. However, it has a downside of multiplying losses as well.
106 Chapter 3 Using Costs in Decision Making
a. Units produced and sold 50,000b. Sales price per unit $70c. Carpenter labor to make shelves 600,000d. Wood to make the shelves 450,000e. Sales staff salaries 80,000f. Office and showroom rental expenses 150,000g. Depreciation on carpentry equipment 50,000h. Advertising 200,000i. Sales commissions based on number of units sold 180,000j. Miscellaneous fixed manufacturing overhead 150,000
k. Rent for the building where the shelves are made 300,000l. Miscellaneous variable manufacturing overhead 350,000
m. Depreciation for office equipment 10,000
(b) What other factors might the manager consider in deciding on the amount of shelf space percategory?
LO LO 2, 4 3-48 Product mix decision Boyd Wood Company makes a regular and a deluxegrade of wood floors. Regular grade is sold at $16 per square yard, and thedeluxe grade is sold at $25 per square yard. The variable cost of making theregular grade is $10 per square yard. It costs an extra $5 per square yard tomake the deluxe grade. It takes 15 labor hours to make 100 square yards ofthe regular grade, and 20 labor hours to make 100 square yards of the deluxegrade. There are 4,600 hours of labor time available for production eachweek. The maximum weekly sales for the regular and the deluxe model are30,000 and 8,000 square yards, respectively. Fixed production costs total$600,000 per year. All selling costs are fixed.
Required
What is the optimal production level in number of square yards for each product?
Problems
LO 3 3-49 Cost classification and target profit Walt’s Woodwork Company makesand sells wooden shelves. Walt’s carpenters make the shelves in thecompany’s rented building. Walt has a separate office at another location thatalso includes a showroom where customers can view sample shelves and askquestions of salespeople. The company sells all the shelves it produces eachyear and keeps no inventories. The following information pertains to Walt’sWoodwork Company for the past year:
Required
Make appropriate assumptions about cost behavior and assume that direct labor costs vary directlywith the number of units produced. How many units must the company sell in order to earn a pre-tax profit of $500,000?
LO 2, 3 3-50 Introducing a new product, profitability Santos Company is consideringintroducing a new compact disc player model at a price of $105 per unit.Santos’s controller has compiled the following incremental cost
108 Chapter 3 Using Costs in Decision Making
COST CATEGORY JOHNSON COMPANY SMITH COMPANY
Selling price per ride $30 $30Variable cost per ride 24 15Contribution margin per ride 6 15Fixed costs per year $300,000 $1,500,000
salaries. Information about the selling prices per ride and cost structures of the two firms is given below.
Required
(a) Calculate the breakeven point in the number of rides for both firms.(b) Draw two graphs plotting profit as a function of the number of rides for the two firms.(c) Explain which firm’s cost structure is more profitable.(d) Explain which firm’s cost structure is riskier.
LO 3 3-54 Multiple breakeven points Last month, Capetini Capacitor Companysold capacitors to its distributors for $250 per capacitor. The sales level of 3,000capacitors per month was less than the single-shift capacity of 4,400 capacitors atits plant located in San Diego. Variable production costs were $100 per capacitor,and fixed production costs were $200,000 per month. In addition, variable sellingand distribution costs are $20 per capacitor, and fixed selling and distributioncosts are $62,500 per month. At the suggestion of the marketing department, thismonth Capetini reduced the sales price to $200 and increased the monthlyadvertising budget by $17,500. Sales are expected to increase to 6,800 capacitorsper month. If the demand exceeds the single-shift capacity of 4,400 capacitors,the plant needs to be operated in two shifts. Two-shift operation will increasemonthly fixed production costs to $310,000.
Required
(a) Determine the contribution margin per capacitor last month.(b) Determine the sales level in number of capacitors at which the profit-to-sales ratio would be
10% for last month.(c) Determine the two breakeven points for this month.(d) Determine the sales level in number of capacitors at which the profit-to-sales ratio this month
is the same as the actual profit-to-sales ratio last month. Is there more than one possible saleslevel at which this equality would occur?
LO 2, 3 3-55 Effect on costs of volume changes Capilano Containers Companyspecializes in making high-quality customized containers to order. Itsagreement with the labor union ensures employment for all its employeesand a fixed payroll of $80,000 per month, including fringe benefits. Thispayroll makes available 4,000 labor hours each month to work on orders thefirm receives. The monthly wages must be paid even if the workers remainidle because of a lack of work. If additional labor hours are required tocomplete jobs, overtime costs $30 per labor hour.
Each job requires 4 labor hours for machine setup and 0.05 labor hour percontainer. Variable costs are $1.60 per container for materials and $8.00 perlabor hour for manufacturing overhead expenses. In addition, the firm mustpay $20,000 per month for selling, general, and administrative expenses, and$36,000 per month lease payments for machinery and physical facilities.
In April, the firm won 90 orders, of which 60 were for 800 containerseach and 30 for 1,600 containers each.
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3) Sensitivity analysis can be used with CVP analysis to measure changes in margin of safety, breakeven, profit, and the like relative to changes in contribution margins and fixed costs.
4) D. Remember that for CVP analysis, it does not matter if a cost is COGS or in operating expenses
under the formal income statement, only that it is variable or fixed. In this particular problem, the per unit variable cost is not given, so you may be surprised. However, note that the question is asking breakeven on a monetary measure.
Breakeven in Sales in Volume = (137,500 + 27,500) / Contribution Margin Per Unit Breakeven Sales in Dollar = (165,000 / Contribution Margin Per Unit) x Selling Price Per Unit Breakeven Sales in Dollar = 165,000/ (Contribution Margin Per Unit/ Selling Price Per Unit Contribution Margin Ratio = Proportion contributed to paying for fixed costs relative to $1 earnings, or contribution margin per unit / selling price per unit. Since this is a ratio, it’s the same if we use total contribution margin / total revnue Contribution Margin Ratio = 275,000 / 500,000 = 55% Each $1 gives 0.55 in contribution. Breakeven Sales in Dollar = 165,000 / 55% = $300,000
5) B. This is a classic of encountering an unfamiliar term, but the solution is similar to other
problems. Contribution to sales ratio is basically contribution margin ratio, and all it is asking you for is getting the weighted average contribution margin ratio, similar to multiple product CVP analysis. 40% x 40% + 25% x 50 % + 35% x 48% = 45.3%
6) 6a) III. The margin of safety requires both budgeted sales and breakeven sales in terms of units. Breakeven sales in units is computed as Fixed Costs / Contribution Margin Per Unit Be warned that sales commission is a variable cost, which we can convert into a per unit basis. Sales Commission = 5% of Selling Price Sales Commission per unit = 5% x 11.60 = .58 Breakeven Sales = ($430,500 + 198,150) / (11.60 – 0.58 – 3.40) Breakeven Sales = 628,650 / 7.62 = 82,500 Margin of Safety = 90,000 – 82,500 = 7,500 As % of Budget = 7,500 / 90,000 =8.3% Be careful to read what the problem is asking for! 6b) III. Recompute but changing the CM. Remember to use the new inputs forcommission and selling price! Sales Commission = 8% of Selling Price Sales Commission per unit = 8% x 12.25 = .98 Breakeven Sales = ($430,500 + 198,150) / (12.25– 0.58 – 3.40) Breakeven Sales = 628,650 / 7.87 = 79,879
7) C. First do the weighted average contribution margin: 20% x 30 + 50% x 20 + 30% x 25 = 23.5 Breakeven in units = 100000 / 23.5 = 4,255.32
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Breakeven in sales = 4,255.32 x 100 = 425,532 Note: If you are given the contribution margin ratio, this can be solved as well. For example, if contribution margin ratio is 30%, 20%, and 25% for A B and C respectively, you can get the weighted average contribution margin ratio and divide the fixed costs with it, without needing to multiply by the selling price.
8) ) You are not given volume, but you do not need it. First solve for the hurdle / target: $5,500,000 + 1,000,000 = 6,500,000 Next, determine the portion already covered by product x and product y. Product X Contribution Margin = 10,000,000 x 15% = 1,500,000 Product Y Contribution Margin = 20,000,000 x 10% = 2,000,000 Fixed Costs and Profit Left to Cover = 6,500,000 – 1,500,000 – 2,000,000 = 3,000,000 Product Z Contribution Margin = 25% of Revenues 3,000,000 = 25% x Product Z Revenues Product Z Revenues = 3,000,000 / 25% = 12,000,000
9) Stand-Alone Breakeven:
Product X = 100,000 / 4 = 25,000 units Product Y = 200,000 / 8 = 25,000 units Company Breakeven: Weighted Average Contribution: 1/3 x 4 + 2/3 x 8 = 5.2 Company Breakeven = 300,000 / 5.2 = 57,692 Why the difference? When you do stand-alone breakeven, 1/3 of the fixed costs are allocate to product X, which has a lower margin. When you do combined, 7/10 of the fixed costs are allocated to product X effectively, meaning that it takes more to cover these fixed costs. Which do you use? You have do stand-alone first to see if the products are profitable by itself. The company breakeven is so you have some flexibility to cover for the losses of other products from time-to-time.
10) a) This is a step function / piece-wise cost equation. Where X = Volume If X <= 30,000: Total Cost = 50,000 + 5X If X > 30,000: Total Cost = 100,000 + 5X
b) Breakeven point is at 20,000 if < 30,000 and at 40,000 for > 30,000
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c) If Toowomba is planning on expansion, then it better makes sure it can sell at least 40,000 to breakeven. Otherwise, it will just lose money. And even then, Toowomba must make sure the profit gained from ramping up capacity is exceeds the profit from not ramping up capacity. At 30,000 units, total profit is 30,000 x 7.5 – 100,000 – 5 x 30,000 = $25,000. So effectively, not only must you produce 40,000 to breakeven, you actually need to produce at this to earn a better return: 7.5 X – 100,000 - 5X > 25,000 X > 50000. In other words, volume must actually be 50,000 for expansion to be worth it. To summarize: If potential sales < 20,000 = Don’t bother producing If potential sales is between 20,000 to 50,000, producing at 30,000 is still better even if you breakeven at 40,000 with the new fixed costs If potential sales is > 50,000, then producing at >50,000 is still better
11) a) Again, we calculate breakeven based on variable and fixed costs (cost behaviors relative to volume) regardless of whether they are COGS, admin, or selling expenses:
You can do this directly via sales revenue and contribution margin ratio, or the long cut (less confusing way). First, determine the fixed costs. Total fixed costs include: 1) Fixed Factory Overhead, 2) Administration Overhead, 3) Fixed sales overhead Total fixed costs = 220,000 + 140,000 + 40,000 = 400,000 Total Revenue = 1,000,000 Total Variable Costs = 100,000 + 350,000 +60,000 + 20,000 + 50,000 = 580,000 Contribution Margin Ratio = (1,000,000 – 580,000) / 1,000,000 Contribution Margin Ratio = 42% Breakeven Sales Revenue = 400,000 / 42% = $952,381 If you don’t want to memorize the contribution margin ratio formula (though I encourage you to understand it), here is another way:
Unit Selling Price: $10 / sweater Direct Materials: $1 / sweater (100,000 / 100,000) Direct Labour: $3.5 / sweater (350,000 /100,000) Variable Overhead: $0.6 / sweater ( 60,000 / 100,000)
0 20,000 40,000 60,000 80,000 100,000 120,000 140,000
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5,000
10,000
15,000
20,000
25,000
30,000
35,000
40,000
45,000
50,000
Total Fixed Cost
Contribution Margin
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Commission: $0.2 / sweater (2% of $10) Delivery Costs: $0.5 / sweater (50,000 / 100,000) Total Variable Costs Per Unit: $5.8 Total Contribution Margin Per Unit = $10 – 5.8 = $4.2 Breakeven Sales in Units = 400,000 / 4.2 = 95,238 units Breakeven Sales in Dollars = 95,238 units x $10 / sweater = 952,381
b) Proposal (i) asks you do actually do a sensitivity / scenario analysis
You can manipulate this on a total revenue or on a per unit basis. Let us say the variable costs remain steady at $5.8, but selling price goes down to $9. Your contribution margin per unit becomes $3.2. Your sales go up by 40%, or by 40,000 sweaters to become 140,000 sweaters. Total Profit = 140,000 x ( 9 – 5.8) – 400,000 Total Profit = $48,000 Better effect than the base case, but still not hitting the $80,000 target. How much do you need to sell in order to reach 80,000? This is a target profit analysis Target Profit + Fixed Costs = 480,000 480,000 / 3.2 = 150,000 units
c) Assuming that the decision will not affect the existing production capacity. This should be
assessed as an independent decision. We will asses the INCREMENTAL costs and INCREMENTAL revenues of the contract.
Additional Fixed Cost = $60,000 Variable Cost = Old Variable Cost – Commission + Special Fee Variable Cost = $5.8 + 0.5 – 0.2 = $6.1 Volume = 50,000 units 1) To breakeven Fixed Cost = Contribution Margin -> Breakeven 60,000 = 50,000 (Selling Price – Variable Cost ) 60,000 = 50,000 (Selling Price - $6.1) $1.2 = Selling Price – 6.1 $7.3 = Minimum Selling Price 2) Same as proposal (i) Proposal (i) has a net profit of 48,000. With the existing 100,000 earning 20,000, the new proposal has to earn $28,000 Target Profit + Fixed Cost = Contribution Margin 20,000 + 60,000 = 50,000 (Selling Price - $6.1) 80,000 = 50,000 (SP – 6.1) 1.60 = SP – 6.1 Minimum Selling Price: $7.7 3) Target Profit of 80,000
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With the existing production earning 20,000, you need to earn 60,000 on the new proposal. 80,000 + 60,000 = 50,000 (SP – 6.1) 140,000 = 50,000 (SP – 6.1) 2.8 = SP – 6.1 Minimum Selling Price = $8.9
d) Selling Price – Variable Cost = Margin Contribution 10 – 5.80 = 4.20 Margin Contribution = $4.20 Total Margin Contribution = $4.20 x 160,000 = $672,000 Fixed Cost = 430,000 Profit = 672,000 – 430,000 = $242,000
12) a) Assuming that you want to make 10,000 on accommodation, this is a target profit analysis problem, wherein fixed costs + target profit = 29,900 + 10,000 = 39,900 While this is an atypical cost formula, all you have to do is translate the sentence into a formula. You are looking for the charge of the single room (X) and the double room (Y), but Y = 1.6x because it is 160% of the single room rate. (woah algebra ☺) To not get confused, frame the timeline of the problem first. This is 20 weeks budget (140 days). Let us solve for the volume first. Double rooms are booked for the whole season. So 35 x 140 = 4,900 double rooms booked in the season Single rooms are booked at 100% for 6 weeks (42 days) and 80% for the remaining 14 weeks (98 days). 60 x 42 + 60 x 80% X 98 = 7,224 single rooms booked in the season 7,224 (x-4) + 4,900 (1.6x – 6.4) = 39,900 7,224x – 28,896 + 7840x – 31,360 = 39,900 15,064x = 100,156 Single Room Rate = 6.65 / night Double Room Rate = 10.64 / night b) Let us use the rates that we solved in A for accommodation. Furthermore, let us count the number of guests. How do we do this? Look at the rooms booked. Remember that single rooms are one person and double rooms are two persons. The way to do this is a sum of the parts analysis (just solve individually and put them together). This is how companies with very diverse products do it. 7,224 + 4900 x 2 = 17,024 guests 30 x 140 = 4,200 casual visitors
Accommodation = $10,000 profit (as given) Sports Center
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Contribution Margin = 2 x 17,024 + 3 x 4,200 = 46,648 Profit = 46,648 – 15,500 Profit = $31,148 Sports Shop
The word used is persons, meaning all the people who go to the resort. This number is the guest plus casual visitors. Contribution Margin = (17,024 + 4,200) x 1 = 21,224 Profit = 21,224 – 8,250 Profit = 12,974 Cafeteria Contribution Margin = (17,024 + 4,200) x 1.5 = 31,836 Profit = 31,836 – 12,750 Profit = 19,086 Total Profit = 73,208 / summer c) At 73,208 profit per summer, the government would be better off operating it on its own and getting $366,040 after 5 years. Assuming we even get the present value using a 10% discount rate, you will still get 277,515.92. The offer is too low.
13) The first thing you have to do is separate the fixed and variable costs through sound judgment.
Variable costs should include, carpenter labor, wood, sales commissions, and miscellaneous variable manufacturing overhead. Depreciation on carpentry equipment, arguably, can be a variable cost if we can allocate this based on volume (like units-of-production method). However, let us not include it for now. Fixed Costs: Depreciation for Carpentry, Sales Staff Salaries, Rental expenses, Advertising, Rent for Factory Building, Depreciation for Office Total Variable Cost = 600,000 + 450,000 + 180,000 + 150,000 + 350,000 = 1,730,000 # of Units Sold = 50,000 Variable Cost per Unit = 1,730,000 / 50,000 = $34.6 / shelf Total Fixed Cost = 80,000 + 50,000 + 150,000 + 200,000 + 300,000 + 350,000 + 10,000 =1,140,000 Target Profit = 500,000 Target Profit and Fixed Costs = 1,140,000 + 500,000 Target Profit and Fixed Costs = 1,640,000 Selling Price Per Unit = $70 Variable Cost Per Unit = $34.60 Contribution Margin = 35.4 Units to Sell = 1,640,000 / 35.4 = 46,328 units
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14) Breakeven Point for Johnson:
300,000 / 6 = 50,000 rides Breakeven Point for Smith: 1,500,000 / 15 = 100,000 rides b)
(c) There is no absolute answer for this. Johnson’s business is more profitable if you are riding under 133,333 cars. After this Smith’s business is more profitable. (d) Smith’s cost structure is riskier due to its higher operating leverage, at any level below 100,000, Smith will lose money. For Johnson’s case, it takes a lower volume to breakeven. e) Indifference point is the point of intersection, which is 133,333. You can do systems for this.
(2,000,000) (1,500,000) (1,000,000) (500,000)
-‐ 500,000
1,000,000 1,500,000 2,000,000
Johnson
Smith
