Cost is something that every business looks to avoid or minimise at least. However, to reduce costs, you first need to understand what it is and how it behaves. Some costs are subject to fluctuation with business activity levels (such as production, services, maintenance and labour) and some costs stay consistent regardless of the activity levels (such as rent or mortgage, insurance and lease repayments). Finally, there are mixed costs such as water and electricity charges, which have both components. In the utilities example, a daily charge (fixed cost) and usage charge (variable cost).
Welcome to Topic 10: Cost Behaviour and Cost-Volume-Profit (CVP) Analysis. In this topic, you will learn about:
- Fixed, variable and other costs
- Contribution margin
- Break-even point
- Cost-volume-profit analysis.
These relate to the Subject Learning Outcomes:
- Understand the role of the finance and accounting functions in an organisation.
- Identify the terminology and concepts that underlie the preparation of general-purpose financial reports.
- Prepare and summarise financial statements to support business decision making.
- Apply mathematics of finance to determine risk, return, evaluation of investment, financing, working capital and distribution decisions.
- Develop analytical skills drawing from key finance theories, concepts and techniques.
Welcome to your pre-seminar learning tasks for this week. Please ensure you complete these prior to attending your scheduled seminar with your lecturer.
Click on each of the following headings to read more about what is required for each of your pre-seminar learning tasks.
Read Chapter 14, pp. 445-449 of the prescribed text - Melicher, RW & Norton, EA 2017, Introduction to finance: Markets, investments, and financial management, 16th edn., John Wiley & Sons, Inc.
Read Chapter 3 of Franklin, M, Graybeal, P & Copper, D 2019, Principles of accounting, volume 2: Managerial accounting, OpenStax.
Read the following journal articles:
- Banker, RD & Byzalov, D 2014, ‘Asymmetric cost behavior’, Journal of Management Accounting Research, 26(2):43-79.
- Stefan, D 2012, ‘Developing a cost-volume-profit model in production decision system based on MAD real options model’, Procedia Economics and Finance, 3:350-354.
- Barbu, I 2015, ‘Cost behavior analysis’, Review of General Management, 21(1):185-197.
Identify the key takeouts from the articles and add these to your reflective journal. You can access the reflective journal by clicking on ‘Journal’ in the navigation bar for this subject.
If you are unsure of any concepts, reach out to your lecturer.
Read the following web article:
- CFI n.d., CVP analysis guide, Corporate Finance Institute.
Read section 14.4 Financial leverage ratios and analysis, on pp. 432-434 of the prescribed text (Melicher & Norton 2017).
Review discussion question 2 on p. 434 and write down your answers to the question in your reflective journal. Be prepared to share your reflections with the class during the scheduled seminar.
Consider these three (3) situations:
- Situation 1: An organisation's current ratio is rising over time while its quick ratio is stable.
- Situation 2: An organisation's total asset turnover ratio is rising but its fixed asset turnover ratio is falling.
- Situation 3: An organisation's equity multiplier is rising and its interest coverage ratio is falling.
Select one (1) of these situations and discuss what may be occurring within the organisation and whether the situation implies potential good news or potential bad news for the business.
The following task has been modified from Horngren, CT, Datar, SM & Rajan, MV 2012, Cost Accounting: A Managerial Emphasis, 14th edn., Pearson Education, Inc., p. 80.
Use the following information to answer the questions. Add your answers to your reflective journal and be prepared to share your calculations during the seminar.
Downunder Tours is a travel agency specialising in ocean cruises between Brisbane and the Whitsundays. It books passengers on P&O Cruises. The Downunder’s fixed costs are $20 000 per month. P&O charges passengers $750 per return trip ticket.
Questions:
Calculate the number of tickets Downunder must sell each month to (a) break-even and (b) make a target operating income of $10 000 per month in each of the following independent cases.
- Downunder’s variable costs are $30 per ticket and P&O Cruises pays Downunder a 10 % commission on the ticket price.
- Downunder’s variable costs are $40 per ticket and P&O Cruises pays Downunder a 10 % commission on the ticket price.
- Downunder’s variable costs are $40 per ticket. It receives a $48 commission per ticket from P&O Cruises. Comment on the results.
- Downunder’s variable costs are $40 per ticket. It receives a $48 commission per ticket from P&O Cruises and charges customers a delivery fee of $12 per ticket. The cost for Downunder to deliver the ticket is $2 per ticket. Comment on the result.
This topic has discussion forum activities, which will enhance your knowledge and give you the opportunity to interact with your peers. You can access the activities by clicking on the following links. You can access the activities by clicking on the links in the topic. You can also navigate to the forum by clicking on 'FIN100 Subject Forum' in the navigation bar for this subject.
Read and watch the following content.
Fixed, variable and other costs
Different costs behave differently. However, the effect of cost can be calculated using the following general formula:
$$Y = a +bx$$
Where:
Y = Total cost
a = Fixed cost
b = Unit cost
x = Number of units produced.
When the previous equation is graphed, a is the y-intercept and b indicates the gradient. The variable x is the independent variable (number of units produced) and y is the dependent variable (total cost) (Graybeal, Franklin & Cooper 2019).
There are six (6) key types of costs to consider:
- Fixed costs
- Variable costs
- Step-fixed costs
- Semi-variable (or mixed) costs
- Curvilinear costs
- Relevant ranges.
Fixed costs
Fixed costs are those that remain constant irrespective of the level of production or activity. Whilst the total cost remains the same, the fixed cost per unit decreases as the level of an activity increases. In other words, “as activity increases, total fixed costs do not change, although unit fixed cost declines” (Langfield-Smith et al. 2018, p. 89).
Fixed cost per unit is often considered when we talk about product costs. However, some contemporary views of cost analysis may argue that very few costs remain truly ‘fixed’ (Langfield-Smith et al. 2018).
Examples of fixed costs include:
- Depreciation
- Interest expense
- Insurance premiums
- Rental expenses
- Higher management salaries
- Utilities – for example, unlimited internet service.
Variable costs
Variable costs are those that are directly or indirectly used to produce and sell goods or services of a business. Therefore, total variable cost is dependent on the number of units produced or the volume of services provided. Increasing units or volume of service increases variable cost.
Examples of variable costs include:
- Direct materials
- Labour per unit or hour
- Sales commissions
- Transportation or delivery.
Step-fixed costs
Step-fixed costs remain “fixed over a wide range of activity levels but jump to a different amount for levels outside that range” (Langfield-Smith et al. 2018, p. 90). For example, the cost of renting a warehouse remains the same regardless of how empty or full that warehouse is. However, if a second warehouse is required because the original one has exceeded its capacity, then costs will increase.
The following figure represents the change in step-fixed costs as activity increases:
Semi-variable costs
Semi-variable (or mixed) costs include both fixed and variable components. For example, water or electricity bills include a ‘daily charge’ (fixed cost) and a ‘usage charge’ (variable cost).
Curvilinear costs
Curvilinear costs have a curved cost line but are often approximated as a semi-variable cost function. The shape of the curve depends on the other variables involved. The following figures represent the curvilinear costs in three (3) different example scenarios.
- The curve in Example A represents a situation in which the unit cost decreases with every additional unit produced. For example, as a new employee becomes increasingly more familiar with the requirements and skilled in production, they can produce many more units per shift than when they started.
- In Example B, the curve indicates the cost per unit increases with higher rates of production. This type of situation can be seen where production is incentivised by paying bonuses for each additional unit produced.
- Example C represents the labour costs of an entire production line workforce who start working slowly then increases their productivity as they develop experience and skills over time, to the point where additional staff must be hired to increase productivity further.
Relevant ranges
Relevant ranges occur where all applicable costs remain the same within a particular range. This is very similar to the step-fixed cost example of renting another warehouse. However, for this situation, let us use production lines instead of warehouses.
The cost of running one production line remains constant regardless of the number of units produced. The addition of a new production line comes with more expenses, such as labour, materials, electricity, maintenance and so on. However, the production process of the business has reached a new range from producing 5 000 units a day with one production line, to 25 000 units per day using both the original (older) production line and the additional (more efficient) production line.
Contribution margin
Contribution refers to the difference between sales revenue and variable costs. In other words, contribution is the direct excess earned when a sale is affected. It is typically used to cover fixed costs.
Contribution margins can be calculated with the following formula:
$$\begin{aligned}\mathsf{Contribution}&=\mathsf{sales\;revenue}-\mathsf{variable\;costs}\\\mathsf{Contribution\;per\;unit}&=\mathsf{selling\;price\;per\;unit}-\mathsf{variable\;cost\;per\;unit}\end{aligned}$$
There are four (4) main types of contribution calculations:
- Unit contribution margin
- Contribution margin ratio
- Contribution margin percentage
- Total contribution margin.
Unit contribution margin
Unit contribution margin per unit is the difference between the sales price per unit and the variable cost per unit.
Contribution margin ratio
Contribution margin ratio is calculated by diving the unit contribution margin by the unit sales price. It is a measure of the proportion of each sales dollar that is available to cover fixed costs and earn a profit.
Contribution margin percentage
Contribution margin percentage is calculated by multiplying the contribution margin ratio by 100. It represents the percentage of each sales dollar that is available to cover fixed costs and earn a profit.
Total contribution margin
Total contribution margin is the difference between the total sales revenue and the total variable costs. It is the total amount available to cover fixed costs and then contribute to profits.
Break-even point
The break-even point is the volume of sales at which the total revenues and costs are equal and the operation ‘breaks even’. At this level of sales, there is no profit or loss. All costs are covered, but without any money left over.
The break-even point can be calculated for an entire organisation or for individual projects, using either of the following formulas:
$$\begin{aligned}\mathsf{Break{\text -}even\;point\;(in\;units)}&=\frac{\mathsf{fixed\;cost}}{\mathsf{unit\;contribution\;margin}}\\\\\mathsf{Break{\text -}even\;point\;(in\;AUD)}&=\frac{\mathsf{fixed\;cost}}{\mathsf{unit\;contribution\;margin\;ratio}}\end{aligned}$$
The break-even (in units) formula determines exactly how many units need to be manufactured or sold to recover all business costs. Tip: Always make sure to provide a whole number as your answer – it assumes whole units must be produced. If your answer is a decimal, always round up to the next whole number.
The break-even (in value) formula works out exactly how much revenue needs to be earned to recover all business costs.
The following figure shows that the total costs increase with every extra unit manufactured because variable costs are in addition to the constant fixed costs. The figure also demonstrates that revenue increases with every unit sold to catch up to (recover) the total costs. Eventually, the total revenues reach the break-even point, where there is no profit or loss but all costs are recovered. Any revenue earnt beyond the break-even point is profit for that period.
Cost-volume-profit analysis
Cost-volume-profit (CVP) analysis also known as break-even analysis, is “a technique or tool used to determine the effects of changes in an organisation’s sales volume based on its costs, revenue and profit” (Langfield-Smith et al. 2018, p. 859). CVP analysis is useful for both profit-seeking organisations, as well as not-for-profit organisations.
Firstly, the business needs to identify its costs and classify them as fixed or variable costs. Secondly, it should calculate the contribution margin per unit by deducting the variable cost per unit from the unit sales price to reach the break-even point unit or in dollar value.
Thereafter, the business can determine its revenue safety margin or the target income expected, to calculate the number of units or the revenue value required to reach the predetermined goal.
Margin of safety
The following formulas are used to calculate the revenue safety margin, in either a dollar amount or as a percentage:
$$\begin{aligned}\mathsf{Margin\;of\;safety\;(AUD)}&=\mathsf{planned\;sales}\,-\,\mathsf{break{\text -}even\;sales}\\\\\mathsf{Margin\;of\;safety\;(\%)}&=\frac{\mathsf{margin\;of\;safety}}{\mathsf{planned\;sales}}\end{aligned}$$
Target income
The following formulas are used to calculate the target income, as either the number of units needing to be sold or a dollar value of revenue required:
$$\begin{aligned}\mathsf{Target\;income\;sales\;(units)}&=\frac{(\mathsf{fixed\;costs}+\mathsf{target\;operating\;income})}{\mathsf{unit\;contribution\;margin}}\\\\\mathsf{Margin\;of\;safety\;(\%)}&=\frac{\mathsf{margin\;of\;safety}}{\mathsf{planned\;sales}}\end{aligned}$$
CVP analysis with multiple products
To conduct a CVP analysis with multiple products you first need to determine the sales mix – that is the relative proportions of each type of product that is sold by the organisation, by income:
$$\mathsf{Sales\;mix\;proportion}=\frac{\mathsf{product\;sales}}{\mathsf{total\;sales}}$$
Next, calculate the unit contribution margin for each product:
$$\mathsf{Unit\;contribution\;margin}=\mathsf{unit\;selling\;price}\,-\,\mathsf{unit\;variable\;cost}$$
Then, use the unit contribution margin for each product to determine the contribution margin mix ratio:
$$\mathsf{Contribution\;margin\;mix\;ratio}=\frac{\mathsf{ unit\;contribution\;margin}}{\mathsf{unit\;selling\;price}}$$
Finally, multiply the relative proportion of the product with its contribution margin mix ratio to find the average of the products’ unit contribution margins, weighted by the sales mix:
$$\mathsf{Weighted\;average\;contribution\;margin\;ratio}=\mathsf{relative\;product\;proportion}\times\mathsf{contribution\;margin\;mix\;ratio}$$
Example
ABC Productions (Pty) Ltd has $100 000 fixed cost per month and their product mix as follows:
| Product | Unit selling price | Unit variable cost | Unit contribution margin |
|---|---|---|---|
| X | $15 | $10 | 15 – 10 = $5 |
| Y | $30 | $10 | 30 – 10 = 20 |
At what point will ABC Production (Pty) Ltd reach its break-even sales?
Solution:
To find the weighted average unit contribution margin:
| Product | Total unit sales mix ratio | Total contribution margin mix ratio | Weighted average contribution margin ratio | ||
|---|---|---|---|---|---|
| X |
$$\frac{15}{45}$$ |
× |
$$\frac{5}{15}$$ |
= | 0.1111111 |
| Y |
$$\frac{30}{45}$$ |
× |
$$\frac{20}{30}$$ |
= | 0.4444444 |
| ∑ (Weighted average contribution margin ratio of all products) | = | 0.5555555 | |||
Calculating the break-even point
The following formula is used to calculate the break-even point:
$$\mathsf{Break{\text -}even\;point}=\frac{\mathsf{fixed\;costs}}{\mathsf{weighted\;average\;unit\;contribution\;margin}}$$
Following on from the previous example and assuming the fixed costs are $100 000:
$$\begin{aligned}\mathsf{Break{\text -}even\;point\;(AUD)}&=\frac{$100\,000}{0.555555}\\\\&=$180\;000\end{aligned}$$
In summary, different costs behave differently from one another. It is important to understand them to manage and find a way to overcome the total cost by revenue to achieve profits. Contribution margin is one of the best ways of identifying the break-even point of a business. Furthermore, it helps management to make decisions about things such as changing price or increasing production to achieve target profits.
Key takeouts
Congratulations, we made it to the end of the tenth topic. Some key takeouts from the Topic 10:
- The linear relationship of cost can be identified by using the formula: Y = a + bx
- Most of the costs are directly connected to and fluctuate with business activity levels (variable costs), whereas some are not (fixed costs).
- Contribution refers to the difference between sales revenue and variable costs.
- Break-even point is the volume of sales where the total revenues and total costs are equal. This can be measured in unit or in value using the following formulas:
$$\begin{aligned}\mathsf{Break{\text -}even\;point\;(in\;units)}&=\frac{\mathsf{fixed\;cost}}{\mathsf{unit\;contribution\;margin}}\\\\\mathsf{Break{\text -}even\;point\;(in\;AUD)}&=\frac{\mathsf{fixed\;cost}}{\mathsf{unit\;contribution\;margin\;ratio}}\end{aligned}$$
Welcome to your seminar for this topic. Your lecturer will start a video stream during your scheduled class time. You can access your scheduled class by clicking on ‘Live Sessions’ found within your navigation bar and locating the relevant day/class or by clicking on the following link and then clicking 'Join' to enter the class.
Click here to access your seminar.
The following learning tasks will be completed during the seminar with your lecturer. Should you be unable to attend, you will be able to watch the recording, which can be found via the following link or by navigating to the class through ‘Live Sessions’ via your navigation bar.
Click here to access the recording. (Please note: this will be available shortly after the live session has ended.)
In-seminar learning tasks
The in-seminar learning tasks identified below will be completed during the scheduled seminar. Your lecturer will guide you through these tasks. Click on each of the following headings to read more about the requirements for each of your in-seminar learning tasks.
Watch the video, Introduction to cost and management accounting - Cost classification.
Working in a breakout room team assigned by your lecturer during the scheduled seminar, discuss the following questions with your teammates. Your lecturer will request that you present the findings back to the class.
- Name and briefly describe all the cost classifications.
- Explain why cost classification is important to a business.
- Working in the same breakout room as previously, read the journal article, Landry, SP & Chan, C 2013, 'A cost analysis case study of a small Chinese manufacturer', Journal of Business Case Studies, 9(3):203-214.
- Discuss the content of the article with your teammates.
Individually answer the three (3) discussion questions on p. 210 of the case study itself. Post your responses to your reflective journal.
Welcome to your post-seminar learning tasks for this week. Please ensure you complete these after attending your scheduled seminar with your lecturer. Your lecturer will advise you if any of these are to be completed during your consultation session. Click on each of the following headings to read more about the requirements for each of your post-seminar learning tasks.
This learning task can be completed during the consultation session.
Knowledge check
Complete the following three (3) tasks. The following questions have been taken from p. 446 of Melicher, RW & Norton, EA 2017, Introduction to finance: Markets, investments, and financial management, 16th edn., John Wiley & Sons, Inc.
Click the arrows to navigate between the tasks.
This learning task can be completed during the consultation session.
Use the following information to answer the question. Add your answer to your reflective journal.
- Adelaide Strikers offers premium tickets for $45 and regular tickets for $30 for each Big Bash League match.
- Variable costs are $10 for each premium and $5 for each regular ticket sold. The difference in costs is because part of the players’ bonuses comes from the number of each type of ticket sold.
- 35 % of tickets sold are premium and 65 % are regular tickets.
- The fixed costs for the season (such as salaries, rent and insurance) are $4 250 000.
Question: How many tickets do the Adelaide Strikers need to sell over the entire season to break even?
This learning task can be completed in the consultation session.
Complete the following review question from p. 450 of the prescribed text (Melicher & Norton 2017) and add your answer in your reflective journal.
What will happen to the break-even point if the contribution margin rises (falls)?
Read the instructions and requirements for Assessment 4 and familiarise yourselves with the client’s financial position. You can access the instructions by clicking “Assessment 4” in the navigation bar for this subject.
Each week you will have a consultation session, which will be facilitated by your lecturer. You can join in and work with your peers on activities relating to this subject. These session times and activities will be communicated to you by your lecturer each week. Your lecturer will start a video stream during your scheduled class time. You can access your scheduled class by clicking on ‘Live Sessions’ found within your navigation bar and locating the relevant day/class or by clicking on the following link and then clicking 'Join' to enter the class.
Click here to access your seminar.
Should you be unable to attend, you will be able to watch the recording, which can be found via the following link or by navigating to the class through ‘Live Sessions’ via your navigation bar.
Click here to access the recording. (Please note: this will be available shortly after the live session has ended.)
- Bradbury, ME & Scott, T 2018, ‘Do managers forecast asymmetric cost behaviour?’, Australian Journal of Management, 43(4):538-554.
- Novák, P & Popesko, B 2014, ‘Cost variability and cost behaviour in manufacturing enterprises’, Economics & Sociology, 7(4):89-103.
References
- Banker, RD & Byzalov, D 2014, ‘Asymmetric cost behavior’, Journal of Management Accounting Research, 26(2):43-79.
- Barbu, I 2015, ‘Cost behavior analysis’, Review of General Management, 21(1):185-197.
- CEOpedia management n.d., Step fixed cost, https://ceopedia.org/index.php/Step_fixed_cost
- CFI n.d., CVP Analysis guide, Corporate Finance Institute, https://corporatefinanceinstitute.com/resources/knowledge/finance/cvp-analysis-guide
- Clancy, D & Madison, T, 1997, ‘Cost-Volume-Profit analysis and changing costs: Reconciling theory and practice', Journal of Cost Analysis, 14(2):89-108.
- Fazal, H n.d., What is a non-linear variable cost?, PakAccountants, https://pakaccountants.com/what-is-a-non-linear-variable-cost/
- Franklin, M, Graybeal, P & Copper, D 2019, Principles of accounting, volume 2: Managerial accounting, OpenStax.
- Graybeal, P, Franklin, M & Cooper, D 2019, Principles of accounting, volume 2: Managerial accounting, OpenStax, https://opentextbc.ca/principlesofaccountingv2openstax/chapter/estimate-a-variable-and-fixed-cost-equation-and-predict-future-costs/
- Horngren, CT, Datar, SM & Rajan, MV 2012, Cost accounting: A Managerial emphasis, 14th edn., Pearson Education.
- Langfield-Smith, K, Smith, D, Andon, P, Hilton, R & Thorne, H 2018, Management accounting, 8th edn., McGraw-Hill.
- Melicher, RW & Norton, EA 2017, Introduction to finance: Markets, investments, and financial management, 16th edn., John Wiley & Sons, Inc.
- Landry, SP & Chan, C 2013, ‘A Cost analysis case study of a small Chinese manufacturer’, Journal of Business Case Studies, 9(3):203-214.
