Semester 1 Week 5 Cost-Volume-Profit Analysis Flashcards
evaluating alternatives on the short-term
How do you decide among alternatives?
Decision making involves selecting from a possible courses of action.
But, before they make their choice, managers need to compare the likely effects of the options they are considering.
This involves answering questions such as:
How many units must be sold to break even?
What would be the effect on profit if we reduce our selling price and sell more units?
What sales volume is required to meet the additional fixed charges arising from advertising campaign?
Begin by considering how management accounting information can be of assistance in providing answers to questions about the consequences of particular courses of action.
What is Cost-Volume-Profit Analysis (CVP)?
CVP analysis is a systematic method that examines the relationship between changes in activity (i.e., output) and changes in sales revenue, costs and net profit.
It allows us to predict what will happen to the financial results if a specified level of activity or volume fluctuates?
Knowledge of this relationship enables management to identify critical output levels, such as the level at which neither a profit or loss will occur (i.e., the break even point).
CVP As a Model:
CVP analysis, as a model, simplifies the real world conditions that the firm will face.
Like most models, which are abstractions from reality, CVP analysis is subject to a number of underlying assumptions and limitations.
For instance, CPV focuses on the short-term, i.e., normally a period of one year, or less, a time in which the output is likely to be restricted to that available from the current operating capacity.
In the short run some inputs can be increased, but other cannot: Additional supplies of materials and unskilled labour may be obtained at short notice, but operating capacity cannot be significantly changed.
Hospital, hotels – cannot increase the number of beds/room to increase the number of patients/beds. Most are Predetermined costs over a short-run period. Therefore, major area of uncertainty will be sales volume. Short-run profitability will, therefore, be most sensitive to sales volume. CVP analysis thus highlights the effects of changes in sales volume on the level of profits in the short run.
The Economist’s Model: Curvilinear CVP Relationships
Curvilinear total revenue (TR) line 0E: Firm is only able to sell increasing quantities of output by reducing the selling price per unit; thus, the total revenue line does not increase proportionally with output.
Total Cost (TC) line A-D rises steeply at first as the firm operates at lower levels of the volume range. -> Difficulties of efficiency using manufacturing facilities designed for much larger volumes. B-C: the efficient range as TC begins to level out and rise less steeply. C-D: TC rises more steeply as the cost per unit increases.
It is also clear that the shape of the total revenues is such that it crosses the total cost line at two points. In other words, there are two output levels at which the total costs are equal to the total revenues; or, more simply, there are two break-even points.
The Accountant’s CVP Model: Linear Relationships
X-Y TR line and 0-V assume that variable cost and selling price are constant per unit of output.
Linear relationship for TR and TC as volume changes. -> Only one break-even point.
Curvilinear relationships appear to be more realistic. So how we justify accountant’s model?
Linear relationships are not intended to provide an accurate representation of TC and TR throughout all ranges of output.
Objective: represent the behaviour of TC/TR over the range of output at which a firm expect to be operating within a short-term planning horizon, i.e., the relevant range Q1-Q2.
Q1-Q2 also broadly represents the output levels that the firms has experience of operating in the past and for which cost information is available.
Fixed Cost Function
Within the short term the firm anticipates that it will operate between output levels Q2 and Q3 and commits itself to fixed costs of 0A.
Costs are fixed in the short term, but can be changed in the longer term.
Total Revenue Function
Fixed selling prices in the short term.
Assume non-price competition.
Beyond the relevant range, increases in output may only be possible by offering substantial reductions in price.
Not the intention of firm to operate outside the relevant range.
Therefore, it is appropriate to assume constant selling prices.
Numerical Approach to CVP Analysis
Example: Panos Enterprises operates in the leisure and entertainment industry and one of its activities is to promote concerts at locations throughout the world
Estimated FC: £ 60,000, VC: £ 10 per ticket, Proposed SP: £ 20 per ticket
1. The number of tickers that must be sold to break-even.
2. How many tickers must be sold to earn £ 30,000 target profit?
3. What profit would result if 80,000 tickets were sold.
4. What selling price would have to be charged to give a profit of £ 30,000 on sales of 8,000 tickets?
5. How many additional tickets must be sold to cover the extra cost of television advertising of £ 8,000?
2: Units (tickets) to be Sold to Obtain a £ 30,000 Profit
To achieve a profit of any size we must first obtain sufficient contribution to cover the fixed costs (i.e., reach the BE point).
If the total contribution is not sufficient to cover the fixed costs then a loss will occur.
Thus, to determine the total contribution to obtain a target profit we simply add the target profit to the fixed costs and divide by the contribution per unit.
3: Profit from the Sale of 8,000 Tickets
Total contribution from 8000 tickers is:
£ 80,000 = (8000 X £ 10).
To ascertain profit: £ 80 000- £ 60 000 = £ 20 000
Any change in tickets increases the net profit by an amount equal to the extra tickets multiplied by the unit contribution margin.
4: Selling Price to be charged to show a Profit of £ 30 000 on sales of 8,000 tickets (i.e., £ 80,000)
An alternative approach is to determine the total required revenue to obtain a profit of £ 30,000. This is £ 170,000, which is derived from the sum of the fixed costs (£ 60,000), variable cost (£ 80,000= 8,000 X £ 10) and the target profit (£ 30,000).
Dividing this required sales revenues of £ 170,000 by the sales volume (8,000 tickets) gives a selling price of £ 21.25.
5: Additional Sales Volume to meet £ 8,000 additional fixed investment advertisement charges
The contribution per unit is £ 10 and fixed costs will increase by 8,000.
Therefore, an extra of 800 tickers (8,000/10) must be sold to cover an additional fixed cost of £ 8,000.
What is the Profit-Volume Ratio?
Also known as contribution margin ratio: the contribution divided by sales (CV/Sales)
It represents the proportion of each £ 1 of sales available to cover fixed costs and provide profit.
In the previous example the profit-volume ratio is contribution per unit divided by SP per unit: £ 10/ £ 20 = 0.5 = 50% .
This means that for each £ 1 sale a contribution of £ 0.5 is earned.
Therefore, profit-volume ratio can be computed using either unit figures or total figures.
Profit-Volume Ratio (Application)
If total sales revenue is estimated to be £ 200,000, the total contribution will be £ 100,000 (£ 200,000 X 0.5).
To calculate the profit, we deduct fixed costs of £ 60,000, thus a profit of £ 40,000 will be obtained from total sales revenue of £ 200,000.
𝑃𝑟𝑜𝑓𝑖𝑡=(𝑆𝑎𝑙𝑒𝑠 𝑅𝑒𝑣𝑒𝑛𝑢𝑒×𝑃𝑉 𝑅𝑎𝑡𝑖𝑜)−𝐹𝑖𝑥𝑒𝑑 𝐶𝑜𝑠𝑡𝑠
𝑃𝑟𝑜𝑓𝑖𝑡+𝐹𝑖𝑥𝑒𝑑 𝐶𝑜𝑠𝑡𝑠=(𝑆𝑎𝑙𝑒𝑠 𝑅𝑒𝑣𝑒𝑛𝑢𝑒×𝑃𝑉 𝑅𝑎𝑡𝑖𝑜)
𝐵𝐸 𝑆𝑎𝑙𝑒𝑠 𝑅𝑒𝑣𝑒𝑛𝑢𝑒=(0+ 𝐹𝑖𝑥𝑒𝑑 𝐶𝑜𝑠𝑡𝑠)/𝑃𝑉 𝑅𝑎𝑡𝑖𝑜
𝑩𝑬 𝑺𝒂𝒍𝒆𝒔 𝑹𝒆𝒗𝒆𝒏𝒖𝒆=𝑭𝒊𝒙𝒆𝒅 𝑪𝒐𝒔𝒕𝒔/𝑷𝑽 𝑹𝒂𝒕𝒊𝒐
If we apply this approach to the example, the break-even sales revenue is £ 120,000 (£ 60,000 FC/0.5 PV ratio)
What does a contribution look like and show?
What does a break even chart look like?
What does a Profit-Volume Graph look like?
What is the Margin of Safety?
What is Multi-Product CVP Analysis?
Our analysis so far has assumed a single product setting. However, firms typically produce and sell a number of different products or services.
This makes breakeven analysis difficult.
To overcome this problem, we adapt CVP analysis to a multi-product setting by assuming a constant product sales mix.
In other words, we have to assume that whenever x units of product A are sold, y units of product B, and z units of product C are also sold.
By assuming a constant sales mix for the product, we can calculate a weighted average contribution per unit sold.
The weighting is based on the quantities or proportion of each product in the constant sales mix.
This means that the unit contribution of the product that makes up the largest proportions of the mix has the greatest impact on the average contribution per mix.
The company sells two products so that there are two unit contribution margins.
If all of the fixed costs are directly attributable to products (i.e., there are no common fixed costs), we can follow the standard approach:
Deluxe BE=Direct FC (€ 90 000)/Unit Contribution (€ 150) = 600 units
Standard BE=Direct FC (€ 27 000)/Unit Contribution (€ 90) = 300 units
However, there are some fixed costs that must be taken into account. Selling 600 deluxe and 300 standard washing machines will generate a contribution that only covers direct fixed costs; the common fixed cost will not be covered (€ 39,000).
A loss equal to the common fixed costs will be reported (€ 39,000). The BE point as whole will not be ascertained.
The common fixed costs cannot be specifically identified with either of the products since they can be only avoided if both products are not sold.
The solution is to convert the sales volume measure of the individual products into standard batches of products based on planned sales mix.
Sales mix 1200:600 -> 2:1
For evert two deluxe machines one standard machine is expected to be sold.
Standard Batch (3 machines)=> 2 deluxe + 1 standard machine
Contribition per batch=(2 x €150) + (1 x €90) = € 390
𝐵𝐸 𝐵𝑎𝑡𝑐ℎ𝑒𝑠=(𝑇𝑜𝑡𝑎𝑙 𝐹𝑖𝑥𝑒𝑑 𝐶𝑜𝑠𝑡𝑠)/(𝐶𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑚𝑎𝑟𝑔𝑖𝑛 𝑝𝑒𝑟 𝑏𝑎𝑡𝑐ℎ)
𝐵𝐸 𝐵𝑎𝑡𝑐ℎ𝑒𝑠=(“€” 156, 000 (117, 000+39, 000))/(“€” 390)=400 𝑏𝑎𝑡𝑐ℎ𝑒𝑠
Thus, 800 deluxe machines (400 batches x 2) and 400 standard machines (400 batches x 1) must be sold to break even.
The BE point is not a unique number: it varies depending on the composition of the sales mix.
PL produces and sell two products, M and N. Product M sells for € 7 per unit and has a total variable cost of € 2.94 per unit, while Product N sells for € 15 and has a total variable cost of € 4.40 per unit.
The marketing department has estimated that for every five units of M sold, one unit of N will be sold. The organisation’s fixed costs per period total € 123 600.
Required: Calculate the breakeven point for PL.
Alternative Cost Structures
CVP-based sensitivity analysis highlights the risk and returns as fixed costs are substituted for a variable costs in a company’s cost structure.
Companies can influence the proportion of fixed and variable costs.
Automated facilities involve: high fixed costs and low variable costs.
Manual systems involve: high variable costs and low fixed costs.
The chosen cost structure can have a significant impact on profits.
Consider the example with the tickets.
Case A, which has higher fixed costs and lower variable costs than Case B, has higher BE point (6 vs 5) but requires fewer units to be sold (9 vs 11) to earn an operating income of 30.
Choice between A and B is a strategic decision.
Which options is associated with a high risk of loss when sales are low?
If the decision maker has a high tolerance for risk, he/she will choose Option A with its potential high awards.
If, however, the decision maker is risk averse, he will prefer Option B, where the rewards are smaller if sales are high but where the potential losses are smaller if sales are low.
The risk-return trade-off across alternative cost structures can be measured by operating leverage.
At any given level of sales:
𝐷𝑒𝑔𝑟𝑒𝑒𝑓 𝑂𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝐿𝑒𝑣𝑒𝑟𝑎𝑔𝑒 = (𝐶𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑀𝑎𝑟𝑔𝑖𝑛)/(𝑂𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝐼𝑛𝑐𝑜𝑚𝑒)
