Cost Volume Profit Analysis
1 Introduction
You are likely to be familiar with elements of cost-volume-profit analysis from your previous studies. P1 advances that knowledge by requiring breakeven techniques to be applied to more complex decisions. You will need to become familiar with profit-volume analysis and with the calculation of a breakeven point in a multi-product environment.
Cost-volume-profit analysis considers the relationship between costs (fixed and variable), sales volume and the level of profit. Its techniques are used in breakeven calculations and contribution/sales ratio analysis, and they can be applied to indicate the level of sales necessary to make a desired profit (target profit) or the amount by which sales can fall before a product becomes loss-making (margin of safety).
This chapter serves component outcome C3b, break-even analysis, and the named topic multi-product break-even analysis. Everything in it rests on one idea from marginal costing.
Contribution
Contribution is selling price less variable cost. It is what each unit sold contributes first towards covering the fixed costs and then, once those are covered, towards profit. Every formula in this chapter is a rearrangement of that one sentence.
Where pricing lives. This chapter takes the selling price as given and asks what volume is needed. The decision about what the price should BE — cost-plus pricing, the price floor for a one-off order, and the difference between maximising revenue and maximising profit — is Chapter 14 §9. The two are complementary: §5 below computes the volume needed for a target profit at a given price, and Chapter 14 §9 computes the price itself.
2 Breakeven
This lecture covers Examples 1 to 3 and both charts, and every figure in it is correct: breakeven at 250 units and $1,500 of revenue, a C/S ratio of 66.67%, a margin of safety of $300 or 16.67%, and a target-profit volume of 330 units. Its passage on how to read a margin of safety — what 1% would tell you and what 80% would — is the best few minutes in the chapter.
Small points: the recording says “exercise one” where these notes say Example 1; at one moment it names a contribution as “$504” where the figure is 500 units × $4 = $2,000; and it quotes the money in pounds, while P1 is in dollars.
Second lecture. Multi-product CVP — section 7 and Example 6 — has its own recording, at section 7.
The breakeven point is the level of sales — in units or in revenue — needed to cover total costs, both fixed and variable. At the breakeven point profit is nil, because total sales income exactly equals total expenditure.
Since the fixed costs are incurred whatever the volume, breaking even means earning just enough total contribution to cover them. Each unit contributes the same amount, so:
Breakeven point (units) = Total fixed costs ÷ Contribution per unit
Sell more than that and the business is profitable; sell less and it is loss-making. The figure matters even when a business expects to sell far more, because it tells management how much of the budget is protecting them from a loss.
3 Contribution to sales ratio (C/S ratio)
The contribution to sales ratio expresses the contribution as a proportion of the selling price. It says how much of every dollar of revenue is contribution.
C/S ratio = Contribution per unit ÷ Selling price per unit
Because revenue, variable cost and contribution all move together with volume, the ratio holds at every level of activity: whether one unit is sold or a thousand, the total contribution is the same percentage of the total revenue. That is what makes it useful, because it allows the breakeven point to be expressed in revenue without knowing the number of units:
Breakeven point (revenue) = Total fixed costs ÷ C/S ratio
It is also called the profit-volume ratio, and it is the key to the multi-product analysis in §7 — where a business sells several products, there is no single “contribution per unit”, but there is still a weighted average C/S ratio.
Do not round the C/S ratio before dividing by it.
A C/S ratio of two-thirds rounded to 0.66 turns a breakeven revenue of $1,500 into $1,515, and a weighted average of 0.302632 rounded to 0.303 moves a breakeven revenue of $26,435 to $26,403. Carry the fraction, or several decimal places, into the division and round only the final answer.
Product X has variable costs of $2 per unit and a selling price of $6 per unit.
The fixed costs are $1,000 per year.
(a) Use the above information to calculate budgeted sales revenue and budgeted costs when planned production is 300 units per year. What is the budgeted profit (or loss) at this level?
(b) What is the breakeven point (in units)?
(c) What is the C/S ratio of this product — explain the meaning.
(d) What is the breakeven revenue ($)?
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4 Margin of safety
The margin of safety measures the difference between budgeted sales and breakeven sales — how far sales can fall short of budget before the product becomes loss-making. It is a direct measure of the risk in a plan, and it is closely related to the sensitivity analysis of Chapter 13 §8: both ask how wrong an estimate can be before the answer changes.
Margin of safety = Budgeted sales − Breakeven sales
It can be stated in units or in revenue, but it is normally given as a percentage, because a shortfall of $300 means one thing against a budget of $400 and quite another against a budget of $10,000:
Margin of safety (%) = (Budgeted sales − Breakeven sales) ÷ Budgeted sales × 100
A margin of safety of 1% should worry management: a tiny shortfall makes the product loss-making, and it is worth asking whether the risk of going ahead is justified at all. A margin of safety of 80% is a comfortable plan.
Calculate the margin of safety percentage for Example 1.
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5 Target profit
Breakeven calculations often ask instead for the level of sales needed to earn a stated profit. The logic is identical: breaking even needs enough contribution to cover the fixed costs, and a target profit needs enough contribution to cover the fixed costs and the target on top.
Sales (units) = (Fixed costs + Target profit) ÷ Contribution per unit
Sales (revenue) = (Fixed costs + Target profit) ÷ C/S ratio
Using Example 1, calculate the sales revenue needed to generate a target profit of $320.
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The other half of the question. A target-profit calculation answers “what volume do we need at this price?”. The mirror question — “what price do we need at this volume?” — is a pricing decision and is dealt with in Chapter 14 §9, where the same $320 target would be approached through a cost-plus mark-up instead. Which question a scenario is asking is worth settling before any arithmetic starts.
6 The breakeven chart and the profit-volume chart
Both relationships can be shown graphically, and each chart answers a different question.
6.1 The breakeven chart
A breakeven chart plots revenue and cost against the level of output. Three lines are drawn:
Sales revenue, from the origin, rising by the selling price for every unit sold.
Fixed costs, a horizontal line at the level of the fixed costs — they do not move with output.
Total costs, starting at the fixed costs when output is nil and rising by the variable cost per unit.
Where the revenue line crosses the total cost line is the breakeven point, and both the breakeven units and the breakeven revenue can be read off the axes. To the right of that point the vertical gap between the two lines is profit; to the left it is loss. The margin of safety is the horizontal distance between the breakeven point and the budgeted level of activity.
Draw a breakeven chart for Example 1.
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6.2 The profit-volume chart
The profit-volume chart is simpler and answers the question management usually asks. Instead of showing revenue and cost separately, it plots profit directly against the level of activity.
Only two points are needed, because the line is straight. At nil sales there is no contribution but the fixed costs are still incurred, so the loss equals the fixed costs — that is the vertical intercept, and it is the starting point for drawing the chart. The line then rises by the contribution per unit, crossing the zero-profit line at the breakeven point.
Draw a profit-volume chart for Example 1.
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7 Multi-product CVP analysis
This lecture works Example 6 from start to finish: the individual C/S ratios, the weighted average by both routes, breakeven revenue at the budgeted mix, both profit-volume lines, and then the limitations in section 8. Two points before you play it.
Selling order: the recording ranks the products correctly — P, then C, then V — but builds the part (e) table with V second. Take C second: cumulative revenue $84,000, $108,000 and $136,800, and cumulative profit $23,800, $29,800 and $33,400 (Answer 6(e)). On the part (f) chart the second segment is C’s, at 25%, not V’s; the end point is the same.
Rounding: it rounds the C/S ratios before dividing, so its breakeven revenues differ slightly from Answer 6’s; $26,435 and $21,132 are the exact figures.
So far the analysis has assumed a single product. In reality a business is likely to sell a range of products, each with a different C/S ratio, and there is then no single contribution per unit to divide by.
Management still wants to know the breakeven sales revenue — the revenue needed to cover the fixed overheads — but the answer now depends on which products are sold as well as how many. The problem is solved by assuming the products are sold in a predetermined budgeted sales mix, which may be taken from forecast sales volumes or from stated ratios or percentages.
7.1 The weighted average C/S ratio
The average C/S ratio cannot be found by adding the individual ratios and dividing by the number of products. That would treat a product selling 200 units a year as equal in importance to one selling 200,000. It must be weighted by the budgeted sales revenue, and the quickest way to do that is to divide total contribution by total revenue at the budgeted mix:
Weighted average C/S ratio = Total contribution at the budgeted mix ÷ Total sales revenue at the budgeted mix
Breakeven revenue = Total fixed costs ÷ Weighted average C/S ratio
The same figure can be reached by taking each product's own C/S ratio and weighting it by that product's share of total budgeted revenue. The two routes give the same answer; the contribution-over-revenue route is faster and avoids the rounding that creeps in when three individual ratios are each rounded before being weighted.
The answer holds only while the mix holds.
A weighted average C/S ratio is valid only if the products continue to be sold in the budgeted proportions. Selling twice as much of everything, or half as much of everything, leaves the ratio unchanged — but selling relatively more of the low-ratio products and less of the high-ratio ones changes it, and with it the breakeven revenue. Every answer based on a weighted average C/S ratio should say so.
7.2 Selling in order of C/S ratio
The constant-mix assumption is a strong one. If sales fall short of budget, a business will not necessarily lose the same proportion of every product; it may push the most profitable product first. A second analysis therefore assumes the products are sold in order of their C/S ratios, highest first.
Plotted on a profit-volume chart this produces a curve of three straight segments rather than one line, each segment flatter than the last as the products get less profitable. It reaches breakeven sooner than the constant-mix line, because the contribution is being earned faster at the start. Both lines start at the same loss (the fixed costs) and finish at the same point (full budgeted revenue and full budgeted profit); it is the path between them that differs.
A company produces and sells three products: C, V and P.
The budget information for the coming year is as follows:
C | V | P | |
Sales (units) | 4,800 | 4,800 | 12,000 |
Selling price (per unit) | $5.00 | $6.00 | $7.00 |
Variable cost (per unit) | $3.75 | $5.25 | $4.35 |
Contribution (per unit) | $1.25 | $0.75 | $2.65 |
The total budgeted fixed overheads for the year are $8,000.
(a) Calculate the C/S ratio for each product individually.
(b) Calculate the weighted average C/S ratio, assuming that the budgeted product mix remains unchanged.
(c) Calculate the breakeven revenue, assuming that the budgeted product mix remains unchanged.
(d) Construct a profit-volume chart, assuming that the budgeted product mix remains unchanged.
(e) Assuming that the products are sold in order of their C/S ratios, construct a table showing the cumulative revenue and cumulative profit associated with this selling order.
(f) Add that information to the profit-volume chart already produced in part (d), and calculate the breakeven sales revenue on this basis.
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8 Limitations of CVP analysis
CVP analysis is sometimes described as a crude, oversimplified model of cost behaviour. Its assumptions are its weaknesses, and a question asking you to comment on a breakeven calculation is asking for these.
Assumption | Why it may not hold |
The selling price per unit remains constant at all levels of activity. | One of the commonest ways of selling more is to reduce the price, and volume discounts are normal. The revenue line is then a curve, not a straight line. |
The variable cost per unit remains constant at all levels of activity. | Buying more materials may earn a bulk discount; running at high volumes may need overtime or less efficient capacity, raising the unit cost. |
Total fixed costs do not change across all levels of production. | Fixed costs are fixed only within a relevant range. High volumes may need a second shift, another supervisor or another factory — the cost steps up. |
Production volume equals sales volume in the period. | The model ignores inventory. If production and sales differ, the profit computed by the model will not be the profit reported. |
The budgeted product mix is known in advance and remains unchanged. | Multi-product analysis only. Both the weighted average C/S ratio and the chart in §7 are invalid the moment the proportions change. |
All costs can be split cleanly into fixed and variable. | Semi-variable and stepped costs have to be separated first, by the high-low method or by regression (Chapter 12), and that separation is itself an estimate. |
None of this makes the technique useless. It makes it a model: it gives a fast, approximately right answer over the range of activity a business is actually planning for, and the further a question moves outside that range the less the answer is worth. Where the estimates behind it are uncertain, the sensitivity analysis of Chapter 13 §8 is the natural next step.
9 Test your knowledge
Two quick checks before you move on: work through the flashcards to fix this chapter’s key terms and definitions, then sit the objective questions for exam-style practice. Both mark themselves and explain the answers as you go.
Cost Volume Profit Analysis
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