Cost Volume Profit Analysis

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1 Introduction

Cost-volume-profit analysis considers how costs and profits change with changes in the volume or level of activity.

2 Breakeven

Breakeven is the level of activity which gives rise to zero profit. Since profit is the difference between total contribution and fixed costs, breakeven is where the total contribution equals total fixed costs.

Breakeven volume

Product X has variable costs of $2 per unit, and selling price of $6 per unit.
The fixed costs are $1,000 per year

If budgeted sales and production are 300 units, what is the budgeted profit (or loss) for the year?
What is the breakeven point (in units)?
What is the breakeven revenue?
How many units need to be sold to achieve a target profit of $300 per year?

Answer to example 1

	$
Selling price	6
Variable costs	2
Contribution	4

(a)		$
	Total contribution (300u × $4)	1,200
	Fixed costs	(1,000)
	Profit	$200

(b) Breakeven

(c) Breakeven revenue = 250 u × $6p.u. = $1,500

(d)		$
	Target profit	300
	Fixed costs	1,000
	Target contribution	$1,300

Number of units

3 Margin of safety

The Margin of Safety measures the %’age fall in budgeted sales that can be allowed before breakeven is reached.

Margin of safety

It is useful in identifying how big a problem any inaccuracy in the budgeted sales is likely to be.

Calculate the margin of safety for example 1

4 Contribution to sales ratio

The contribution to sales ratio (or C/S ratio) is calculated as follows:

C/S ratio

Since the contribution and the sales revenue both vary linearly with the volume, the C/S ratio will remain constant.

[Note: the C/S ratio is sometimes called the profit to volume (or P/V ratio)].

Calculate the C/S ratio for example 1

What sales revenue is needed to generate a target profit of $320?

Answer to example 3

C/S ratio

	$
Target profit	320
Fixed overheads	1,000
Target contribution	$1,320

Sales revenue required = Target contribution ÷ C/S ratio = 1320 ÷ 4/6 = $1,980

5 Breakeven chart

The breakeven chart plots total costs and total revenues at different levels of volume, and shows the activity level at which breakeven is achieved.

Draw a breakeven chart for example 1

6 Profit-volume chart

The profit volume chart shows the net profit or loss at any level of activity

Draw a profit-volume chart for example 1

7 Multi-product CVP analysis

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In practice a company is likely to make several products, each with different CS ratios.

They are still likely to be interested in the break-even sales revenue (in order to cover the fixed overheads), but the existence of several products makes it less certain and all we can really do is calculate breakeven on the assumption that the mix of products remains as per the budgeted mix – even if total sales are lower.

However, as will be illustrated in the following example, the company could reach the breakeven position sooner if it were to sell the product with the highest CS ratio first.

‘Overall’ means the weighted average C/S ratio: total contribution divided by total revenue. Check that it falls between the individual products’ ratios. Selling more of the product with the lowest C/S ratio pulls the average down, so breakeven revenue rises — explaining that link is what the discussion marks are for.

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 (p.u.)	$5	$6	$7
Variable cost (p.u.)	$3.75	$5.25	$4.35
Contribution (p.u.)	$1.25	$0.75	$2.65

The total budgeted fixed overheads for the year are $8,000

Calculate the CS ratio for each product individually
Calculate the average CS ratio (assuming that the budget mix of production remains unchanged)
Calculate the breakeven revenue (assuming that the budget mix of production remains unchanged)
Construct a PV chart (assuming that the budget mix of production remains unchanged)

Assuming that the products are produced in order of their CS ratios, construct a table showing the cumulative revenue and cumulative profits

Calculate the breakeven sales revenue on this basis

Add the information to the P/V chart already produced for Example 6

Answer to example 6

(a) CS ratios:

C = 1.25 / 5.00 = 0.25	(or 25%)
V = 0.75 / 6.00 = 0.125	(or 12.5%)
P = 2.65 / 7.00 = 0.379	(or 37.9%)

(b) Average CS ratio:

Based on budget sales,

Total revenue	= (4800 x 5) + (4800 x 6) + (12000 x 7)
	= $136,800
Total contribution	= (4800 x 1.25) + (4800 x 0.75) + (12000 x 2.65)
	= $41,400
Average CS ratio	= 41400/136800 = 0.303 (or 30.3%)

(Alternatively, the average CS ratio may be calculated by taking the weighted average of the individual CS ratios, weighting by the budgeted sales revenues.)

= 8000/0.303

= $26,400

(d) See graph below

(e) P has the highest CS ratio, followed by C, followed by V.

		Cumulative Sales		Cumulative Profit
P	(12,000 × 7 =)	84,000	((12,000 × 2.65) – 8000)	23,800
C	(4,800 × 5 = 24,000)	108,000	(4,800 × 1.25 = 6000)	29,800
V	(4,800 × 6 = 28,800)	136,800	(4,800 × 0.75 = 3600)	33,400

Breakeven sales for P are 8000/0.379 = $21,108

8 Limitations of CVP analysis

The selling price per unit is assumed to remain constant at all levels of activity
The variable cost per unit is assumed to remain constant at all levels of activity
It is assumed that the total fixed costs remain constant
It is assumed that the level of production is equal to the level of sales (i.e. that there are no changes in the levels of inventory)

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