Lesson 1, Topic 1

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PREVIOUS SEMESTERS

Cost Volume and Profit Analysis (CVP)

Cost volume profit (CVP) analysis is the study of the effects on future profit of changes in fixed cost, variable costs, sales price quantity and mix.

The purpose of the C.V.P analysis is to understand the relationship amongst the aforesaid variables to forecast profits, determine the volumes to be achieved to meet target profit, and such other short term decisions. The CVP analysis is based on the premise of marginal costing.

The marginal costing technique recognizes variable cost as the product costs and fixed costs as period costs. The principle is that only variable costs will change with a change in volume of production and sales, but the fixed costs will remain the same.

Cost volume profit (CVP) analysis is a systematic approach of examining the relationship between changes in volume and changes in total sales, expenses and net profit. The underlying objective of CVP is to know the effect of fluctuation in the activity volume on financial results.

The following is a typical cost volume profit diagram that depicts how sales revenue, fixed costs and variable costs respond to changes in the volume of sales and production. The volume of production and sales is measured by the X-axis and revenue, costs and profit (loss) are measured by –axis in the CVP chart.

The short run decisions where CVP analysis may be useful include choice of product mix, product pricing, special order acceptance, shut down of a plant etc.

Assumptions of CVP analysis

Revenues, costs and profit functions are assumed to be linear with respect to volumes of output.
Costs can be split into fixed and variable statement
Fixed costs remain constant throughout the analysis
The selling price per unit remains constant
Variable cost per unit remains constant
The only factor affecting cost and revenue is output i.e. output is the only revenue and cost driver
Technology in production and efficiency level remains constant.
Only production is produced and sold. In case of multiple productions the sale mixture will remain constant.
All units produced will be sold.

Let X: No of units produced and sold/activity level

D= Price per unit

V = Variable cost per unit

F = Fixed costs

R = Total sales revenues in monetary form and activity level in monetary terms. C = Total costs TI = Profits

Marginal costs equation

Contribution signifies an alternative measure of profit which is computed as sales less total variable costs of sales

Accordingly Contribution = Sales – Variables

Contribution for the period provides a pool (since it recognizes a surplus generated by sale revenue over variable costs) out of which fixed costs for the period are met and any surplus constitutes the profit. It is called contribution because it literally contributes towards fixed costs and profit)

Therefore Contribution = Fixed costs + Profit

The elements in tradition break even chart (in a single product situation)

A traditional break even chart records revenues and cost on the vertical axis and volume of activity on other horizontal axis. The lines representing sales revenue and total costs signify break-even point.

At any volume level the space between the total cost line and fixed costs line signifies variable cost. In traditional chart, the fixed cost line is drawn first and thereupon the variable cost is drawn in order to signify total cost

The contribution break even chart (in a single product situation)

The basic elements of a contribution break even chart are the same as that of the traditional break even chart.

The only difference is that it shows the variable cost line instead of the fixed cost line. This is done in order to overcome the major problem with traditional break even chart that it is not possible to read contribution directly from the chart.

The same lines for total costs and sales revenue are shown so the breakeven point and profit can be interpreted in the same way as with convectional chart.

The contribution can read as the difference between the sales revenue line and the variable costs line.

Profit/ volume chart (in simple product situation)

This is yet another mode of presentation of break-even chart. This is also known as contribution volume graph. In this, a single a single line is drawn depicting the profit or loss at each level of activity. The point of intersection of the line and the horizontal axis is the breakeven point. The basic feature of this chart is that the vertical axis indicates profits and losses and the horizontal axis is drawn at zero profit or loss.

Cost Volume Profit (C.V.P) analysis by formula

C-V-P analysis can be undertaken by graphical means which are dealt with later in this chapter, or by simple formulae which are listed below and illustrated by examples

Break-even point (in units) = Fixed Costs

Contribution/unit

C/S Ratio = Contribution/unit x 100

Sales price/unit

Break-even point (£sales) = Fixed Costs x Sales price/unit

Contribution/unit

= Fixed Costs x 1

C/S ratio

Level of sales to result in target profit (in units) = Fixed Costs + Target profit

Contribution/unit e) Level of sales to result in target profit after tax (in units)

= Fixed Cost + [ Target profit](1 – Tax rate)

Contribution/unit

f) Level of sales to result in target profit £sales)

= (Fixed Cost + Target profit) x Sales price/unit

Contribution/unit

Note: The above formulae relate to a single firm or one with an unvarying mix of sales. With a multi -product firm it is possible to calculate the break- even point as follows:

Break-even point (sh. sales) = Fixed Costs × Sales Value

Contribution

Illustration

A company makes a single product with a sales price sh10 and a marginal cost of sh6. Fixed costs are sh60,000 per annum.

Number of units to break even
Sales at break-eve point
C/S ratio
What number of units will need to be sold to achieve a profit of sh20,000 p.a.?
What level of sales will achieve a profit of sh20,000 p.a.?
As (d) with a 40% tax rate.
Because of increasing costs the marginal cost is expected to rise to £6.50 per unit and fixed costs to sh70,000 p.a. If the selling price cannot be increased what will be the number of units required to maintain a profit of £20,000 p.a. (ignore tax)?

Solution

Contribution	= Selling price – Marginal Cost
	= sh10 – sh6
	= sh4
a) Break-even point (units)	= sh60,000 4

	= 15,000
b) Break-even point (shs. sales)	= 15,000 x sh10 = sh150,000
c) C/S ratio	= sh4 10 = 40%

Number of units for target profit = sh60,000 + sh20,000

= 20,000

Sales for target profit = 20,000 x sh10 = 200,000

(Alternatively, this figure can be deduced by the following reasoning. After break-even point the contribution per unit becomes net profit per unit, so that as 15,000 units were required at break-even point, 5000 extra units would be required to make sh.20,000 profit.

Therefore total units = 15,000 + 5,000 = 20,000

20,000 x sh10 = sh.200,000

Number of units for target profit with 40% tax = 60,000 + 20,000 (1-0.4 ) sh4

= 23,333

Note that the fixed costs, marginal cost and contribution have changed

No. of units for target profit = Sh70,000 + sh20,000

Sh3.50

= 25,714 units

Note: The C/S ratio is sometimes known as the P/V ratio

LIMITATIONS OF CVP ANALYSIS

It can be time consuming
The analysis can only be applied to a single product
Where there is difficulty in classifying costs between fixed costs variable , it is difficult to apply break even analysis
At all levels of output , it assumes that the fixed costs are fixed or constant
At all levels of output, it assumes that the per unit variable costs are the same or fixed
At all levels of output , it assumes that sales price are fixed or constant
Inventory is not taken into consideration
It is not useful for production planning