Cost-Volume-Profit (CVP) Analysis

1 Introduction

This chapter looks at how analysing costs and contribution can be used for decision making.

2 Recap

Some definitions:

Marginal cost (MC):   the additional cost caused when one more unit is made. Marginal cost will be the sum of all variable costs per unit.

Total absorption cost (TAC):   the total cost of manufacturing a unit. This is the sum of the marginal cost and a fair share of the fixed production costs.

Fixed overhead absorption rate:   budgeted fixed production costs divided by budgeted output in units.

Profit per unit:   selling price per unit less total absorption cost per unit ie less marginal costs and all fixed production costs.

Contribution per unit:   selling price per unit less marginal cost per unit

Here is a cost card showing selling price and costs per unit:

Remember, the volume of items made will not alter the total fixed costs.

The contribution is always fundamental to decision-making; profit is usually irrelevant.

3 Breakeven calculations

In the above example, if no units are made and sold, fixed costs of $30,000 are still expected to be incurred and this will result in the business making a loss of $30,000.

If one unit is made and sold, there will be extra costs of $40 incurred (the marginal cost) and revenue of $100 will be earned, so the business will be richer by $100 - $40 = $60. The initial loss of $30,000 will be reduced by $60 to $29,940.

Gradually, as each additional item is made and sold, the loss will become smaller by $60/unit. So, to eliminate the initial loss of $30,000 (caused by the fixed costs) the business will have to make and sell:

  $30,000/$60 = 500 units.

Check:   Total contribution = 500 units x 60   = $30,000

  Fixed costs that have to be covered   = $30,000

At an output of 500 units, there will be zero profit (fixed costs = contribution) and the business is at break-even point.

The following diagram shows what’s going on:

When no units are made and sold, there is a loss of $30,000. The organisation can ‘climb’ out of that position by making and selling units. Each unit lifts the organisation by $60, the contribution.

The number of steps needed to just break even will be 30,000/60 = 500.

The break even revenue = 500 x 100 = $50,000

4 Margin of safety

The margin of safety is a measure of how much budgeted sales can fall by before the break even point is reached. It is usually expressed as the percentage fall from budgeted production that can be tolerated before falling in a loss.

5 Break even charts and P/V charts.

These charts display revenue, costs, profits and contribution in various formats.

For all of the following examples, the following information will be used:

Selling price = $20. Variable (marginal) cost per unit = $12. Fixed costs = $16,000

Budgeted output and sales = 3,000

The basic break even chart

Steps in drawing a break even chart:

1. Work out the break even point. Here, 16,000/(20 – 12) = 2,000 units

2. Draw the fixed cost line – horizontal at $16,000.

3. Draw the revenue line. This starts at the origin.

4. Draw the total cost line. This starts at Units = 0 and Total cost = Fixed cost.

5. Note that the revenue line rises more quickly ($20 for each extra unit) than the total cost line ($12 for each extra unit).

The budgeted profit is the difference between revenue and total costs at the budgeted volume of sales.

To the left of the breakeven point, total costs exceed total revenue so a loss is made.

The margin of safety (in units) is the distance between the budgeted volume and the breakeven volume.

Contribution break even chart

You can see that at the break even point, the contribution (revenue less variable costs) is equal to the fixed costs.

The profit volume graph

This graph allows you to immediately see the profit at any level of sales. It is not very helpful in identifying the break even point (which you would calculate before drawing the graph).

6 Contribution to sales ratio

The contribution to sales ratio is: contribution per unit/sales price per unit.

It allows you to calculate how much contribution is generated per $ of sales.

Contribution = Sales x C/S ratio

The C/S ratio can also be used to work out the break even point in terms of sales revenue.

We know that breakeven point occurs when the contribution just matches the fixed costs.

At break-even point   Sales x C/S ratio = Fixed costs

7 Achieving target profits

Remember what was said near the start of this chapter: contribution is always fundamental to decision-making; profit is usually irrelevant.

So, if you are asked to work out what volume of product needs to be made and sold to achieve a target profit, work out what target contribution is needed and calculate how many units need to be made to achieve that.

Target contribution = Target profit + fixed costs

The contribution has to be enough to first cover the fixed costs then it will start contributing towards profits.

8 The effects of changing selling prices and costs

Businesses often have the option to change selling prices and costs – but usually these changes affect other amounts as well.

For example, if selling prices are lowered, sales volume is likely to increase. Or, if new machinery is installed, fixed costs might rise but the variable cost of manufacturing might fall because the machines are more efficient.

As always, concentrate on working out the new contribution. The new profit can then be calculated easily.

The effect on break-even point and margin of safety

A change in price or cost also moves the break-even point and the margin of safety, and you may be asked for those rather than for profit. Work out the new contribution per unit first, then simply redo the two calculations.

So a $5 price cut — 10% off the price — pushes break-even up by 20% and eats into the safety margin, even though the same volume is still expected to be sold. The rules are worth remembering: anything that reduces contribution per unit (a lower price, a higher variable cost) raises the break-even point and cuts the margin of safety, and so does a rise in fixed costs. Anything that raises contribution per unit, or cuts fixed costs, does the opposite. And a change in fixed costs alone moves the break-even point but never the contribution per unit.