1. WYCAS follow up notes re. Costing and Pricing course February 2011
In these notes I’ll show you the relationship between your costs, the volume of sales and
your profits. Actually figuring out how a particular price affects the volume of sales is
another matter – that depends on your understanding of your market. The purpose of
these notes is to help you understand the consequences of delivering a service at a
particular price and therefore aid your decision making.
For this, all you really need is the following formula:
Net profit = Total sales – Total costs
I’m sure that will seem pretty obvious to you but with that basic statement you can answer
most of your costing and pricing questions. Though it will be a bit more helpful to expand it
a little and add a couple of definitions.
So here’s a more detailed version:
Net Profit = (Unit selling price x units sold) – (Unit variable cost x units sold) - total
fixed costs
Definitions:
Variable costs are only those things that vary with the volume of sales eg if you hire
freelancers to deliver services, you only hire them when there is work to do. In
manufacturing or retailing the variable costs will be the stock purchases – ie every
purchase can potentially by sold.
Fixed costs are those that you incur regardless of the volume of sales, these would
include things like management and admin salaries and your office costs like rent, rates,
utilities, consumables etc. Note, if your front line staff are salaried then those will be fixed
costs too.
If your organisation provides a number of different services the fixed costs relating to any
one service will be some calculated proportion of all of your fixed costs. Eg you might
attribute some of the premises costs on the basis of floor space used by the service and
then the central office costs like management and admin salaries, office consumables and
office premises costs etc on the basis of expected delivery hours on the service.
Finally, let’s assign some letters to the elements of the formula to make it easier to write.
NP = Net Profit, P = Selling price, x = Units sold
a = Unit variable cost, b = Total fixed costs
So now our formula is: NP = Px – ax – b

2. Basic profit calculation
Now we can actually get it to answer some questions. Lets start with something easy.
We’ll imagine our organisation runs training courses:
What profit would we make if we delivered 20 courses over the course of a year with an
expected average enrolment of 10 people on each course if we charge the learners £200
for a course? (ie total income per course = £2000)
We’ll use a freelance tutor who charges £1200 per course and let’s say we have
calculated the share of our total fixed costs attributable to this work as £10000.
So putting these figures in the formula we get:
NP = (£2000 x 20) – (£1200 x 20) - £10000
= £40000- £24000 - £10000
= £6000
Okay but a more common question might be: How many courses do we need to deliver
just to cover our costs or ‘break even’?
Break-even point in sales
The break-even point is when net profit = nil, so using the formula again:
Px – ax – b = 0
So: £2000x - £1200x - £10000 = 0
Therefore: £800x - £10000 = 0
And so: £800x = £10000
Ie: x = £10000 / £800 = 12.5
So whilst we expect to run 20 courses, provided we run 13 with an average of 10 learners
we’ll cover our costs (we can’t run half a course). That seems like a healthy margin of
safety and we can actually quantify this as a %:
Margin of safety = (Expected sales – Break-even sales) / Expected sales
So in our example this is (20 – 13) / 20 = 35%
In other words we can take a 35% reduction in our expected sales and still break even.
What selling price should we charge?
We can use the formula to answer this question too but this time we know the volume of
sales but not the selling price. We will also need to put in a figure for the target net profit –

3. we’ll try £8000 but note that if we put in nil this would tell us the price we would need to
charge in order to break even for a given volume of sales.
Ie: (P x 20) – (£1200 x 20) - £10000 = £8000
Therefore: P x 20 - £34000 = £8000, so: P x 20 = £42000
Ie: P = £42000 / 20 = £2100.
If we average 10 learners per course this means charging £210 per learner.
Hopefully you can see how powerful this formula is provided you have a bit of basic
information and a reasonable grasp of maths.
A note on fixed and variable costs
If your organisation has no variable costs, your formula will look like this:
NP = Px – b
ie there is no variable cost element, however you will soon realise that for the same
expected volume of sales and selling price, an organisation whose costs are all fixed will
have a higher break-even point in sales than one with a mixture of fixed and variable
costs.
Contribution
You might have noticed that if you do have significant variable costs you can work out how
much each sale ‘contributes’ to fixed costs. This is a quicker way of calculating the break-
even point.
In our example the unit selling price was £2000 per course and the unit variable cost was
£1200 per course. Therefore every course contributes £800 towards the total fixed costs of
£10000.
This means that the break-even point can be calculated by dividing the fixed costs by the
contribution:
Ie Break even point in sales = £10000 / £800 = 12.5
Therefore every course beyond this level yields £800 profit.
Note you could not use this method if your tutors were salaried as you would have to pay
them whether you ran all the courses or not – ie their salary would actually be part of the
fixed costs.
Remember, true variable costs are only incurred when you actually make a sale.

4. Capacity
Clearly what underpins all of these calculations is your understanding the organisation’s
capacity to deliver a particular volume of sales. If your delivery staff are salaried, you need
to work out how much of their contracted hours can be used for actual delivery, ie their
‘chargeable’ time. To do this you will need to deduct things like annual leave, an allowance
for sickness, and some notion of time spent on admin tasks, travel or training etc.
You also need to understand the capacity of your management and admin staff – ie one
manager can only manage a finite number of staff. You need to consider the physical
capacity of your premises to accommodate your staff or in which to deliver your services,
again this is a finite resource and at some point you may need to rent another room or
move to larger premises. The fixed costs can change but they go up in steps rather than
varying immediately with sales.
Expected sales
This comes down to your knowledge of the market you intend to work in. The difficulty
here is that the selling price and the expected sales are actually related, depending on
how ‘price elastic’ the service is. Ie if the price goes up, to what extent does the sales
volume go down and vice versa? The level of competition in the market will have an effect
too – more competitors will tend to drive prices down so how you structure your
organisation and market your services will be very important.
Summary
What you actually arrive at as a price for a service is up to you but it is essential that you
run your examples through the formula above in order to test the effect on your profits,
establish a break-even point and get an idea of the margin of safety. You might even
choose to deliver a service at or below cost, provided another service yields sufficient
profits to subsidise it.
For more information or training on this subject contact WYCAS on 0113 270 6269 or
check our website: http://www.wycas.org.uk/