The Maths of VAT on Delivery of Mixed Rate Goods

If you managed to get past the title of this post and are still here then this article could potentially be of great help to you.  If you’re bemused by the title but have stuck around thinking this might be an entertaining read, leave now – you are horribly mistaken.

OK, let’s start with the context, which can be summarised as follows.  I’m referring to the situation in the UK here, I’m not sure how it works elsewhere, though I imagine it could be similar:

• A common doubt amongst online sellers is whether they should charge VAT on their delivery charge.
• HMRC are quite clear that if you are charging a separate fee for delivery of orders, then whether this should have VAT added or not depends on the nature of the goods in the box, so to speak.
• If you are sending out standard rated goods (i.e. 20% VAT as of May 2012), then you should add VAT to the delivery charge.
• If you are sending out zero-rated goods (e.g. books, children’s clothes, food), then you can zero-rate the delivery charge (so no VAT).
• The difficulty arises when an order contains both standard rate and zero rate goods – a typical example from my company is an order that contains food (0% VAT) and cooking utensils (20% VAT).
• In such cases, HMRC’s position is not quite as clear.
• Some have interpreted HMRC documentation as suggesting that if an order contains any standard-rated goods at all, then the whole delivery charge should have VAT added.
• Others, myself included, have a different interpretation.

In either case there is a single supply for which the VAT liability is based on the liability of the goods being delivered. For example, any element of the price attributed to the doorstep delivery of milk and newspapers will also be zero rated. On the other hand any element attributed to the delivery of standard rated mail order goods will be standard rated.

Although the terminology (“any element attributed”) isn’t crystal clear, I think it’s obvious that they are suggesting a proportional approach, i.e, that the delivery charge can be broken down into a VATable component and a non-VATable component based on the composition of the order being sent out.  So an order consisting of half food and half, say, frying pans, would need to have VAT applied to 50% of the delivery charge.  Not only does that appear to be the intention of HMRC wording, it would also seem to be the fairest and most sensible way of applying the VAT law to this situation, and let’s assume that’s what they want!

Assuming that this is the correct way to interpret the VAT rules, this concept of proportionality can cause a huge mathematical headache for online sellers.  Let me explain why.  In the vast majority of online transactions, the customer will pay a fee for delivery which will be fixed and independent of the VAT composition of their basket.  It is highly unlikely either that they will have any notion of the above VAT laws, or even whether the items they are buying even attract VAT.  They will expect to pay £4.99 for delivery if that is what is advertised.  Full stop.  In that case, the responsibility for adjusting the VAT charges will fall on the retailer, and probably after the sale has been made.

Let’s try an example. A customer places the following order:

1. A frying pan. £25 ex. VAT. £30.00 inc. VAT.
2. Some food to the value of £60 ex. VAT, therefore £60 inc. VAT.
3. Order subtotal £85 ex. VAT, £90.00 inc. VAT.
4. Delivery charge £5.99.
5. Grand Total £95.99

So, the customer pays £95.99 by card and doesn’t expect to pay a penny more or a penny less.  Would you know how to split the delivery charge up correctly into VATable and non-VATable components?  The maths are pretty tricky.  Here’s how you do it.

The goal is to end up with two delivery charges – one that will carry 20% VAT, and another that will be zero-rated.  Each of these charges should be in proportion to the VAT composition of the order and the total delivery charge, once VAT has been added to the VATable component, should be £5.99.  Head spinning already?  We haven’t even begun.

OK, so let’s agree that the new delivery charge, excluding VAT, is going to be less than £5.99 – this is obvious as there’s going to be some VAT on it, bringing the Net total up to £5.99.  Let’s call this new ex. VAT delivery charge x.

What we know is that the VATable portion of x with VAT added on, plus the non-VATable portion of x will equal £5.99.  Algebraically that’s:

1.2(Sx) + Zx = T,

where S is the proportion, from 0 to 1, of VATable goods in the order, Z is the proportion of zero-rated goods in the order, and T is the total inc. VAT delivery charge, in this case £5.99.

With a little algebra magic that you should remember from school, you get:

x = T / (1.2S + Z)

So, now all we need are S and Z and we’ll be on our way.

Let’s work out the composition of the order.  The total excluding VAT was £85, of which 29.4% (£25/£85) is represented by standard-rated goods, and 70.6% by zero-rated goods.  So, S = 0.294 and Z = 0.706.

Plug that into the above formula and you get:

x = 5.99 / ((1.2 x 0.294) + 0.706)
   = 5.99 / 1.0588
   = 5.657

So, the new ex. VAT delivery charge is going to be £5.66.  Going back to the composition of the order, we know that 29.5% were VATable goods, so £5.66 x 0.294 = £1.66.  Thus, we know that the VATable portion of the delivery charge should be £1.66 ex. VAT, which amounts to £1.99 inc. VAT.

We also know that the zero-rated portion was 70.6%, so £5.66 x 0.706 = £4.

Add those up, and what do you get? £1.99 + £4 = £5.99.  So, we’re back at our original delivery charge.

So just to summarise – on the above order, which was comprised by value of 29% VATable goods and 71% VAT free goods, we have worked out that to arrive at a final VAT inclusive delivery charge of £5.99, we need to charge two components of £1.66 plus VAT and £4 with no VAT.

If you are paranoid, you can check the percentages and you’ll see that £1.66 out of £5.66 is 29% and £4 out of £5.66 is 71%.  Perfect.

Go back to the original order now and recalculate the subtotals.  Total ex VAT is £90.66.  Total amount of VAT is £5.33.

Grand total, unbelievably, is correct at £95.99.

Bet you wish you paid more attention in maths class now, don’t you?