VAT and Discount Calculator

What this calculator does

VAT and discounts are the two percentage operations most people perform weekly, and both have a trap that catches a surprising number of otherwise careful people.

The VAT trap is removing it by subtraction. If a price includes 7.5 per cent VAT, taking 7.5 per cent off that price does not give you the net figure, because the VAT was calculated on the smaller number in the first place. You have to divide by 1.075 instead. Invoices go out wrong over this every day.

The discount trap is stacking. Twenty per cent off followed by a further ten per cent is not thirty per cent off. It is twenty eight per cent, because the second reduction applies to an already reduced price. The gap is small on one item and significant across a full basket.

This calculator handles both directions of VAT, single and stacked discounts, and the reverse calculation from a discounted price back to the original.

How the calculation works

Adding VAT is straightforward: multiply the net price by the rate and add it, or equivalently multiply by 1.075 at the standard Nigerian rate of 7.5 per cent.

Removing VAT reverses that multiplication, so you divide by 1.075. The VAT element is then the difference between the gross and net figures. Expressed as a share of the gross price, VAT at 7.5 per cent is about 6.98 per cent of the total, which is why subtraction gives the wrong answer.

Discounts work through multipliers. A twenty per cent discount multiplies the price by 0.80. A second discount of ten per cent multiplies the result by 0.90. The combined multiplier is 0.72, giving an effective discount of 28 per cent rather than 30.

Working backwards from a discounted price divides by the multiplier. A price of ₦7,500 after a 40 per cent discount was originally 7,500 divided by 0.60, which is ₦12,500.

The formula

Adding VAT = Net price × (1 + VAT rate ÷ 100)

Removing VAT = Gross price ÷ (1 + VAT rate ÷ 100)

VAT element of a gross price = Gross price − (Gross price ÷ 1.075)

Single discount = Price × (1 − Discount ÷ 100)

Two stacked discounts = Price × (1 − D1) × (1 − D2)

Original from a discounted price = Discounted price ÷ (1 − Discount ÷ 100)

A worked example

A service is quoted at ₦45,000 before VAT. Adding 7.5 per cent gives ₦3,375 of VAT and a total of ₦48,375.

Now reverse it. An invoice shows ₦48,375 including VAT. Dividing by 1.075 gives ₦45,000 net and ₦3,375 of VAT, which is correct. Subtracting 7.5 per cent from ₦48,375 instead would give ₦44,747, understating the net by ₦253. On a single invoice that is an irritation. Across a year of invoicing it is a reconciliation problem.

For discounts, take an item at ₦45,000 with 20 per cent off and a further 10 per cent at the till. The first discount brings it to ₦36,000. The second takes ten per cent of ₦36,000, not of ₦45,000, giving ₦32,400. The total saving is ₦12,600, which is 28 per cent, not the 30 per cent the two signs together imply.

Things worth knowing

Divide to remove VAT

Never subtract the VAT percentage from a gross price. Divide by one plus the rate. At 7.5 per cent, VAT is roughly 6.98 per cent of the gross figure rather than 7.5, and the difference compounds across every line of an invoice.

Stacked discounts are smaller than they look

Two discounts never add. Twenty and ten combine to twenty eight. Thirty and twenty combine to forty four. Work out the effective figure before deciding whether an offer is as good as the signage suggests.

Check the reference price

A discount is only meaningful relative to a genuine original price. Use the reverse calculation to see what the stated original actually implies, and compare it against what the item sells for elsewhere.

VAT is not your revenue

A registered business collects VAT on behalf of the tax authority and remits it. Treating it as income produces a shortfall at filing time. Work out your margins on net prices, not gross ones.

Common mistakes to avoid

Subtracting the VAT percentage from a VAT inclusive price instead of dividing.
Adding two discount percentages together rather than applying them in sequence.
Calculating profit margins on VAT inclusive prices.
Applying VAT to a price that already includes it, which double charges the customer.
Assuming every good and service carries VAT, when some are zero rated or exempt.
Adding the discount percentage back to a reduced price to find the original.

Frequently asked questions

What is the VAT rate in Nigeria?

The standard rate is 7.5 per cent. Certain goods and services, including some basic food items, medical supplies and educational materials, are zero rated or exempt. Check the current schedule if you are unsure whether a specific item carries VAT.

How do I remove VAT from a price?

Divide the gross price by 1.075 at the standard rate. Subtracting 7.5 per cent gives a figure that is too low, because the VAT was originally calculated on the net amount rather than the gross.

Do two discounts add together?

No. They multiply. Twenty per cent followed by ten per cent gives an effective discount of 28 per cent, not 30. Each successive discount is applied to the already reduced price.

Should VAT be added before or after a discount?

VAT is normally calculated on the final amount actually charged, so after any discount. If VAT were applied first and the discount second, the customer would be paying tax on money they did not spend.

How do I find the original price from a sale price?

Divide the sale price by one minus the discount as a decimal. A price of ₦8,000 after a 20 per cent discount was originally 8,000 divided by 0.80, which is ₦10,000.