Three similar concepts, three different calculations
VAT, discount and cash discount feel similar in everyday life – they all end with a percentage and a final amount. Mathematically and economically, however, the three topics are cleanly separated:
| Topic | What is calculated? | Typical calculator |
|---|---|---|
| VAT | Tax amount, net and gross value | VAT calculator |
| Discount | Price reduction and final price | Discount calculator |
| Cash discount | Amount payable on early payment | Cash-discount calculator |
Keeping the three apart avoids the most common errors in invoice checking and price comparison.
VAT: gross, net and tax amount
Value-added tax (also called turnover tax) is levied on virtually all supplies of goods and services. In Germany there are essentially three rates:
| Rate | Application |
|---|---|
| 19% | Standard rate for most goods and services |
| 7% | Reduced rate: foodstuffs, books, newspapers, local public transport, hotels, concerts |
| 0% | Exempt services: medical treatment, certain educational services, intra-EU supplies |
The base formulas are:
- Gross = net × (1 + rate)
- Net = gross ÷ (1 + rate)
- Tax amount = gross − net = net × rate
Worked example: an item costs 100 € net, the tax rate is 19 %.
| Quantity | Calculation | Result |
|---|---|---|
| Net | given | 100.00 € |
| Tax amount | 100 × 0.19 | 19.00 € |
| Gross | 100 × 1.19 | 119.00 € |
The other way around: a gross of 119 € is decomposed. Net = 119 ÷ 1.19 = 100 €, tax amount = 19 €. At 7 % the net would be 119 ÷ 1.07 ≈ 111.21 €.
Under Section 14 of the German VAT Act, invoices must show the tax amount separately (except for small-amount invoices below 250 € gross). Anyone writing an invoice must report net and tax separately. The VAT calculator handles the conversion in both directions.
Discount: unconditional price reduction
Discounts are price reductions without further conditions. They can refer to list price (list discount), quantity (quantity discount), loyalty (loyalty discount) or season (seasonal discount). The base formula:
- Final price = original × (1 − discount ÷ 100)
- Saving = original × (discount ÷ 100)
Example: 80 € minus 15 % discount:
| Quantity | Calculation | Result |
|---|---|---|
| Original price | given | 80.00 € |
| Discount (saving) | 80 × 0.15 | 12.00 € |
| Final price | 80 × 0.85 | 68.00 € |
Key pitfall: multiple discounts in sequence must not be added. "10 % off everything" plus "another 10 % in sale" is not a 20 % total discount. Cutting 100 € by 10 % (= 90 €) and then another 10 % yields 81 € – that is 19 % total discount, not 20 %. This is true for multiplicative discounts, the typical online-shop case.
For additive discounts ("20 % total reduction with two promotions"), the final price relates to the list price: 100 € × 0.80 = 80 €. The small print decides which form is meant.
The discount calculator shows both the saving and the new price and makes the relation transparent.
Cash discount: price advantage for early payment
Cash discount differs from a discount mainly in that it is tied to a payment condition. An invoice might read:
Payment within 10 days with 2 % cash discount, otherwise within 30 days net.
If you pay within the cash-discount deadline, you may deduct the cash-discount amount. The base formula:
- Amount payable = invoice amount × (1 − cash discount rate ÷ 100)
- Cash-discount saving = invoice amount × cash discount rate ÷ 100
Example: 1,250 € invoice, 2 % cash discount:
| Quantity | Calculation | Result |
|---|---|---|
| Invoice amount | given | 1,250.00 € |
| Cash-discount saving | 1,250 × 0.02 | 25.00 € |
| Amount payable | 1,250 × 0.98 | 1,225.00 € |
The effective annual rate of cash discount is surprisingly high. Using 2 % cash discount with a 10-day instead of 30-day payment deadline improves liquidity by 20 days. Annualised, this is an effective rate of about 36 %:
- Effective rate ≈ cash discount rate ÷ (payment term − cash discount term) × 360
- 2 ÷ 20 × 360 = 36 %
Such values beat almost any cheap overdraft facility. In any business relationship that offers cash discount, you should almost always use the cash-discount deadline – even if other open balances stretch out longer. The cash-discount calculator returns both the amount payable and the cash-discount saving.
Reverse charge and tax special cases
For B2B transactions inside the EU, the reverse-charge procedure often applies: the supplier invoices without VAT, the recipient reports the tax in their home country and can deduct it as input tax. Invoices then read "tax liability of the recipient" or "reverse charge".
Private individuals rarely see this. For companies, freelancers and clubs it is standard, however, when software, advertising or consulting services are sourced from abroad. Important: in your own books, the gross amount is not taken from the invoice but composed from net plus calculated tax.
Small-amount invoices and document obligations
Invoices up to 250 € gross qualify as small-amount invoices. For them, the gross amount with a note on the included VAT rate suffices; a separate breakdown of net and tax is not required. Above that, net, tax rate and tax amount must be shown separately.
For private people charging VAT (e.g. when selling on online platforms or as a small-business owner), the small-business rule (Kleinunternehmerregelung) is worth knowing: with a previous-year turnover of up to 25,000 € (from 2025) and an expected annual turnover of 100,000 €, you can opt out of stating VAT. This makes invoices simpler, but also forfeits the right to input-tax deduction.
Common errors in invoice checks
- Mixing up net and gross: wholesale often quotes net, retail gross. Without care, you compare apples and pears.
- Adding cash discount and discount: cash discount is taken from the gross or net amount, not from an already discounted price – unless explicitly agreed.
- Adding several percentages: with multiplicative discounts this is wrong.
- Wrong tax rate: in mixed shipments (books and toys) the items must be shown separately with 7 % and 19 %.
- Applying cash discount on gross to net: cash discount usually refers to the gross amount, unless otherwise agreed.
Worked example: all three combined
A furniture store issues the following invoice:
| Item | amount |
|---|---|
| Sofa (net) | 1,000.00 € |
| Delivery (net) | 100.00 € |
| Net subtotal | 1,100.00 € |
| 10 % discount | -110.00 € |
| Net assessment basis | 990.00 € |
| 19 % VAT | 188.10 € |
| Gross invoice amount | 1,178.10 € |
| 2 % cash discount on 10-day payment | -23.56 € |
| Amount payable with cash discount | 1,154.54 € |
Important: discount is deducted before VAT because it reduces the taxable turnover. Cash discount is deducted after VAT; the cash-discount amount is then accounted for as a turnover reduction in the next VAT pre-return.
Conclusion
VAT, discount and cash discount look similar but solve different tasks. The right order in invoices is usually: discount – VAT – cash discount. Once you understand that, every invoice can be checked, every price comparison is on a solid base and every term of business is easier to read. With the VAT calculator, the discount calculator and the cash-discount calculator you have three sharply focused tools.
Sources
- VAT Act (UStG), especially Sections 14 and 19 – gesetze-im-internet.de/ustg_1980
- Federal Ministry of Finance circulars on small-amount invoices and the small-business rule – bundesfinanzministerium.de
- IHK overviews of cash discount and payment terms – dihk.de