The premium is charged on 110 per cent of the CIF price it belongs to, so the price has to be solved, not stacked.
To convert an FOB price to CIF, add the freight and then gross up for insurance, because the premium is charged on 110 per cent of the CIF price you are trying to find: CIF = (FOB + freight) ÷ (1 − 1.1 × premium rate). An illustrative $480,000 FOB order with $18,500 of freight and a 0.30 per cent premium rate gives a CIF price of $500,150.50, a premium of $1,650.50 and an insured value of $550,165.55. Insure 110 per cent of FOB plus freight instead and, under a letter of credit, the insurance document is short.
Worked in full in Trade Finance by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The conversion looks like a pricing chore, and in dollars the error is tiny. Its real weight is documentary. Under a letter of credit the insurance certificate is examined against a percentage of the CIF value, and an exporter who computes the insured amount the easy way presents a document that is short of the minimum. The bank does not care that the shortfall is a rounding of the circular formula; it is a discrepancy.
Both rules refer to the CIF value, which includes the premium itself. That is what makes the calculation circular.
| Item | Value |
|---|---|
| FOB price, goods loaded on board at the port of shipment | 480,000 |
| Ocean freight to the destination port | 18,500 |
| CFR price (FOB + freight) | 498,500 |
| Insurance premium rate, on the insured amount | 0.30% |
| Cover required | 110% of CIF |
The premium rate is illustrative. Cargo rates depend on the goods, the packing, the route and the clauses chosen, and war and strikes cover is often priced separately.
CIF = FOB + freight + premium, and premium = rate × 1.1 × CIF
CIF × (1 − 1.1 × rate) = FOB + freight
CIF = 498,500 ÷ (1 − 1.1 × 0.30%) = 498,500 ÷ 0.9967 = 500,150.50
Insured value = 1.1 × 500,150.50 = 550,165.55
Premium = 0.30% × 550,165.55 = 1,650.50
Check: 480,000 + 18,500 + 1,650.50 = 500,150.50
Excel, with FOB in B1, freight in B2, rate in B3 and cover in B4: =(B1+B2)/(1-B4*B3) for the CIF price and =B4*B5 for the insured value, where B5 holds the CIF result. To go back from a CIF quote to FOB: =CIF*(1-B4*B3)-B2, which returns 480,000.00.
The insurance costs 0.33 per cent of the CIF price, and the whole CIF price is 4.20 per cent above FOB, almost all of it freight.
| Method | Quoted CIF | Insured | 110% of quoted CIF | Shortfall |
|---|---|---|---|---|
| Gross-up formula | 500,150.50 | 550,165.55 | 550,165.55 | 0.00 |
| 110% of FOB + freight | 500,145.05 | 548,350 | 550,159.56 | 1,809.56 |
| 110% of FOB | 500,084 | 528,000 | 550,092 | 22,092 |
The first shortcut is the one most exporters use: insure 110 per cent of the CFR price, 548,350, pay a premium of 1,645.05, and invoice the total. The price is off by only 5.45, but the insurance certificate now covers 1,809.56 less than 110 per cent of the invoiced CIF value. If the credit is silent on cover, or asks for 110 per cent of the invoice value, that certificate does not comply. The second shortcut forgets the freight altogether and is short by 22,092.
A short insurance document is a discrepancy like any other: the issuing bank may refuse, and payment then depends on the applicant agreeing to waive it. The cost of a refusal, in fees, delay and a buyer who may now negotiate, is worked in what a letter of credit discrepancy actually costs. The practical rule is to compute the exact figure and ask for the insured amount rounded up, never down.
| Premium rate | CIF price | Premium | Insured, 110% | Price error of the CFR shortcut |
|---|---|---|---|---|
| 0.10% | 499,049 | 549 | 548,954 | 0.60 |
| 0.30% | 500,150 | 1,650 | 550,166 | 5.45 |
| 0.60% | 501,812 | 3,312 | 551,993 | 21.86 |
| 1.00% | 504,044 | 5,544 | 554,449 | 60.99 |
| 1.50% | 506,863 | 8,363 | 557,550 | 137.99 |
The price error grows with the square of the rate and stays small even on expensive cover. The documentary error does not shrink at all: whatever the rate, the shortcut always leaves the certificate below 110 per cent of the CIF value, because it leaves the premium out of the base.
| Cover | CIF price | Insured value | Premium |
|---|---|---|---|
| 100% | 500,000 | 500,000 | 1,500 |
| 110% | 500,150 | 550,166 | 1,650 |
| 120% | 500,301 | 600,361 | 1,801 |
A buyer who asks for 120 per cent cover in the credit costs the exporter only 151 more in premium on this order, but the formula must be rerun with the new cover: the gross-up factor changes with it.
The common mistake is to treat insurance as a line added after the price is known. Under CIF the premium is part of the price on which the cover is measured, so the calculation must be solved, not stacked. The second mistake is to forget the premium in the margin: an exporter that converts its FOB price list to CIF by adding freight only gives away 1,650.50, 0.34 per cent of the FOB value, on every order, before any finance cost is counted.
The order's full economics, with every route to payment priced, are in the free workbooks for Trade Finance. For the bank's own charges on the same credit, see how letter of credit fees are calculated.
The minimum is 110 per cent of the contract price under Incoterms 2020 CIF, and UCP 600 article 28(f)(ii) requires at least 110 per cent of the CIF or CIP value when a credit does not state the cover. On a $500,150.50 CIF invoice that means at least $550,165.55 insured. A credit can ask for more, such as 120 per cent, and the documents must then follow the credit.
Remove the premium first, then the freight: FOB = CIF x (1 - 1.1 x premium rate) - freight. On the worked order, 500,150.50 x 0.9967 - 18,500 returns the 480,000 FOB price. Subtracting a premium computed on the CIF figure alone gives a slightly different result, because the cover is 110 per cent, not 100.
It is a discrepancy. In the worked case, insuring 110 per cent of FOB plus freight gives cover of $548,350 against a required $550,159.56 on the resulting invoice, $1,809.56 short. The bank may refuse the documents, and payment then waits on the applicant's waiver, which a buyer can use to reopen the price.
This article is one calculation from Trade Finance. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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