The break-even price premium for granting credit, solved in closed form on one export order, and why the shortcut most sales teams use falls short.
Charge the premium that leaves the margin after finance where it would have been at sight. On a 4,200,000 export order on a confirmed usance credit discounted without recourse, that is 2.27 per cent of the price for 90 days, 3.05 per cent for 120 and 4.64 per cent for 180. The formula is premium = R ÷ [V × (1 − k)] − 1, where R is the money to recover whatever the term and k the cost rate that scales with the price.
Worked in full in Trade Finance by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Buyers ask for longer terms as if they were free, and sales teams concede them with a small price lift that feels proportionate. The question is how large the lift has to be before the longer term costs the seller nothing. It can be answered before the quotation leaves the building.
| Input | Value |
|---|---|
| Contract value V | 4,200,000 |
| Cost of goods sold / overhead | 3,423,000 / 470,400 |
| Operating margin before finance | 306,600 |
| Days to cash, any term (production, transit, documents, bank, refusals) | 116.82 |
| Financing of the cost at 8.4% | 93,304.13 |
| Confirmation, a year, shipment to maturity | 1.85% |
| Bank discount, a year, on the face | 6.9% |
| Document examination, share of the drawing | 0.125% |
| Flat fees: advising, couriers, amendment | 1,770 |
Because the confirming bank discounts the accepted draft at presentation, the exporter is paid on day 116.82 whatever term the buyer gets. The term is paid for in confirmation and discount, both charged on the price, not in a longer wait for cash.
=B10/(B2*(1-B11))-1, with R in B10 and k in B11The formula needs no iteration. Raising the price raises the confirmation, the discount, the examination fee and the expected loss in proportion, and nothing else, so the premium has to cover its own share of those charges: that is the 1 − k in the denominator.
| Days of credit | Total cost at list | Margin at list | k | Premium | Premium, money |
|---|---|---|---|---|---|
| 30 | 139,498 | 167,102 | 1.0577% | 0.74% | 31,286 |
| 60 | 170,452 | 136,148 | 1.7947% | 1.50% | 63,041 |
| 90 | 201,406 | 105,194 | 2.5317% | 2.27% | 95,275 |
| 120 | 232,358 | 74,242 | 3.2687% | 3.05% | 127,999 |
| 180 | 294,258 | 12,342 | 4.7425% | 4.64% | 194,962 |
| 270 | 387,101 | -80,501 | 6.9530% | 7.13% | 299,374 |
| 360 | 479,934 | -173,334 | 9.1633% | 9.73% | 408,856 |
Each day of credit costs about 1,031.75 on this order, almost exactly the same early in the term as late in it. Beyond 180 days the margin at list is already negative, so the last two rows are not a pricing strategy: they measure the damage a term of that length would have to undo.
In Case B of the companion workbook, the order is won on 180 days for a 1.5 per cent premium, 63,000. The operating margin rises to 369,600, because the extra price carries no extra cost of goods. The longer term then adds 188,703.58 of confirmation, discount and loss:
| Line | At sight | 180 days, +1.5% |
|---|---|---|
| Contract value | 4,200,000 | 4,263,000 |
| Operating margin | 306,600 | 369,600 |
| Total cost of finance | 108,542.64 | 297,246.22 |
| Margin after finance | 198,057.36 | 72,353.78 |
| Days to cash | 116.82 | 116.82 |
The premium bought back 63,000 of a 188,704 cost: 125,703.58 of margin destroyed, 36.5 per cent of the sight margin left. The term needed 4.64 per cent and was sold for 1.5, a shortfall of 3.14 percentage points. Days to cash did not move, so no receivables report flagged it.
A credit policy enforced through DSO has no grip on orders that are discounted at presentation, and those are usually the largest orders. Price the term on the quotation, not on the ageing.
Cost of funds times days. 8.4 per cent × 120 ÷ 360 = 2.80 per cent, against the 3.05 needed. It prices a wait that does not happen and misses the confirmation and the gross-up.
Discount rate times days. 6.9 per cent × 120 ÷ 360 = 2.30 per cent, or 96,600: exactly the discount and nothing else. At 180 days the same shortcut gives 3.45 per cent against 4.64.
Re-applying overhead to the higher price. The 470,400 of selling and administrative cost is sized on the list price. Charging 11.2 per cent on the achieved price as well would invent a cost that scales with the premium, make the term look dearer than it is and push the break-even premium above what the order actually needs.
The free workbook for this case, on the Trade Finance companion page, includes a quote calculator that prices any term on your own order. Why the discount is the dearer part of the money is worked in is a 6.90 per cent discount cheaper than an 8.40 per cent facility.
Separate the costs that scale with the price (confirmation, discount, examination fee, expected loss) from those that do not (cost of goods, overhead, financing, flat fees). The premium is the fixed money plus the margin at sight, divided by the price times one less the scaling cost rate, less one. On a 4,200,000 order at 120 days that is 3.05 per cent, or 127,999.
Because when the exporter discounts the buyer's accepted draft, cash arrives at presentation whatever the term. On this order days to cash are 116.82 at sight and at 180 days alike. The term is paid for through the discount and the confirmation fee on the price, so a DSO target sees nothing while 125,704 of margin disappears.
On this order about 1,031.75 a day, the 185,715.81 difference between sight and 180 days divided by 180. The line is nearly straight because confirmation and discount are rates on a principal that does not change. At that pace the margin after finance reaches zero shortly after 180 days.
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.
Get the book on Amazon →Free companion files
Also on Amazon UK · Amazon Germany · Amazon France · Amazon Canada
Reading guide: business operations: cost, contracts, pricing and supply chain → · All 681 articles →
If this book helped, or didn’t, a few lines on Amazon are worth more than they look: they are what the next reader goes on. Write a review. The workbook stays free either way.