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Is a 6.90 per cent discount cheaper than an 8.40 per cent facility?

A bank discount is charged on the price. The exporter’s own facility is charged on the cost. Until the two rates sit on one base, the lower one only looks cheaper.

Harrowgate Instruments can fund ninety days of buyer credit on its own facility at 8.40 per cent, or have a confirming bank discount the accepted draft at 6.90 per cent. The discount is a point and a half cheaper on the quotation. On the 4,200,000 Meridian order it costs 72,450, and the facility costs 71,883. The lower rate is the dearer money by 567.

The difference is small, and the point is not its size but its sign. Two rates were compared that are charged on different things. The facility funds what the factory was paid, 3,423,000 of cost of goods sold. The discount is taken on the face of the bill, which is the whole invoice, margin included. A rate is a number attached to a base, and comparing two rates without their bases is a coincidence rather than a comparison.

The same ninety days, priced twice

Both columns use actual/360, the convention of the trade, and the same tenor. Nothing differs except the rate and what it is charged on.

Own facilityBank discount
Rate, a year8.40%6.90%
Charged on3,423,000 (cost)4,200,000 (price)
Cost of the money, 90 days71,88372,450
Cost of the money, 180 days143,766144,900
Discount less facility, 90 days / 180 days567 / 1,134
The Meridian order. Cost of goods sold is 81.5 per cent of the price; money is actual/360.

At 90 days the discount costs 567 more, which is 0.79 per cent of the facility’s own cost. At 180 days it costs 1,134 more, exactly twice as much, and the same 0.79 per cent. Lengthening the tenor changes the money but not the ranking, because both sides of the comparison carry the same days.

That is why the answer can be solved rather than searched for. Set the cost of funds times the cost equal to the discount rate times the price, and the days cancel. Break-even discount rate = own cost of funds × cost ÷ price. Here that is 8.40 per cent × 0.815 = 6.8460 per cent. The quoted 6.90 sits 5.4 basis points above it, so the discount is the dearer money at every tenor.

Four numbers for one rate

A careful treasurer knows that a bank discount is not a yield, and corrects for it. The discount is computed on the face and earned on the proceeds: at 90 days the bank takes 72,450 from 4,200,000, the exporter has the use of 4,127,550, and the rate actually borne on the money received is 7.0211 per cent. That correction is right, and it is not the one that decides this question. Set 7.0211 against 8.40 and the discount still looks well over a point cheaper.

The conversion that decides it is the base. Here is the same pair of facilities stated every way the workbook states them.

StatementBaseRate
The discount as quotedface of the bill (price)6.9000%
The discount as a yieldproceeds, 4,127,5507.0211%
The discount restated on the costcost, 3,423,0008.4663%
Own facility restated on the priceprice, 4,200,0006.8460%
Own facility as quotedcost, 3,423,0008.4000%
Only rates on the same base can be compared: 6.9000 against 6.8460 on the price, or 8.4663 against 8.4000 on the cost. Either way the gap is the discount’s.

On the price, the discount is 6.9000 per cent against a facility worth 6.8460. On the cost, the discount is 8.4663 per cent against 8.4000. The honest spread between the two, once both are on one base, is 6.63 basis points a year against the discount, and it is that spread, applied to 3,423,000 for 90 days, that produces the 567.

The face-and-proceeds correction still matters, just for a different question. It grows with the tenor: 12.1 basis points at 90 days, 16.2 at 120, 24.7 at 180 and 51.1 at 360. When two banks quote discounts at different tenors, it is the correction that makes the quotations comparable with each other. It does not make either of them comparable with the exporter’s own facility.

What decides the answer is the margin, not the rate

The whole of the conversion sits in one ratio, cost over price. An exporter whose goods cost less relative to what it charges finances less on its own facility and is still discounted on the whole invoice, so the richer the margin, the dearer the discount. Holding the facility at 8.40 per cent and the discount at 6.90, and moving only the cost of goods sold:

Cost of goods, % of priceFacility, 90 daysDiscount, 90 daysDiscount less facilityBreak-even discount rateCheaper
70.0%61,74072,45010,7105.8800%own facility
75.0%66,15072,4506,3006.3000%own facility
80.0%70,56072,4501,8906.7200%own facility
81.5%71,88372,4505676.8460%own facility
85.0%74,97072,450−2,5207.1400%discount
90.0%79,38072,450−6,9307.5600%discount
The discount never moves: it is charged on the price. Only the facility’s base does. The bold row is the Meridian order.

The crossing point is a cost of goods of 82.14 per cent of the price, 6.90 divided by 8.40, which is a gross margin of 17.86 per cent. Harrowgate’s gross margin on this order is 18.5 per cent, so it sits just on the wrong side of the line. An exporter on thinner margins can accept a dearer discount; an exporter on fatter ones should refuse a cheaper one. The same 6.90 per cent quotation is good business for one company and poor business for another, and the difference is on the income statement, not in the bank’s offer.

It follows that the rule of thumb most treasuries use, discount whenever the bank’s rate is below our own, is correct only for an exporter selling at cost. Every point of gross margin moves the break-even further below the facility rate. At a 30 per cent gross margin the discount has to come in under 5.88 per cent before it is cheaper than money costing 8.40.

What the 567 actually buys

None of this says the discount is a mistake. It says what the discount costs, which is a different and more useful statement. Discounting the draft repays the facility for those 90 days, and 3,423,000 of borrowing capacity is released. The price of that release is 567, or 6.63 basis points a year on the capacity freed. The book’s own Chapter 10 says that a treasurer three quarters drawn “may reasonably pay” the 567, and leaves it there.

The second of the three cases that ship with the companion files takes the facility question to a number at route level. Once the limit binds, a route’s price is its cost plus the margin of the order it crowds out, and the confirmed discounted credit earns 9.47 per cent of margin a year per dollar of facility against 7.27 for insured open account, the cheapest route at held terms. On that framing, if a dollar of spare headroom is worth more than 3.55 per cent a year, the confirmed credit wins. Set beside either of those figures, 6.63 basis points is not a large number.

So the practical answer has two halves. For an exporter with room on its facility, the discount at 6.90 is dearer than its own 8.40 money, and it should say so to the bank or keep the draft. For an exporter whose facility is the constraint, 567 is a cheap price for 3,423,000 of headroom, and it should take the discount knowing what it paid. Either way the decision belongs to the cost-to-price ratio and the headroom, and neither of them appears on the bank’s term sheet.

Reproducing it in the workbook

Everything above is in The_Cost_of_the_Money.xlsx, the third of the four workbooks.

Then put your own cost ratio into C8 and your own facility rate into C15 before the next discount quotation comes in. The break-even in C20 is the only rate on the bank’s offer worth reading against.

The workbooks behind this article

Every figure above is a live formula in the free companion files for Trade Finance. Each workbook ends with a Checks sheet setting the printed figure beside the computed one. No account and no email address.

Open the companion files →

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