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 facility
Bank discount
Rate, a year
8.40%
6.90%
Charged on
3,423,000 (cost)
4,200,000 (price)
Cost of the money, 90 days
71,883
72,450
Cost of the money, 180 days
143,766
144,900
Discount less facility, 90 days / 180 days
567 / 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.
Statement
Base
Rate
The discount as quoted
face of the bill (price)
6.9000%
The discount as a yield
proceeds, 4,127,550
7.0211%
The discount restated on the cost
cost, 3,423,000
8.4663%
Own facility restated on the price
price, 4,200,000
6.8460%
Own facility as quoted
cost, 3,423,000
8.4000%
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 price
Facility, 90 days
Discount, 90 days
Discount less facility
Break-even discount rate
Cheaper
70.0%
61,740
72,450
10,710
5.8800%
own facility
75.0%
66,150
72,450
6,300
6.3000%
own facility
80.0%
70,560
72,450
1,890
6.7200%
own facility
81.5%
71,883
72,450
567
6.8460%
own facility
85.0%
74,970
72,450
−2,520
7.1400%
discount
90.0%
79,380
72,450
−6,930
7.5600%
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.
The inputs are on the Inputs sheet: cost of goods sold as a share of the price in C8
(81.5 per cent), the exporter’s cost of funds in C15 (8.40 per cent) and the confirming
bank’s discount rate in C41 (6.90 per cent).
The sheet Discount Against Own Funding holds the comparison: the facility cost in C10,
the discount in C13, the 567 in C14, the break-even rate in C20, its distance from the quote in
C23 (−5.4 basis points), and the two restated rates in C27 and C28 with the 6.63 basis-point
spread in C29. Column D repeats the whole comparison at 180 days.
The sheet Discount Is Not a Yield carries the face-and-proceeds conversion at 90, 120
and 180 days in C12 to E13, and the ladder from 30 to 360 days in rows 28 to 34.
To rebuild the margin table, overtype Inputs C8 with 0.70, 0.75, 0.80, 0.85 and 0.90 in turn
and read C10, C13, C14 and C20 on the comparison sheet. Rows 34 to 39 of Checks hold the
printed 71,883, 72,450, 567, 0.815 and 6.8460 against the computed ones; with C8 changed those
checks will read FAIL, which is the workbook working, not breaking.
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.
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