Straight discount and discount to yield on a series of avalised notes, the equivalent yield, and the gross-up that keeps the exporter whole.
A forfaiting discount is calculated note by note: face value × discount rate × (days to maturity + grace days) ÷ 360. Four avalised notes of 1,050,000 falling due over two years, discounted at an illustrative 6.50 per cent with 3 grace days, lose 348,075 on a straight discount, 8.29 per cent of face. Quoted as discount to yield, the same 6.50 per cent costs 316,933, 31,142 less.
Worked in full in Trade Finance by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Forfaiting is the without-recourse purchase of medium-term receivables, usually promissory notes or bills of exchange guaranteed (avalised) by the buyer's bank. The exporter ships, receives the notes, sells them to a forfaiter and is paid in cash, leaving the forfaiter with the bank and country risk. The price is set by one quoted rate, but two conventions turn that rate into money, and they differ by more than most people expect.
| Input | Value |
|---|---|
| Contract price | 4,200,000 |
| Notes, equal semi-annual instalments | 4 × 1,050,000 |
| Days to maturity from the discount date | 182, 365, 547, 730 |
| Grace days added to each note | 3 |
| Discount rate, all-in (illustrative) | 6.50% |
| Day basis | 360 |
| Commitment fee, per month from commitment to discounting | 0.10% × 2 months |
=F*r*(t+g)/360 for the straight discount, =F/(1+r*(t+g)/360) for proceeds to yield.| Days | Straight discount | Proceeds | Proceeds to yield | Yield of the straight discount |
|---|---|---|---|---|
| 182 | 35,073 | 1,014,927 | 1,016,061 | 6.725% |
| 365 | 69,767 | 980,233 | 984,580 | 6.963% |
| 547 | 104,271 | 945,729 | 955,148 | 7.217% |
| 730 | 138,965 | 911,035 | 927,277 | 7.491% |
| Total | 348,075 | 3,851,925 | 3,883,067 |
On a straight discount the exporter receives 3,851,925 for 4,200,000 of notes, 91.71 per cent of face, and 3,843,525 after the commitment fee. The all-in cost is 356,475, 8.49 per cent of the price. On discount to yield it would receive 3,883,067, 31,142 more, at the same quoted rate.
The gap grows with tenor. A straight discount is computed on the face value but earned on the proceeds, which are smaller, so the yield it represents rises with time: 6.725 per cent on the six-month note, 7.491 per cent on the two-year one. A forfaiter quoting “6.50 straight” on a two-year series is pricing the last note at almost a point more than a competitor quoting “6.50 to yield”. Ask which convention the quote uses before comparing two quotes.
The same face-versus-proceeds effect is why a bank discount at a lower rate can cost more than an overdraft at a higher one, worked on this order in whether a 6.90 per cent discount is cheaper than an 8.40 per cent facility.
| Case | Cost | Share of price |
|---|---|---|
| Rate 5.00% | 276,150 | 6.58% |
| Rate 6.50% | 356,475 | 8.49% |
| Rate 8.00% | 436,800 | 10.40% |
| 6.50%, no grace days | 354,200 | |
| 6.50%, 7 grace days | 359,508 |
Each 1.5 points of rate moves the cost by 80,325 on this series, because the average note is outstanding 456 days. Grace days matter less, a few thousand, but they are charged at the full rate and are worth negotiating on a long series.
The commercial question is usually the reverse one: what face value must the notes carry for the exporter to net the 4,200,000 it priced? Each note has to be grossed up by its own discount factor, holding the commitment fee at 8,400: face = (1,050,000 + share of commitment fee) ÷ (1 − r × (t + g) ÷ 360). The four notes become 1,088,458, 1,126,982, 1,168,099 and 1,212,582, a total of 4,596,120, an uplift of 9.43 per cent. Simply adding the 356,475 cost to the price gives a face of 4,556,475, which nets only 4,170,457: 29,543 short, because the uplift is itself discounted.
Comparing quotes across conventions. A straight discount and a discount to yield at the same rate are different prices. Convert both to proceeds before choosing.
Using a 365-day basis. Forfaiting in euro and dollar paper is normally quoted on a 360-day basis (sterling paper uses 365). On euro or dollar notes, computing the discount on 365 understates it by 4,768 on this series.
Adding the cost to the price instead of grossing up. As above, the shortfall is the discount on the uplift. On this two-year series it is 29,543.
The cost of each length of buyer credit on this order, and the price premium it requires, is in the free workbook for this case, and in how much to charge for extended payment terms.
Straight discount deducts rate times time from the face value; discount to yield divides the face value by one plus rate times time. On the same 6.50 per cent the second is cheaper for the exporter: on a 730-day note of 1,050,000 the straight discount is 138,965, the discount to yield 122,723. A straight discount of 6.50 per cent is a 7.491 per cent yield on that note.
Days added to each maturity to cover the time the forfaiter expects to wait for the funds to arrive after the due date. They are charged at the full discount rate. Three grace days on four notes of 1,050,000 at 6.50 per cent add 2,275 to the discount; seven grace days add 5,308.
More than the discount, because the uplift is discounted too. Adding the 356,475 cost to a 4,200,000 price nets only 4,170,457, 29,543 short. Grossing up each note by one minus rate times days gives a total face of 4,596,120, an uplift of 9.43 per cent rather than 8.49.
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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