What it means
In the market sense, the rate is applied to the face value of the instrument to produce a discount amount, and you pay face value less that discount. At maturity you receive the full face value, so the discount is your entire return.
In the central banking sense, the discount rate is what an institution pays to borrow from the central bank's lending facility, sometimes called the discount window. That rate is deliberately set a little above normal market rates, so banks use the facility as a backstop rather than a routine funding source.
The two meanings are connected by history rather than by mathematics. Central banks originally lent by buying, or rediscounting, commercial bills at a discount, and the name stuck even after the mechanics changed to straightforward secured lending.
For a business, the market meaning is the one that turns up in practice, usually when a bank offers to discount a trade bill or a receivable. The rate you are quoted determines the cash you receive today, and it should be compared against the cost of an overdraft or an invoice finance facility over the same number of days.
The nuance to hold onto is that a discount rate is not the same as an interest rate on the money you receive. Because the charge is calculated on the larger face value but deducted from the smaller sum you actually get, the effective cost of the borrowing is always a little higher than the quoted rate.
In practice
Real-world examples.
Example
An exporter asks its bank to discount a 60-day bill of exchange with a face value of $200,000 at a 6% bank discount rate. The charge is $200,000 x 0.06 x 60 / 360 = $2,000, so the exporter receives $198,000 immediately instead of waiting two months.
Example
A regional bank facing an unexpected deposit outflow borrows $12,000,000 from the central bank's discount window for 30 days at a 5% discount rate. The cost is $12,000,000 x 0.05 x 30 / 360 = $50,000, which the bank accepts as the price of avoiding a fire sale of assets.
Example
A treasurer choosing between two bills, one 90-day at 4.5% and one 180-day at 4.6%, converts both to the return on money actually invested before deciding. The longer bill wins on yield but ties up cash past a scheduled tax payment, so the shorter bill is bought instead.
Formula
Calculation
Discount amount = Face value x discount rate x (days to maturity / 360), and Purchase price = Face value - discount amount.
A cash manager buys a 90-day instrument with a face value of $500,000 quoted at a bank discount rate of 4.5%. The time factor is 90 / 360 = 0.25, so the rate applied is 0.045 x 0.25 = 0.01125. The discount is $500,000 x 0.01125 = $5,625, and the price paid is $500,000 - $5,625 = $494,375.
Measured against the money actually committed, the return is $5,625 / $494,375 = 1.138% over 90 days. Annualising over a 365-day year gives 1.138% x (365 / 90) = about 4.61%, comfortably above the 4.5% quote.Case study
Seen in the real world.
Copperline Freight is an illustrative, invented haulage operator used here to make the arithmetic concrete. It had a $360,000 receivable from a reliable customer on 120-day terms and needed the cash immediately to fund a truck purchase, with two options on the table.
Its bank offered to discount the bill at a 7% bank discount rate. The charge worked out at $360,000 x 0.07 x 120 / 360 = $8,400, leaving proceeds of $351,600. The alternative was to draw the same $351,600 on the overdraft at 11% for the same 120 days, which would have cost $351,600 x 0.11 x 120 / 360 = $12,892.
Discounting the bill therefore saved $12,892 - $8,400 = $4,492, and it also kept the overdraft facility free for the seasonal dip that Copperline knew was coming in the winter. This fictional comparison is the calculation any owner should run before assuming the overdraft is the cheapest short-term option.
Watch out
Common mistakes.
- Reading the quoted discount rate as the effective cost of the borrowing, when the charge is calculated on face value but deducted from the smaller amount you actually receive.
- Mixing up the central bank discount window rate with the market discount rate used to price bills, and then drawing conclusions about the wrong market.
- Forgetting the 360-day convention and calculating the discount on a 365-day year, which produces a figure that will not match the bank's own quote.
Questions
People also ask.
Is a higher bank discount rate good or bad for me?
It depends which side you are on, since a buyer of a bill earns more when the rate is higher, while a business discounting its own receivable pays more.
How does the discount rate differ from a coupon or interest rate?
Interest is paid on top of the principal over time, whereas a discount is deducted from the amount you receive at the start.
Does the central bank discount rate affect my business loan?
Usually only indirectly, since it anchors the very short end of the market and feeds through to the base rates that variable business loans are priced against.
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