Discounting

In finance, discounting is a mechanism in which a debtor obtains the right to delay payments to a creditor, for a defined period of time, in exchange for a charge or fee.

[1] Essentially, the party that owes money in the present purchases the right to delay the payment until some future date.

{\displaystyle {\text{Discount yield}}={\frac {\text{Charge to delay payment for 1 year}}{\text{debt liability}}}}

Since a person can earn a return on money invested over some period of time, most economic and financial models assume the discount yield is the same as the rate of return the person could receive by investing this money elsewhere (in assets of similar risk) over the given period of time covered by the delay in payment.

[1][2][5] The concept is associated with the opportunity cost of not having use of the money for the period of time covered by the delay in payment.

[1][2][6] The person delaying the payment of the current liability is essentially compensating the person to whom he/she owes money for the lost revenue that could be earned from an investment during the time period covered by the delay in payment.

[6] Therefore, the "discount yield", which is predetermined by a related return on investment that is found in the different markets in the financial sector, is what is used within the time-value-of-money calculations to determine the "discount" required to delay payment of a financial liability for a given period of time.

Some adjustment may be made to the discount rate to take account of risks associated with uncertain cash flows, with other developments.

For a zero-rate (also called spot rate) r, taken from a yield curve, and a time to cash flow T (in years), the discount factor is: In the case where the only discount rate one has is not a zero-rate (neither taken from a zero-coupon bond nor converted from a swap rate to a zero-rate through bootstrapping) but an annually-compounded rate (for example if the benchmark is a US Treasury bond with annual coupons) and one only has its yield to maturity, one would use an annually-compounded discount factor: However, when operating in a bank, where the amount the bank can lend (and therefore get interest) is linked to the value of its assets (including accrued interest), traders usually use daily compounding to discount cash flows.

In that case, the discount factor is then (if the usual money market day count convention for the currency is ACT/360, in case of currencies such as United States dollar, euro, Japanese yen), with r the zero-rate and T the time to cash flow in years: or, in case the market convention for the currency being discounted is ACT/365 (AUD, CAD, GBP): Sometimes, for manual calculation, the continuously-compounded hypothesis is a close-enough approximation of the daily-compounding hypothesis, and makes calculation easier (even though its application is limited to instruments such as financial derivatives).