Discount rate

Discount rate

Overview
For the fees charged to merchants for accepting credit cards, see Discount Rate under Merchant Account.
For discount rate as a term in investment financing, see Discounted cash flow

The discount rate can mean
  • an interest rate a central bank
    Central bank
    A central bank, reserve bank, or monetary authority is a public institution that usually issues the currency, regulates the money supply, and controls the interest rates in a country. Central banks often also oversee the commercial banking system of their respective countries...

     charges depository institution
    Depository institution
    A depository institution is a financial institution in the United States that is legally allowed to accept monetary deposits from consumers...

    s that borrow reserves
    Bank reserves
    Bank reserves are banks' holdings of deposits in accounts with their central bank , plus currency that is physically held in the bank's vault . The central banks of some nations set minimum reserve requirements...

     from it, for example for the use of the Federal Reserve's discount window
    Discount window
    The discount window is an instrument of monetary policy that allows eligible institutions to borrow money from the central bank, usually on a short-term basis, to meet temporary shortages of liquidity caused by internal or external disruptions...

    .

  • the same as interest rate
    Interest rate
    An interest rate is the rate at which interest is paid by a borrower for the use of money that they borrow from a lender. For example, a small company borrows capital from a bank to buy new assets for their business, and in return the lender receives interest at a predetermined interest rate for...

    ; the term "discount" does not refer to the common meaning of the word, but to the meaning in computations of present value
    Present value
    Present value, also known as present discounted value, is the value on a given date of a future payment or series of future payments, discounted to reflect the time value of money and other factors such as investment risk...

    , e.g.
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Encyclopedia
For the fees charged to merchants for accepting credit cards, see Discount Rate under Merchant Account.
For discount rate as a term in investment financing, see Discounted cash flow

The discount rate can mean
  • an interest rate a central bank
    Central bank
    A central bank, reserve bank, or monetary authority is a public institution that usually issues the currency, regulates the money supply, and controls the interest rates in a country. Central banks often also oversee the commercial banking system of their respective countries...

     charges depository institution
    Depository institution
    A depository institution is a financial institution in the United States that is legally allowed to accept monetary deposits from consumers...

    s that borrow reserves
    Bank reserves
    Bank reserves are banks' holdings of deposits in accounts with their central bank , plus currency that is physically held in the bank's vault . The central banks of some nations set minimum reserve requirements...

     from it, for example for the use of the Federal Reserve's discount window
    Discount window
    The discount window is an instrument of monetary policy that allows eligible institutions to borrow money from the central bank, usually on a short-term basis, to meet temporary shortages of liquidity caused by internal or external disruptions...

    .

  • the same as interest rate
    Interest rate
    An interest rate is the rate at which interest is paid by a borrower for the use of money that they borrow from a lender. For example, a small company borrows capital from a bank to buy new assets for their business, and in return the lender receives interest at a predetermined interest rate for...

    ; the term "discount" does not refer to the common meaning of the word, but to the meaning in computations of present value
    Present value
    Present value, also known as present discounted value, is the value on a given date of a future payment or series of future payments, discounted to reflect the time value of money and other factors such as investment risk...

    , e.g. net present value
    Net present value
    In finance, the net present value or net present worth of a time series of cash flows, both incoming and outgoing, is defined as the sum of the present values of the individual cash flows of the same entity...

     or discounted cash flow
    Discounted cash flow
    In finance, discounted cash flow analysis is a method of valuing a project, company, or asset using the concepts of the time value of money...


  • the annual effective discount rate, which is the annual interest divided by the capital including that interest; this rate is lower than the interest rate; it corresponds to using the value after a year as the nominal value, and seeing the initial value as the nominal value minus a discount
    Discounts and allowances
    Discounts and allowances are reductions to a basic price of goods or services.They can occur anywhere in the distribution channel, modifying either the manufacturer's list price , the retail price , or the list price Discounts and allowances are reductions to a basic price of goods or services.They...

    ; it is used for Treasury Bills and similar financial instruments

Annual effective discount rate


The annual effective discount rate is the annual interest divided by the capital including that interest, which is the interest rate divided by 100% plus the interest rate. It is the annual discount factor to be applied to the future cash flow, to find the discount, subtracted from a future value to find the value one year earlier.

For example, suppose there is a government bond
Government bond
A government bond is a bond issued by a national government denominated in the country's own currency. Bonds are debt investments whereby an investor loans a certain amount of money, for a certain amount of time, with a certain interest rate, to a company or country...

 that sells for $95 and pays $100 in a year's time. The discount rate according to the given definition is


The interest rate is calculated using 95 as its base:


For every annual effective interest rate
Effective interest rate
The effective interest rate, effective annual interest rate, annual equivalent rate or simply effective rate is the interest rate on a loan or financial product restated from the nominal interest rate as an interest rate with annual compound interest payable in arrears.It is used to compare the...

, there is a corresponding annual effective discount rate, given by the following formula:


or inversely,


where the approximations apply for small i and d; in fact i - d = id.

See also notation of interest rates.

Business calculations


Businesses need to consider the discount rate when deciding whether to spend some of their profits on buying a new piece of equipment, or whether to give the profit back to their shareholders. In an ideal world, they would only buy a piece of equipment if the shareholders would get a bigger profit later. The amount of extra profit that a shareholder requires in the future in order to prefer that the company buy the equipment rather than giving them the profit now is based on the shareholder's discount rate. There is a widely used way of estimating shareholder's discount rates using share price data. It is known as the capital asset pricing model
Capital asset pricing model
In finance, the capital asset pricing model is used to determine a theoretically appropriate required rate of return of an asset, if that asset is to be added to an already well-diversified portfolio, given that asset's non-diversifiable risk...

. Businesses normally apply this discount rate to their decisions about purchasing equipment by calculating the net present value
Net present value
In finance, the net present value or net present worth of a time series of cash flows, both incoming and outgoing, is defined as the sum of the present values of the individual cash flows of the same entity...

 of the decision

See also

  • Discounting
  • Social discount rate
    Social discount rate
    Social discount rate is a measure used to help guide choices about the value of diverting funds to social projects. It is defined as "the appropriate value of r to use in computing present discount value for social investments"...

  • Ramsey growth model
    Ramsey growth model
    The Ramsey–Cass–Koopmans model or the Ramsey growth model is a neo-classical model of economic growth based primarily on the work of the economist and mathematician Frank P. Ramsey, with significant extensions by David Cass and Tjalling Koopmans...

  • Compare and contrast with federal funds
    Federal funds
    In the United States, federal funds are overnight borrowings by banks to maintain their bank reserves at the Federal Reserve. Banks keep reserves at Federal Reserve Banks to meet their reserve requirements and to clear financial transactions...


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