Discounting is a financial mechanism in which a

rate of return
In finance, return is a profit on an investment. It comprises any change in value of the investment, and/or cash flows (or securities, or other investments) which the investor receives from that investment, such as interest payments, coupons, c ...

denoted ''r'' on a similar investment asset means the future value of ''P'' is $P(1\; +\; r)^t$, and the discount can be calculated as
: $\backslash text\; =\; P(1+r)^t-P.$
We wish to calculate the

rate of return
In finance, return is a profit on an investment. It comprises any change in value of the investment, and/or cash flows (or securities, or other investments) which the investor receives from that investment, such as interest payments, coupons, c ...

on the financial asset mixture the firm uses to finance capital investment. Some adjustment may be made to the discount rate to take account of risks associated with uncertain cash flows, with other developments.
The discount rates typically applied to different types of companies show significant differences:
* Start-ups seeking money: 50–100%
* Early start-ups: 40–60%
* Late start-ups: 30–50%
* Mature companies: 10–25%
The higher discount rate for start-ups reflects the various disadvantages they face, compared to established companies:
* Reduced marketability of ownerships because stocks are not traded publicly
* Small number of investors willing to invest
* High risks associated with start-ups
* Overly optimistic forecasts by enthusiastic founders
One method that looks into a correct discount rate is the

debtor
A debtor or debitor is a legal entity (legal person) that owes a debt to another entity. The entity may be an individual, a firm, a government, a company or other legal person. The counterparty is called a creditor. When the counterpart of this ...

obtains the right to delay payments to a creditor
A creditor or lender is a party (e.g., person, organization, company, or government) that has a claim on the services of a second party. It is a person or institution to whom money is owed. The first party, in general, has provided some property ...

, for a defined period of time, in exchange for a charge or fee.See "Time Value", "Discount", "Discount Yield", "Compound Interest", "Efficient Market", "Market Value" and "Opportunity Cost" in Downes, J. and Goodman, J. E. ''Dictionary of Finance and Investment Terms'', Baron's Financial Guides, 2003. Essentially, the party that owes money in the present purchases the right to delay the payment until some future date.See "Discount", "Compound Interest", "Efficient Markets Hypothesis", "Efficient Resource Allocation", "Pareto-Optimality", "Price", "Price Mechanism" and "Efficient Market" in Black, John, ''Oxford Dictionary of Economics'', Oxford University Press, 2002. This transaction is based on the fact that most people prefer current interest to delayed interest because of mortality effects, impatience effects, and salience effects. The discount, or charge, is the difference between the original amount owed in the present and the amount that has to be paid in the future to settle the debt.
The discount is usually associated with a ''discount rate'', which is also called the ''discount yield''.Here, the ''discount rate'' is different from the discount rate the nation's Central Bank charges financial institutions. The discount yield is the proportional share of the initial amount owed (initial liability) that must be paid to delay payment for 1 year.
:$\backslash text\; =\; \backslash frac$
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
In finance, return is a profit on an investment. It comprises any change in value of the investment, and/or cash flows (or securities, or other investments) which the investor receives from that investment, such as interest payments, coupons, c ...

the person could receive by investing this money elsewhere (in assets of similar risk
In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty about the effects/implications of an activity with respect to something that humans value (such as health, well-being, wealth, property or the environm ...

) over the given period of time covered by the delay in payment. The concept is associated with the opportunity cost
In microeconomic theory, the opportunity cost of a particular activity is the value or benefit given up by engaging in that activity, relative to engaging in an alternative activity. More effective it means if you chose one activity (for example ...

of not having use of the money for the period of time covered by the delay in payment. The relationship between the discount yield and the rate of return
In finance, return is a profit on an investment. It comprises any change in value of the investment, and/or cash flows (or securities, or other investments) which the investor receives from that investment, such as interest payments, coupons, c ...

on other financial assets is usually discussed in economic and financial theories involving the inter-relation between various market price
A price is the (usually not negative) quantity of payment or compensation given by one party to another in return for goods or services. In some situations, the price of production has a different name. If the product is a "good" in th ...

s, and the achievement of Pareto optimality through the operations in the capitalistic price mechanism, as well as in the discussion of the efficient (financial) market hypothesis.Competition from other firms who offer other financial assets that promise the market rate of return
In finance, return is a profit on an investment. It comprises any change in value of the investment, and/or cash flows (or securities, or other investments) which the investor receives from that investment, such as interest payments, coupons, c ...

forces the person who is asking for a delay in payment to offer a "discount yield" that is the same as the market rate of return. 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. Accordingly, it is the relevant "discount yield" that determines the "discount", and not the other way around.
As indicated, the rate of return is usually calculated in accordance to an annual return on investment
Return on investment (ROI) or return on costs (ROC) is a ratio between net income (over a period) and investment (costs resulting from an investment of some resources at a point in time). A high ROI means the investment's gains compare favourably ...

. Since an investor earns a return on the original principal amount of the investment as well as on any prior period investment income, investment earnings are "compounded" as time advances. Therefore, considering the fact that the "discount" must match the benefits obtained from a similar investment asset, the "discount yield" must be used within the same compounding mechanism to negotiate an increase in the size of the "discount" whenever the time period of the payment is delayed or extended. The "discount rate" is the rate at which the "discount" must grow as the delay in payment is extended. This fact is directly tied into the time value of money
The time value of money is the widely accepted conjecture that there is greater benefit to receiving a sum of money now rather than an identical sum later. It may be seen as an implication of the later-developed concept of time preference.
The ...

and its calculations.
The "time value of money" indicates there is a difference between the "future value" of a payment and the "present value" of the same payment. The rate of return on investment should be the dominant factor in evaluating the market's assessment of the difference between the future value and the present value of a payment; and it is the market's assessment that counts the most. Therefore, the "discount yield", which is predetermined by a related return on investment
Return on investment (ROI) or return on costs (ROC) is a ratio between net income (over a period) and investment (costs resulting from an investment of some resources at a point in time). A high ROI means the investment's gains compare favourably ...

that is found in the financial market
A financial market is a market in which people trade financial securities and derivatives at low transaction costs. Some of the securities include stocks and bonds, raw materials and precious metals, which are known in the financial marke ...

s, 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.
Basic calculation

If we consider the value of the original payment presently due to be ''P'', and the debtor wants to delay the payment for ''t'' years, then a marketpresent value
In economics and finance, present value (PV), also known as present discounted value, is the value of an expected income stream determined as of the date of valuation. The present value is usually less than the future value because money has in ...

, also known as the "discounted value" of a payment. Note that a payment made in the future is worth less than the same payment made today which could immediately be deposited into a bank account and earn interest, or invest in other assets. Hence we must discount future payments. Consider a payment ''F'' that is to be made ''t'' years in the future, we calculate the present value as
: $P=\backslash frac$
Suppose that we wanted to find the present value, denoted ''PV'' of $100 that will be received in five years time. If the interest rate ''r'' is 12% per year then
: $=\backslash frac=\backslash \$56.74.$
Discount rate

The discount rate which is used in financial calculations is usually chosen to be equal to thecost of capital
In economics and accounting, the cost of capital is the cost of a company's funds (both debt and equity), or from an investor's point of view is "the required rate of return on a portfolio company's existing securities". It is used to evaluate ne ...

. The cost of capital, in a financial market equilibrium, will be the same as the market capital asset pricing model
In finance, the capital asset pricing model (CAPM) is a model used to determine a theoretically appropriate required rate of return of an asset, to make decisions about adding assets to a well-diversified portfolio.
The model takes into accou ...

. This model takes into account three variables that make up the discount rate:
1. Risk free rate: The percentage of return generated by investing in risk free securities such as government bonds.
2. Beta: The measurement of how a company's stock price reacts to a change in the market. A beta higher than 1 means that a change in share price is exaggerated compared to the rest of shares in the same market. A beta less than 1 means that the share is stable and not very responsive to changes in the market. Less than 0 means that a share is moving in the opposite direction from the rest of the shares in the same market.
3. Equity market risk premium: The return on investment that investors require above the risk free rate.
: Discount rate = (risk free rate) + beta * (equity market risk premium)
Discount factor

The discount factor, ''DF(T)'', is the factor by which a future cash flow must be multiplied in order to obtain the present value. For a zero-rate (also called spot rate) ''r'', taken from ayield curve
In finance, the yield curve is a graph which depicts how the yields on debt instruments - such as bonds - vary as a function of their years remaining to maturity. Typically, the graph's horizontal or x-axis is a time line of months or ye ...

, and a time to cash flow ''T'' (in years), the discount factor is:
: $DF(T)\; =\; \backslash frac.$
In the case where the only discount rate one has is not a zero-rate (neither taken from a zero-coupon bond
A zero coupon bond (also discount bond or deep discount bond) is a bond in which the face value is repaid at the time of maturity. Unlike regular bonds, it does not make periodic interest payments or have so-called coupons, hence the term zer ...

nor converted from a swap rate to a zero-rate through bootstrapping
In general, bootstrapping usually refers to a self-starting process that is supposed to continue or grow without external input.
Etymology
Tall boots may have a tab, loop or handle at the top known as a bootstrap, allowing one to use fingers ...

) 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
The yield to maturity (YTM), book yield or redemption yield of a bond or other fixed-interest security, such as gilts, is an estimate of the total rate of return anticipated to be earned by an investor who buys a bond at a given market price, h ...

, one would use an annually-compounded discount factor:
: $DF(T)\; =\; \backslash frac.$
However, when operating in a bank, where the amount the bank can lend (and therefore get interest) is linked to the value of its asset
In financial accounting, an asset is any resource owned or controlled by a business or an economic entity. It is anything (tangible or intangible) that can be used to produce positive economic value. Assets represent value of ownership that can ...

s (including accrued interest), traders usually use daily compounding to discount cash flows. Indeed, even if the interest of the bonds it holds (for example) is paid semi-annually, the value of its book of bond will increase daily, thanks to accrued interest being accounted for, and therefore the bank will be able to re-invest these daily accrued interest (by lending additional money or buying more financial products). In that case, the discount factor is then (if the usual money market
The money market is a component of the economy that provides short-term funds. The money market deals in short-term loans, generally for a period of a year or less.
As short-term securities became a commodity, the money market became a compon ...

day count convention for the currency is ACT/360, in case of currencies such as United States dollar
The United States dollar (symbol: $; code: USD; also abbreviated US$ or U.S. Dollar, to distinguish it from other dollar-denominated currencies; referred to as the dollar, U.S. dollar, American dollar, or colloquially buck) is the official ...

, euro
The euro ( symbol: €; code: EUR) is the official currency of 19 out of the member states of the European Union
The European Union (EU) is a supranational political and economic union of member states that are located prim ...

, Japanese yen
The is the official currency of Japan. It is the third-most traded currency in the foreign exchange market, after the United States dollar (US$) and the euro. It is also widely used as a third reserve currency after the US dollar and th ...

), with ''r'' the zero-rate and ''T'' the time to cash flow in years:
: $DF(T)\; =\; \backslash frac$
or, in case the market convention for the currency being discounted is ACT/365 ( AUD, CAD
Computer-aided design (CAD) is the use of computers (or ) to aid in the creation, modification, analysis, or optimization of a design. This software is used to increase the productivity of the designer, improve the quality of design, improve co ...

, GBP
Sterling (abbreviation: stg; Other spelling styles, such as STG and Stg, are also seen. ISO code: GBP) is the currency of the United Kingdom and nine of its associated territories. The pound ( sign: £) is the main unit of sterling, and ...

):
: $DF(T)\; =\; \backslash frac.$
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). In that case, the discount factor is:
: $DF(T)\; =\; e^.\; \backslash ,$
Other discounts

For discounts inmarketing
Marketing is the process of exploring, creating, and delivering value to meet the needs of a target market in terms of goods and services; potentially including selection of a target audience; selection of certain attributes or themes to empha ...

, see 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 (determined by the manufacturer and often printed on the package) ...

, sales promotion
Sales promotion is one of the elements of the promotional mix. The primary elements in the promotional mix are advertising, personal selling, direct marketing and publicity/public relations. Sales promotion uses both media and non-media marketing ...

, and pricing. The article on discounted cash flow
The discounted cash flow (DCF) analysis is a method in finance of valuing a security, project, company, or asset using the concepts of the time value of money.
Discounted cash flow analysis is widely used in investment finance, real estate devel ...

provides an example about discounting and risks in real estate investments.
See also

*Coupon
In marketing, a coupon is a ticket or document that can be redeemed for a financial discount or rebate when purchasing a product.
Customarily, coupons are issued by manufacturers of consumer packaged goods
or by retailers, to be used in r ...

* Coupon (bond)
In finance, a coupon is the interest payment received by a bondholder from the date of issuance until the date of maturity of a bond.
Coupons are normally described in terms of the "coupon rate", which is calculated by adding the sum of coupons ...

* High-low pricing
* Hyperbolic discounting
In economics, hyperbolic discounting is a time-''inconsistent'' model of delay discounting. It is one of the cornerstones of behavioral economics and its brain-basis is actively being studied by neuroeconomics researchers.
According to the dis ...

References

NotesExternal links

{{Wiktionary Actuarial science Loans