Discounting

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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. [2] 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. [3] 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. [1]

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The discount is usually associated with a discount rate, which is also called the discount yield. [1] [2] [4] The discount yield is the proportional share of the initial amount owed (initial liability) that must be paid to delay payment for 1 year.

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. The relationship between the discount yield and the rate of return on other financial assets is usually discussed in economic and financial theories involving the inter-relation between various market prices, and the achievement of Pareto optimality through the operations in the capitalistic price mechanism, [2] as well as in the discussion of the efficient (financial) market hypothesis. [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. [1] 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. 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. [1] [2] 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. [2] [6] The "discount rate" is the rate at which the "discount" must grow as the delay in payment is extended. [7] This fact is directly tied into the time value of money and its calculations. [1]

The present value of $1,000, 100 years into the future. Curves representing constant discount rates of 2%, 3%, 5%, and 7% Economics of climate change chapter3 discounting curves.png
The present value of $1,000, 100 years into the future. Curves representing constant discount rates of 2%, 3%, 5%, and 7%

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. [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.

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 market rate of return denoted r on a similar investment asset means the future value of P is , [2] [7] and the discount can be calculated as

[2]

We wish to calculate the present value, 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

[2]

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

Discount rate

The discount rate which is used in financial calculations is usually chosen to be equal to the cost of capital. The cost of capital, in a financial market equilibrium, will be the same as the market rate of return 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:

The higher discount rate for start-ups reflects the various disadvantages they face, compared to established companies:

One method that looks into a correct discount rate is the capital asset pricing model. 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 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. 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 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). In that case, the discount factor is:

Other discounts

For discounts in marketing, see discounts and allowances, sales promotion, and pricing. The article on discounted cash flow provides an example about discounting and risks in real estate investments.

See also

Related Research Articles

The discounted cash flow (DCF) analysis, in financial analysis, is a method used to value a security, project, company, or asset, that incorporates the time value of money. Discounted cash flow analysis is widely used in investment finance, real estate development, corporate financial management, and patent valuation. Used in industry as early as the 1700s or 1800s, it was widely discussed in financial economics in the 1960s, and U.S. courts began employing the concept in the 1980s and 1990s.

The net present value (NPV) or net present worth (NPW) applies to a series of cash flows occurring at different times. The present value of a cash flow depends on the interval of time between now and the cash flow. It also depends on the annual effective discount rate. NPV accounts for the time value of money. It provides a method for evaluating and comparing capital projects or financial products with cash flows spread over time, as in loans, investments, payouts from insurance contracts plus many other applications.

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 interest-earning potential, a characteristic referred to as the time value of money, except during times of negative interest rates, when the present value will be equal or more than the future value. Time value can be described with the simplified phrase, "A dollar today is worth more than a dollar tomorrow". Here, 'worth more' means that its value is greater than tomorrow. A dollar today is worth more than a dollar tomorrow because the dollar can be invested and earn a day's worth of interest, making the total accumulate to a value more than a dollar by tomorrow. Interest can be compared to rent. Just as rent is paid to a landlord by a tenant without the ownership of the asset being transferred, interest is paid to a lender by a borrower who gains access to the money for a time before paying it back. By letting the borrower have access to the money, the lender has sacrificed the exchange value of this money, and is compensated for it in the form of interest. The initial amount of borrowed funds is less than the total amount of money paid to the lender.

<span class="mw-page-title-main">Interest</span> Sum paid for the use of money

In finance and economics, interest is payment from a borrower or deposit-taking financial institution to a lender or depositor of an amount above repayment of the principal sum, at a particular rate. It is distinct from a fee which the borrower may pay to the lender or some third party. It is also distinct from dividend which is paid by a company to its shareholders (owners) from its profit or reserve, but not at a particular rate decided beforehand, rather on a pro rata basis as a share in the reward gained by risk taking entrepreneurs when the revenue earned exceeds the total costs.

An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed. The total interest on an amount lent or borrowed depends on the principal sum, the interest rate, the compounding frequency, and the length of time over which it is lent, deposited, or borrowed.

<span class="mw-page-title-main">Time value of money</span> Conjecture that there is greater benefit to receiving a sum of money now rather than later

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In finance, the duration of a financial asset that consists of fixed cash flows, such as a bond, is the weighted average of the times until those fixed cash flows are received. When the price of an asset is considered as a function of yield, duration also measures the price sensitivity to yield, the rate of change of price with respect to yield, or the percentage change in price for a parallel shift in yields.

The current yield, interest yield, income yield, flat yield, market yield, mark to market yield or running yield is a financial term used in reference to bonds and other fixed-interest securities such as gilts. It is the ratio of the annual interest (coupon) payment and the bond's price:

In finance, return is a profit on an investment. It comprises any change in value of the investment, and/or cash flows which the investor receives from that investment over a specified time period, such as interest payments, coupons, cash dividends and stock dividends. It may be measured either in absolute terms or as a percentage of the amount invested. The latter is also called the holding period return.

The expectations hypothesis of the term structure of interest rates is the proposition that the long-term rate is determined purely by current and future expected short-term rates, in such a way that the expected final value of wealth from investing in a sequence of short-term bonds equals the final value of wealth from investing in long-term bonds.

In finance, a zero coupon swap (ZCS) is an interest rate derivative (IRD). In particular it is a linear IRD, that in its specification is very similar to the much more widely traded interest rate swap (IRS).

References

Notes

  1. 1 2 3 4 5 6 7 8 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.
  2. 1 2 3 4 5 6 7 8 9 10 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.
  3. ↑ Chabris, C.F.; Laibson, D.I. & Schuldt, J.P. (2008). "Intertemporal Choice". The New Palgrave Dictionary of Economics.
  4. ↑ Here, the discount rate is different from the discount rate the nation's Central Bank charges financial institutions.
  5. ↑ Kazmi, Kumail (February 26, 2021). "Discount Calculator - Find discounted product price". Smadent.com. Smadent. Retrieved February 26, 2021. Since a person can earn a return on money
  6. 1 2 3 Competition from other firms who offer other financial assets that promise the market rate of return 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.
  7. 1 2 Chiang, Alpha C. (1984). Fundamental Methods of Mathematical Economics (Third ed.). New York: McGraw-Hill. ISBN   0-07-010813-7.
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