discount

discount

[v. dis-kount, dis-kount; n., adj. dis-kount]
discount, in banking and investment, fee for lending money, which the banker deducts from the loan when it is given. Thus, with a $1,000 loan at a 6% discount, the borrower receives $940 and repays $1,000. Unlike a discount, interest is paid periodically. Central banks, as in the U.S. Federal Reserve System, charge a discount when lending notes to member banks. Such a fee is often called a rediscount. When bills of exchange are cashed in advance, a percentage is discounted from the price they would bring at maturity. When securities are sold at less than par, they are said to be sold at a discount. Trade discount is a deduction from the list price. Discounts from transportation rates are called rebates. Certain banks specializing in banks' and bankers' acceptances, U.S. Treasury certificates of indebtedness, U.S. bonds approaching maturity, U.S. Treasury bills, and other high-quality, short-term credit obligations call themselves discount corporations.
or bank rate

Interest rate charged by a central bank for loans of reserve funds to commercial banks and other financial intermediaries. The discount rate is one important indicator of the condition of monetary policy in an economy. Because raising or lowering the discount rate alters the rates that commercial banks charge on loans, adjustment of the discount rate is used as a tool to combat recession and inflation.

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Set of institutions, conventions, and practices whose aim is to facilitate the lending and borrowing of money on a short-term basis. The money market is, therefore, different from the capital market, which is concerned with medium- and long-term credit. The transactions that occur on the money market involve not only banknotes but assets that can be turned into cash at short notice, such as short-term government securities and bills of exchange. Though the details and mechanism of the money market vary greatly from country to country, in all cases its basic function is to enable those with surplus short-term funds to lend and those with the need for short-term credit to borrow. This function is accomplished through middlemen who provide their services for a profit. In most countries the government plays a major role in the money market, acting both as a lender and borrower and often using its position to influence the money supply and interest rates according to its monetary policy. The U.S. money market covers financial instruments ranging from bills of exchange and government securities to funds from clearinghouses and certificates of deposit. In addition, the Federal Reserve System provides considerable short-term credit directly to the banking system. The international money market facilitates the borrowing, lending, and exchange of currencies between countries.

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In finance and economics, discounting is the process of finding the present value of an amount of cash at some future date, and along with compounding cash forms the basis of time value of money calculations. The discounted value of a cash flow is determined by reducing its value by the appropriate discount rate for each unit of time between the time when the cashflow is to be valued to the time of the cash flow. Most often the discount rate is expressed as an annual rate.

Example

To calculate the present value of a single cash flow, it is divided by one plus the interest rate for each period of time that will pass. This is expressed mathematically as raising the divisor to the power of the number of units of time.

Consider the task to find the present value PV of $100 that will be received in five years. Or equivalently, which amount of money today will grow to $100 in five years when subject to a constant discount rate?

Assuming a 12% per year interest rate it follows

{rm PV}=frac{$100}{(1+0.12)^5}=$56.74.

Discount rate

The discount rate which is used in financial calculations is usually chosen to be equal to the cost of capital. Some adjustment may be made to the discount rate to take account of risks associated with uncertain cashflows, with other developments.

The discount rates typically applied to different types of companies show significant differences:

  • Startups seeking money: 50 – 100 %
  • Early Startups: 40 – 60 %
  • Late Startups: 30 – 50%
  • Mature Companies: 10 – 25%

Reason for high discount rates for startups:

  • Reduced marketability of ownerships because stocks are not traded publicly
  • Limited number of investors willing to invest
  • Startups face high risks
  • Over optimistic forecasts by enthusiastic founders.

One method that looks into a correct discount rate is the capital asset pricing model. This model takes in 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 of the market change.

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, P(T), is the number which a future cash flow, to be received at time T, must be multiplied by in order to obtain the current present value. Thus, a fixed annually compounded discount rate is

P(T) = frac{1}{(1+r)^T}

For fixed continuously compounded discount rate we have

P(T) = e^{-rT} ,

Other discounts

For discounts in marketing, see discounts and allowances, sales promotion, and pricing.

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