## Discounting and Rates

Discounting is a financial 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. Essentially, the party that owes money in the present purchases the right to delay the payment until some future date.

Discounting is the process of determining the present value of a payment or a stream of payments that is to be received in the future. Given the time value of money, a dollar is worth more today than it would be worth tomorrow. Discounting is the primary factor used in pricing a stream of tomorrow’s cash flows.

For example, the coupon payments found in a regular bond are discounted by a certain interest rate and added together with the discounted par value to determine the bond’s current value. From a business perspective, an asset has no value unless it can produce cash flows in the future. Stocks pay dividends. Bonds pay interest, and projects provide investors with incremental future cash flows. The value of those future cash flows in today’s terms is calculated by applying a discount factor to future cash flows.

Time Value of Money and Discounting

When a car is on sale for 10% off, it represents a discount to the price of the car. The same concept of discounting is used to value and price financial assets. For example, the discounted, or present value, is the value of the bond today. The future value is the value of the bond at some time in the future. The difference in value between the future and the present is created by discounting the future back to the present using a discount factor, which is a function of time and interest rates.

For example, a bond can have a par value of \$1,000 and be priced at a 20% discount, which is \$800. In other words, the investor can purchase the bond today for a discount and receive the full face value of the bond at maturity. The difference is the investor’s return. A larger discount results in a greater return, which is a function of risk.

Present Value

Present value (PV) is the current worth of a future sum of money or stream of cash flows given a specified rate of return. Future cash flows are discounted at the discount rate, and the higher the discount rate, the lower the present value of the future cash flows. Determining the appropriate discount rate is the key to properly valuing future cash flows, whether they be earnings or obligations.

PV is also referred to as the discounted value. The basis is that receiving \$1,000 now is worth more than \$1,000 five years from now, because if you got the money now, you could invest it and receive an additional return over the five years.

Discounting and Risk

In general, a higher the discount means that there is a greater the level of risk associated with an investment and its future cash flows. For example, the cash flows of company earnings are discounted back at the cost of capital in the discounted cash flows model. In other words, future cash flows are discounted back at a rate equal to the cost of obtaining the funds required to finance the cash flows. A higher interest rate paid on debt also equates with a higher level of risk, which generates a higher discount and lowers the present value of the bond. Indeed, junk bonds are sold at a deep discount. Likewise, a higher the level of risk associated with a particular stock, represented as beta in the capital asset pricing model, means a higher discount, which lowers the present value of the stock.

Discount Window

The discount window is a central bank lending facility meant to help commercial banks manage short-term liquidity needs.

The Federal Reserve and other central banks maintain discount windows, referring to the loans they make at an administered discount rate to commercial banks and other deposit-taking firms. Discount window borrowing tends to be short-term – usually overnight – and collateralized. These loans are different from the uncollateralized lending banks with deposits at central banks do among themselves; in the U.S. these loans are made at the federal funds rate, which is lower than the discount rate.

Banks borrow at the discount window when they are experiencing short-term liquidity shortfalls and need a quick cash infusion. (The term refers to the now-obsolete practice of sending bank employees to actual, physical windows in Federal Reserve branch lobbies to ask for loans.) Banks generally prefer to borrow from other banks, since the rate is cheaper and the loans do not require collateral. For this reason discount window borrowing jumps during spells of economy-wide distress, when all banks are experiencing some degree of liquidity pressure: after the tech bubble burst in 2001, for example, borrowing at the Fed’s discount window hit its highest level in 15 years.

The 2008 financial crisis saw the Fed’s discount window take on a central role in maintaining a semblance of financial stability. Lending periods were extended from overnight to 30 days, then 90. The rate was cut to within 0.25 percentage points of the federal funds rate; the spread had previously been 1 pp, and as of November 2017 it is 0.5 pp. In October 2008, the month after Lehman Brothers’ collapse, banks borrowed \$403.5 billion at the discount window; the previous recession had seen borrowing peak at \$3.4 billion (September 2001).

The Fed’s discount window actually lends at three rates; discount rate is shorthand for the primary rate offered to the most financially sound institutions.

Discount Rate

The discount rate is the interest rate charged to commercial banks and other depository institutions for loans received from the Federal Reserve’s discount window.

The discount rate also refers to the interest rate used in discounted cash flow analysis to determine the present value of future cash flows.

The Fed’s discount rate is an administered rate set by the boards of the Federal Reserve Banks and approved by the Board of Governors; it is not a market rate. The Fed’s 12 regional branches offer very short-term – generally overnight – loans to banks that are experiencing funding shortfalls in order to prevent liquidity problems or, in the worst-case scenario, bank failures. This lending facility is known as the deposit window; it is different from the interbank borrowing that institutions with deposits at the Fed do among themselves, which is governed by the federal funds rate.

The discount rate is actually three separate but related rates. The primary credit rate, which is sometimes referred to simply as the discount rate and should not be confused with the prime rate, is available to institutions with good credit. The secondary credit rate is available to institutions that do not qualify for the primary rate and is set 50 basis points higher than the primary rate. Both of these rates are set without regard to market rates. The seasonal credit rate is available to institutions that experience predictable seasonal fluctuations, such as banks serving agricultural and tourist communities. It is set every 14 days at the average of the daily effective federal funds rate and the three-month CD rate over the previous 14 days, meaning it’s affected by market interest rates.

Discounted Cash Flow Analysis

The discount rate also refers to the rate used to determine the present value of cash flows in discounted cash flow analysis. For example, to determine the present value of \$1,000 a year from now, you need to discount it by a particular interest rate

Bank Discount Rate

The bank discount rate is the interest rate for short-term money-market instruments like commercial paper and Treasury bills. The bank discount rate is based on the instrument’s par value and the amount of the discount. The bank discount rate is the required rate of return of a safe investment guaranteed by the bank.

Bank Rate

A bank rate is the interest rate at which a nation’s central bank lends money to domestic banks, often in the form of very short-term loans. Managing the bank rate is method by which central banks affect economic activity. Lower bank rates can help to expand the economy by lowering the cost of funds for borrowers, and higher bank rates help to reign in the economy when inflation is higher than desired.

In the United States, the bank rate is often referred to as the federal funds rate or the discount rate. In the United States, the Board of Governors of the Federal Reserve System sets the discount rate as well as the reserve requirements for banks. The Federal Open Market Committee (FOMC) buys or sells Treasury securities to regulate the money supply. Together, the federal funds rate, the value of Treasury bonds and reserve requirements have a huge impact on the economy. The management of the money supply in this way is referred to as monetary policy.

Discount Rate Versus Overnight Rate

The discount rate, or bank rate, is sometimes confused with the overnight rate. While the bank rate refers to the rate the central bank charges banks to borrow funds, the overnight rate refers to the rate banks charge each other when they borrow funds among themselves. Banks borrow money from each other to cover deficiencies in their reserves.

Banks are required to have a certain percentage of their deposits on hand as reserve. If they don’t have enough cash at the end of the day to satisfy their reserve requirements, they borrow it from another bank at the overnight rate. If the discount rate falls below the overnight rate, banks typically turn to the central bank, rather than each other, to borrow funds. As a result, the discount rate has the potential to push the overnight rate up or down.

How the Bank Rate Affects Consumer Interest Rates

As the bank rate has such a strong effect on the overnight rate, it also affects consumer lending rates. Banks charge their best, most creditworthy customers a rate that is very close to the overnight rate, and they charge their other customers a rate that is a bit higher. For example, if the bank rate is 0.75%, banks are likely to charge their customers relatively low interest rates. In contrast, if the discount rate is 12% or a similarly high rate, banks are going to charge borrowers comparatively higher interest rates.

Discounted Future Earnings

Discounted future earnings is a method of valuation used to estimate a firm’s worth. The discounted future earnings method uses forecasts for the earnings of a firm and the firm’s estimated terminal value at a future date, and discounts these back to the present using an appropriate discount rate. The sum of the discounted future earnings and discounted terminal value equals the estimated value of the firm.

As with any estimate based on forecasts, the estimated value of the firm using the discounted future earnings method is only as good as the inputs – the future earnings, terminal value and the discount rate. While these may be based on rigorous research and analysis, the problem is that even small changes in the inputs can give rise to widely differing estimated values.

Market Discount

The market discount is the difference between a bond’s stated redemption price and its purchase price on the secondary market, if it has been purchased at a price below par. Market discount arises when a bond’s value on the secondary market decreases after it has been issued, usually because of an increase in interest rates. In the case of original issue discount (OID) securities such as zero-coupon bonds, the market discount is the difference between the purchase price and the issue price plus accrued OID.

Market discount is not subject to taxation annually in the U.S., but it becomes taxable as ordinary interest income in the year that the bond is sold or redeemed. The bond investor can also elect to include amortized market discount annually in income for tax purposes, although this would mean paying tax on it now rather than in the future. Note that market discount is taxable even if regular interest income from the bond in question is tax-exempt, such as for municipal securities.

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