Pricing
Perpetual bonds are valued using the formula:
where:
- is an annual coupon interest on a bond.
- is an expected yield for maximum term available. [8]
A perpetual bond, also known colloquially as a perpetual or perp, is a bond with no maturity date, [1] therefore allowing it to be treated as equity, not as debt. Issuers pay coupons on perpetual bonds forever, and they do not have to redeem the principal. Perpetual bond cash flows are, therefore, those of a perpetuity.
Perpetual bonds are valued using the formula:
where:
In finance, a bond is a type of security under which the issuer (debtor) owes the holder (creditor) a debt, and is obliged – depending on the terms – to provide cash flow to the creditor. The timing and the amount of cash flow provided varies, depending on the economic value that is emphasized upon, thus giving rise to different types of bonds. The interest is usually payable at fixed intervals: semiannual, annual, and less often at other periods. Thus, a bond is a form of loan or IOU. Bonds provide the borrower with external funds to finance long-term investments or, in the case of government bonds, to finance current expenditure.
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.
A government bond or sovereign bond is a form of bond issued by a government to support public spending. It generally includes a commitment to pay periodic interest, called coupon payments, and to repay the face value on the maturity date.
In corporate finance, a debenture is a medium- to long-term debt instrument used by large companies to borrow money, at a fixed rate of interest. The legal term "debenture" originally referred to a document that either creates a debt or acknowledges it, but in some countries the term is now used interchangeably with bond, loan stock or note. A debenture is thus like a certificate of loan or a loan bond evidencing the company's liability to pay a specified amount with interest. Although the money raised by the debentures becomes a part of the company's capital structure, it does not become share capital. Senior debentures get paid before subordinate debentures, and there are varying rates of risk and payoff for these categories.
In finance, a perpetuity is an annuity that has no end, or a stream of cash payments that continues forever. There are few actual perpetuities in existence. For example, the United Kingdom (UK) government issued them in the past; these were known as consols and were all finally redeemed in 2015.
In finance, a convertible bond, convertible note, or convertible debt is a type of bond that the holder can convert into a specified number of shares of common stock in the issuing company or cash of equal value. It is a hybrid security with debt- and equity-like features. It originated in the mid-19th century, and was used by early speculators such as Jacob Little and Daniel Drew to counter market cornering.
United States Treasury securities, also called Treasuries or Treasurys, are government debt instruments issued by the United States Department of the Treasury to finance government spending in addition to taxation. Since 2012, U.S. government debt has been managed by the Bureau of the Fiscal Service, succeeding the Bureau of the Public Debt.
Preferred stock is a component of share capital that may have any combination of features not possessed by common stock, including properties of both an equity and a debt instrument, and is generally considered a hybrid instrument. Preferred stocks are senior to common stock but subordinate to bonds in terms of claim and may have priority over common stock in the payment of dividends and upon liquidation. Terms of the preferred stock are described in the issuing company's articles of association or articles of incorporation.
In economics and accounting, the cost of capital is the cost of a company's funds, 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 new projects of a company. It is the minimum return that investors expect for providing capital to the company, thus setting a benchmark that a new project has to meet.
In finance, bond convexity is a measure of the non-linear relationship of bond prices to changes in interest rates, and is defined as the second derivative of the price of the bond with respect to interest rates. In general, the higher the duration, the more sensitive the bond price is to the change in interest rates. Bond convexity is one of the most basic and widely used forms of convexity in finance. Convexity was based on the work of Hon-Fei Lai and popularized by Stanley Diller.
A collateralized mortgage obligation (CMO) is a type of complex debt security that repackages and directs the payments of principal and interest from a collateral pool to different types and maturities of securities, thereby meeting investor needs.
Floating rate notes (FRNs) are bonds that have a variable coupon, equal to a money market reference rate, like LIBOR or federal funds rate, plus a quoted spread. The spread is a rate that remains constant. Almost all FRNs have quarterly coupons, i.e. they pay out interest every three months. At the beginning of each coupon period, the coupon is calculated by taking the fixing of the reference rate for that day and adding the spread. A typical coupon would look like 3 months USD LIBOR +0.20%.
A corporate bond is a bond issued by a corporation in order to raise financing for a variety of reasons such as to ongoing operations, M&A, or to expand business. The term is usually applied to longer-term debt instruments, with maturity of at least one year. Corporate debt instruments with maturity shorter than one year are referred to as commercial paper.
Daily inflation-indexed bonds are bonds where the principal is indexed to inflation or deflation on a daily basis. They are thus designed to hedge the inflation risk of a bond. The first known inflation-indexed bond was issued by the Massachusetts Bay Company in 1780. The market has grown dramatically since the British government began issuing inflation-linked Gilts in 1981. As of 2019, government-issued inflation-linked bonds comprise over $3.1 trillion of the international debt market. The inflation-linked market primarily consists of sovereign bonds, with privately issued inflation-linked bonds constituting a small portion of the market.
In finance, a bond option is an option to buy or sell a bond at a certain price on or before the option expiry date. These instruments are typically traded OTC.
The bond market is a financial market where participants can issue new debt, known as the primary market, or buy and sell debt securities, known as the secondary market. This is usually in the form of bonds, but it may include notes, bills, and so on for public and private expenditures. The bond market has largely been dominated by the United States, which accounts for about 39% of the market. As of 2021, the size of the bond market is estimated to be at $119 trillion worldwide and $46 trillion for the US market, according to the Securities Industry and Financial Markets Association (SIFMA).
Hybrid securities are a broad group of securities that combine the characteristics of the two broader groups of securities, debt and equity.
Gilt-edged securities are bonds issued by the UK Government. The term is of British origin, and then referred to the debt securities issued by the Bank of England on behalf of His Majesty's Treasury, whose paper certificates had a gilt edge. Hence, they are known as gilt-edged securities, or gilts for short.
In finance, subordinated debt is debt which ranks after other debts if a company falls into liquidation or bankruptcy.
An inverse floating rate note, or simply an inverse floater, is a type of bond or other type of debt instrument used in finance whose coupon rate has an inverse relationship to short-term interest rates. With an inverse floater, as interest rates rise the coupon rate falls. The basic structure is the same as an ordinary floating rate note except for the direction in which the coupon rate is adjusted. These two structures are often used in concert.
 | This finance-related article is a stub. You can help Wikipedia by expanding it. |
