Zero coupon bond payment formula

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Contents:
  1. Zero Coupon Bond Value Formula: How to Calculate Value of Zero Coupon
  2. Bond Valuation
  3. 2) Key Bond Characteristics

Some bonds contain a provision that enables the buyer to sell the bond back to the issuer at a pre-specified price prior to maturity. This price is known as the put price. A bond containing such a provision is said to be putable. This provision enables bond holders to benefit from rising interest rates since the bond can be sold and the proceeds reinvested at a higher yield than the original bond. Since a put provision is advantageous to the bond holder, the bond will offer a lower yield than an otherwise identical bond with no put provision.

Some bonds are issued with a provision that requires the issuer to repurchase a fixed percentage of the outstanding bonds each year, regardless of the level of interest rates. A sinking fund reduces the possibility of default ; default occurs when a bond issuer is unable to make promised payments in a timely manner. Since a sinking fund reduces credit risk to bond holders, these bonds can be offered with a lower yield than an otherwise identical bond with no sinking fund. Bonds are issued by borrowers to raise funds for long-term investments; the main issuers of bonds in the U.

Treasury securities are issued by the U. These are free of default risk , which is the risk that the investor will not receive all promised payments. They are not taxed by state and local governments, but are taxed at the federal level. Another key difference between these securities is that Treasury bills are sold at a discount from their face value and redeemed at face value; Treasury notes and bonds are sold and redeemed at face value and pay semi-annual coupons to investors.

Corporations can raise funds by issuing debt in the form of corporate bonds.

Zero Coupon Bond Value Formula: How to Calculate Value of Zero Coupon

These bonds offer a higher promised coupon rate than Treasuries, but expose investors to default risk. The riskiest corporations offer the highest coupon rates to investors as compensation for default risk.


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  • What is a Zero Coupon Bond?.
  • What it is:!

A municipal bond is issued by a state or local government; as a result, they carry little or no default risk. Occasionally, municipalities do default on their debts; in , the city of Detroit filed for bankruptcy as a result of being unable to pay its debts. Municipal bonds offer an extremely favorable tax treatment to investors. They are not taxed by federal, state or local governments as long as the bond holder lives in the municipality in which the bonds were issued. As a result, municipal bonds can be issued with very low yields.

Foreign bonds are issued by foreign governments and corporations and are denominated in dollars.

If they are denominated in a foreign currency, they are known as eurobonds. Dollar-denominated bonds issued in the U. This formula shows that the price of a bond is the present value of its promised cash flows. The bond makes annual coupon payments. These results also demonstrate that there is an inverse relationship between yields and bond prices:. For a bond that makes semi-annual coupon payments, the following adjustments must be made to the pricing formula:.

Bond Valuation

As an alternative to this pricing formula, a bond may be priced by treating the coupons as an annuity; the price is therefore equal to the present value of an annuity the coupons plus the present value of a sum the face value. This method of valuing bonds will use the formula:. The bond in the previous example can be priced using this alternate bond valuation formula as follows:.

A zero-coupon bond does not make any coupon payments; instead, it is sold to investors at a discount from face value. The difference between the price paid for the bond and the face value, known as a capital gain , is the return to the investor. The pricing formula for a zero coupon bond is:. What is the market price of this bond? In order to be consistent with coupon-bearing bonds, where coupons are typically made on a semi-annual basis, the yield will be divided by 2, and the number of periods will be multiplied by There are different types of yield measures that may be used to represent the approximate return to a bond.

These include:. This equals the rate of return earned by a bond holder known as the holding period return if:. It is impossible to solve for the yield to maturity algebraically; instead, this must be done using a financial calculator or Microsoft Excel. The variables in brackets fv, type and guess are optional values; the value of type is set to zero if it is not specified.

Guess can be used to provide an initial estimate of the rate, which could potentially speed up the calculation time. Note that either pv or fv must be negative, and the other must be positive. The negative value is considered to be a cash outflow, and the positive value is considered to be a cash inflow. In other words, if you invest it, let's just take an example.

But the zero coupons build that in, so you get actually about twice as much appreciation for given declining interest rates with a zero coupon, as with a coupon bond, and the longer the maturity, the more bang for the buck. Now, it works both ways. You'll lose more money if rates go up. But actually, I started in with the zero coupon bonds from my own account in And by the mids, the Shilling family, on that one investment, had achieved financial independence. Well, I've never, never, never bought Treasury bonds for yield.

I couldn't care less what the yield is as long as it's going down. Because when it goes down, they increase in price, and I bought it for the same reason most people buy stocks. Most people don't buy stocks for dividends, you have some for utilities and real estate investments, but most people are looking for appreciation. And that's what my interest is in Treasury bonds. That difference in price is capital appreciation.

The first disadvantage is they do not throw off any income as the capital is stored in the bond. In some countries the imputed interest may be taxed as income even though the bond has not yet been redeemed or reached maturity. The IRS requires zero-coupon bond holders to pay tax on the "phantom" imputed interest income just as they would if they had received coupon payments, even though there wasn't any interest paid to the bond holder.

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For the subsequent years you would start with the base from prior years to calculate the new imputed interest value. The second major disadvantage is when interest rates rise significantly they can see a drastic decline in capital value, as they have a significant duration risk because no capital is paid out until the bond reaches maturity risk remains embedded in the instrument until it is redeemed. Bonds can be traded on the secondary market, with valuations reflecting the current interest rate envirnoment.

Treasury Instruments Bills, Notes, Bonds Many people refer to any fixed-income treasury instrument as a bond, however the duration determines the specific name.

Bills: These mature in 1 year or less. Longer duration bonds are more sensitive to shifts in interest rates. And zero-coupon long duration bonds are more sensitive to rate shifts than bonds which regularly pay interest. Typically the yield curve is upward sloping with longer duration bonds offering a higher return to compensate for the added risk. When shorter duration bonds offer a higher yield than longer duration bonds that is called yield curve inversion. If investors are willing to lock their money up for a longer period of time at low rates it usually indicates they think there might be significant economic risks ahead.

2) Key Bond Characteristics

Inversion frequently happens anywhere from about 6 to 18 months before a recession happens. The most widely watched segment is the 2-year versus the year. This limitatio does not apply to rollover reinvestment. Rate data sources: Treasury. Some municipal bonds are exempt from income taxes, which boost their equivalent yield when compared against other bonds. Gift purchases are attributed to the recipient. The Treasury also offers zero-percent certificate of indebtedness C of I which can be used to fund TreasuryDirect purchases.