A bond has a par value, a maturity date, and a coupon rate. The maturity date is the date the company must repay the investor an amount equal to the par value. The par value is the amount the lender will receive at the maturity date. The coupon rate is the interest rate on the bond. A coupon is typically semi-annually. So if the bond has a coupon rate of 8%, the investor will receive two payments per year, each equal to 4% of the bond’s par value.

Rating agencies rate the creditworthiness of bonds. High quality bonds are considered investment grade. Low quality bonds are considered noninvestment grade, or junk bonds.

Zero coupon bonds are a debt security that does not have periodic interest payments. The bond, issued at a deep discount from par value, compensates for the lack of interest payments. Then they are redeemed at par value at maturity.

Stripped Bond

Banks or dealers create strip bonds, synthetic zero-coupon bonds. Therefore, separate the principal amount (the corpus) from the interest payments (the coupon payments) and sell the two parts separately to investors. Thus, this creates zero-coupon bonds. The investors then receive a lump sum at the maturity date, equal to the value of corpus or the coupon payments, depending on their contract. The contracts are known as STRIPS (Separate Trading of Registered Interest and Principal of Securities).

Imputed Interest

According to the IRS, the holder of a zero-coupon bond owes income tax on the bond’s imputed interest. Imputed interest refers to the implied periodic interest payments that the bondholder does not actually receive until maturity. Imputed interest on zero-coupon bonds issued by municipalities is tax exempt.

The yield to maturity (YTM) of a bond represents the annual rate of return for the full life of the bond. The YTM assumes the investor will hold the bond to maturity, and that all interestpayments will (hypothetically) be reinvested at the YTM rate.

For example, a bond with a maturity of 10 years and a YTM of 5% implies that buying this bond and holding it for the full ten years would give the investor an annual return of 5% on the invested capital.

The current yield of a bond differs from the yield to maturity. The current yield of a bond represents the implied return on the bond for one year, given the coupon payments and the current marketprice. For example, if an investor buys a bond for $95 with an annual coupon payment of $5, the current yield for that bond would be 5.26% (.0526 = 5/95). The current yield formula is:

Current Yield = Annual Payment/Current Market Price

Yield to Maturity – Bond Price

If a bond’s yield to maturity is greater than its current yield, the bond is selling at a discount, or a price less than par value. If YTM is less than current yield, the bond is selling at a premium, or a price above the par value. If YTM equals current yield, the bond is selling at par value.

Par Value Price – Yield to Maturity = Current Yield

Bond Yield To Maturity Formula

The formula for a bond’s yield to maturity is complicated and solving it mathematically often requires a process of trial and error. It is possible to get an approximate YTM for a bond using a bond yield table. The best way to compute the YTM for a bond is to use a financial calculator. Using a financial calculator, punching in four out of five of the relevant variables (price, par value, maturity, coupon payment, YTM) will give you the fifth variable.

To calculate the bond’s YTM, solve this formula for YTM:

A yield curve can be normal, flat, or inverted. In a normal yield curve, investments with longer maturities have higher yields than investments with shorter maturities. Whereas, in a flat yield curve, investments with long maturities and investments with short maturities have similar yields. In an inverted yield curve, investments with shorter maturities have higher yields than investments with longer maturities.

Consider a normal yield curve a sign of a healthy economy. However, if long-term yields are significantly higher than short-term yields, it may be a sign of inflation. A flat yield curve is considered a sign of a transitional period in an economy. An inverted yield curve is considered a sign of a troubled economy, or even a recession.

Because treasury bills do not pay coupons they are sold at a discount in an auction held by the Bureau of Public Debt. A t-bill is essentially risk free and highly liquid due to its short term nature. There are four different types of t bills which are sold according to their respective maturities. T bills are sold with maturities of 28 days, 91 days, 182 days, and 364 days. T-bills are also sold in certain denominations which range from $10,000 to $1 million.

Treasury Bill (t bill) Formula

Treasury bill rates can be calculated using the following formula:

((Face Value – Purchase Price)/Face Value) * (360/Days until Maturity) = Yield or Rate

Treasury Bills (t bills) Example

A $10,000 face value 91 day (3 month) t bill is currently being sold at auction. Lumber Co. purchases this t bill for a discount at a price of $9,833. What is the yield on this particular treasury bill at the time of sale.

1) Bond prices and their yields are inversely related. Thus, if a interest rate increases the bond price falls or drops to a discount, and if the interest rate drops the bondprices rises or is considered at a premium. The fluctuations in the market is an interest rate risk that must be accounted for accordingly when investing.

2) The longer the maturity the more sensitive a bond or debt instrument is to interest rate changes. As a bond comes closer to its maturity the price fluctuates less and less from changes in the market. This means that a shorter term security has less interest raterisk.

3) An increase in interest rates will yield a much larger change in a bond than a decrease of the same amount. This means that a bond has the ability to lose its overall value in price than it does in gaining or selling at a premium.

4) Prices of low coupon bonds are much more sensitive to market yield changes than the prices of higher coupon bonds.

5) A bond or debt instrument’s price is much more sensitive if that particular bond has a lower yield to maturity. Thus, the higher the yield to maturity the less sensitive the bond price.

Note: None of these factors matter if a person plans on holding a bond or debt instrument until its maturity. If a person holds a bond until its maturity the fact that interest rates fluctuate is irrelevant because all bonds pay coupons and finally the face value at maturity. This means that this person will automatically make the desired return and therefore need not worry about interest raterisk measures.

Interest Rate Risk Example

Chuck wants to invest in a debt instrument, and comes across some lucrative bonds. He has narrowed the search down to two, and is trying to decide between bond A and bond B. Both bonds pay a coupon of 8% and have a current yield to maturity of 6%. The only large difference between them is that the maturity for bond A is 5 years and B has a maturity of 30 years. After consulting with a close friend Chuck decides to buy bond A because his friend tells him there is less interest rate risk inherent in bond A.

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