Bond Valuation and Yield Measures - Example

Bond Yield Measures A bond serves as an instrument to show that the issuer of the bond in indebted to the bond holders. It is a kind of debt security through which the one issuing it had the debt of the holder and going by the terms of a particular bond, the issuer should pay interest to the holders and later on at a maturity date, pay the principal (Brown, 1998). Interest on bonds is paid only at fixed intervals especially monthly, semi annually and annually. A bond is always negotiable. In this sense the bond acts as a loan where the lender is the bond holder and the borrower is the one issuing it. The coupon serves as the interest. A bond is something that an investor chooses to use in order to finance long term investments or current expenditure for government bonds. Public authorities, supranational institutions, companies and credit institutions are responsible for issuing bonds. A bond is in most cases issued by way of underwriting of bond issues (Wilson, Fabozzi, CFA 1995). When this happens banks or security firms in a syndicate buy the issue to sell them later to investors. There are different measures applicable to bond yields. The measures of bond yields are important since they inform investors about the rate of return on bonds in different assumptions. Face value The face value of a bond is that amount of money paid to the person holding the bond after the date of maturity if the issuer does not default. This is also called par value or face value. Bonds that are on sale on the secondary market go up and down depending on the interest rates. Price risk: maturity, yield Price risk comes about as a result of the variation in the prices of bonds resulting from the existing inverse relationship between the bonds and interest rates. The maturity of a bond is a particular date in the future at which the principal of the investor is paid back. The maturity of a bond could be anything between one days and 30 years. In certain cases some bonds have a maturity of 100 years. The ranges in the maturity of bonds fall in the following categories. Maturities of less than five years have the short term notes, those of between 5 and 12 years have intermediate bonds while those with 12 years or more have long term bonds. The choice of maturity is dependent on the time at which the principal should be repaid and the type of investment being sought within a particular period of risk tolerance. Some people opt for short term bonds for their relative safety and stability even though their returns on investment are lower when compared to cases of long term securities. Alternative to this, those investors with the need to have higher returns overall can be go for long term securities even though their value is can easily be affected by the fluctuations in interest rates, credit risk and other market risks (Crabbe, Fabozzi, CFA, 2003). Reinvestment risk Bond investors face a risk called reinvestment risk. This risk comes as a result of reinvesting proceeds at a rate that is lower compared to the rate at which the funds were earning earlier on. This risk appears whenever the rates of interest drop in the course of time and those issuing the bonds start exercising callable bonds (Parameswaran, 2007).  By using the callable feature, the issuer is able to redeem the bond even before its maturity. Because of this, the holder of the bond gets the principal payment and in most cases this payment is at a small premium to the par value of the bond. The disadvantage of a bond call comes when the investor is compelled to remain with a lot of cash money that cannot be reinvested at a rate that is comparable to the one of the bond call. A reinvestment risk can have a very bad effect on the investment returns of a person over time. For them to get compensation for this type of risk, investors get a bigger yield on that bond compared to what they would get from a bond same to it that is not callable. Bond investors may solve the problems of reinvestment risks by delaying the predetermined call dates for differing bonds. This reduces the chances of so many bonds being called at a go (Fabozzi, Fabozzi, 2005). Credit risk Investors buy bonds and these bonds are certificates of debt which may not be stated. This money has been borrowed and should be paid back after some time with interest. Corporate bonds do not have full credit and faith of government. They only rely on the ability of the corporation to repay the debt. An investor should think about default and incorporate the risk in his decision to invest (Fabozzi, Fabozzi, 2005). As away of assessing the probability of default, investors and analysts may opt to seek out and know the coverage ratio of a company prior to any act of investment. To determine the probability of a default occurring, they analyze the cash flow and income statement of the corporation before they compare it to the debt service expense. Investment analysts believe that the investment is only safe when the cash flow and operating income or coverage is bigger compared to debt service expenses (Parameswaran, 2007).  Coupon rates i) Coupon rate > market interest rate If the coupon rate on the bond is higher than the interest rates the bond sells at a premium or above par. A drop in the interest rates below the original coupon rate causes a rise in the bond prices which means the interest is higher than what was there on the market originally. ii) Coupon rate < market interest rate If the interest rates rise above the coupon rate on the bond, the bond is then sold at a discount or simply below par. There always an inverse relationship between interest rates and the prices of bonds. A fall in interest rates is interpreted to mean that prices of bond on the market must go up. On the inverse, rising interest rates is an indication of falling bond prices (Parameswaran, 2007). This tends to happen because when the rates of interest are falling the investors try their best to capture the highest rates for the longest time possible. To accomplish this they simply take all the existing bonds with a bigger interest than the existing market rate. This high demand causes the prices of bonds to go up. On the other side, if the existing interest rates are increasing, investors get rid of those bonds with a low interest rate. This causes the prices of bonds to go down (Parameswaran, 2007).  The three kinds of bond yields i) Yield to maturity (promised yield). This is the estimated amount of what the investor gets if the bond is allowed to reach its date of maturity. Municipal bonds that are not taxable tend to have on them a tax equivalent yield whose determination depends on the tax bracket of the investor. Basically, the yield to maturity of a bond otherwise known as redemption yield is normally the internal rate of return which is the overall rate of interest that an investor earns if he purchases the bond at the present time at the market price. This is so if the bond is kept to maturity and every principal and coupon payment is done within the expected time period (Brown 1998). Contrary to what some people believe, and even what is written in many advanced financial publications, the yield to maturity is not dependent on dividend reinvestment. Instead, yield to maturity is the rate of discount at which the total cash flows for the future from both the principal and coupons are equal to bond price. Yield to maturity is expressed as the Annual Percentage Rate although normally market convention is adhered to. In some big markets the norm is quoting the yields after a half a year. This means a yearly effective yield at 10.25% is quoted as 5.00% since 1.05 x 1.05 is 1.1025 (Wilson, Fabozzi, CFA 1995).  ii) Realized yield The realized yield is different from the yield at maturity in situations where the maturity date is greater than holding period. This is to say that the selling of the security is done before the date of maturity determined during the time of purchase. For instance, one investor can buy a bond with a maturity date of 10 years at $ 1,000 with an annual coupon of 5%. The investor can sell this bond at $ 1,000 after the first year has ended and after the first coupon payment has been made. In this case, he would get a realized yield including only the coupon payment of $50. iii) Expected yield This is the yield predicted for a certain holding period that is lesser than the maturity period. Promised yield, realized yield and expected yield To calculate the promised yield, the following formula is used. P = An online or financial calculator is used to do the bulk of the calculation. A bond has Coupon rate of 11% Maturity of 18 years Par value of $1,000 First par call in 13 years Only put date in five years and putable at par value Market price of the bond is $1,169. To verify the yield as 9.077%, = = $55[17.57569] = $966.663. = = $1,000[0.2023273] = $202.327. Therefore when a 9.077% / 2 = 4.5285% semiannual interest rate is applied, the existing value for cash flows is $966.663 + $202.327 = $1,168.99 or approximately $1,169. Therefore, the yield to maturity for the bond becomes 9.077%. How interest affects bond price Interest rates and the prices of bonds move in an inverse manner to each other. The rising of interest rates means that bond prices are going down and the falling of interest rates means that bond prices will go up. For example, if a bond with a 5 percent interest rate is issued at $ 10, 000 for 5 years and the payment is made every 6 months (Brown 1998). Interest rates on the market rise up to six percent. If this bond is to be sold, it will present the problem because its price it 1% less than the market price. The buyer should be able to get a market rate for this bond yet the seller cannot change the interest rate since it has been fixed to 5%. The price to be taken for this bond can however be altered. The yearly payment of $ 500 or $100 x 500 percent must be equal to a payment of 6 percent. The face value on the bond has to be discounted to exactly $ 8, 333 to make the $ 500 fixed payment equal to a 6 percent yield on the investment of th3e buyer which is $ 8, 333 x 6 percent which equal to $ 500. If the rates of interest dropped instead of rising, the bond can be sold at a premium over the face value since fixed interest rate would be bigger than the market rate (Wilson, Fabozzi, CFA 1995).  Conclusion In conclusion, this essay has examined the various bond yield measures. The essay also explores how the changes in the rates of interest affect the prices of bonds. A bond is something that an investor chooses to use in order to finance long term investments or current expenditure for government bonds. Various risks are associated with bond yields. These risks include price risks, reinvestment risk and credit risk. Coupon rates or bond prices vary inversely with the market interest rates such that when one goes down the other rises. There are three kinds of bond yields which include yield to maturity, realized yield and expected yield. Interest rates have an impact on bond prices. The rising of interest rates means that bond prices are going down and the falling of interest rates means that bond prices will go up. References Brown, P. J. (1998). Bond Markets: Structures and Yield Calculations. Global Professional Publishers.  Crabbe, L. E., Fabozzi, F. J., CFA (2003). Managing a Corporate Bond Portfolio. John Wiley & Sons. Fabozzi, F., Fabozzi, J. (2005). The Handbook of Fixed Income Securities. Chapter 5- Bond Pricing, Yield Measures and Total Return. McGraw-Hill. Parameswaran, S. (2007). Bond Valuation, Yield Measures and the Term Structure. Tata McGraw-Hill Education. Wilson, R.C., Fabozzi, F.J., CFA (1995). Corporate Bonds: Structure and Analysis. John Wiley & Sons. Read More