In our preceding article of the series on bonds, we looked at what bonds are, characteristics of bonds and the various types of bonds. Our focus in this article will be on bond pricing and bond yields.
It is very important for every bond investor to know the price of the bond being purchased since it will determine the cash flows that will accrue to the investor. Bond prices are determined by key factors such as the face/ par value of the bond, the coupon rate, the prevailing market interest rates and the credit rating of the issuer among others.
Bonds can be priced at a premium, discount, or at par. A bond trades at a premium when the coupon rate is higher than the rate of return. Similarly, a bond trades at a discount when the coupon rate is lower than the rate of return. Also, a bond will trade at par value when the coupon rate is equal to the rate of return.
The price of a bond is the Present Value of all cash flows generated by the bond (i.e. coupons and face value) discounted at the required rate of return.
|+ … +|| Cn + P
C = coupon, or interest, payment per period
n = number of years until maturity
r = annualized market interest rate
P = face/par value of bond
For example, the price of a 3-year bond with a face value of GH₵1,000, a 5% annual coupon, and a required return of 2.15% is calculated as:
Bond Price= GH₵108.95
Similarly, the price of a 3-year bond with a face value of GH₵1,000, a 5% semiannual coupon, and a required return of 2.15% is calculated as:
Rate of return= =0.1075
Bond Price= GH₵1082.37
If you examine a price sheet put out by a bond dealer, you will usually see information regarding each bond’s maturity date, price and coupon rate and the bond’s reported yield. In the previous article we stated that the coupon rate is fixed. Unlike the coupon rate, the bond’s yield varies from day to day depending on the current market conditions. A bond yield is the amount of return an investor will realize on a bond. The yield of a bond can be calculated in three different ways; the current yield, the yield to maturity, and the yield to call.
The current yield is the interest payment on a bond divided by the bond’s current price.
For instance, a bond trading at a face value of GH₵2000 and pays a coupon of rate of 10% will have a current yield of
Current Yield= Annual cedi coupon interest =200
Bond price 2000
Current Yield = 10%.
Unlike the yield to maturity, the current yield does not represent the return that investors should expect to receive from holding a bond. The current yield gives information regarding the amount of cash income that a bond will generate in a given year. However, since it does not take account of the capital gains and losses that will be realized if the bond is held to maturity, it does not provide an accurate measure of the bond’s total expected return.
Yield to Maturity (YTM)
The yield to maturity is the rate of return earned on a bond if it’s held to maturity. In other words, the yield to maturity (YTM) is the total return anticipated on a bond if the bond is held until the end of its lifetime or tenor.
It is the summation of all the interest payments you will receive plus any gain (if the bond is purchased at a discount) or loss (if the bond is purchased at a premium). The yield to maturity assumes that the interest payment will be reinvested at the same rate as the current yield on the bond. Since the yield to maturity is the interest rate an investor would earn by reinvesting every coupon payment from the bond at a constant interest rate until the bond’s maturity date, the present value of all of these future cash flows equals the bond’s market price.
The yield to maturity can be quite useful for estimating whether or not buying a bond is a good investment. An investor will often determine a required yield, or the return on a bond that will make the bond worthwhile, which may vary from investor to investor. Once an investor has determined the YTM of a bond he or she is considering buying, the investor can compare the YTM with the required yield to determine if the bond is a good buy. (Source: http://www.investopedia.com/terms/r/requiredyield.asp).
Let’s assume that an investor purchased a ten year bond with a face value of GH₵ 1000 and 8% annualized coupon rate for GH₵ 936, the YTM will be:
YTM= GH₵ 80+ (GH₵ 1000- GH₵ 936)/10
Yield to Call (YTC)
Investors who purchase a callable bond (a type of bond which the issuer has the right to redeem the bonds under specified terms prior to the normal maturity date at a call price, which is greater than the face value of the bond, to the bondholder.), will not have the option to hold the bond until it matures. In other words, when the present market interest rate is lower than the stated interest rate on a callable bond, it is likely that the bond will be called because it is financially advantageous for an issuer to retire a high rate debt and issue a low rate bond. Consequently, the yield to maturity will not be realized. In such a situation, yield to call (YTC) is a better estimate of expected return on the bond than the yield to maturity (YTM). Therefore, in calculating the yield of the callable bond, there is need to replace the maturity value with the call price and take into account only those coupon payments that are expected to be received by the call date. The Yield to Call can be calculated using the formula below:
- B0 = the bond price,
- C = the annual coupon payment,
- CP = the call price,
- YTC = the yield to call on the bond, and
- CD = the number of years remaining until the call date.
Assuming the yield to call on a semiannual coupon bond with a face value of GH₵1000, a 10% coupon rate, 15 years remaining until maturity given that the bond price is GH₵1175 and it can be called 5 years from now at a call price of GH₵1100. The Yield to Call can be calculated as:
- Top of Form
- Bottom of Form
In the second article of the series on bonds, we have looked at bond pricing and bond yields. In our subsequent article, we will discuss bonds and their associated risks.
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