When you are buying a bond, the first thing that you will want to know is the returns that you can get for it. For stocks or unit trusts, the return will be the difference between the price that you bought and sold the investment plus dividends, if any. However, the dividends tend to be a relatively small contributor to total returns. For bonds, the interest component (coupon payments) is often the main contributor to total returns. In addition, changes in the prices of the bonds affect the overall returns. Hence, bond returns are calculated differently. We need to look at the periodic coupon payments and the current price of the bond to determine the yield or return for the bond.
For example, let's assume you are thinking of purchasing a bond that matures in 10 years and is currently priced at $100. Coupon payments are made annually at 4% of the $100 face value, which means that $4 is paid to you annually. The face value of the bond will be returned to you after 10 years. Since the coupon that you get annually is $4 and $100 will be returned to you at the end of 10 years, your annualised yield would be 4%.
Let's take another scenario, where you purchase the same bond at a higher price, for example $105. What will happen? You will still continue to get an annual coupon payment of $4 and will be paid the face value of your bond when it matures. In this case, the yield to maturity that you obtain will be 3.4%. What happens is that because you are paying a higher price for the bond, you will have a smaller yield.
However, the reverse is true if you had purchased the bond at a lower price. Let's assume the bond costs $95. You still obtain a $4 coupon annually with the face value of $100 returned to you when the bond matures. The yield to maturity that you will get is 4.6%. This is because $4 works out to be more than 4% of the $95 you paid for the bond and upon maturity you get a capital profit of $5.
Calculating Yield To Maturity
The yields calculated in the examples above are the annualised return that you will get when you hold the bonds to maturity. Now, how do you calculate this yield to maturity? We can use the formula below:
P = c(1 + r)-1 + c(1 + r)-2 + . . . + c(1 + r)-n + B(1 + r)-n
r = yield to maturity
c = annual coupon payment (in dollars)
n = number of years to maturity
B = par value
P = purchase price
Using the figures from the second example when the bond price is $105:
105 = 4(1 + r)-1 + 4(1 + r)-2 + . . . + 4(1 + r)-10 + 100(1 + r)-10
r = yield to maturity
The "r" calculated using this formula will be the return that you will be getting when the bond is held until it matures and assuming that the periodic coupon payments are reinvested at the same yield. We can use a bond calculator to calculate the "r". In this example, the "r" is 3.4%.
On our website, we have a bond calculator that can calculate the yield to maturity. This is a useful tool if you want to know the price to purchase a bond in order to attain a specific yield.
Coupon Payments Versus Yield
Investors often buy bonds with a high periodic coupon payment, without looking at its yield to maturity. This is a mistake as it is the yield to maturity that accurately reflects the bond's returns. Let us look at the example in table below:
Table 1: Coupon Versus Yield Prices as at 5 Dec 2004
When you look at the bond with a maturity of 5.03 years, you can see that although this bond has a high annual coupon rate of 4.375% the yield is only 2.9%. The reason behind the low yield is the high current price of $107.05. Looking at the bond with a maturity of 14.65 years, we can see that the coupon is 4% but the yield of this bond is 4.2%. This is due to the low current price of $97.90. Note that the offer price is the price that we can purchase the bond. The offer yield is the yield to maturity by purchasing at offer price.
Investing in bonds is unlike stocks or unit trusts where you look at stock valuations to determine whether if it is a good buy. For bonds, it is important to take note of the yield that you will get from purchasing a bond at a certain price. The yield to maturity will eventually be the profit that you get from holding the bond until maturity and assuming reinvestment of the coupon payments at the same yield. The yield to maturity takes into account all the future cash flows that you will get from the bond. Future cash flows will include periodic coupon payments and the principal payment when the bond matures.
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