Introduction
It is critical for investors to understand how to calculate the value of a bond and the risk associated with bonds. This paper uses General Dynamic’s bonds to show the impact of changes in interest rates on the value of a bond. A bond is recognized as a long-term debt which is issued by a company to raise additional capital. When investors buy bonds, they become creditors of the company but have no voting right. If a firm fails to meet the obligation of its debt holders, they have a greater claim on the asset of a company than equity shareholders. Usually, bonds are exchanged at a higher nominal value than the par value or a price below par value. When a bond is selling above the par value, it is said to be trading at a premium. However, if the bond is trading below the par value, it is said to be selling at a discount. Therefore, it is imperative that investors understand how to value bonds in order to earn adequate returns on their investment. The theory behind bond valuation helps investors to understand the expected yield when they decided to purchase a bond (Bond & Brown, 2011, p. 34). Investors should understand when a bond is selling at a premium or discount. In part I, it is assumed that the bond outstanding will mature in 20 years. This bond has a coupon interest rate of 6.5% and a par value of $1000. The bond has a yield to maturity of 8 percent. To calculate the value of the bond, the calculations were done in the Microsoft Excel provided as an appendix. However, the results of the calculation are shown in tables for easy interpretation the bond selling at a premium or discount.
In order to determine whether a bond is selling at a premium of discount, we must calculate the value of the bond. Ideally, the value of a bond is the present value of both interest payments and maturity. The interest rate is calculated by multiplying the coupon interest rate with the par value. In this case, the interest rate is the value of 6.5%*1000= $65. The value of the bond to maturity is the present value of the par value of debt which is given as $1000.
In the example above, the yield to maturity can also be referred to as the required rate of return of the bond. It can also be called the discounted rate of the present value of future cash flow of the bond. Therefore, the yield to maturity, which is given as 8%, is the discounting factor. It will be used to discount the interest payments and the lump sum during maturity of the bond. As a rule, when the coupon interest rate is higher than the yield to maturity, the bond is said to be trading at a discount. Conversely, if the coupon interest rate is lower than the yield to maturity, the bond will be trading at a discount (Damodaran, 2002, p. 883).
From the calculation in the excel, the present value of the bond is $852.67. The value of the bond is calculated as shown in the table below.
From the table above, it can be seen that the value of a bond is the total present value of interest and the present value of maturity. Since the bond matures after 20 years, the present value of the bond will be in lump sum. The present value of maturity will be the present value at par value of $1000. From the calculations above, the bond is selling at a discount because the par value is higher than the value of the bond. As a rule, a bond is said to be selling at a discount if the par value is higher than the value of the bond (Ulrici, 2007, p. 3). It is easy to determine when a bond is trading at a premium or discount by looking at the coupon rate and the yield to maturity. A bond that is trading at a discount has a higher yield to maturity or required rate of return. In this example, General Dynamics’ bond is trading at a discount because the required rate of return (8%) is higher than the coupon interest rate (6.5%). Since investors want a high yield, they will pay less for this bond because it pays low-interest rate. It should be noted that investors receive annual interest rates depending on the number of bonds held. The coupon rate multiplied by the par value of the bond determines the interest rate. Therefore, investors pay lower prices for a bond that is paying small coupon interest rates.
In bond valuation, lower prices mean the cost of borrowing will be high. The price investors are willing to pay is determined by the interest rate of the debt. For instance, if the prevailing interest rate rises above the rate at which the bond was issued, the prices will drop. This is because there will be new bonds in the market that will be issued at a higher coupon rate which will make the old bond unattractive to investors (Parameswaran, 2007, p. 19). However, the bond can be made attractive by lowering the price to compensate the impact of low-interest rates. If the interest rate goes up, the price of the bond will decline. When interest rates decline, the prevailing prices will rise, which will allow investors to sell their bond at a higher price. In some cases, investors are willing to pay a premium price for bonds that pay higher interest rates. However, it is normal for investors to pay lower prices for bonds that pay low coupon interest rates in comparison with the prevailing interest rates.
Value of a bond when its pay semiannually
Semiannual compounding is normal in the market because many bonds make two interest payments. When calculating the price of a bond that pays semiannual compounding, we divided both the coupon interest and yield to maturity by two. In this case, the coupon interest will be 6.5/2 = 3.25. Since the bond is paying semiannually, the number of payments will double or each payment will be half the annual payments. Therefore, in this case, the number of years will double to 40 payments. Although the number of payments doubles, the value of the bond does not change as shown below.
When the interest rate changes, the market price of the bond will either increase or decrease. However, a long-term bond fluctuates more than the short-term bond prices. The price of a bond is determined by the prevailing interest rates in the market. If the interest rates increase, the price of the bond will drop because there will be new bonds issued at a higher coupon rate which will be more attractive to investors. However, if the interest rate decreases, the value of the bond will increase which will allow investors who holder it to sell it because they will earn a high return. In the example given, the price of the bond will increase because interest rates declined. During a recession, interest rates decline, this makes the bond attractive to investors. This means that it will be trading at a premium or above the par value. The value of the bond is shown in the table below.
From the calculations on the table, it can be seen that the value of the bond increased to $1,186.94. Therefore, we can conclude that the value of a bond increases when the interest rate decreases because the interest rate is inversely related to the value of a bond.
Calculating the yield of a bond
From the example given, the bond is trading at $1,125 with a par value of $1000. If the market interest rate is 10.25%, then we can be able to calculate the coupon interest rate. From this information, we can infer that the bond is trading at a premium because the market price is higher than the par value. This also shows that the coupon interest is higher than the yield to maturity. Therefore, we can calculate the value of the bond using 12% to determine if it is the current yield.
From the calculations, the current yield of the bond is 12%.
Comparing reinvestment risk and interest rate risk
There are many differences and similarities between interest rate risk and reinvestment risk. Interest rate risk relates to the value of a bond while reinvestment risk relates to the income generated in a portfolio (Olsens, 2009, p. 904). Interest rate risk is associated with long-term bonds. For instance, an investor who holds a long-term bond will be exposed to interest rate risk because the value of the bond will decline when interest rates increase. However, long-term bondholders do not face reinvestment risk. If an investor purchases short-term bonds, they will be exposed to considerable reinvestment risk because the amount of interest received will fluctuate with changing interest rates. In other words, no bond in the market can be considered risk-free. In fact, even most of the risk-free Treasury bonds are exposed to both interest rate risk and reinvestment risk.
The price of a bond shows the trading activities in the market which can be altered by those who have large sums of money to determine bond prices. Graham, Smart and Megginson (2012, p. 121) argue that although some investors are risk averse to reinvestment risk than interest rate risk, marginal investors are more likely to be risk averse to interest rate risk than reinvestment risk. Marginal investors will only buy bonds that expose them to interest rate risk if the expected rate of return is higher than short-term bonds. When holding all factors constant, the additional return is the risk premium (Keane, 2013). Reinvestment risk occurs when the bond (which is a portion of a loan to an entity) is paid back before it matures. When interest rate increases, there is less likelihood that companies will call back their bond which reduces reinvestment risk. However, when interest rate declines, there is high likelihood a bond will be called before it reaches its maturity. Interest related risk is inversely related to reinvestment risk.
Investors to hedge against both investment and reinvestment risk can use many strategies. For instance, the simplest way to hedge against interest and reinvestment risk when interest rate increases is by holding the bond to maturity (Fang & Moser, 2009, p. 56). This strategy will allow the investor to receive the principal at maturity. This method has been proved to eliminate interest rate risk because the investor will receive all the money they invested in the bond at maturity depending on market price.
The other alternative is to invest in a bond fund when interest rates are expected to increase. This fund absorbs interest rate risk which will see their market value decline. An investor can also be able to hedge against reinvestment risk and interest rate risk by investing in short-term maturing bonds. The period of a bond determines its sensitivity to prices changes in the market. When an investor purchases a bond with a short maturity period, they are less likely to suffer from interest rate risk.
References
Bond, P. & Brown, P. (2011). Rating valuation principles and practice. Amsterdam: Elsevier/EG Books.
Damodaran, A. (2002). Investment valuation: tools and techniques for determining the value of any asset. New York: Wiley.
Fang, Z., & Moser, J. (2009). Use of Derivatives and Bank Holding Companies’ Interest-Rate Risk. Banking & Finance Review, 1(1), 51-62.
Graham, J., Smart, S., & Megginson, W. (2012). Introduction to corporate finance. Australia Mason, Ohio: South-Western/Cengage Learning.
Keane, F. M. (2013). Securities Loans Collateralized by Cash: Reinvestment Risk, Run Risk, and Incentive Issues. Current Issues in Economics & Finance, 19(3), 1-8.
Olsens, R. A. (2009). The effect of interest-rate risk on liquidity premiums: an empirical investigation. Journal of Financial & Quantitative Analysis, 9(5), 901-910.
Parameswaran, S. (2007). Bond valuation, yield measures and the term structure. New Delhi: Tata McGraw-Hill.
Ulrici, V. (2007). Bond valuation in emerging markets. LohmarKöln: Eul.
Appendix
