Value of Bonds
Bonds are debt securities issued by companies, governments, and other organizations to raise capital. The value of a bond is determined by its present value, which is the sum of the discounted future cash flows generated by the bond. In other words, the value of a bond is equal to the sum of the present value of all the interest payments and the principal repayment.
To calculate the present value of a bond, investors use the bond’s yield-to-maturity (YTM) and the bond’s coupon rate. The coupon rate is the annual interest rate that the bond pays, and the YTM is the annual rate of return that the investor will receive if the bond is held until maturity. The present value is calculated using the formula:
PV = C / (1+r)^1 + C / (1+r)^2 + … + C / (1+r)^n + F / (1+r)^n
PV is the present value of the bond
C is the annual coupon payment
r is the YTM
F is the face value of the bond
n is the number of periods until maturity
To illustrate, let’s say an investor purchases a 10-year bond with a face value of $1,000 and a coupon rate of 5%. The bond pays interest twice a year, so the annual coupon payment is $50 ($1,000 x 5%). If the YTM is 4%, the present value of the bond can be calculated as follows:
PV = $50 / (1+0.04)^1 + $50 / (1+0.04)^2 + … + $50 / (1+0.04)^20 + $1,000 / (1+0.04)^20
PV = $50 / 1.04^1 + $50 / 1.04^2 + … + $50 / 1.04^20 + $1,000 / 1.04^20
PV = $50 x (1 – 1 / 1.04^20) / 0.04 + $1,000 / 1.04^20
PV = $50 x 13.5909 + $456.39
PV = $1,000
Therefore, the value of the bond is $1,000, which is equal to its face value. If the YTM changes, the value of the bond will also change accordingly. When the YTM is higher than the coupon rate, the bond will trade at a discount to its face value, while when the YTM is lower than the coupon rate, the bond will trade at a premium.
Value of Debentures
Debentures are long-term debt instruments issued by companies to raise funds. They are similar to bonds but are not secured by any specific assets of the company. The value of debentures depends on various factors such as interest rates, creditworthiness of the issuer, market demand, and the terms of the debenture agreement.
The value of a debenture can be calculated using the following formula:
Debenture Value = (Interest payment / Discount rate) + (Principal payment / (1 + Discount rate)^n)
Interest payment: The periodic interest payment made by the issuer to the debenture holder.
Discount rate: The rate of return required by investors to invest in a debenture of similar risk.
Principal payment: The amount that the issuer will pay to the debenture holder on the maturity of the debenture.
n: The number of periods until the maturity of the debenture.
The discount rate used to calculate the value of a debenture depends on various factors such as the credit rating of the issuer, the prevailing interest rates in the market, and the maturity of the debenture. Higher credit ratings and shorter maturities generally result in lower discount rates, which in turn result in higher debenture values.
Debentures may also be issued with a call option, which allows the issuer to redeem the debenture before its maturity. The value of a callable debenture is calculated using a different formula that takes into account the possibility of early redemption.
In general, the value of a debenture is affected by changes in interest rates. As interest rates rise, the value of a debenture falls, as investors demand a higher rate of return to compensate for the increased risk. Conversely, when interest rates fall, the value of a debenture rises, as investors are willing to accept a lower rate of return for the lower risk.
Investors who wish to invest in debentures should carefully consider the creditworthiness of the issuer and the terms of the debenture agreement, including the interest rate, maturity date, and any call or put options. They should also consider the prevailing market conditions and the outlook for interest rates, as these factors can have a significant impact on the value of the debenture.
Current Yield, YTM, YTC
Current yield, yield to maturity (YTM), and yield to call (YTC) are important measures used to evaluate the returns of fixed income securities such as bonds, debentures, and other debt instruments.
The current yield is a simple measure that calculates the annual interest payment on a bond as a percentage of its current market price. It is calculated as follows:
Current Yield = (Annual Interest Payment / Market Price) x 100
For example, if a bond has a face value of $1,000, a coupon rate of 6%, and is trading at a market price of $950, then the current yield would be:
Current Yield = (6% x $1,000 / $950) x 100 = 6.32%
The yield to maturity (YTM) is a more complex measure that takes into account the total return an investor will receive if the bond is held until maturity. It represents the average annual return that an investor will earn over the life of the bond if all interest and principal payments are made on time and the bond is held until maturity.
YTM can be calculated using the following formula:
PV = C/(1 + r) + C/(1 + r)^2 + … + C/(1 + r)^n + FV/(1 + r)^n
PV is the present value of the bond,
C is the periodic coupon payment,
r is the discount rate,
n is the number of periods until maturity,
FV is the face value of the bond.
The yield to call (YTC) is similar to YTM, but it represents the return an investor would earn if the bond were called by the issuer before maturity. This can occur if the issuer has the right to redeem the bond early, usually at a specified call price.
YTC can be calculated using the same formula as YTM, but with the call price as the final payment instead of the face value. The yield to call is only relevant if the bond has a call feature and is trading above the call price.
In general, YTM and YTC are more useful measures of bond returns than current yield because they take into account the time value of money and the bond’s price fluctuations. However, they are based on certain assumptions about the bond’s cash flows and future interest rates, and may not accurately reflect the actual return that an investor will receive if the bond is sold before maturity or if interest rates change.