# Bonds: Term Definition

## Introduction

Bonds are fixed-income securities having long-term yields. Bonds are of two types: government bonds and corporate bonds. Bond valuation is easier than stock valuation because the probable cash flow streams and the time horizon are well specified and fixed for bonds.

## Zero coupon bonds

It is a special type of bond which does not pay annual interest. The return on this type of bond is in the form of a discount that the investor enjoys at the time of issue of the bond to him. For example, a two-year bond of the face value of Rs. 2000 is issued at a discount of Rs. 594.38. This means that the investor who pays Rs. 1405.62 now, gets 2000 on maturity after two years. The returns received can be expressed on an annualized basis and are called the spot interest rate. The returns that an investor gets from bonds can be expressed in different ways. They are coupon yield, current yield, yield to maturity, yield to call, etc.

## Coupon yield

When bonds are issued, the issuing party undertakes to pay a fixed interest to the subscriber and that rate may be printed on the bond certificate. This interest is called the nominal rate of interest and is calculated on the face value of the bond. As an example, in the case of the coupon rate of a bond with a face value of Rs. 1115.00(without interest) is a 7 percent annual coupon, Rs. 100 is the interest payable by the company to the bondholder annually till maturity. In this example, the coupon yield is 7%.

## Current Yield

In the stock exchange, debt instruments are also bought and sold. If so, the current market price of a bond may differ from its face value. A bond with a face value of Rs. 100 may be traded at a premium of Rs. 10 or a discount of Rs. 15. In such an event, the market price of the bond is Rs. 110 in the first case and Rs. 85 in the second case. Then the return that an investor will get from the bond investment is to be calculated with the interest rate offered on the bond at its face value and the market price. It is shown as follows.

Current yield =In ∕ Po* 100

Here, In = Annual interest

Po = Current price

For example, A bond of the face value of Rs.1000 with a coupon rate of 7 percent, traded at Rs. 1110.00, 2 year. The current yield of the bond is calculated as

In = 1000*70/ 100 = **70**

Current yield = 70/ 1115*100 = **6.3%**

The current yield would be higher than the coupon rate when the bond is traded at a discount. On the other hand, the yield will be lower than the coupon rate if it is acquired at a premium by the investor. When the current yield is arrived at, it is assumed that the investor buys the bond and sells it before the maturity period at the same price the investor acquired the bond.

## Yield to maturity

For arriving at the return that an investor gets from bonds, usually yield to maturity is worked out. Yield to maturity can be defined as the average rate of return expected on an investment in bond security in the current market price and received in maturity. At the time of acquisition, there is a cash outflow and after that yearly cash inflows are expected by way of interest, and during the last year capital repayment is also obtained. Yield to maturity is the internal rate of return earned from holding the bond till maturity. Find out the probable cash outflows and inflows. To reach the internal rate of return, the present values of inflows have to be balanced with the present value of outflow. It is known as yield to maturity. It is the discount rate that makes the present value of cash inflows from the bond equal to the cash outflow for acquiring the bond.

Mp = ∑n [C1/ (1+ YTM) ]+ [TV/ I+ YTM)] n

T=1

Here MP= Market price of the bond

CI = cash inflow from the bond (interest) throughout the holding period.

TV= Terminal cash inflow received at the end of the holding period

By using trial and error, the value of YTM that equates the two sides of the equation can be arrived at.

Face value of bond = 1000. The coupon rate is 7%. The current market price is Rs. 1110. The maturity period from now is 2 years.

Here we assume 2%, that means : 980 and. 961

(70* 1.941) + (1000*.961)

135.87+ 961= **1096.87**

Assume 1% that means. 990 and. 980

(70* 1.97 + (1000*.980)

137.9+ 980

**1117.9**

This means that the YTM is lying between 1 % and 2%. To find out the exact YTM rate the interpolation technique is adopted.

= A+ C/ C-D(B-A)

A= YTM rate at the lower trial (1%)

B= YTM rate at the higher trial (2%)

C= Excess value of right-hand side figure over left-hand side figure

D= Deficit value of right-hand side figure over left-hand side figure.

1+ 17.9/21.03*1

1+.85 = **1.85%**

*Yield to call*

Some bonds are available which are redeemable before the maturity period. The redemption may be done either at the option of the issuer or of the investor. This type of option can be applied in a specified period and price. The decision to exercise the option of redemption is taken by the investor as well as the issuer based on the yield. Sometimes it will be beneficial for the investor to exercise the call before the maturity date. In certain cases, it will be attractive to wait for the entire period of the bond. Everything depends upon the yield.

Here interest is not given. So we assume the interest is 14%. The formula is

Po= ∑n CF/ (1+ I)t

T=1

(70*1.646)+ (1000*.769)

115.22+769 = **884**

Bonds are generally issued with a fixed rate of interest known as the coupon rate. This offered fixed rate is calculated on the face value of the bond and it remains fixed till maturity. Generally, the coupon rate will be lower than the prevailing market interest rate. When the market interest rate changes, then the market price of bonds will also change. It may be upwards or downwards. If the interest rate prevailing is more than the offered coupon rate, the market price of the bond will come down and vice versa. So the bond prices vary inversely with changes in market interest rates. The amount of price variation necessary to adjust to a given change in interest rates is a function of the number of years to maturity. In the case of long-term maturity bonds, a change in market interest rate results in a relatively large price change when compared to a short maturity bond. In other words, long-term bonds are more sensitive to interest rate changes than short-term bonds.

## Bond Duration

The important risk in the bond market is interest rate risk. This risk is verified using a concept is known as duration. When changing the interest rate, estimate how much it is possible for the price of the bond to increase or decrease. The important and essential inputs are maturity time and coupon rate.

## Conclusion

Bond valuation is not as much challenging as stock valuation. The returns from bonds are variously mentioned as current yield, coupon yield, yield to maturity and yield to call. The returns from the bond investment are fixed. The bond prices do not fluctuate widely like equity shares.