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# Valuation of Bonds-Debentures Assignment Help

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Valuation of Bonds and Shares - Valuation of Bonds-Debentures

Valuation of Bonds/Debentures

Bonds are long term debt instruments issued by big corporate clientele or government delegacies or agencies to promote large amount . Bonds brought out by government agencies are secured and those issued by private sector companies may be unsecured or secured. The rate of interest on bonds is determined and they are reformable after a particular period. Here are some significant terms in bond valuation,they are as follows:

**Face value: **

Face value is also referred as par value. It is the value declared on the face of the bond. It makes up the amount that the unit borrows which is to be re-compensated at the time of maturity, after a certain period of time. A bond is in general issued at values such as Rs. 100 or Rs. 800.

Coupon rate is the assigned rate of interest in the bond. The interest payable at regular intervals is the product of the par value and the coupon rate crumbled to the given time horizon.

Maturity period brings up to the number of years after which the par value becomes payable to the bond holder. In general, corporate bonds have a maturity period of 7-10 years and government bonds 20 to 25 years.

Redemption value is the amount the bond holder develops on maturity. A bond may be delivered at par, at a premium bond holder acquires more than the par value of the bond or at a discount bond holder acquires less than the par value of the bond.

Market value is the price in the stock exchange at which the bond is traded. Market price is the price at which the bonds can be sold or bought and this price may be different from par value and redemption value.

Types of Bonds

There are three forms of bonds:

i) Irredeemable Bonds also known as perpetual bonds

ii) Redeemable Bonds, also known as Bonds with finite maturity period.

iii) Zero Coupon Bonds.

i) Irredeemable Bonds or Perpetual Bonds

Bonds which will never mature are known as perpetual bonds or irredeemable. Indian Companies Acts limits the issue of such bonds and thus these are very rarely issued by corporates these days. In case of these bonds the maturity value or terminal value

does not exist because they are not redeemable. The face value is known, the interest

received on such bonds is fixed and obtained at steady intervals and hence the interest receipts resemble a perpetuity. The present value (the intrinsic value) is computed as:

V0=I/id .

Redeemable Bonds:

There are two forms , bonds with annual interest payments and bonds with semi annual interest payments.

Bonds with annual interest payments:

Fundamental Bond Valuation Model:

The holder of a bond receives a fixed annual interest for a determined number of years and a constant principal repayment at the time of maturity. The intrinsic value (present value of bond) can be

expressed as:

V0 or P0=∑ n t=1 I/(I+kd) n +F/(I+kd) n

Which can also be stated as follows

V0=I*PVIFA(kd, n) + F*PVIF(kd, n)

Where V0= Intrinsic value of the bond

P0= Present Value of the bond

I= Annual Interest payable on the bond

F= Principal amount (par value) repayable at the maturity time

n= Maturity period of the bond

Kd= requisite rate of return

For instance : Mr. Verma purchases a bond whose face value is Rs. 1000, with a maturity period 5 years paired with a nominal rate of interest 8%. The requisite rate of return is 10%. In that case:

Interest payable is 1000*8%=Rs. 80

Principal repayment will be Rs. 1000

requisite rate of return will be 10%

Based on the formula:

V0=I*PVIFA(kd, n) + F*PVIF(kd, n)

The value of the bond is

80*PVIFA(10%, 5y) + 1000*PVIF(10%, 5y)

= 80*3.791 + 1000*0.621=Rs. 924.28

This implies that the company is bidding the bond at Rs. 1000 but is deserving Rs. 924.28 at the requisite 10% rate of return. The investor may not be inclined to pay more than Rs. 924.28 for the bond.

** **Bond Values with Semi Annual Interest payment:

Actually it is quite popular to pay interest on bonds semi-annually. From the consequence of

compounding, the bond value with semiannual interest is more than the one with annual interest payments. Therefore, the bond valuation equation can be specified as:

V0 or P0=∑ n t=1 I/2/(I+id/2) n +F/(I+id/2) 2n

Where V0=Intrinsic value of the bond

P0=Present Value of the bond

I/2=Semi annual Interest payable on the bond

F=Principal amount (par value) repayable at the maturity time

2n=Maturity period of the bond expressed in half yearly periods

kd/2=requisite rate of return semi annually.

Valuation of Zero Coupon Bonds

Zero coupon bonds are referred as Deep Discount Bonds in India. For more than a

decade, these bonds became very popular in India due to issue of such bonds at

regular intervals by ICICI and IDBI . Zero coupon bonds have no coupon rate, i.e. there is no interest to be compensated. Instead, these bonds are issued at a discount to their face value, and the face value is the amount payable to the investor of the instrument on maturity. The difference amongst the discounted issue price and face value is effective interest earned by the investor. They are called deep discount bonds because these bonds are long-term bonds, whose maturity some time extends up to 25 to 30 years.

For instance :

River Valley Authority brought out Deep Discount Bond of the face value of Rs. 60000 payable 11.5 years later, at an issue price of Rs. 7300.The effective interest rate gained by an

investor from this bond will be:

As the bond is a zero coupon or deep discount bond. It does not contain any coupon rate.

Thus, the entailed interest rate could be computed as follows:

Step 1:

Principal amount invested at present is Rs. 7300 at a rate of interest of "r"% over 11.5 years to amount to

Rs.60000.

Step 2:

It can be stated as

A = P0 (1+r) n

60000 = 7300 (1+r) 11.5

8.22 = (1+r) 11.5

Reading the compound value (FVIF) table, horizontally along the 11.5 year line, we find 'r' equals 9%. Therefore, bond gives an effective return of 9% per annum.

Current Yield:

Current yield appraises the rate of return earned on a bond if it is bought at its current market price and the coupon interest received.

Current Yield = Coupon Interest / Current Market Price

For instance : Continuing with the same instance above calculate the CY if the current market price is Rs. 460

Solution:

CY=Coupon Interest / Current Market Price

=40/460

=11.5%

Yield to Maturity is the rate earned by an investor who purchases a bond and holds it till its maturity. The Yield to Maturity is the discount rate equaling the present values of cash flows to the current market price.

The formula is:

V0 or P0=∑ n t=1 I/(I+kd) n +F/(I+kd) n

The following formula may be used to get a raw idea about Kd as Trial & Error Method is a very long-winded procedure and involves lots of time. This formula can be employed as a reference formula.

Yield to Maturity={I+(FP)/n} / {(F+P)/2}

Where Yield to Maturity =Yield to Maturity

I=Annual interest payment

F=Face value of the bond

P=Current market price of the bond

n=Number of years to maturity.

Yield to Maturity determining the market value of the bond, the bond price will fluctuate to the

varies in market interest rates. A bond's price moves inversely proportional to its Yield to Maturity.

The following elements involve the bond values:

Relationship amongst the requisite rate of interest (Kd) and the discount rate.

No. of years to maturity.

Yield to Maturity

**Relationship amongst the requisite rate of interest (Kd) and the discount rate:**

When Kd is equal to the coupon rate, the intrinsic value of the bond is equal to its face value, if Kd=coupon rate, then value of bond=face value.

When Kd is greater than the coupon rate, the intrinsic value of the bond is very low than its face value i.e. if Kd>coupon rate, then value of bond<face value.

When Kd is lesser than the coupon rate, the intrinsic value of the bond is greater than its face value, that is, if Kd<coupon rate, then value of bond>face value.

Number of years to maturity

When Kd is greater than the coupon rate, the discount on the bond declines as maturity approaches.

When Kd is less than the coupon rate then the premium on the bond declines as maturity approaches.

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**Face value:**

Face value is also referred as par value. It is the value declared on the face of the bond. It makes up the amount that the unit borrows which is to be re-compensated at the time of maturity, after a certain period of time. A bond is in general issued at values such as Rs. 100 or Rs. 800.

V0=I*PVIFA(kd, n) + F*PVIF(kd, n)

80*PVIFA(10%, 5y) + 1000*PVIF(10%, 5y)

**Bond Values with Semi Annual Interest payment:**

Principal amount invested at present is Rs. 7300 at a rate of interest of "r"% over 11.5 years to amount to

It can be stated as

The following formula may be used to get a raw idea about Kd as Trial & Error Method is a very long-winded procedure and involves lots of time. This formula can be employed as a reference formula.

**Relationship amongst the requisite rate of interest (Kd) and the discount rate:**

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