Value of Bond

8/2/2019 Value of Bond

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The coupon rate of a bond is the statedrate of interest that the bond will pay

The coupon rate does not normallychange during the life of the bond,instead the price of the bond changes asthe coupon rate becomes more or lessattractive relative to other interest rates

The coupon rate determines the dollaramount of the annual interest payment:


4/25

Bonds with maturity Pure discount bonds Perpetual bonds

4


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Bond value = Present value of interest +Present value of maturity value:

5

0

0

INT

( ) ( )0 0

n

t n

t n

t d d

B

B k k=

= ++ +

1. Required rate of return

2. Time to maturity


6/25

When required rate = coupon rate, bondvalue = par value

RR> coupon rate, bond value < par value

RR< coupon rate, bond value > par value Discount=?

Bn-B0 Premium=?

B0-Bn


7/25

The value of thebond declines as themarket interest rate(discount rate)

increases.The value of a 10-

year, 12 per cent Rs1,000 bond for the

market interest ratesranging from 0 percent to 30 percent.

.00

.0000

.0000

.0000

.0000

.00000

.00000

%0 %0 %00 %00 %00 %00 %00

Interest Rate

BondValu

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8/25

The intensity of interest rate risk would behigher on bonds with long maturities thanbonds with short maturities.

The shorter the time period to maturity, lessresponsive is its market value to changes inrequired rate


9/25

The yield to maturity is the average annualrate of return that a bondholder will earnunder the following assumptions: The bond is held to maturity

The interest payments are reinvested at the YTM

The yield to maturity is the same as thebonds internal rate of return (IRR)

If bond value equals par then YTM equals CR


10/25

The yield-to-maturity(YTM) is themeasure of a bonds rate of return thatconsiders both the interest income and

any capital gain or loss. YTM is bondsinternal rate of return. perpetual bonds yield-to-maturity:

10

0

0

INT INT

( )0

n

t

t d d

Bk k

=

=

= =+


11/25

Most corporate bonds, and many oldergovernment bonds, have provisions which allowthem to be called if interest rates should dropduring the life of the bond

Normally, if a bond is called, the bondholder ispaid a premium over the face value (known as thecall premium)

The YTC is calculated exactly the same as YTM,

except: The call premium is added to the face value, and

The first call date is used instead of the maturity date


12/25

For calculating the yield to call, the call periodwould be different from the maturity period andthe call (or redemption) value could be differentfrom the maturity value.

Example: Suppose the 10% 10-year Rs 1,000bond is redeemable (callable) in 5 years at a callprice of Rs 1,050. The bond is currently selling forRs 950.

The bonds yield to call is 12.7%.

( ) ( )

0

0

0

,111 1111000

YTC YTC0 0t

t=

= ++ +


13/25

The current yield is a measure of thecurrent income from owning the bond.Current yield is the annual interest

divided by the bonds current value. Current yield does not account for the

capital gain or loss. Example: The annual interest is Rs 60 on

the currentinvestment of Rs 883.40. the current rate of return or the current

yield is: 60/883.40 = 6.8 per cent.

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A bond (debenture) may be amortised everyyear, i.e., repayment of principal every yearrather at maturity.

The formula for determining the value of abond or debenture that is amortised everyyear, can be written as follows:

Note that cash flow, CF, includes both theinterest and repayment of the principal.

14

0

0( )0

n

tt

t d

CF

Bk

=

=+


15/25

Pure discount bond do not carry anexplicit rate of interest. It provides for thepayment of a lump sum amount at a futuredate in exchange for the current price of the

bond. The difference between the facevalue of the bond and its purchase pricegives the return or YTM to the investor.

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Pure discount bonds are called deep-discount bonds orzero-interest bondsor zero-coupon bonds.

The market interest rate, also calledthe market yield, is used as the discountrate.

Value of a pure discount bond = PV of theamount on maturity:

16

( )0

0

n

n

d

MB

k

=+


17/25

Perpetual bonds, also called consols, hasan indefinite life and therefore, it has nomaturity value. Perpetual bonds or

debentures are rarely found in practice.

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18/25

B0= I/2* (PVIFA k/2,2n) + M* (PVIF k/2, 2n)

Value of bond selling at discount is lowerwith semi-annual interest than annual

interest Value of bond selling at premium is higher

with semi-annual interest than annualinterest


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Trustee Indenture Bond rating Sinking Fund Call/put provision Claim on Income/ Assets Security

Convertibility Covenants


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DEFININTION: a legal document formallydescribing the terms of the legal relationshipbetween a bond issuer and bondholders.

The Trustee1acts to protect the interests of bondholders

0facilitates communications between them and the

issuer the indenture promises the trustee that it will

comply with a number of stated provisions

includes other terms such as the sale of assets,issuance of other bonds, dividends paymentchanges, and other issues that may change theprofitability and solvency of the issuer


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requires issuer to make annual payments to afund

the fund pays part of the principal each year

trustee may also repurchase bonds in the open

market


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Zero interest bonds Deep discount bonds SPN

FRB Income Bonds Convertible Bonds Foreign Bonds


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Restrictive Covenants Legal obligation Financial risk

0 Cash outflows

No voting rights Debenture prices are vulnerable to interest

rates

Documents

Value of Bond