Bonds and Their Valuation
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Key features of bonds
Bond valuation
Measuring yield
Assessing risk
7-1
What is a bond?
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A long-term debt instrument in which
a borrower agrees to make payments
of principal and interest, on specific
dates, to the holders of the bond.
7-2
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Par value (face value)
Coupon rate
Coupon payment
Maturity date
7-3
Key Features of a Bond
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Face Value
Face value is called par value. A bond is
generally issued at a par value of taka
100 or 1000 and interest is paid on face
value.
Face amount of the bond, which
is paid at maturity
7-4
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Interest rate/ Coupon Interest Rate
stated interest rate (generally fixed) paid by
the issuer.
Interest rate is fixed and known to the
bondholders.
Interest is also called coupon rate.
It is a rate mentioned on the certificate.
Multiply by par to get taka payment of
interest
7-5
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Maturity
A bond is issued for a specified period
of time.
It is paid repaid on maturity.
Issue date – when the bond was issued.
7-6
Present Value of Cash Flows as Rates
Change
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Bond Value = PV of coupons + PV of
par
Bond Value = PV annuity + PV of lump
sum
Remember, as interest rates increase
present values decrease
So, as interest rates increase, bond
prices decrease and vice versa
7-7
Perpetual Bond:
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Bonds which will never mature are
known as perpetual bonds.
In case of perpetual bond, there is no
maturity or terminal value, the value of
the bonds would simply be discounted
value of the infinite stream of interest
flows.
7-8
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Example:
A bond will pay tk 70 interest annually.
What would be its value if the required
rate of return is 8%. What would be the
value of the bond?
7-9
Discount Rate
4
5
6
7
8
9
10
Value of Bond
1750
1400
1166.67
1000
875
777.78
700
7-10
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If the interest rate is 7%, the value of
the bond will be tk. 1,000 and if it is
9% the value will be tk. 777.78.
Thus, value of the bond will decrease as
the interest rate increase.
7-11
Yield to Maturity
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We have so far assumed that the bond’s
required rate of return is given for
calculating its value.
We may be required rate to calculate
the required rate of return when the
bond’s price and cash flows are known.
This rate is also known as yield to
maturity (YTM) or internal rate of return
7-12
Bond maturity and interest
Rate Risk:
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The value of the bond depends upon the
interest rate.
As the interest changes, the value of a bond
also varies. There is an inverse relationship
between the value of the bond and interest
rate.
The value will decline when the interest rate
rises and vice-versa.
Interest rates have the tendency of rising or
falling in practice. Thus, investors investing
their funds in bonds are exposed to risk from
increasing or falling interest rates.
7-13
Interest
Rate
4
5
6
7
8
9
10
Value of 5 Value of
year bond 10 year
bond
1134
1244
1087
1155
1042
1073
1000
1000
961
933
922
871
886
816
Value of
perpetual
bond
1750
1400
1167
1000
875
778
700
7-14
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Example:
The value of a 5 year bond comes down to 960.51
from 1,000 when interest rate is assumed to rise
from 7% to 8%, resulting in a loss of 39.49 to the
bondholder.
At 7% interest rate, values of all three bonds are
same, tk.1000. When interest rate rises to say 8%, 5
year bond falls to 961, 10 year bond to 933 and
perpetual bond further to 875.
Similarly, the value of long term bond will fluctuate
(increase) more when rates fall below 7 percent.
7-15
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The differential value response to
interest rates changes between short
and long term bond will always be true.
Two bonds have different exposure to
interest ate risk- the one with longer
maturity is exposed to greater degree
of risk from increasing interest rates
7-16
Behavior of Bond Price
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When the market required rate of return is
more than the stated coupon rate, the price
of the bond will be less than its face value.
Such a bond is said to be selling at a discount
from face value. The amount by which the
face value exceeds the current price is the
bond discount.
If a bond sells at a discount, then P0<Par
and YTM > Coupon Rate
7-17
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When the market required rate of return is
less than the stated coupon rate, the price of
the bond will be more than its face value.
Such a bond is said to be selling at a
premium over face value. The amount by
which the current price exceeds the face
value is the bond premium.
If a bond sells at a premium, then P0>Par
and YTM<Coupon Rate
7-18
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When the market required rate of
return equals the stated coupon rate,
the price of the bond will equal its face
value. Such a bond is said to be selling
at par.
If a bond sells at par, then P0 =Par and
YTM= Coupon Rate.
7-19
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If interest rates rise so that the market
required rate of return increases, the bond’s
price will fall. If interest rate falls, the bond’s
price will increase. In short, interest rates and
bond prices move n opposite directions.
For a given change in market required return,
the price of a bond will change by a greater
amount, the longer its maturity.
7-20
Bond Prices: Relationship Between
Coupon and Yield
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If YTM = coupon rate, then par value =
bond price
If YTM > coupon rate, then par value >
bond price
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Why?
Selling at a discount, called a discount bond
If YTM < coupon rate, then par value <
bond price
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Why?
7-21
Selling at a premium, called a premium bond
Zero Coupon Bonds
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A bond that pays no interest but sells at a
deep discount from its face value; it provides
compensation to investors in the form price
appreciation.
In other words, a bond that pays no coupons
at all must be offered at a price much lower
than its face value. Such bonds are called
zero coupon bonds.
7-22
Why buy a bond that pays no
interest?
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The buyer of such a bond does receive
a return. This return consists of the
gradual increase (appreciation) in the
value of the security from its original,
below face value purchase price until it
is redeemed at face value on its
maturity date.
Value of Bond= (Face value) /(1+kd)^n
7-23
7-24