BBA 7th semeseter

1. Portfolio Management
LECTURE SEVEN
Bond Evaluation
Prepared By:
Noorulhadi Qureshi
Lecturer Govt College of Management Sciences 1
Peshawar

2. Bonds
• A bond is a tradable instrument that represents
a debt owed to the owner by the issuer. Most
commonly, bonds pay interest periodically
(usually semiannually) and then return the
principal at maturity.
• Most corporate, and some government, bonds
are callable. That means that at the company’s
option, it may force the bondholders to sell them
back to the company. Ordinarily, there are
restrictions on the timing of the call and the
amount that must be paid.
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3. • Par or Face Value:
The amount of money hat is paid to the bond
holder at maturity. i.e. its generally represent
the amount of money borrowed by the bond
issuer.
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4. Bond Return
• Bond Return can be calculated and
expressed in different ways. It is necessary
to understand the meaning of each of these
expressions.
• Coupon rate: It is the nominal rate of interest
fixed and printed on the bond certificate. It is
calculate on the face value of the bond. For
example if the coupon rate on a bond of face
value of Rs. 1000 is 12%, Rs. 120 would be
payable by the company to the bondholder
annually till maturity. And amount Rs. 120 is
known coupon payment. 4

5. Current yield
Bond may be trader at secondary market
at different price from face value. The
current yield relates the annual interest
receivable on a bond to its current
market price. For example if a bond face
value is Rs. 1000 with coupon rate of
12% and current selling for Rs. 800, the
current yield would be
Current yield may be
In higher than coupon if
CurrentYield = .100 bond trader at discount
Po and may be low if
In= annual interest traded at premium
Po= Current market price
120
CurrentYield = x100
800
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CurrentYield = 15%

6. Spot Interest Rate
Zero Coupon bond is special type of bond
which does not pay annual interest. The
return on bond is in the form of discount on
issue of the bond. Or example , two year
bond of face value is Rs. 1000 at discount
for Rs. 797.19 with no coupon or with no
annual interest. This type of bond is also
called pure discount bond or deep discount
bond. And it is calculated as
Discounted Price= (Face value)/(1+k)n
(1+k)n =(Face value)/ Discounted Price
K = n FaceValue / Di csc ount Pr ice − 1
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7. Spot Interest Rate (con’t)
Consider a zero coupon bond whose face value is
Rs. 1000 and maturity period is 5 year. If the
issue rice of the bond is Rs. 519.37, what is
spot interest rate.
K = n FaceValue / Di csc ount Pr ice −1
K = 5 1000 / 519.37 −1
K = 14%
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8. Bond
• Maturity date: The maturity date represent
on which the bond is mature and repaid to
the bond holder:
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9. Yield to Maturity
• The compounded rate of return an investor
expected to receive from bond purchased at
the current market price and held to
n
maturity: Ct
MP = (
∑ TV
(1 + YTM )t
)+(
(1 + YTM )n
)
MP is the current market price of the bond
Ct is the cash inflow from the bond throughout the holding period
TV is the terminal cash inflow received at the end of the holding period.
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10. YTM (con’t)
• A bond face value with Rs. 1000 and coupon rate is 15%, market
price is Rs. 900 with five years maturity period,
n
∑
MP = (
Ct
(1 + YTM )t
)+(
TV
(1 + YTM )n
)
It will be on the basis on trail and error, assuming 20% YTM, the value of
if calculated, is 850.49, so the value is less the market value so this rate
to be reduced with another assumption i.e 18% rate is inserted in
equation, it gives Rs. 906.18 Now to calculate YTM
HigheCalculatedValue − MP
YTM = LowerRate + ( HigherRate − LowerRate)
HighCacultedValue − LowerCalculatedValue
906.18 − 900
YTM = 18 + (20 −18)
906.18 − 850.49
YTM = 18.22
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11. YTM(alternative way Approx)
To avoid trail and error which tedious calculation, YTM maturity can
be calculated approximately as
I is annual interest=150
MV is maturity value and=1000
MP is market price, and =900
n is holding period to maturity= 5
I +( MV −MP) / n
YTM =
( MV +MP) / 2
150 +(1000 −900) / 5
YTM =
(1000 +900) / 2
150 +20
YTM =
950
YTM =0.1789or17.89% 11

12. Bond Price
• Bond price refers to the Present value of
Bond.
CFt It MV
Po = ∑ Po = ∑ +
(1 + k )t
(1 + K )t (1 + K )t
Po = Present value, It is the annual interest, MV is maturity value, n is the
number of year to maturity and k is the appropriate discount rate.
Let a bond face value is Rs. 1000 issued five years ago at coupon rate of 10%
the had had a maturity period of 10 years, so five years are more left from
today to maturity the current market rate is 14% the present value would be
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13. Calculating the Value of a Bond
• There are two types of cash flows that are
provided by a bond investments:
– Periodic interest payments (usually every six
months, but any frequency is possible)
– Repayment of the face value (also called the
principal amount, which is usually $1,000) at
maturity
• The following timeline illustrates a typical
bond’s cash flows: 1,000
100 100 100 100 100
0 1 2 3 4 5
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14. Calculating the Value of a Bond (cont.)
• We can use the principle of value additivity to
find the value of this stream of cash flows
• Note that the interest payments are an
annuity, and that the face value is a lump
sum
• Therefore, the value of the bond is simply the
present value of the annuity-type cash flow
and the lump sum:
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15. Bond Terminology
• There are several terms with which you must be
familiar to solve bond valuation problems:
– Coupon Rate - This is the stated rate of interest on the
bond. It is fixed for the life of the bond. Also, this rate time
the face value determines the annual interest payment
amount.
– Face Value - This is the principal amount (nominally, the
amount that was borrowed). This is the amount that will be
repaid at maturity
– Maturity Date - This is the date after which the bond no
longer exists. It is also the date on which the loan is repaid
and the last interest payment is made.
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16. Bond Valuation: An Example
• Assume that you are interested in
purchasing a bond with 5 years to maturity
and a 10% coupon rate. If your required
return is 12%, what is the highest price
that you would be willing to pay? 1,000
100 100 100 100 100
0 1 2 3 4 5
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17. Some Notes About Bond
Valuation
• The value of a bond depends on several factors
such as time to maturity, coupon rate, and
required return
• We can note several facts about the relationship
between bond prices and these variables
(ceteris paribus):
– Higher required returns lead to lower bond prices, and
vice-versa
– Higher coupon rates lead to higher bond prices, and
vice versa
– Longer terms to maturity lead to lower bond prices,
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and vice-versa

18. Bond Risk
1. Default Risk:
Default risk refers to the possibility that a
company may fail to pay the interest rate
or principal amount on maturity date
3. Interest Rate Risk
Interest rate risk refers to variation of market
interest rate or discount rate compare to
coupon rate.
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