this slides contain: definitions related to bonds, bond value formula and some exercises, comparison between market interest and coupon interest and interest rate risk

1. Bonds valuation
houssem chkili
ID 175252430712

2. BOND VALUATION
All bonds have the following characteristics:
1. A maturity date- typically 20-25 years.
2. A coupon rate- the rate of interest that the issuing
company pays to the holder.
3. A face value- usually $1000 or $5000.
%
8
18

3. BOND VALUATION
The value of a bond is the sum of the present value of the
annual interest payments plus the present value of the face
value;
nn
r
Face
r
Interest
pv
)1()1( +
+
+
=
Where; interest = coupon rate x face value
r = discount rate
n = years to maturity

4. BOND VALUATION
nn
r
Face
r
CouponPV
)1(
1
)1(
1
+
+
+
=
Where 1/(1+r) = discount rate

5. BOND VALUATION
Where 1/(1+r) = discount rate
t
t
YTM)(1
F
YTM
YTM)(1
1
-1
CValueBond
+
+












+
=
- As interest rates increase present values decrease ( r
→ PV  )
- As interest rates increase, bond prices decrease
and vice versa

6. BOND VALUATION
EXAMPLE
Find the value of a 20 year, 10%, $1000 face value bond.
The interest payment is given by: .10 x $1000 = $100/year
THE FORMULA IS:
PV = ∑= +
+
+
20
1
20
)1(
1000$
)1(
100$
N
N
rr
PV = $100(6.145) + $1000(.386) = $614.50 + $386 = $1000

7. BOND VALUATION
if the coupon rate is 8%, then the formula for the value of
the bond is;
20
20
1 )1(
1000$
)1(
80$
rr
PV
n
n
+
+
+
= ∑=
PV = $80(6.145) + $1000(.386) = $877.60
THE BOND SELLS AT A DISCOUNT

8. BOND VALUATION
if the coupon rate is 12%, then the formula for the value of
the bond is;
20
20
1 )1(
1000$
)1(
120$
rr
PV
n
n
+
+
+
= ∑=
PV = $120(6.145) + $1000(.386) = $1123.40
THE BOND SELLS AT A PREMIUM

9. Bond
Price
Yield-to-maturity
Graphical Relationship Between Price and
Yield-to-maturity

10. Bond
Price
Yield-to-maturity
Bond Value ($) vs Years remaining to
Maturity
M
Premium
1,000
Discount
30 25 20 15 10 5 0
CR>YTM
CR<YTM
YTM = CR

11. Interest Rate Risk
Price Risk
-Change in price due to changes in interest
rates –
Long-term bonds have more price risk than
short-term bonds
-Low coupon rate bonds have more price risk
than high coupon rate bonds