Discussion 3
wtfbm69
Ch7-Bondvalution.pptxChapter 7. Bond Valuation
1
What is a bond?
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.
2
Coupon payment is the periodic interest payment paid by the issuer to the bondholder. It is typically paid every six months
Coupon rate is the interest rate to be paid on the face value of a bond
Yield to maturity is the average rate of return an investor will receive from a bond if a purchased at the current market price and held to maturity
Current yield is the ratio of the interest payment to the current market value of the bond
How Bond Markets Facilitate the Flow of Funds
Characteristics
Par (face) value
the amount the issuer provides to the bondholder, once maturity is reached.
Coupon rate and coupon payment
the interest rate to be paid on the face value of a bond
the periodic interest payment paid by the issuer to the bondholder
Maturity Date
the date on which the principal amount of a bond – also known as the “par value” – is to be paid in full.
Characteristics
Call provisions:
Require the firm to pay a price above par value when it calls its bonds
The difference between the call price and par value is the call premium
Are used to:
Issue bonds with a lower interest rate
Retire bonds as required by a sinking-fund provision
Are a disadvantage to bondholders
Sinking Fund Provision
A requirement to retire a certain amount of the bond issue each year
Valuation of Bonds
First Principle
Value of financial securities = PV of expected future cash flows
Bonds
Find PV of coupons and par value
Remember, interest rates are inversely related to present values
6
Bond Values
Information needed to value bonds:
Coupon payment dates and time to maturity (T)
Coupon payment (C) per period and Face value (F)
Discount rate
Value of a bond= PV of coupon payment annuity + PV of face value
7
Bond Values
Consider a corporate bond:
The Par Value of the bond is $1,000;
Coupon rate is 8%, coupon payments are made semi-annually;
Maturity is 10 years;
Yield to maturity is 6%.
Coupon = 4%*1,000 = 40 (Semiannual)
Discount Rate = 3% (Semiannual)
Number of payments= 20 periods
Par Value = 1,000
8
Bond Values
PMT
I/Y
FV
PV
N
40
20
1,000
– 1,148.77
3
9
Bond Rate of Return
There are several ways that we can describe the rate of return on a bond:
Coupon rate
Current yield
Yield to maturity
Yield to call
10
The Coupon Rate
The coupon rate of a bond is the stated rate of interest that the bond will pay
The coupon rate determines the dollar amount of the annual interest payment:
11
The Current Yield
The current yield is a measure of the current income from owning the bond
It is calculated as:
Annual Coupon Payment
Current Yield =
Bond Price
12
The Yield to Maturity
The yield to maturity is the average annual rate of return that a bondholder will earn under 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 the bond’s internal rate of return (IRR)
13
The Yield to Maturity
To calculate the yield to maturity, we solve the bond price equation for the interest rate, given the bond's price:
Using financial calculator to calculate yield to maturity.
20 -1148.77 40 1000 3
3% is the semiannual rate. The annual rate is 6%. The yield to maturity is 6%.
N
I/Y
PV
FV
PMT
YTM with Annual Coupons
Consider a bond with a 10% annual coupon rate, 15 years to maturity, and a par value of $1,000. The current price is $928.09. Is the yield more than or less than 10%?
The yield to maturity has to satisfy the following equation:
N = 15; PV = -928.09; FV = 1,000; PMT = 100
Compute: I/Y = 11
15
The students should be able to recognize that the YTM is more than the coupon since the price is less than par.
YTM with Semiannual Coupons
Suppose a bond with a 10% coupon rate and semiannual coupons has a face value of $1,000, 20 years to maturity, and is selling for $1,197.93.
Is the YTM more or less than 10%?
What is the semi-annual coupon payment?
How many periods are there?
N = 40; PV = -1,197.93; PMT = 50; FV = 1,000; CPT I/Y =4
The yield to maturity is 8%. The interest rate is 8%.
The Yield to Call
Most corporate bonds, and many older government bonds, have provisions which allow them to be called if interest rates should drop during the life of the bond
Normally, if a bond is called, the bondholder is paid a premium over the face value (known as the call 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
17
Calculating Bond Yield Measures
As an example of the calculation of the bond return measures, consider the following:
You are considering the purchase of a 2-year bond (semiannual interest payments) with a coupon rate of 8% and a current price of $964.54. The bond is callable in one year at a premium of 3% over the face value. Calculate the various return measures.
18
Calculating Bond Yield Measures (cont.)
0
1
2
3
4
40
1,000
40
40
40
-964.54
0
1
2
40
1,030
40
-964.54
Timeline if called
Timeline if not called
19
Calculating Bond Yield Measures (cont.)
The yields for the example bond are:
Current yield = 80/964.54 = 8.294%
YTM = 5% per period, or 10% per year
YTC = 7.42% per period, or 14.84% per year
20
Relation between bond prices and interest rates
Example: Determine the market value of a corporate bond with 20 years to maturity that has a 9% coupon rate (coupon is paid annually), if the market’s required rate of return is
7%
9%
11%
Fundamental fact about the relation between bond prices and interest rates: bond prices move inversely to interest rates!
N=20, FV=1000, PMT=90, I/Y=7
PV=-1221.88
N=20, FV=1000, PMT=90, I/Y=9
PV=-1000
N=20, FV=1000, PMT=90, I/Y=11
PV=-840.73
21
YTM and Bond Value
22
Bond Ratings – Investment Quality
High Grade
Moody’s Aaa and S&P AAA – capacity to pay is extremely strong
Moody’s Aa and S&P AA – capacity to pay is very strong
Medium Grade
Moody’s A and S&P A – capacity to pay is strong, but more susceptible to changes in circumstances
Moody’s Baa and S&P BBB – capacity to pay is adequate, adverse conditions will have more impact on the firm’s ability to pay
23
Bond Ratings - Speculative
Low Grade
Moody’s Ba and B / S&P BB and B
Considered speculative with respect to capacity to pay.
Very Low Grade
Moody’s C / S&P C & D
Highly uncertain repayment and, in many cases, already in default, with principal and interest in arrears.
24
T
T
T
T
t
t
T
T
r
F
r
r
C
r
F
r
C
r
F
r
C
r
C
r
C
PV
)
1
(
)
1
(
1
1
)
1
(
)
1
(
)
1
(
)
1
(
...
)
1
(
)
1
(
1
2
+
+
ú
û
ù
ê
ë
é
+
-
=
+
+
+
=
+
+
+
+
+
+
+
+
=
å
=
FC$$
T
0
C$
1
C$
2
C$
1T
20
40
$
40
$
40
$
19
1000
$
40
$
+
77
.
1148
)
3
.
0
1
(
1000
)
3
.
0
1
(
1
1
3
.
0
40
)
3
.
0
1
(
1000
)
3
.
0
1
(
40
...
)
3
.
0
1
(
40
)
3
.
0
1
(
40
20
20
20
20
2
=
+
+
ú
û
ù
ê
ë
é
+
-
=
+
+
+
+
+
+
+
+
=
PV
Annual
Pmt
Coupon
Rate
Face
Value
=
´
T
T
1
t
t
r)
(1
ParValue
r)
(1
Coupon
Bond_Price
+
+
+
=
å
=
20
1
20
)1(
000,1$
)1(
40$
77.1148
t
t
rr
15
15
3
2
)
1
(
1000
)
1
(
100
...
)
1
(
100
)
1
(
100
)
1
(
100
09
.
928
r
r
r
r
r
+
+
+
+
+
+
+
+
+
+
=
