

Money
& Banking MGT411
VU
Lesson
13
BONDS
& BONDS PRICING
Bond
& Bond pricing
Zero
Coupon Bond
Fixed
Payment Loan
Coupon
Bonds
Consols
Bond
Yield
Yield
to Maturity
Current
Yield
Bonds
Virtually
any financial arrangement involving the
current transfer of resources from a
lender to
a
borrower, with a transfer back at some
time in the future, is a form of
bond.
Car
loans, home mortgages, even credit
card balances all create a
loan from a financial
intermediary
to an individual making a
purchase
Governments
and large corporations sell
bonds when they need to
borrow
The
ease with which individuals,
corporations, and governments borrow is
essential to the
functioning
of our economic system.
Without
this free flow of resources
through the bond markets, the economy
would grind to a
halt.
Historically,
we can trace the concept of
using bonds to borrow to
monarchs' almost insatiable
appetite
for resources.
The
Dutch invented modern bonds to
finance their lengthy war of
independence
The
British refined the use of
bonds to finance government
activities.
The
practice was soon popular among
other countries
A
standard bond specifies the fixed amount
to be paid and the exact dates of the
payments
How
much should you be paying
for a bond?
The
answer depends on bond's
characteristics
Bond
Prices
Zerocoupon
bonds
Promise
a single future payment,
such as a Treasury
bill.
Fixed
payment loans
Conventional
mortgages.
Car
loans
Coupon
Bonds
Make
periodic interest payments and repay the
principal at maturity.
Treasury
Bonds and most corporate bonds are
coupon bonds.
Consols
Make
periodic interest payments forever,
never repaying the principal
that was borrowed.
ZeroCoupon
Bonds
These
are pure discount bonds
since they sell at a price
below their face
value
The
difference between the selling price and
the face value represents the interest on
the bond
The
price of such a bond, like a
Treasury bill (called
"Tbill"), is the present
value of the future
payment
40
Money
& Banking MGT411
VU
Price
of a $100 face value zerocoupon
bond
$
100
=
(1
+
i
)
n
Where
i
is the interest rate in decimal form
and
n
is time until the payment is
made in the same time units
as the interest rate
Given
n, the price of a bond and the interest rate
move in opposite
directions
The
most common maturity of a Tbill is 6
months; the Treasury does not
issue them with a
maturity
greater than 1 year
The
shorter the time until the payment is
made the higher the price of the
bond, so 6 month T
bills
have a higher price that a
oneyear Tbill
Examples:
Assume
i=4%
Price
of a OneYear Treasury
bill
100
=
=
$ 96
. 15
(1
+
0 .
04 )
Price
of a SixMonth Treasury
bill
100
=
=
$ 98
. 06
(1
+
0 .
04 )
1/
2
The
interest rate and the price for the
Tbill move
inversely.
If
we know the face value and
the price then we can solve
for the interest rate
Fixed
Payment Loans
They
promise a fixed number of equal payments
at regular intervals
Home
mortgages and car loans are examples of
fixed payment loans;
These
loans are amortized, meaning
that the borrower pays off
the principal along with
the
interest
over the life of the
loan.
Each
payment includes both interest and
some portion of the
principal
The
price of the loan is the present
value of all the
payments
Value
of a Fixed Payment Loan =
FixedPayme
t +
FixedPayme
t +
... +
FixedPayment
n
n
(1
+
i)
(1
+
i)
(1
+
i)
2
n
Coupon
Bond
The
value of a coupon bond is the
present value of the periodic interest
payments plus the present
value
of
the principal repayment at
maturity
⎡
CouponPayment
CouponPayment
CouponPayment
⎤
FaceValue
PCB = ⎢
+
+
......
+
⎥
+ (1
+
i)n
(1
+
i)1
(1
+
i)2
(1
+
i)n
⎣
⎦
The
latter part, the repayment of the
principal, is just like a zerocoupon
bond.
41
Money
& Banking MGT411
VU
Consols
A
consol offers only periodic interest
payments; the borrower never repays the
principal
There
are no privately issued
consols because only governments
can credibly promise to make
payments
forever
The
price of a consol is the present value of
all the future interest payments, which
is a bit
complicated
because there are an infinite number of
payments
Bond
Yields
Now
that we know how to price a
bond while interest rate is known; we
now move to other
direction
and calculate the interest rate or return to an
investor
So
combining information about the promised
payments with the price to obtain
what is called
the
yield a measure of cost of
borrowing or reward for
lending.
Interest
rate and yield are used
interchangeably
Yield
to Maturity
The
most useful measure of the
return on holding a bond is
called the yield to maturity
(YTM).
This
is the yield bondholders receive if
they hold the bond to its
maturity when the
final
principal
payment is made
It
can be calculated from the
present value formula
Price
of OneYear 5 percent Coupon Bond
=
$5
$100
+
(1
+
i
)
(1 +
i
)
The
value of i that solves this
equation is the yield to
maturity
If
the price of the bond is $100,
then the yield to maturity
equals the coupon rate.
Since
the price rises as the yield
falls, when the price is above
$100, the yield to maturity
must
be
below the coupon rate.
Since
the price falls as the yield
rises, when the price is
below $100, the yield to
maturity must
be
above the coupon rate.
Yield
to Maturity
Considering
5% coupon bond
If
YTM is 5% then price is
$5
$
100
+
=
$100
(1
+
.05)
(1 +
.05)
If
YTM is 4% then price is
$5
$
100 =
$100.96
+
(1
+
.04)
(1 +.04)
If
YTM is 6% then price is
$5
$
100
+
=
$99.06
(1
+
.06)
(1 +.06)
Generally
If
the yield to maturity equals the coupon
rate, the price of the bond is the same
as its face value.
If
the yield is greater than the coupon
rate, the price is lower;
If
the yield is below the coupon rate, the
price is greater
42
Table of Contents:

