

Investment
Analysis & Portfolio Management
(FIN630)
VU
Lesson
# 28
BOND
FUNDAMENTALS Contd...
BOND
PRICING AND
RETURNS:
As
with any timevalueofmoney
application, there is a deterministic
relationship between
the
current prices of a security, it's
promised future cash flows,
and the riskiness of those
cash
flows. The current price is
the market's estimation of
what the expected cash flows
are
worth
in today's dollars.
Valuation
Equations:
Annuities:
For
an ordinary annuity bond
paying interest semiannually and
assuming it has just made
an
interest
payment, the valuation
equation is as follows:
Po=∑
Ct/ (1+r/2)t
where;
n =
term of the bond in
semiannual periods
Ct = cash flow at time
t
r =
discount rate
Po = current price of the
bond
t =
time in semiannual periods from
the present
The
bond pricing relationship is
customarily expressed in terms of
the number of
semiannual
payment periods. An eightyear bond,
for example, has 16
semiannual
payments.
This procedure also requires
dividing the annual discount
rate, r, by two to turn
it
into
a semiannual equivalent.
To
illustrate, we split equation
into two parts, one for
the interest component (the
cash flows
Ct and one for the
principal:
Po=∑
Ct/ (1+r/2)t +
Par/1+r/2)n
Bond
price = PV (interest) +PV
(principal)
Suppose
a bond currently sells for
$900, pays $95 per year (interest paid
semiannually), and
returns
the par value of $1,000 in exactly
eight years. What discount rate is
implied in these
numbers?
To find out, we solve the
following valuation
equation:
$900=∑
$47.50/(l+r/2)t + $1,000/(l+r/2)16
This
equation can be solved using
timevalueofmoney tables, a finance
calculator, or a
spreadsheet
package such as Lotus 125
or Microsoft Excel. We find r =
11.44%.
This
bond's return comes from two
sources: periodic interest and the
return of the bond
principal
in eight years. These two
components can be valued separately
after determining
the
appropriate interest rate.
Using 11.44%, the value of
the interest component is
$489.40,
170
Investment
Analysis & Portfolio Management
(FIN630)
VU
while
the principal value is $410.60 in
current dollars. These two
values sum to the
bond's
current
market price of $900.
The
bond pricing relationship is customarily
expressed in terms of semiannual
periods.
Yield
to Maturity:
In
the preceding valuation
equations, investors call
the discount rate, r, the
yield to maturity.
This
concept is precisely the
same as internal rate of return in
corporate finance
applications.
Calculating
the Yield to Maturity:
An
easytouse approximation method
usually provides an estimate within a
few basis
points
of the true yield to
maturity.
YTM
approximate
= (annual
interest ((market pricepar
value)/years until
maturity))/0.6(market
price) + 0.4(par
value)
Plugging
in the values from the
previous example, we find an
approximate yield to
maturity
of
6.32%
In
this case, the value
from the approximation
formula is near the true
value from the
complete
valuation equation. When the
bond sells for near par,
the approximation method
is
accurate.
Some error is introduced
when a bond sells for a
substantial discount or
premium.
Spot
Rates:
For a
given issuer, all securities of a
particular maturity will not
necessarily have the
same
yield
to maturity, even if they
have the same default
risk. A spot rate is the yield to
maturity
of a
zero coupon security of the
chosen maturity. You can observe spot rates
directly from
the
U.S. Treasury strips portion
of the government bond. A
treasury strip is a
government
bond
or note that has been
decomposed into two parts,
one for the stream of
interest
payments
and one for the return of
principal at maturity These are
sometimes called
interest
only and principal only
securities, respectively. The
codes in the newspaper
listing
are
ci for coupon
interest, np for note
principal, and bp for bond
principal The
principal
only
version of a U.S. treasury
strip is a manufactured zero
coupon security, but one
whose
price
reflects the prevailing spot
rate.
The
yield to maturity is the
single interest rate that,
when applied to the stream of
cash
flows
associated with a bond,
causes the present value of those
cash flows to equal
the
bond's
market price. Yield to
maturity is a useful and frequently
cited statistic. It is akin
to
an
average of the various spot
rates over the security's
life. The market, however,
does not
value
a bond using the yield to
maturity concept. Rather,
the yield to maturity is a
derived
statistic
after the bond value is
already known; we need to
know the bond price in
order to
get
the yield to
maturity.
For
valuation purposes, a bond should be
thought of as a package of zero
coupon securities,
each
providing a single cash
flow, and each valued using
the appropriate spot rate. In
other
words,
each component is discounted by a
specific rate rather than by
some average rate.
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