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Information Report

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FINS1613

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Chapter
6
Basic
questions
(1–16)
1.
The
yield
to
maturity
(YTM)
is
the
required
rate
of
return
on
a
bond
expressed
as
a
nominal
annual
interest
rate.
For
non
‐
callable
bonds,
the
yield
to
maturity
and
required
rate
of
return
are
interchangeable
terms.
Unlike
YTM
and
required
return,
the
coupon
rate
is
not
a
return
used
as
the
interest
rate
in
bond
cash
flow
valuation,
but
it
is
a
fixed
percentage
of
face
value
over
the
life
of
the
bond
used
to
set
the
coupon
payment
amount.
For
the
example
given,
the
coupon
rate
on
the
bond
is
still
10%,
and
the
YTM
is
8%.
2.
Price
and
yield
move
in
opposite
directions;
if
interest
rates
rise,
the
price
of
the
bond
will
fall.
This
is
because
the
fixed
coupon
payments
determined
by
the
fixed
coupon
rate
are
not
as
valuable
when
interest
rates
rise.
Hence,
the
price
of
the
bond
decreases.
NOTE:
Most
problems
do
not
explicitly
list
a
par
value
for
bonds.
Even
though
a
bond
can
have
any
par
value,
in
general,
we
have
adopted
a
par
value
of
$1000.
We
will
use
this
par
value
in
all
problems
unless
a
different
par
value
is
explicitly
stated.
3.
The
price
of
any
bond
is
the
PV
of
the
interest
payment,
plus
the
PV
of
the
par
value.
Notice
this
problem
assumes
an
annual
coupon.
The
price
of
the
bond
will
be:
P
=
$60({1
–
[1/(1
+
0.08)]
9
}
/
0.08)
+
$1000[1
/
(1
+
0.08)
9
]
P
=
$875.06
We
would
like
to
introduce
shorthand
notation
here.
Rather
than
write
(or
type,
as
the
case
may
be)
the
entire
equation
for
the
PV
of
a
lump
sum,
or
the
PVA
equation,
it
is
common
to
abbreviate
the
equations
as:
PVIF
R,t
=
1
/
(1
+
R
)
t
which
stands
for
Present
Value
Interest
Factor
PVIFA
R,t
=
({1
–
[1/(1
+
R
)]
t
}
/
R
)
which
stands
for
Present
Value
Interest
Factor
of
an
Annuity
These
abbreviations
are
shorthand
notation
for
the
equations
in
which
the
interest
rate
and
the
number
of
periods
are
substituted
into
the
equation
and
solved.
We
will
use
this
shorthand
notation
in
the
remainder
of
the
solutions
key.
The
bond
price
equation
for
this
problem
would
be:
P
=
$60(PVIFA
8%,9
)
+
$1000(PVIF
8%,9
)
P
=
$875.06
4.
Here,
we
need
to
find
the
YTM
of
a
bond.
The
equation
for
the
bond
price
is:
P
=
$1038.50
=
$70(PVIFA
R%
,9
)
+
$1000(PVIF
R
%,9
)
Notice
the
equation
cannot
be
solved
directly
for
R
.
Using
a
spreadsheet,
a
financial
calculator,
or
trial
and
error,
we
find:
R
=
YTM
=
6.42%
If
you
are
using
trial
and
error
to
find
the
YTM
of
the
bond,
you
might
be
wondering
how
to
pick
an
interest
rate
to
start
the
process.
First,
we
know
the
YTM
has
to
be
lower
than
the
coupon
rate
since
the
bond
is
a
premium
bond.
That
still
leaves
a
lot
of
interest
rates
to
check.
One
way
to
get
a
starting
point
is
to
use
the
following
equation,
which
will
give
you
an
approximation
of
the
YTM:
Approximate
YTM
=
[Annual
interest
payment
+
(Par
value
–
Price)
/
Years
to
maturity]
/
[(Price
+
Par
value)
/
2]
Solving
for
this
problem,
we
get:
Approximate
YTM
=
[$70
+
(–$38.50
/
9)]
/
[($1038.50
+
1000)
/
2]
Approximate
YTM
=
0.0645,
or
6.45%
This
is
not
the
exact
YTM,
but
it
is
close,
and
it
will
give
you
a
place
to
start.
5.
Here
we
need
to
find
the
coupon
rate
of
the
bond.
All
we
need
to
do
is
to
set
up
the
bond
pricing
equation
and
solve
for
the
coupon
payment
as
follows:
P
=
$963
=
C
(PVIFA
7.5%,12
)
+
$1000(PVIF
7.5%,12
)
Solving
for
the
coupon
payment,
we
get:
C
=
$70.22
The
coupon
payment
is
the
coupon
rate
multiplied
by
par
value.
Using
this
relationship,
we
get:
Coupon
rate
=
$70.22
/
$1000
Coupon
rate
=
0.0702,
or
7.02%
6.
To
find
the
price
of
this
bond,
we
need
to
realise
that
the
maturity
of
the
bond
is
19
years.
The
bond
was
issued
one
year
ago,
with
20
years
to
maturity,
so
there
are
19
years
left
on
the
bond.
Also,
the
face
value
is
$200
000
and
the
coupons
are
semi
‐
annual,
so
we
need
to
use
the
semi
‐
annual
interest
rate
and
the
number
of
semi
‐
annual
periods.
The
price
of
the
bond
is:
The
coupon
is
$200
000
x
6.1%/2
=
6100
P
=
$6100(PVIFA
2.65%,38
)
+
$200
000(PVIF
2.65%,38
)
P
=
$219
014.80
7.
Here,
we
are
finding
the
YTM
of
a
semi
‐
annual
coupon
bond.
The
bond
price
equation
is:
P
=
$188
000
=
$6900(PVIFA
R%
,26
)
+
$200
000(PVIF
R%
,26
)
Since
we
cannot
solve
the
equation
directly
for
R
,
using
a
spreadsheet,
a
financial
calculator,
or
trial
and
error,
we
find:
R
=
3.818%
Since
the
coupon
payments
are
semi
‐
annual,
this
is
the
semi
‐
annual
interest
rate.
The
YTM
is
the
APR
of
the
bond,
so:
YTM
=
2
3.818%
YTM
=
7.64%
8.
To
find
the
price
of
the
bill,
we
need
to
realise
that
the
maturity
of
the
bill
is
105
days.
Also,
the
face
value
is
$500
000.
The
price
of
the
bill
is:
P
=
$500
000
/
(1
+3.5%x105/365)
P
=
$495
015.94
9.
To
find
the
price
of
this
bill,
we
need
to
realise
that
the
maturity
of
the
bill
is
now
50
days
(105–55).
The
face
value
remains
unchanged
at
$500
000
The
price
of
the
bill
is:
P
=
$500
000
/
(1
+3.25%x50/365)
P
=
$497
783.84
10.
Here,
we
need
to
find
the
coupon
rate
of
the
bond.
All
we
need
to
do
is
to
set
up
the
bond
pricing
equation
and
solve
for
the
coupon
payment
as
follows:

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