Today’s semiannual inflation rate is given by: [(1 + 4%) / (1 + 2%)] -1 = 1.9608%.
Likewise, the semiannual inflation rate six months from today is: [(1 + 5%) / (1 +
2.5%)] -1 = 2.4390%.
The inflation-adjusted principal of this TIPS at the end of one year from now is:
$50,000 × (1 + 1.9608%) × (1 + 2.4390%) = $52,223.82 or about $52,224.
3. (Q.
7 in B) A firm has two $1,000 par value bonds both selling for $701.22.
The first bond has a coupon rate of 8% and 20 years of maturity. The second
bond has the same yield as the first bond but only 5 years of maturity. Both
bonds pay coupons annually. What is the annual coupon payment on the second
bond?
A) $18.56
B) $28.65
C) $35.18
D) $37.12
E)
$38.24
Answer D
The YTM on the first bond is:
80(PMT), 1,000(FV), 20(N), -701.22(PV), CPT (I/Y)
⇒
YTM = 12%.
This is also the YTM on the second bond. So the price of the second bond
is calculated as:
.
12
.
37
$
]
)
12
.
1
(
12
.
0
1
12
.
0
1
[
)
12
.
1
(
000
,
1
$
22
.
701
$
coupon
)
12
.
1
(
000
,
1
$
]
)
12
.
1
(
12
.
0
1
12
.
0
1
[
coupon
22
.
701
$
5
5
5
5
=
×
−
−
=
⇒
+
×
−
×
=
4. (Q. 8 in B) Compute the price of the following Treasury bond: $600 par, 5%
coupon payable semiannually, and a maturity of 3.5 years. The T-bill rates at 6
months and 1 year are 3.2% and 3.6%, respectively. The Treasury spot rates at
1.5 years, 2 years, 2.5 years, 3 years, and 3.5 years are 3.7%, 4%, 3.8%, 4.2%,
and 4.5%, respectively. All the interest rates are reported on a bond-equivalent
basis.
A) $585.87