1)
Staind, Inc., has 7.5 percent coupon bonds on the market that have 10 years left to
maturity. The bonds make annual payments. If the YTM on these bonds is 8.75% what is
the current market price?
The price of any bond is the PV of the interest payment, plus the PV of the par value.
Notice this bond
as an annual coupon. The price of the bond will be:
Price = PV of coupon payments + PV of face value
PV of coupon payments: PV=75 ($1000*.075), n=10, i=8.75
PV of face value: FV=1000,n=10,i=8.75
Price = 75({1 – [1/(1 + .0875)]
10
} / .0875) + 1,000[1 / (1 + .0875)
10
] = $918.89
2)
Grohl Co. issued 11-year bonds a year ago at a coupon rate of 6.9 percent. The
bonds make semiannual payments. If the YTM on these bonds is 7.4 percent, what is the
current bond price?
Start with the coupon payments:
How many coupon payments do you expect to receive if you buy this bond and hold it to
maturity? (n)
How does the interest rate match the periods of the coupon payments? (i)
What is the amount of the coupon payment? (pmt)
What is the face value? (FV)
3)
To find the price of this bond, we need to realize that the maturity of the bond is
10 years. The bond was issued one year ago, with 11 years to maturity, so there are 10
years left on the bond. Also, the coupons are semiannual, so we need to use the
semiannual interest rate and the number of semiannual periods. The price of the bond is:
PMT=34.50,n=20,i=3.7, solve for PV
FV=1000,n=20,i=3.45
P=$34.50(PVIFA
3.7%,20
) + $1,000(PVIF
3.7%,20
) = $965.10
4)
If Treasury bills are currently paying 7 percent and the inflation rate is 3.8
percent, what is the approximate real rate of interest? The exact real rate?
The approximate relationship between nominal interest rates (
R
), real interest rates (
r
),
and inflation (
h
) is:
R
=
r
+
h
Approximate
r
= .07 – .038 =.032 or 3.20%
The Fisher equation, which shows the exact relationship between nominal interest rates,
real interest rates, and inflation is:
(1 +
R
) = (1 +
r
)(1 +
h
)
(1 + .07) = (1 +
r
)(1 + .038)
Exact
r
= [(1 + .07) / (1 + .038)] – 1 = .0308 or 3.08%