CHAPTER 7
B-121
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 = $1,045 =
C
(PVIFA
7.5%,13
) + $1,000(PVIF
7.5%,36
)
Solving for the coupon payment, we get:
C
= $80.54
The coupon payment is the coupon rate times par value. Using this relationship, we get:
Coupon rate = $80.54 / $1,000 = .0805 or 8.05%
6.
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:
P = $34.50(PVIFA
3.7%,20
) + $1,000(PVIF
3.7%,20
) = $965.10
7.
Here we are finding the YTM of a semiannual coupon bond. The bond price equation is:
P = $1,050 = $42(PVIFA
R%
,20
) + $1,000(PVIF
R%
,20
)
Since we cannot solve the equation directly for
R
, using a spreadsheet, a financial calculator, or trial
and error, we find:
R
= 3.837%
Since the coupon payments are semiannual, this is the semiannual interest rate. The YTM is the APR
of the bond, so:
YTM = 2
3.837% = 7.67%
8.
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 = $924 =
C
(PVIFA
3.4%,29
) + $1,000(PVIF
3.4%,29
)
Solving for the coupon payment, we get:
C
= $29.84
Since this is the semiannual payment, the annual coupon payment is:
2 × $29.84 = $59.68
And the coupon rate is the annual coupon payment divided by par value, so:
Coupon rate = $59.68 / $1,000
Coupon rate = .0597 or 5.97%