FNAN 301, fall 2011, quiz 2, version B, solutions
1. Bonds A, B, C, and D have face values of $1000, pay semi-annual coupons with the next
coupon due in 6 months, and mature in T years.
Bond A and B have different coupon rates, and
bonds C and D have different yields-to-maturity.
Which assertion is true if PB > PA > 0, PD >
PC > 0, T > 0, Y > 0, and C > 0?
Note that all bonds with a time-to-maturity of T have the same
time-to-maturity, all bonds with a yield-to-maturity of Y have the same yield-to-maturity (YTM),
and all bonds with a coupon rate of C have the same coupon rate.
Bond
Bond Price
Time-to-maturity
Yield-to-maturity
A
PA
T
Y
B
PB
T
Y
Bond
Bond Price
Time-to-maturity
Coupon rate
C
PC
T
C
D
PD
T
C
A. Bond A has a higher coupon rate than bond B and bond C has a higher YTM than bond D
B. Bond A has a higher coupon rate than bond B and bond D has a higher YTM than bond C
C. Bond B has a higher coupon rate than bond A and bond C has a higher YTM than bond D
D. Bond B has a higher coupon rate than bond A and bond D has a higher YTM than bond C
E. None of the above assertions is true
Bond A and bond B
If two bonds have the same YTM, face value, time to maturity, and coupon payment
schedule, but different coupon rates, then the only difference between the two bonds would
be their regular coupon payments.
The one with the higher coupons would be worth more
than the one with the lower coupons.
Therefore, the bond with the higher coupon rate
would have the greater value and the bond with the lower coupon rate would have the
lower.
Since bonds A and B are alike in all respects except for their coupon rates and since
PB > PA, the coupon rate of bond B is greater than the coupon rate of bond A.
Coupon rate of B > coupon rate of A
Bond C and bond D
If two bonds have the same coupon rate, face value, time to maturity, and coupon payment
schedule, but different YTMs, then the bond with the higher YTM has the lower value and
the bond with the lower YTM has the higher value.
Since bonds C and D are alike in all
respects except for their YTMs and since PD > PC, the yield-to-maturity of bond C is
greater than the yield-to-maturity of bond D.
YTM of C > YTM of D
Answer:
C. Bond B has a higher coupon rate than bond A and bond C has a higher YTM than bond D
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