Solutions-Chapter6
Posted: Tue Aug 03, 2021 7:43 am
6-3. The following table summarizes prices of various default-free, zero-coupon bonds (expressed as a percentage of face value):
a. Compute the yield to maturity for each bond.
a. Use this equation: 1 YTM FVn 1/ n
100 1/1 1YTM1
95.51
100 1/2 1YTM1
91.05
YTM1 YTM1
4.70%
4.80%
100 1/3 86.38
100 1/4 1YTM4
81.65
100 1/5 1YTM5
76.51
1YTM3 YTM3 5.00%
n P
YTM4 YTM5
5.20% 5.50%
6-4. Suppose the current zero-coupon yield curve for risk-free bonds is as follows:
a. b. c. a.
b. c.
What is the price per $100 face value of a two-year, zero-coupon, risk-free bond? What is the price per $100 face value of a four-year, zero-coupon, risk-free bond? What is the risk-free interest rate for a five-year maturity?
P100/(1.055)2 $89.85 P100/(1.0595)4 $79.36
6.05%
6-6. Suppose a 10-year, $1000 bond with an 8% coupon rate and semiannual coupons is trading for a price of $1034.74.
a. b.
a.
What is the bond’s yield to maturity (expressed as an APR with semiannual compounding)? If the bond’s yield to maturity changes to 9% APR, what will the bond’s price be?
40 40 401000
$1,034.74 YTM YTM YTM YTM 7.5%
(1 ) (1 )2 (1 )20 222
Use your financial calculator:
PV = -1034.74, FV = 1000, N = 20, PMT = 40, Solve for rate => 3.75% (a 6-month rate).
Therefore, YTM = 3.75% × 2 = 7.50%
@ Using P=40×!Ts[1-
6-8. The prices of several bonds with face values of $1000 are summarized in the following table:
For each bond, state whether it trades at a discount, at par, or at a premium.
Bond A trades at a discount. Bond D trades at par. Bonds B and C trade at a premium.
6-10. Suppose a seven-year, $1000 bond with an 8% coupon rate and semiannual coupons is trading with a yield to maturity of 6.75%.
FORMULA : Cpnxtyftettypiftdffsn
THE P=
Bond -
vawnnon
,÷ys⇒tlF÷w=
934.96
a. Is this bond currently trading at a discount, at par, or at a premium? Explain.
b. If the yield to maturity of the bond rises to 7% (APR with semiannual compounding), what price will the bond trade for?
a. Because the yield to maturity is less than the coupon rate, the bond is trading at a premium. 40 40 401000
b. (10.035)(10.035)2 (10.035)14 $1,054.60
OR -
Formula : cpnxtyftettypiftdffygn
THE P=
Bond -
valuation
Using
P=
.
loot 40×1=[1-1]
=
1054.60
035 1.0354
+
1.0
354
a. Compute the yield to maturity for each bond.
a. Use this equation: 1 YTM FVn 1/ n
100 1/1 1YTM1
95.51
100 1/2 1YTM1
91.05
YTM1 YTM1
4.70%
4.80%
100 1/3 86.38
100 1/4 1YTM4
81.65
100 1/5 1YTM5
76.51
1YTM3 YTM3 5.00%
n P
YTM4 YTM5
5.20% 5.50%
6-4. Suppose the current zero-coupon yield curve for risk-free bonds is as follows:
a. b. c. a.
b. c.
What is the price per $100 face value of a two-year, zero-coupon, risk-free bond? What is the price per $100 face value of a four-year, zero-coupon, risk-free bond? What is the risk-free interest rate for a five-year maturity?
P100/(1.055)2 $89.85 P100/(1.0595)4 $79.36
6.05%
6-6. Suppose a 10-year, $1000 bond with an 8% coupon rate and semiannual coupons is trading for a price of $1034.74.
a. b.
a.
What is the bond’s yield to maturity (expressed as an APR with semiannual compounding)? If the bond’s yield to maturity changes to 9% APR, what will the bond’s price be?
40 40 401000
$1,034.74 YTM YTM YTM YTM 7.5%
(1 ) (1 )2 (1 )20 222
Use your financial calculator:
PV = -1034.74, FV = 1000, N = 20, PMT = 40, Solve for rate => 3.75% (a 6-month rate).
Therefore, YTM = 3.75% × 2 = 7.50%
@ Using P=40×!Ts[1-
6-8. The prices of several bonds with face values of $1000 are summarized in the following table:
For each bond, state whether it trades at a discount, at par, or at a premium.
Bond A trades at a discount. Bond D trades at par. Bonds B and C trade at a premium.
6-10. Suppose a seven-year, $1000 bond with an 8% coupon rate and semiannual coupons is trading with a yield to maturity of 6.75%.
FORMULA : Cpnxtyftettypiftdffsn
THE P=
Bond -
vawnnon
,÷ys⇒tlF÷w=
934.96
a. Is this bond currently trading at a discount, at par, or at a premium? Explain.
b. If the yield to maturity of the bond rises to 7% (APR with semiannual compounding), what price will the bond trade for?
a. Because the yield to maturity is less than the coupon rate, the bond is trading at a premium. 40 40 401000
b. (10.035)(10.035)2 (10.035)14 $1,054.60
OR -
Formula : cpnxtyftettypiftdffygn
THE P=
Bond -
valuation
Using
P=
.
loot 40×1=[1-1]
=
1054.60
035 1.0354
+
1.0
354