(Bond valuation) You are examining three bonds with a par value of $1,000 (you r
ID: 2790989 • Letter: #
Question
(Bond valuation) You are examining three bonds with a par value of $1,000 (you receive $1,000 at maturity) and are concerned with what would happen to their market value if interest rates (or the market discount rate) changed. The three bonds are Bond A-a bond with 5 years left to maturity that has an annual coupon interest rate of 12 percent, but the interest is paid semiannually. Bond B-a bond with 8 years left to maturity that has an annual coupon interest rate of 12 percent, but the interest is paid semiannually. Bond C-a bond with 16 years left to maturity that has an annual coupon interest rate of 12 percent, but the interest is paid semiannually.
What would be the value of these bonds if the market discount rate were
a. 12 percent per year compounded semiannually?
b. 7 percent per year compounded semiannually?
c. 16 percent per year compounded semiannually?
d. What observations can you make about these results?
a. If the market discount rate were 12 percent per year compounded semiannually, the value of Bond A is $ . (Roundtothenearestcent.)
If the market discount rate were 12 percent per year compounded semiannually, the value of Bond B is $ . (Roundtothenearestcent.)
If the market discount rate were 12 percent per year compounded semiannually, the value of Bond C is $ . (Roundtothenearestcent.)
b. If the market discount rate were 7 percent per year compounded semiannually, the value of Bond A is $ . (Round to the nearest cent.)
If the market discount rate were 7 percent per year compounded semiannually, the value of Bond B is $ . (Round to the nearest cent.)
If the market discount rate were 7 percent per year compounded semiannually, the value of Bond C is $ . (Round to the nearest cent.)
c. If the market discount rate were 16 percent per year compounded semiannually, the value of Bond A is $ . (Roundtothenearestcent.)
If the market discount rate were 16 percent per year compounded semiannually, the value of Bond B is $ . (Roundtothenearestcent.)
If the market discount rate were 16 percent per year compounded semiannually, the value of Bond C is $ . (Roundtothenearestcent.)
Explanation / Answer
When market interest rate is 12%
A-
PVAF at 6% semiannually for the period of 10 semiannual
1-(1+r)^-n / r
1-(1.06)^-10 / .06
7.3608
PVAF at 6% semiannually for the period of 16 semiannual
1-(1+r)^-n / r
1-(1.06)^-16 / .06
10.1059
PVAF at 6% semiannually for the period of 32 semiannual
1-(1+r)^-n / r
1-(1.06)^-32 / .06
14.08404
PVF at 6% semiannually at 10 semiannual period
1/(1+r)^n
1/1.06^10
0.558395
PVF at 6% semiannually at 16 semiannual period
1/(1+r)^n
1/1.06^16
0.393646
PVAF at 6% semiannually for the period of 32 semiannual
1/(1+r)^n
1/1.06^32
0.154957
value of bonds when market interest rate is 12% i.e 6% per semiannual
value of bond A
interest*PVAF + face value*PVF)
60*7.3608 +1000*.558395
1000.043
value of bond B
interest*PVAF + face value*PVF)
60*10.1059 +1000*.393646
1000
value of bond C
interest*PVAF + face value*PVF)
60*14.08404 +1000*.154957
999.9994
When market interest rate is 7%
B-
PVAF at 3.5% semiannually for the period of 10 semiannual
1-(1+r)^-n / r
1-(1.035)^-10 / .035
8.316605
PVAF at 3.5% semiannually for the period of 16 semiannual
1-(1+r)^-n / r
1-(1.035)^-16 / .06
12.09412
PVAF at 3.5% semiannually for the period of 32 semiannual
1-(1+r)^-n / r
1-(1.035)^-32 / .035
19.06887
PVF at 3.5% semiannually at 10 semiannual period
1/(1+r)^n
1/1.035^10
0.708919
PVF at 3.5% semiannually at 16 semiannual period
1/(1+r)^n
1/1.035^16
0.576706
PVAF at 3.5% semiannually for the period of 32 semiannual
1/(1+r)^n
1/1.035^32
0.33259
value of bonds when market interest rate is 7% i.e 3.5% per semiannual
value of bond A
interest*PVAF + face value*PVF)
60*8.3166+1000*.708919
1207.915
value of bond B
interest*PVAF + face value*PVF)
60*12.09412+1000*.576706
1302.353
value of bond C
interest*PVAF + face value*PVF)
60*19.06887 +1000*.33259
1476.722
When market interest rate is 16%
C-
PVAF at 8% semiannually for the period of 10 semiannual
1-(1+r)^-n / r
1-(1.08)^-10 / .08
6.710081
PVAF at 8% semiannually for the period of 16 semiannual
1-(1+r)^-n / r
1-(1.08)^-16 / .08
8.851369
PVAF at 8% semiannually for the period of 32 semiannual
1-(1+r)^-n / r
1-(1.08)^-32 / .08
11.435
PVF at 8% semiannually at 10 semiannual period
1/(1+r)^n
1/1.08^10
0.463193
PVF at 8% semiannually at 16 semiannual period
1/(1+r)^n
1/1.08^16
0.29189
PVAF at 8% semiannually for the period of 32 semiannual
1/(1+r)^n
1/1.08^32
0.0852
value of bonds when market interest rate is 16% i.e 8% per semiannual
value of bond A
interest*PVAF + face value*PVF)
60*8.3166+1000*.463193
962.189
value of bond B
interest*PVAF + face value*PVF)
60*8.851369+1000*.29189
822.9721
value of bond C
interest*PVAF + face value*PVF)
60*11.435 +1000*.0852
771.3
D-
When market interest rate is less than coupon rate bonds price would be higher than it face value and when market interest rate would be greater than coupon rate, value of the bond would be less than par value and when both the rates are same bonds would be issued at par
When market interest rate is 12%
A-
PVAF at 6% semiannually for the period of 10 semiannual
1-(1+r)^-n / r
1-(1.06)^-10 / .06
7.3608
PVAF at 6% semiannually for the period of 16 semiannual
1-(1+r)^-n / r
1-(1.06)^-16 / .06
10.1059
PVAF at 6% semiannually for the period of 32 semiannual
1-(1+r)^-n / r
1-(1.06)^-32 / .06
14.08404
PVF at 6% semiannually at 10 semiannual period
1/(1+r)^n
1/1.06^10
0.558395
PVF at 6% semiannually at 16 semiannual period
1/(1+r)^n
1/1.06^16
0.393646
PVAF at 6% semiannually for the period of 32 semiannual
1/(1+r)^n
1/1.06^32
0.154957
value of bonds when market interest rate is 12% i.e 6% per semiannual
value of bond A
interest*PVAF + face value*PVF)
60*7.3608 +1000*.558395
1000.043
value of bond B
interest*PVAF + face value*PVF)
60*10.1059 +1000*.393646
1000
value of bond C
interest*PVAF + face value*PVF)
60*14.08404 +1000*.154957
999.9994
When market interest rate is 7%
B-
PVAF at 3.5% semiannually for the period of 10 semiannual
1-(1+r)^-n / r
1-(1.035)^-10 / .035
8.316605
PVAF at 3.5% semiannually for the period of 16 semiannual
1-(1+r)^-n / r
1-(1.035)^-16 / .06
12.09412
PVAF at 3.5% semiannually for the period of 32 semiannual
1-(1+r)^-n / r
1-(1.035)^-32 / .035
19.06887
PVF at 3.5% semiannually at 10 semiannual period
1/(1+r)^n
1/1.035^10
0.708919
PVF at 3.5% semiannually at 16 semiannual period
1/(1+r)^n
1/1.035^16
0.576706
PVAF at 3.5% semiannually for the period of 32 semiannual
1/(1+r)^n
1/1.035^32
0.33259
value of bonds when market interest rate is 7% i.e 3.5% per semiannual
value of bond A
interest*PVAF + face value*PVF)
60*8.3166+1000*.708919
1207.915
value of bond B
interest*PVAF + face value*PVF)
60*12.09412+1000*.576706
1302.353
value of bond C
interest*PVAF + face value*PVF)
60*19.06887 +1000*.33259
1476.722
When market interest rate is 16%
C-
PVAF at 8% semiannually for the period of 10 semiannual
1-(1+r)^-n / r
1-(1.08)^-10 / .08
6.710081
PVAF at 8% semiannually for the period of 16 semiannual
1-(1+r)^-n / r
1-(1.08)^-16 / .08
8.851369
PVAF at 8% semiannually for the period of 32 semiannual
1-(1+r)^-n / r
1-(1.08)^-32 / .08
11.435
PVF at 8% semiannually at 10 semiannual period
1/(1+r)^n
1/1.08^10
0.463193
PVF at 8% semiannually at 16 semiannual period
1/(1+r)^n
1/1.08^16
0.29189
PVAF at 8% semiannually for the period of 32 semiannual
1/(1+r)^n
1/1.08^32
0.0852
value of bonds when market interest rate is 16% i.e 8% per semiannual
value of bond A
interest*PVAF + face value*PVF)
60*8.3166+1000*.463193
962.189
value of bond B
interest*PVAF + face value*PVF)
60*8.851369+1000*.29189
822.9721
value of bond C
interest*PVAF + face value*PVF)
60*11.435 +1000*.0852
771.3
D-
When market interest rate is less than coupon rate bonds price would be higher than it face value and when market interest rate would be greater than coupon rate, value of the bond would be less than par value and when both the rates are same bonds would be issued at par
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