Miller Corporation has a premium bond making semiannual payments. The bond has a
ID: 2780818 • Letter: M
Question
Miller Corporation has a premium bond making semiannual payments. The bond has a coupon rate of 9 percent, a YTM of 7 percent, and 19 years to maturity. The Modigliani Company has a discount bond making semiannual payments. This bond has a coupon rate of 7 percent, a YTM of 9 percent, and also has 19 years to maturity What is the price of each bond today? (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).) Price of Miller bond 1,208.41 Price of Modigliani bond 819.50 If interest rates remain unchanged, what do you expect the price of these bonds to be 1 year from now? In 10 years? In 14 years? In 18 years? In 19 years? (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).) Price of bond 1 year 10 years 14 years 18 years 19 years Miller bond Modigliani bond in: $ 1,459.80 882.93 $ 1,000.00 $ 1,000.00Explanation / Answer
Miller bond
Modigiliani bond
PVAF at 19 year period
PVAF at 19 year period
present value annuity factor at 3.5% for 38 semiannual period
[1-(1+r)^-n / r]
[1-(1.035)^-38 /.035]
10.4205
present value annuity factor at 3.5% for 38 semiannual period
[1-(1+r)^-n / r]
[1-(1.045)^-38 /.045]
18.0499
present value factor at 3.5% for 38th period
1/(1+r)^n
1/(1.035)^38
0.270562
present value factor at 3.5% for 38th period
1/(1+r)^n
1/(1.035)^38
0.18775
value of miller bond today
interest*PVAF + face value*PVF
45*20.8419 + 1000*.2705
1208.386
value of miller bond today
interest*PVAF + face value*PVF
35*18.0499 + 1000*.1877
819.4465
price of bond 1 year from now
price of bond 1 year from now
present value annuity factor at 3.5% for 36 semiannual period
[1-(1+r)^-n / r]
[1-(1.035)^-36 /.035]
20.2904
present value annuity factor at 3.5% for 36 semiannual period
[1-(1+r)^-n / r]
[1-(1.045)^-36 /.045]
17.666
present value factor at 3.5% for 36th period
1/(1+r)^n
1/(1.035)^36
0.289833
present value factor at 3.5% for 36th period
1/(1+r)^n
1/(1.045)^36
0.205028
value of miller bond one year from now
interest*PVAF + face value*PVF
45*20.2904 + 1000*.2898
1202.868
value of miller bond one year from now
interest*PVAF + face value*PVF
35*17.666 + 1000*.2050
823.31
price of bond 10 year from now
price of bond 10 year from now
present value annuity factor at 3.5% for 36 semiannual period
[1-(1+r)^-n / r]
[1-(1.035)^-18 /.035]
13.1896
present value annuity factor at 3.5% for 36 semiannual period
[1-(1+r)^-n / r]
[1-(1.045)^-18 /.045]
12.159
present value factor at 3.5% for 36th period
1/(1+r)^n
1/(1.035)^18
0.538361
present value factor at 3.5% for 36th period
1/(1+r)^n
1/(1.035)^18
0.4528
value of miller bond one year from now
interest*PVAF + face value*PVF
45*13.1896 + 1000*.5383
1131.832
value of miller bond one year from now
interest*PVAF + face value*PVF
35*12.159 + 1000*.4528
878.365
price of bond 14 year from now
price of bond 14 year from now
present value annuity factor at 3.5% for 36 semiannual period
[1-(1+r)^-n / r]
[1-(1.035)^-10 /.035]
8.3166
present value annuity factor at 3.5% for 36 semiannual period
[1-(1+r)^-n / r]
[1-(1.045)^-10 /.045]
7.912
present value factor at 3.5% for 36th period
1/(1+r)^n
1/(1.035)^10
0.708919
present value factor at 3.5% for 36th period
1/(1+r)^n
1/(1.035)^10
0.643928
value of miller bond one year from now
interest*PVAF + face value*PVF
45*8.3166 + 1000*.7089
1083.147
value of miller bond one year from now
interest*PVAF + face value*PVF
35*7.912 + 1000*.6439
920.82
price of bond 18 year from now
price of bond 18 year from now
present value annuity factor at 3.5% for 36 semiannual period
[1-(1+r)^-n / r]
[1-(1.035)^-02 /.035]
1.8996
present value annuity factor at 3.5% for 36 semiannual period
[1-(1+r)^-n / r]
[1-(1.045)^-02 /.045]
1.872
present value factor at 3.5% for 36th period
1/(1+r)^n
1/(1.035)^02
0.933511
present value factor at 3.5% for 36th period
1/(1+r)^n
1/(1.045)^02
0.91573
value of miller bond one year from now
interest*PVAF + face value*PVF
45*1.8996 + 1000*.9335
1018.982
value of miller bond one year from now
interest*PVAF + face value*PVF
35*1.872 + 1000*.9157
981.22
price of bond 19 year from now
price of bond 19 year from now
present value annuity factor at 3.5% for 36 semiannual period
[1-(1+r)^-n / r]
[1-(1.035)^-0 /.035]
0
present value annuity factor at 3.5% for 36 semiannual period
[1-(1+r)^-n / r]
[1-(1.045)^-0 /.045]
0
present value factor at 3.5% for 36th period
1/(1+r)^n
1/(1.035)^0
1
present value factor at 3.5% for 36th period
1/(1+r)^n
1/(1.045)^0
1
value of miller bond one year from now
interest*PVAF + face value*PVF
45*0 + 1000*1
1000
value of miller bond one year from now
interest*PVAF + face value*PVF
45*0 + 1000*1
1000
value of bond
miller
Modigliani
Year
1
1202.868
823.31
10
1131.832
878.365
14
1083.147
920.82
18
1018.982
981.22
19
1000
1000
Miller bond
Modigiliani bond
PVAF at 19 year period
PVAF at 19 year period
present value annuity factor at 3.5% for 38 semiannual period
[1-(1+r)^-n / r]
[1-(1.035)^-38 /.035]
10.4205
present value annuity factor at 3.5% for 38 semiannual period
[1-(1+r)^-n / r]
[1-(1.045)^-38 /.045]
18.0499
present value factor at 3.5% for 38th period
1/(1+r)^n
1/(1.035)^38
0.270562
present value factor at 3.5% for 38th period
1/(1+r)^n
1/(1.035)^38
0.18775
value of miller bond today
interest*PVAF + face value*PVF
45*20.8419 + 1000*.2705
1208.386
value of miller bond today
interest*PVAF + face value*PVF
35*18.0499 + 1000*.1877
819.4465
price of bond 1 year from now
price of bond 1 year from now
present value annuity factor at 3.5% for 36 semiannual period
[1-(1+r)^-n / r]
[1-(1.035)^-36 /.035]
20.2904
present value annuity factor at 3.5% for 36 semiannual period
[1-(1+r)^-n / r]
[1-(1.045)^-36 /.045]
17.666
present value factor at 3.5% for 36th period
1/(1+r)^n
1/(1.035)^36
0.289833
present value factor at 3.5% for 36th period
1/(1+r)^n
1/(1.045)^36
0.205028
value of miller bond one year from now
interest*PVAF + face value*PVF
45*20.2904 + 1000*.2898
1202.868
value of miller bond one year from now
interest*PVAF + face value*PVF
35*17.666 + 1000*.2050
823.31
price of bond 10 year from now
price of bond 10 year from now
present value annuity factor at 3.5% for 36 semiannual period
[1-(1+r)^-n / r]
[1-(1.035)^-18 /.035]
13.1896
present value annuity factor at 3.5% for 36 semiannual period
[1-(1+r)^-n / r]
[1-(1.045)^-18 /.045]
12.159
present value factor at 3.5% for 36th period
1/(1+r)^n
1/(1.035)^18
0.538361
present value factor at 3.5% for 36th period
1/(1+r)^n
1/(1.035)^18
0.4528
value of miller bond one year from now
interest*PVAF + face value*PVF
45*13.1896 + 1000*.5383
1131.832
value of miller bond one year from now
interest*PVAF + face value*PVF
35*12.159 + 1000*.4528
878.365
price of bond 14 year from now
price of bond 14 year from now
present value annuity factor at 3.5% for 36 semiannual period
[1-(1+r)^-n / r]
[1-(1.035)^-10 /.035]
8.3166
present value annuity factor at 3.5% for 36 semiannual period
[1-(1+r)^-n / r]
[1-(1.045)^-10 /.045]
7.912
present value factor at 3.5% for 36th period
1/(1+r)^n
1/(1.035)^10
0.708919
present value factor at 3.5% for 36th period
1/(1+r)^n
1/(1.035)^10
0.643928
value of miller bond one year from now
interest*PVAF + face value*PVF
45*8.3166 + 1000*.7089
1083.147
value of miller bond one year from now
interest*PVAF + face value*PVF
35*7.912 + 1000*.6439
920.82
price of bond 18 year from now
price of bond 18 year from now
present value annuity factor at 3.5% for 36 semiannual period
[1-(1+r)^-n / r]
[1-(1.035)^-02 /.035]
1.8996
present value annuity factor at 3.5% for 36 semiannual period
[1-(1+r)^-n / r]
[1-(1.045)^-02 /.045]
1.872
present value factor at 3.5% for 36th period
1/(1+r)^n
1/(1.035)^02
0.933511
present value factor at 3.5% for 36th period
1/(1+r)^n
1/(1.045)^02
0.91573
value of miller bond one year from now
interest*PVAF + face value*PVF
45*1.8996 + 1000*.9335
1018.982
value of miller bond one year from now
interest*PVAF + face value*PVF
35*1.872 + 1000*.9157
981.22
price of bond 19 year from now
price of bond 19 year from now
present value annuity factor at 3.5% for 36 semiannual period
[1-(1+r)^-n / r]
[1-(1.035)^-0 /.035]
0
present value annuity factor at 3.5% for 36 semiannual period
[1-(1+r)^-n / r]
[1-(1.045)^-0 /.045]
0
present value factor at 3.5% for 36th period
1/(1+r)^n
1/(1.035)^0
1
present value factor at 3.5% for 36th period
1/(1+r)^n
1/(1.045)^0
1
value of miller bond one year from now
interest*PVAF + face value*PVF
45*0 + 1000*1
1000
value of miller bond one year from now
interest*PVAF + face value*PVF
45*0 + 1000*1
1000
value of bond
miller
Modigliani
Year
1
1202.868
823.31
10
1131.832
878.365
14
1083.147
920.82
18
1018.982
981.22
19
1000
1000