This is an actuarial science question What is a bond amortization schedule? How
ID: 2799122 • Letter: T
Question
This is an actuarial science question
What is a bond amortization schedule? How can we construct a bond amortization schedule? How it does work? Why do we amortize a bond? What is a book value?
What is the amortization of premium? or discount?
An example: A $1000 par value five-year bond with a coupon rate of 10% payable semiannually and redeemable at par is bought to yield 12% convertible semiannually.
Please construct for me a bond amortization schedule table showing on the table the columns of Period, coupon, Interest earned, Principal adjustment, Book value, all showing with formulas how to calculate. Is the principal amount same as premium? What is a premium of a bond?
Please explain me all terms and example in details, and if possible of your own example to clarify the topic
Thanks in advance for help
Explanation / Answer
1-
A bond amortization schedule is a table that depicts the amount of interest expense, interest payment, and discount or premium amortization of a bond in each successive period.
2-
Step 1
find the face value of bonds payable
Step 2
Find the issue price of bond
Step 3
Bonds are issued either at Par value, at premium or discount
if bonds are issued at premium or discount we shall prepare the bond amortization schedule
Step 4
on coupon payment date we shall calculate amount of coupon payment on the date by applying coupon rate on face value
Step 5
On the same date we shall also calculate amount of interest expense by applying the effective interest rateon carrying value of bonds
Step 6
Now we shall deduct the amount of interest expense from the amount of interest paid and we shall get the value of discount amortized
Step 7
now we shall reduce the balance in discount on bonds payable by subtsract the amount of discount on bonds payable amortized and will get the balance in discount on bonds payable
Step 8
Now we shall reduce the amount of balance in discount on bonds payable from face value of bond
These steps will continue on each coupon payment date till the balance reaches to zero in discount on bonds payable or throughout the life of bonds
3-
Bond are issued either at discount or at premium so either it is a loss or gain to the issuing company so issuing company amortize the discount or premium through out the life of bond to bring down the carrying value of bond equal to its face value
4-
Book value refers to face value of bond
5-
Amortization of bond discount or premium is a kind of writing off premium or discount over the life of bond
It is assumed that bonds are issued for a value of 1000000
value of bond
interest*PVAF at 6% for 10 semiannual period + face value*PVF at 6% at 20th semiannual period
50000* 7.360 + 1000000*.5583
926300
interest
1000000*5%
50000
face value
1000000
PVAF at 6%
1-(1+r)^-n / r
1-(1.06)^-10 /.06
7.36
PVF at 6% at 10th semiannual period
1/(1+r)^n
1/(1.06)^10
0.558395
6-
date
cash paid = face value* coupon rate
interest expense = carrying value*market rate
discount amortized
carrying value in discount on bonds payable
book value
carrying value in bonds payable
Semiannual period
0
73700
1000000
926300
1
50000
55578
5578
68122
1000000
931878
2
50000
55912.68
5912.68
62209.32
1000000
937790.7
3
50000
56267.44
6267.441
55941.88
1000000
944058.1
4
50000
56643.49
6643.487
49298.39
1000000
950701.6
5
50000
57042.1
7042.096
42256.3
1000000
957743.7
6
50000
57464.62
7464.622
34791.67
1000000
965208.3
7
50000
57912.5
7912.5
26879.17
1000000
973120.8
8
50000
58387.25
8387.25
18491.92
1000000
981508.1
9
50000
58890.48
8890.485
9601.439
1000000
990398.6
10
50000
59423.91
9423.914
177.5258
1000000
999822.5
No it is not same as principal amount same as premium, premium amount is the excess price paid by the investor over the face value
1-
A bond amortization schedule is a table that depicts the amount of interest expense, interest payment, and discount or premium amortization of a bond in each successive period.
2-
Step 1
find the face value of bonds payable
Step 2
Find the issue price of bond
Step 3
Bonds are issued either at Par value, at premium or discount
if bonds are issued at premium or discount we shall prepare the bond amortization schedule
Step 4
on coupon payment date we shall calculate amount of coupon payment on the date by applying coupon rate on face value
Step 5
On the same date we shall also calculate amount of interest expense by applying the effective interest rateon carrying value of bonds
Step 6
Now we shall deduct the amount of interest expense from the amount of interest paid and we shall get the value of discount amortized
Step 7
now we shall reduce the balance in discount on bonds payable by subtsract the amount of discount on bonds payable amortized and will get the balance in discount on bonds payable
Step 8
Now we shall reduce the amount of balance in discount on bonds payable from face value of bond
These steps will continue on each coupon payment date till the balance reaches to zero in discount on bonds payable or throughout the life of bonds
3-
Bond are issued either at discount or at premium so either it is a loss or gain to the issuing company so issuing company amortize the discount or premium through out the life of bond to bring down the carrying value of bond equal to its face value
4-
Book value refers to face value of bond
5-
Amortization of bond discount or premium is a kind of writing off premium or discount over the life of bond
It is assumed that bonds are issued for a value of 1000000
value of bond
interest*PVAF at 6% for 10 semiannual period + face value*PVF at 6% at 20th semiannual period
50000* 7.360 + 1000000*.5583
926300
interest
1000000*5%
50000
face value
1000000
PVAF at 6%
1-(1+r)^-n / r
1-(1.06)^-10 /.06
7.36
PVF at 6% at 10th semiannual period
1/(1+r)^n
1/(1.06)^10
0.558395
6-
date
cash paid = face value* coupon rate
interest expense = carrying value*market rate
discount amortized
carrying value in discount on bonds payable
book value
carrying value in bonds payable
Semiannual period
0
73700
1000000
926300
1
50000
55578
5578
68122
1000000
931878
2
50000
55912.68
5912.68
62209.32
1000000
937790.7
3
50000
56267.44
6267.441
55941.88
1000000
944058.1
4
50000
56643.49
6643.487
49298.39
1000000
950701.6
5
50000
57042.1
7042.096
42256.3
1000000
957743.7
6
50000
57464.62
7464.622
34791.67
1000000
965208.3
7
50000
57912.5
7912.5
26879.17
1000000
973120.8
8
50000
58387.25
8387.25
18491.92
1000000
981508.1
9
50000
58890.48
8890.485
9601.439
1000000
990398.6
10
50000
59423.91
9423.914
177.5258
1000000
999822.5
No it is not same as principal amount same as premium, premium amount is the excess price paid by the investor over the face value
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