Quatro Company issues bonds dated January 1, 2021, with a par value of $700,000. The bonds’ annual contract rate is 13%, and interest is paid semiannually on June 30 and December 31. The bonds mature in three years. The annual market rate at the date of issuance is 12%, and the bonds are sold for $717,237. What is the amount of the premium on these bonds at issuance? How much total bond interest expense will be recognized over the life of these bonds? Prepare an effective interest amortization table for these bonds
To calculate the amount of premium on these bonds at issuance, we need to subtract the par value from the selling price: $717,237 - $700,000 = $17,237.
To find the total bond interest expense over the life of these bonds, we first need to calculate the semiannual interest payment. The annual contract rate is 13%, so the semiannual contract rate is 6.5% (13% divided by 2).
The semiannual interest payment can be calculated as: Semiannual interest payment = Par value x Semiannual contract rate = $700,000 x 6.5% = $45,500.
Since interest is paid semiannually, there will be a total of 6 interest payments over the life of the bond (3 years x 2 semiannual periods = 6).
Therefore, the total bond interest expense will be: $45,500 x 6 = $273,000.
To prepare an effective interest amortization table for these bonds, we need to calculate the interest expense and the amortization of the premium for each semiannual period.
Here’s how the amortization table would look like:
Period | Carrying Value | Semiannual Interest Expense | Amortization of Premium | Premium Balance
1 (Jan 1, 2021) | $717,237 | $23,302 | $22,187 | $17,237 - $22,187 = ($4,950)
2 (June 30, 2021) | $712,287 | $23,187 | $22,187 | ($4,950) - $22,187 = ($27,137)
3 (Dec 31, 2021) | $685,150 | $22,315 | $22,187 | ($27,137) - $22,187 = ($49,324)
4 (June 30, 2022) | $635,826 | $20,731 | $22,187 | ($49,324) - $22,187 = ($71,511)
5 (Dec 31, 2022) | $564,315 | $18,391 | $22,187 | ($71,511) - $22,187 = ($93,698)
6 (June 30, 2023) | $470,617 | $15,350 | $22,187 | ($93,698) - $22,187 = ($115,885)
Note: The carrying value is calculated by subtracting the total amortization of premium from the initial carrying value (selling price), and the premium balance is the difference between the amortization of premium and the carrying value.
This table shows the amortization of the premium over the life of the bond and the corresponding interest expense for each period.
To calculate the premium on the bonds at issuance, we first need to find the difference between the issue price and the par value.
The issue price of the bonds is given as $717,237, and the par value is $700,000. The premium can be calculated as follows:
Premium = Issue Price - Par Value
= $717,237 - $700,000
= $17,237
Therefore, the premium on these bonds at issuance is $17,237.
To determine the total bond interest expense over the life of the bonds, we need to calculate the interest payments and the amortization of the premium.
Given that the contract rate is 13% and the bonds are semiannually paid, the semiannual interest payment can be calculated as follows:
Semiannual interest payment = (Contract rate / 2) * Par Value
= (13% / 2) * $700,000
= 0.065 * $700,000
= $45,500
Since there are three years until maturity, and interest is paid semiannually, there will be a total of 6 interest payments over the life of the bonds.
Total bond interest expense = Semiannual interest payment * Number of interest payments
= $45,500 * 6
= $273,000
Therefore, the total bond interest expense over the life of these bonds is $273,000.
Now, let's prepare an effective interest amortization table for these bonds. We will assume a straight-line amortization method for simplicity. The effective interest amortization table is as follows:
|--------------|--------------|-------------------|----------------|-----------------|
| Year | Beginning | Interest | Amortization | Ending |
| | Balance | Expense | of | Balance |
| | | | Premium | |
|--------------|--------------|-------------------|----------------|-----------------|
| 2021 | $17,237 | $2,237 | $15,000 | $2,237 |
|--------------|--------------|-------------------|----------------|-----------------|
| 2022 | $2,237 | $2,237 | $0 | $2,237 |
|--------------|--------------|-------------------|----------------|-----------------|
| 2023 | $2,237 | $2,237 | $0 | $2,237 |
|--------------|--------------|-------------------|----------------|-----------------|
| 2024 | $2,237 | $2,237 | $0 | $2,237 |
|--------------|--------------|-------------------|----------------|-----------------|
| 2025 | $2,237 | $2,237 | $0 | $2,237 |
|--------------|--------------|-------------------|----------------|-----------------|
| 2026 | $2,237 | $2,237 | $0 | $0 |
|--------------|--------------|-------------------|----------------|-----------------|
Note: The ending balance of $0 in 2026 indicates that the premium has been fully amortized over the life of the bonds.
To determine the amount of the premium on the bonds at issuance, we need to compare the market rate and the contract rate. A premium occurs when the contract rate is higher than the market rate.
1. Calculate the interest payment per period:
The bonds pay interest semiannually, so divide the annual contract rate by 2:
Interest payment per period = ($700,000 * 13%) / 2 = $45,500
2. Calculate the present value of the bond:
To find the present value, we will discount the future cash flows of the bond using the market rate. Since the bond has semiannual payments, we need to adjust the market rate accordingly.
Periods = 3 years * 2 = 6 periods
Interest rate per period = 12% / 2 = 6%
Present value of interest payments:
PV of interest payments = $45,500 * [(1 - (1 + 6%)^(-6)) / (6%)] = $246,717.39
Present value of the bond's face value:
PV of face value = $700,000 / (1 + 6%)^6 = $470,155.58
Total present value of the bond = PV of interest payments + PV of face value = $246,717.39 + $470,155.58 = $716,872.97
3. Calculate the premium on the bonds:
Premium on bonds = Selling price - Total present value of the bond = $717,237 - $716,872.97 = $364.03
Therefore, the amount of the premium on these bonds at issuance is $364.03.
Next, let's calculate the total bond interest expense that will be recognized over the life of these bonds. Bond interest expense is the difference between the interest payment per period and the bond discount or premium amortization.
1. Calculate the total interest payments over the life of the bonds:
Number of interest payment periods = 3 years * 2 = 6 periods
Total interest payments = Interest payment per period * Number of interest payment periods = $45,500 * 6 = $273,000
2. Calculate the total premium amortization:
Premium amortization per period = Premium on bonds / Number of interest payment periods = $364.03 / 6 = $60.67
Total premium amortization = Premium amortization per period * Number of interest payment periods = $60.67 * 6 = $364.02
3. Calculate the total bond interest expense:
Total bond interest expense = Total interest payments - Total premium amortization = $273,000 - $364.02 = $272,635.98
Therefore, the total bond interest expense recognized over the life of these bonds is $272,635.98.
Now, let's prepare an effective interest amortization table for these bonds to track the interest expense, premium amortization, and carrying value of the bond at each period.
Period | Beginning Carrying Value | Interest Expense | Premium Amortization | Ending Carrying Value
--------------------------------------------------------------------------------------
1 | $716,872.97 | $21,442.19 | $3,560.51 | $719,854.19
2 | $719,854.19 | $21,595.63 | $3,407.08 | $724,041.74
3 | $724,041.74 | $21,721.25 | $3,281.46 | $727,081.52
4 | $727,081.52 | $21,812.45 | $3,190.26 | $728,083.33
5 | $728,083.33 | $21,842.50 | $3,160.21 | $728,161.21
6 | $728,161.21 | $21,844.84 | $3,157.87 | $728,164.18
Each period, the interest expense is calculated using the beginning carrying value multiplied by the market rate per period (12% / 2 = 6%). The premium amortization is calculated as the difference between the interest expense and the interest payment per period.
The ending carrying value is the sum of the beginning carrying value, interest expense, and premium amortization for that period.
Please note that the carrying value in the table might differ slightly from the exact amounts due to rounding errors.