Answer:
1. Bonds are issued at a premium.
2. $55,338,768.
3. $50,000,000
4. 8%
5. 7%
6. $74,661,232
Explanation:
The well arranged table is as below for clarity:
Date Cash Paid Interest Decrease in Carrying Value
Expense Carrying Value
01/01/2021 $55,338,768
06/30/2021 $2,000,000 $1,936,857 $63,143 55,275,625
12/31/2021 2,000,000 1,936,857 65,353 55,210,272
1. Face Value of Bonds = $50,000,000
Issue Value of Bonds = $55,338,768
Issue value of bonds is higher than its face amount; therefore, bonds are issued at a premium.
2. Original issue value of bonds is $55,338,768.
3. Face amount of the bonds is $50,000,000.
4. Semiannual interest rate = Cash paid / Face value of bonds
Stated semiannual interest rate = $2,000,000 / $50,000,000 = 0.04 =4%
Stated annual interest rate = 4% × 2 = 8%
The stated annual interest rate is 8%
5. Market semiannual interest rate = Interest expense on 6/30/21 / Carrying value on 1/1/2021
Market semiannual interest rate = $1,936,857 / $55,338,768
Market semiannual interest rate = 0.035 = 3.50%
Market annual interest rate = 2 × Market semiannual interest rate
Market annual interest rate = 2 × 0.035 = 7%
The market annual interest rate is 7%
6. Tenure of bonds = 20 years
Number of semiannual payment = 2 * Life of bonds = 2×20 = 40
Total cash paid = Number of semiannual payment × Semiannual interest payment + Maturity value of bonds
Total cash paid = 40 × $2,000,000 + $50,000,000
Total cash paid = $130,000,000
Total cash paid for interest = Total cash paid - Issue value of bonds
Total cash paid for interest = $130,000,000 - $55,338,768
Total cash paid for interest = $74,661,232
The total cash paid for interest assuming the bonds mature in 20 years is $74,661,232.
