Sun City issues $50 million of bonds on January 1, 2021 that pay interest semiannually on June 30 and December 31. A Portion of the bond amortization schedule appears below: Cash Interest Decrease in Carrying Date Paid Expense Carrying Value 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 1,934,647 65,353 55,210,272
Required:
1. Were the bonds issued at face amount, a discount, or a premium?
2. What is the original issue price of the bonds?
3. What is the face amount of the bonds?
4. What is the stated annual interest rate?
5. What is the market annual interest rate?
6. What is the total cash paid for interest assuming the bonds mature in 20 years?

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.

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