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29 March, 13:07

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?

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Answers (1)
  1. 29 March, 13:19
    0
    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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