Question

On January 1, 2017, ARC Inc. issued 100 5-year bonds, with a face value of $1,000 each and a coupon rate of 10%, payable semiannually. The interest is paid on June 30 and December 31 of each year. The market rate of interest at the time that the bonds were issued was 13%, so that the bonds were sold for $892 each.

1. Interest expense for the January 1–June 30 period was $_____
2. Interest expense for the July1–December 31 period was $_____
3. Book value of Bonds on June 30 was $_____
4. Book value of Bonds on December 31 was $_____
5. Interest payment on June 30 was $_____

Answer 1

Answer 2

To calculate the values requested, we need to follow the steps below:

Step 1: Calculate the semi-annual coupon payment. Step 2: Calculate the interest expense for each period. Step 3: Calculate the book value of the bonds on each date. Step 4: Calculate the interest payment on June 30.

Given data:

• Face value of the bond (FV) = $1,000

• Coupon rate (CR) = 10%

• Market rate of interest (MR) = 13%

• Number of bonds issued (N) = 100

• Bonds sold for = $892 each

Step 1: Calculate the semi-annual coupon payment. Coupon Payment = FV * CR / 2 Coupon Payment = $1,000 * 0.10 / 2 Coupon Payment = $50

Step 2: Calculate the interest expense for each period. Interest Expense = Book Value * MR / 2

Step 3: Calculate the book value of the bonds on each date. For the first period (January 1 - June 30, 2017): Book Value on June 30 = (Bonds sold for) - (Coupon Payment * Number of Bonds) Book Value on June 30 = $892 - ($50 * 100) Book Value on June 30 = $892 - $5,000 Book Value on June 30 = -$4,108 (Note: A negative value indicates a loss)

For the second period (July 1 - December 31, 2017): Book Value on December 31 = (Book Value on June 30) - (Coupon Payment * Number of Bonds) Book Value on December 31 = -$4,108 - ($50 * 100) Book Value on December 31 = -$4,108 - $5,000 Book Value on December 31 = -$9,108 (Note: A negative value indicates a loss)

Step 4: Calculate the interest payment on June 30. Interest Payment = Book Value * MR / 2 Interest Payment = (-$4,108) * 0.13 / 2 Interest Payment = -$266.94 (Note: A negative value indicates a loss)

Answers to the questions:

1. Interest expense for the January 1 - June 30 period was $266.94 (rounded to two decimal places).

2. Interest expense for the July 1 - December 31 period was $649.34 (rounded to two decimal places).

3. Book value of Bonds on June 30 was -$4,108 (negative value indicates a loss).

4. Book value of Bonds on December 31 was -$9,108 (negative value indicates a loss).

5. Interest payment on June 30 was -$266.94 (negative value indicates a loss).