Question

Astro World issues $58 million in bonds on January 1,2024 , that pay interest semiannually on June 30 and December 31 . Portions of the bond amortization schedule appear below: 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? Complete this question by entering your answers in the tabs below. Were the bonds issued at face amount, a discount, or a premiun? Astro World issues $58 million in bonds on January 1,2024 , that pay interest semiannually on June 30 and December the bond amortization schedule appear below: 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? Complete this question by entering your answers in the tabs below. What is the original issue price of the bonds? (Enter your answer in whole dollars, not millions (i.e., $5.5 million should be entered as 5,500,000).) Astro World issues $58 million in bonds on January 1,2024 , that pay interest semiannually on June 30 and the bond amortization schedule appear below: 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? Complete this question by entering your answers in the tabs below. What is the face amount of the bonds? (Enter your answer in whole dollars, not millions (i.e., $5.5 million should be ei as 5,500,000).) Astro World issues $58 million in bonds on January 1,2024 , that pay interest semiannually on June the bond amortization schedule appear below: 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? Complete this question by entering your answers in the tabs below. What is the stated annual interest rate? Astro World issues $58 million in bonds on January 1,2024 , that pay interest semiannually on June 30 and December 31 . Portions of the bond amortization schedule appear below: 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? Complete this question by entering your answers in the tabs below. What is the market annual interest rate? (Round your answer to the nearest whole percent.) Astro World issues $58 million in bonds on January 1,2024 , that pay interest semiannually on June 30 and December 31 . Portions of the bond amortization schedule appear below: 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? Complete this question by entering your answers in the tabs below. What is the total cash paid for interest assuming the bonds mature in 20 years? (Enter your answer in dollars, not millions. L.e., $5.5 million should be entered as 5,500,000, )

Answer 1

1. The bonds were issued at a premium.

2. The original issue price of the bonds is $59,011,900, with a face amount of $58,000,000 and a stated annual interest rate of 4%, generating a total cash payment for interest of $46,800,000 over 20 years.

Step-by-step explanation:

The bonds were issued at a premium, as the original issue price of $59,011,900 exceeds the face amount of $58,000,000. The difference between the issue price and the face value represents the premium paid by investors for acquiring the bonds.

The original issue price of the bonds is calculated using the present value formula, considering the semiannual interest payments and the final principal repayment at maturity. The face amount of $58,000,000 multiplied by the present value annuity factor for 20 periods at a semiannual interest rate of 2% yields the original issue price of $59,011,900.

The face amount of the bonds represents the principal amount to be repaid at maturity, which is $58,000,000. The stated annual interest rate, mentioned in the bond contract, is 4%. The market annual interest rate, used to calculate the present value of the bond payments, is 3.5%. Lastly, the total cash paid for interest assuming a 20-year maturity period is calculated by multiplying the total number of interest payments (40 semiannual periods) by the semiannual interest payment amount of $587,500. This results in a total interest payment of $46,800,000 over the life of the bonds.

Answer 2

Bonds can be issued at face value, discount, or premium, based on the relationship between the stated interest rate and the market interest rate. The total cash paid for interest over the bond's life is calculated based on the interest payment per period times the number of periods. Present value calculations are used to determine a bond's price when market interest rates change.

Step-by-step explanation:

When a bond is issued, it can be at face value, at a discount, or at a premium. This depends on how the interest rate stated on the bond (stated interest rate or coupon rate) compares to the market interest rate at the time of issuance. To determine whether the bonds were issued at a discount or premium, one must compare the original issue price to the face amount (also known as the principal or par value).

If the original issue price is less than the face value, the bonds are issued at a discount. Conversely, if the original issue price is more than the face value, the bonds are considered to be issued at a premium. When the original issue price equals the face amount, the bonds are issued at face value. The distinction between the issue price and the face amount also impacts how much interest is actually paid over the life of the bond.

To calculate the total cash paid for interest over the entire term of a bond, you multiply the interest payment per period by the number of periods. For a semiannual interest payment schedule over 20 years, there would be 40 periods of interest payments. If the bonds were issued at a discount or premium, this total cash paid will differ from the interest that would be calculated strictly based on the bond's face value and stated interest rate.

A simple two-year bond issued for $3,000 with an 8% interest rate will pay $240 annually in interest. If discounted back at the same rate, the present value would be equal to the issue price. But if market rates rise to 11%, a calculation using present value formulas would show that the bond's price will drop, to the point where the present value of those cash flows equals what the bond is worth in today's terms when compared to alternative investments yielding 11%.