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In: Finance

On January 1, 2020, Caliber Corporation issued 9% bonds dated January 1, 2020, with a face...

On January 1, 2020, Caliber Corporation issued 9% bonds dated January 1, 2020, with a face amount of $10 million. The bonds mature in 2029 (10 years). For bonds of similar risk and maturity, the market yield is 10%. Interest is paid annually on December 31.

1. What is the amount of the annual interest payment?

2. What is the price of the bond on the issue date? (state method used)

3. Was the bond sold at a discount or a premium? Explain why.

4. What is the "actual" cost of this debt?

5. What is the price of the bond if the market yield is 8%? (state method used)

6. Is this bond sold at a discount or premium? Explain why.

7. What is the "actual" cost of this debt?

Solutions

Expert Solution

1.

Interest rate = 9%

Face Value = $10 million

Amount of Annual Interest = $10 million x 0.09 = $ 0.9 million

2. Theoretical price of the bond shall be calulated discounting the future coupons and the redeemable value at the time of the maturity. This will help in establishing the maximum cost of the bond that the investor will be willing to pay.

Price of the Bond = C/ PVFA(10%,10) + Face Value / (1+r)^t

= 0.9 / PVFA(10%,10) + 10 / (1.1)^10

= 5.53 + 3.86 = $ 9.39 million

3. As the theoretical price is less than the face value, the bond was sold for premium.

Premium on Bond = $ 10 mn - $ 9.39 mn = $ 0.614 mn

4. Actual cost of the bond is the theorectical price of the bond i.e. $ 9.39 million

5. Theoretical price of the bond shall be calulated discounting the future coupons and the redeemable value at the time of the maturity. This will help in establishing the maximum cost of the bond that the investor will be willing to pay.

Price of the Bond = C/ PVFA(10%,10) + Face Value / (1+r)^t

= 0.9 / PVFA(8%,10) + 10 / (1.08)^10

= 6.04 + 4.63 = $ 10.67 million

6. As the theoretical price is more than the face value, the bond was sold for discount.

Premium on Bond = $ 10.67 mn - $ 10 mn =  $ 0.67 mn

7. Actual cost of the bond is the theorectical price of the bond i.e. $ 10.67 million

jeff jeffy answered 1 year ago
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