Question

X2 issued callable bonds on January 1, 2015. The bonds pay interest annually on December 31 each year. X2's accountant has projected the following amortization schedule from issuance until maturity:
Date Cash Paid Interest
Expense Decrease in Carrying Value Carrying Value
1/12015 $107,167
12/31/2015 $8,755 $8,038 $717 106,450
12/31/2016 8,755 7,984 771 105,678
12/31/2017 8,755 7,926 829 104,849
12/31/2018 8,755 7,864 891 103,958
12/31/2019 8,755 7,797 958 103,000
What is the annual market interest rate on the bonds?

Answer 1

Answer:

market rate is 7.5%

Explanation:

We will work with the formulas for bonds amortization under effective rate method:

1.-  Face value x rate = cash proceeds

2.- Carring Value x market rate = interest expense

3.- Cash proceds - interest expense = amortization

With the second formula, and the givne value we are able to solve for market rate:

carrying value at 12/31/2015 is used to calcualte the 2016 interest expense:

106,450 x market rate= 7,984

market rate = 7,984/106,450 = 0.07500 = 7.5%

carrying value at 12/31/2016 is used to calcualte the 2017 interest expense:

105,678 x market rate = 7,926 = 0.07500 = 7.5%

So, we can conclude the market rate is 7.5%