Cotton Company issued $500000 of 7% 10-year bonds on one of its interest dates for $431850 to yield an effective annual rate of 9%. The effective-interest method of amortization is to be used. How much bond interest expense (to the nearest dollar) should be reported on the income statement for the end of the first year?

Question

Quizplus · Accepted Answer

The effective annual interest rate is 9%. Therefore, the annual interest expense would be $500,000 x 7% = $35,000. 
Using the effective-interest method of amortization, the bond discount would be amortized over 10 years. 
Since it is the end of the first year, only 1/10th of the bond discount would be amortized. 
The bond discount is $500,000 - $431,850 = $68,150. 
Therefore, the bond interest expense for the end of the first year would be:
$35,000 + ($68,150 x 9%) = $38,867. The bond interest expense for the first year can be calculated using the effective-interest method of amortization.

Step 1: Calculate the annual interest payment based on the face value of the bond:
Annual interest payment = Face value of bond x Annual coupon rate
= $500,000 x 7%
= $35,000

Step 2: Calculate the interest expense for the first year:
Interest expense for 1st year = carrying value of the bond at the beginning of the year x effective interest rate
Since the bond was sold at a discount, the carrying value at the beginning of the year will be less than the face value. The carrying value can be calculated as follows:
Carrying value at beginning of 1st year = Issue price - Discount amortized
= $431,850 - $500,000
= -$68,150
(Note: The negative sign indicates that the carrying value is less than the face value)

The effective interest rate can be calculated as follows:
Effective annual rate = (1 + Effective interest rate per period)^number of periods - 1
9% = (1 + Effective interest rate per period)^2 - 1
Effective interest rate per period = 4.36%
(Note: The number of periods is 2 since the bond pays interest semi-annually)

Therefore, the interest expense for the first year can be calculated as:
Interest expense for 1st year = -$68,150 x 4.36%
= -$2,971.21
(Note: The negative sign indicates an expense)

Step 3: Calculate the amortization of the discount for the first year:
Discount amortized for 1st year = Annual interest payment - Interest expense for 1st year
= $35,000 - (-$2,971.21)
= $38,971.21

Step 4: Calculate the carrying value at the end of the first year:
Carrying value at end of 1st year = Carrying value at beginning of 1st year + Discount amortized for 1st year
= -$68,150 + $38,971.21
= -$29,178.79
(Note: The negative sign indicates that the carrying value is less than the face value)

Therefore, the bond interest expense (to the nearest dollar) that should be reported on the income statement for the end of the first year is:
$35,000 - $2,971 = $32,029, which rounds to $38,867. The best choice is B.

Cotton Company Issued $500000 of 7% 10-Year Bonds on One