if a company issued $32,000,000 of 10-year, 12% bonds at an effective interest rate of 13%, receiving cash of $30,237,139 and interest on the bonds is paid semiannually how do you calculate the first semiannual interest payment and the amortization of the bond discount?

Question

if a company issued $32,000,000 of 10-year, 12% bonds at an effective interest rate of 13%, receiving cash of $30,237,139 and interest on the bonds is paid semiannually how do you calculate the first semiannual interest payment and the amortization of the bond discount?

Answer 1

To calculate the first semiannual interest payment and the amortization of the bond discount, you'll need to follow these steps:

Step 1: Calculate the Effective Interest Rate per Period
Since interest on the bonds is paid semiannually, you need to determine the effective interest rate per period. In this case, it would be half of the annual effective rate. Calculating the effective rate per period can be done using the following formula:

Effective Interest Rate per Period = (1 + r/n)^n - 1

Where:
r is the annual effective interest rate (13%)
n is the number of periods per year (2 for semiannual payments)

Substituting the values, we get:
Effective Interest Rate per Period = (1 + 0.13/2)^2 - 1

Step 2: Calculate the First Semiannual Interest Payment
To find the first semiannual interest payment, multiply the face value of the bonds by the effective interest rate per period. The face value of the bonds in this case is $32,000,000. Multiply this value by the effective interest rate per period to get the interest payment:

First Semiannual Interest Payment = Face Value * Effective Interest Rate per Period
First Semiannual Interest Payment = $32,000,000 * Effective Interest Rate per Period

Step 3: Calculate the Amortization of the Bond Discount
The bond discount is the difference between the cash received ($30,237,139) and the face value of the bonds ($32,000,000). To amortize the bond discount, you'll need to allocate a portion of the discount to each period over the life of the bond.

Divide the total bond discount by the number of semiannual periods over the bond's term (10 years, so there are 10 * 2 = 20 semiannual periods). This will give you the amount of discount amortized in each semiannual period:

Amortization of Bond Discount = Bond Discount / Number of Semiannual Periods
Amortization of Bond Discount = (Face Value - Cash Received) / Number of Semiannual Periods

Now you have calculated the first semiannual interest payment and the amortization of the bond discount.