a company issues 7% 10 year bonds with a par value of $150,000 and semi annual payments. On the side date the annual market rate for these bonds are 8%, which implies a selling price of 93 1/4 the straight line is used to allocate interest expense
what is the total amount of bond interest expense that will be recognized over the life of these bonds and what is the first amount of bond interest exp recorded on the first payment? thanks alot!
To calculate the total amount of bond interest expense over the life of the bonds, we need to find the interest expense for each semi-annual payment and multiply it by the total number of payments over the 10-year period.
First, let's determine the semi-annual coupon payment. The bonds have a par value of $150,000 with a coupon rate of 7%. Since the coupon payments are made semi-annually, we need to divide the annual coupon rate by 2:
Coupon Rate = 7% / 2 = 3.5%
Next, let's calculate the interest expense for each semi-annual payment. The interest expense is the difference between the market interest rate and the coupon rate, multiplied by the carrying value of the bonds. However, in this case, we are given that the straight-line method is used to allocate interest expense instead.
The straight-line method means that the interest expense will be evenly distributed over the life of the bond. To calculate the interest expense per payment, we divide the total interest expense by the total number of payments. The total interest expense is the difference between the face value of the bond and the selling price.
Selling Price = 93 1/4% = 93.25%
Interest Expense = Face Value - Selling Price
= $150,000 - ($150,000 * 93.25%)
= $150,000 - ($150,000 * 0.9325)
= $150,000 - $139,875
= $10,125
Now, let's calculate the total number of payments over the 10-year period. Since the payments are made semi-annually, the total number of payments is 2 payments per year multiplied by 10 years:
Total Number of Payments = 2 payments/year * 10 years
= 20 payments
Therefore, the total amount of bond interest expense over the life of the bonds is:
Total Bond Interest Expense = Interest Expense per Payment * Total Number of Payments
= $10,125 * 20
= $202,500
Now let's find the first amount of bond interest expense recorded on the first payment. Since the payments are made semi-annually, the first payment will occur at the end of the 6-month period after the bond issuance. Therefore, the first interest expense recorded will be half of the interest expense per payment:
First Interest Expense = Interest Expense per Payment / 2
= $10,125 / 2
= $5,062.50
So, the total amount of bond interest expense recognized over the life of the bonds is $202,500, and the first amount of bond interest expense recorded on the first payment is $5,062.50.