Price is the sum of the present values of the cash flows...
Here, since the market rate = the coupon rate, the bonds will sell at par: $75m
FYI, when market rate > coupon rate, the bonds sell at a discount to par (less than par)
when market rate < coupon rate, the bonds sell at a premium to par (more than par)
"On January 1, a company issued 7%, 15-year bonds with a face amount of $90 million for $82,218,585 to yield 8%. Interest is paid semiannually. What was interest expense at the effective interest rate on June 30, the first interest date? "
Notice that the yield (market rate) is greater than coupon rate, the bonds have sold at a discount.
Since the bonds pay interest semi-annually, the effective interest rate is 1/2 the 8% yield. Interest EXPENSE is calculated based on the sale price of the bond and the yield, so you have....
$82,218,585 * 0.08/2
= $82,218,585 * 0.04
= $3,288,743.40
FYI, the company's CASH interest paid is Face * Coupon rate / 2...
90,000,000 * 0.07 / 2 = $3,150,000
The difference between the interest EXPENSE and the CASH coupon paid (3288743.40 - 3150000) = $138,743.40 is accounted for as an amortization of the discount on the bonds. Remember, the bonds sold for $82,218,585 (cash received by the company for the bonds), but $90m is due at maturity. The difference between the interest expense and the cash coupon paid is "added" to the 82,218,585 each semi-annual period, such that at maturity, the bond obligation = the $90m they must pay in par at maturity. Each time you add that difference to the balance, that becomes the new amount you use to calculate the next interest EXPENSE, using the effective interest rate of 8%/2. The link is a good source for understanding the amortization of bond discounts and premiums. Hope this helps...
The bonds sold at par (face amount) since the stated interest rate of the bonds and market yield for similar bonds are the same are the same.
Using the effective interest method, the interest expense for the first interest payment was (82,218,585 x .08 x 1/2). The interest is calculated by multiplying the carrying amount of the bonds (82,218,585) by the effective interest rate (8%) multiplied by 1/2 since interest in paid semiannually.
The journal entry for the first interest payment would be:
DR Interest Expense 3,288,743
CR Cash 3,150,000 (the face amount x stated rate x 1/2 (since its semiannual payment))
CR Discount on Bonds Payable 138,743 (the difference in the two amounts above)
The carrying amount of the bonds after this interest payment will be: (90,000,000 - 7,781,415 (the original discount amount) + 138,743 (the amount of discount amortized) = 7,920,158.
When you calculate the next interest payment, you'd use the new carrying amount x 8% x 1/2 to determine Interest Expense.
I go to school online(bad ideal) and I am having trouble understanding how to do the interest on a bond.Below is a question thats in my book.. PLEASE HELP ME..
Thank you
A company issued 6%, 15-year bonds with a face amount of $75 million. The market yield for bonds of similar risk and maturity is 6%. Interest is paid semiannually. At what price did the bonds sell?
On January 1, a company issued 7%, 15-year bonds with a face amount of $90 million for $82,218,585 to yield 8%. Interest is paid semiannually. What was interest expense at the effective interest rate on June 30, the first interest date?
