A company issues a 10-year, $1,000,000 bond on January 1, Year 1, with a stated interest rate of 5%, payable annually on December 31. The market interest rate on the date of issuance is 6%. The bond was issued at a discount. Which of the following statements is true regarding the interest expense recognized for this bond in Year 1, using the effective interest method?
- AInterest expense cannot be determined without the bond's issue price.
- BInterest expense will be greater than $50,000.
- CInterest expense will be $50,000.
- DInterest expense will be less than $50,000.
Show answer & explanationAnswer & explanation
Correct answer: B. Interest expense will be greater than $50,000.
When a bond is issued at a discount, the market interest rate is higher than the stated interest rate. Under the effective interest method, interest expense is calculated by multiplying the carrying value of the bond by the effective (market) interest rate. Since the bond is issued at a discount, its carrying value starts at less than face value, but the effective interest rate (6%) is applied to this carrying value. Crucially, because the bond was issued at a discount, the interest expense (carrying value * market rate) will always be greater than the cash interest paid (face value * stated rate), as the difference amortizes the discount. The cash interest paid is $1,000,000 * 5% = $50,000. Therefore, interest expense will be greater than $50,000.
Why the other options are wrong
- A. While the exact amount requires the issue price, the relationship (greater than $50,000) can be determined from the fact it's a discount bond.
- C. This is the cash interest payment, not the interest expense under the effective interest method for a discount bond.
- D. This would be true if the bond was issued at a premium.
Effective Interest Method (Bonds)
A method of amortizing bond discounts or premiums that results in a constant interest rate (the effective rate) over the life of the bond when applied to the bond's carrying value.
- Interest expense = Carrying Value x Market (Effective) Interest Rate.
- Cash interest paid = Face Value x Stated (Coupon) Interest Rate.
- Difference between interest expense and cash interest amortizes the discount/premium.
Memory trick: Bond's Interest: Effective Rate on Carrying keeps the balance flowing.