Premium and discount
Bonds are issued at a discount when the stated (coupon) rate is below the market rate, and at a premium when the stated rate exceeds the market rate. Either way, the bond is initially recorded at the present value of its future cash flows (interest + principal), discounted at the market rate.
Effective-interest amortization
US GAAP requires the effective-interest method (straight-line is only permitted if not materially different):
- Interest expense = Carrying value × Market (effective) rate
- Cash paid = Face value × Stated (coupon) rate
- Discount amortization = Interest expense − Cash paid (increases carrying value)
- Premium amortization = Cash paid − Interest expense (decreases carrying value)
EXAMPLE: $1,000,000 face value bond, 6% stated rate, issued to yield 8%, carrying value $940,000. Cash interest = $1,000,000 × 6% = $60,000. Interest expense = $940,000 × 8% = $75,200. Discount amortized = $75,200 − $60,000 = $15,200. New carrying value = $955,200.
IMPORTANT: Bond issuance costs (legal, underwriting fees) are presented as a direct reduction of the carrying amount of the debt (not a separate asset), effectively amortized as part of the effective-interest calculation.
Troubled debt restructuring (debtor's books)
If the total future cash flows under modified terms are less than the carrying value of the debt, the debtor recognizes a gain immediately for the difference, and no further interest expense is recognized (all future payments reduce principal). If total future cash flows exceed carrying value, no gain is recognized; instead, a new effective rate is calculated so that future cash flows equal the current carrying value.