Unamortized Bond Premium

Unamortized Bond Premium — Meaning and How It Works

An unamortized bond premium is the portion of the price paid for a bond that exceeds its face (par) value and has not yet been written off (amortized) as interest expense. If a bond with a $1,000 par value sells for $1,090, the total premium is $90. The part of that premium that remains to be amortized over the life of the bond is the unamortized bond premium.

Why premiums arise

• When prevailing market interest rates fall below a bond’s fixed coupon rate, existing bonds with higher coupons become more valuable and trade above par.
• Buyers pay a premium to acquire those higher-coupon bonds; the premium compensates the seller for the bond’s higher-than-market interest payments.

Accounting treatment

• For issuers: The unamortized bond premium is recorded on the balance sheet in a liability account often called “Unamortized Bond Premium.” The premium is amortized over the bond’s life and reduces interest expense recognized on the income statement (under GAAP the effective-interest method is commonly used).
• For investors: Premium amortization reduces the bond’s cost basis gradually. For taxable bonds, amortizing the premium can reduce reported interest income for tax purposes (subject to tax rules). For tax-exempt bonds, the premium must be amortized to reduce basis, but the amortization is not deductible.

Tax considerations

• Taxable premium bonds: Investors generally benefit from amortizing the premium because the amortized amount offsets interest income, lowering taxable income from the bond.
• Tax-exempt interest bonds: Investors must amortize the premium but cannot deduct the amortization; it only reduces the bond’s cost basis.

Example calculation (annual coupon, effective-interest approach)

Assumptions:
– Par value: $1,000
– Coupon rate: 5% → annual coupon = $50
– Market yield (YTM): 4%
– Purchase price: $1,090
– Initial premium: $1,090 − $1,000 = $90

Year 1:
– Income from yield on purchase price = $1,090 × 4% = $43.60
– Coupon received = $50
– Amortizable amount = coupon − (price × YTM) = $50 − $43.60 = $6.40
– Investor’s taxable interest reported = $50 − $6.40 = $43.60
– Unamortized premium after Year 1 = $90 − $6.40 = $83.60
– New cost basis = $1,090 − $6.40 = $1,083.60

Year 2:
– Income from yield on new basis = $1,083.60 × 4% = $43.34
– Amortizable amount = $50 − $43.34 = $6.66 (rounded; original example shows $6.64 due to rounding differences)
– Unamortized premium after Year 2 ≈ $83.60 − $6.66 = $76.94
– New cost basis ≈ $1,083.60 − $6.66 = $1,076.94

Repeat the same steps each year until the premium is fully amortized at maturity. (Actual amortization depends on the method used and rounding rules; the effective-interest method yields a varying amortization schedule based on the changing basis.)

Key takeaways

• Unamortized bond premium = amount of purchase price above par that remains to be amortized.
• Issuers record it as a liability and amortize it to reduce interest expense over the bond’s life.
• Investors amortize premium to reduce taxable interest income (for taxable bonds) and to reduce cost basis (for both taxable and tax-exempt bonds).
• The effective-interest method (using yield to maturity) is commonly used to calculate amortization amounts.