What is an amortizable bond premium?
– Definition: An amortizable bond premium is the amount by which the price you pay for a bond exceeds its face (par) value. When you buy a bond above par, that excess is the premium. For many tax purposes the premium is spread (amortized) over the remaining life of the bond so the investor’s reported interest income and the bond’s cost basis are adjusted each period.
Why premiums happen (brief)
– Market interest rates and coupon rates move in opposite directions. If market rates fall below a bond’s coupon rate, that bond becomes more valuable and trades above par. The difference between the market price and par is the premium.
Key tax concepts (short)
– Cost basis: The investor’s purchase price in the bond, which includes any premium paid.
– Amortization: Systematic reduction of the premium across the remaining life of the bond.
– Tax effect (taxable bonds): If you elect to amortize, the amortized premium reduces the amount of interest income you report each period and also reduces the bond’s basis.
– Tax-exempt interest: The IRS requires amortization of premium on tax-exempt bonds; the amortized amount reduces basis but does not produce a deduction against taxable income.
– Method required: For IRS purposes, amortization is done using the constant yield method (see below).
Constant yield method — concept and formula
– Concept: The constant yield method allocates interest income based on the bond’s yield to maturity (YTM) rather than on the coupon cash payment. Each accrual (interest) period you:
1) compute the interest equivalent at the bond’s periodic yield using the current adjusted basis, and
2) compare that to the coupon cash received. The difference is the premium amortization for the period.
– Formula (per period):
Periodic yield = (YTM) / (number of periods per year)
Interest-by-yield = Adjusted basis × Periodic yield
Amortization for period = Coupon payment − Interest-by-yield
New adjusted basis = Old adjusted basis − Amortization for period
Note: For bonds priced at a premium, amortization will be a positive number (it reduces the basis). If coupon < yield (discount bond), the analogous concept is OID/amortization in the other direction.
Step-by-step checklist for amortizing a premium (practical)
1. Confirm you want/need to amortize (taxable bond election; required for tax-exempt bonds).
2. Determine the bond’s yield to maturity (YTM) at purchase and the payment frequency (annual, semiannual, etc.).
3. Convert YTM and coupon to periodic rates (divide by number of periods per year).
4. Start with the purchase price as the initial adjusted basis.
5. For each period:
a. Calculate Interest-by-yield = Adjusted basis × Periodic yield.
b. Calculate coupon cash = Coupon rate per period × Par value.
c. Amortization = Coupon cash − Interest-by-yield.
d. Subtract amortization from adjusted basis to get the next period’s basis.
6. Continue until
the bond matures, you sell it, or the adjusted basis equals the par (face) value. If you elected to amortize the premium for tax purposes, the amortization in each period reduces the amount of interest income you report (for taxable bonds) and reduces the bond’s adjusted basis for capital-gains purposes when you later sell or it matures.
Practical notes and caveats
– Election to amortize (taxable bonds): For taxable bonds, investors may elect to amortize bond premium so that each period’s reported interest income is reduced by the amortized amount. Check your tax reporting rules or tax advisor—IRS Publication 550 explains the treatment and how the election is handled.
– Tax-exempt bonds: For tax-exempt interest (for example, municipal bonds), amortization of premium typically adjusts basis but does not make the tax-exempt interest taxable. The premium still reduces your basis and affects gain/loss on sale or maturity.
– Yields and payment frequency: Use the bond’s yield-to-maturity (YTM) at purchase as the periodic yield; match the periodic yield to the coupon payment frequency (e.g., semiannual). The constant-yield (effective-interest) method is standard.
– Accrued interest and purchase between coupon dates: If you bought the bond between coupon dates, your purchase price included accrued interest paid to the seller. Amortization applies to the premium portion of the clean price (purchase price minus accrued interest). Handle accrued interest separately.
– Callable and puttable bonds: If the bond can be called (redeemed early) or put, amortization stops at call/put/sale; adjusted basis at that event is what matters for gain/loss and final interest reporting.
– Sales before maturity: When you sell, your adjusted basis equals the original purchase price minus cumulative amortization. That adjusted basis is used to compute capital gain or loss on sale.
Worked numeric example (semiannual, constant-yield method)
Assumptions
– Par (face) value = $1,000.
– Coupon = 6% annual → $30 every six months (semiannual payments).
– Purchase price = $1,080 (bond bought at a $80 premium).
– Yield to maturity (YTM) at purchase = 4% annual → 2% per semiannual period.
Period 1
– Adjusted basis (start) = 1,080.00
– Periodic yield = 0.02
– Interest-by-yield = 1,080.00 × 0.02 = 21.60
– Coupon cash = 30.00
– Amortization = Coupon cash − Interest-by-yield = 30.00 − 21.60 = 8.40
– Adjusted basis (end) = 1,080.00 − 8.40 = 1,071.60
Period 2
– Adjusted basis (start) = 1,071.60
– Interest-by-yield = 1,071.60 × 0.02 = 21.43 (rounded)
– Coupon cash = 30.00
– Amortization = 30.00 − 21.43 = 8.57
– Adjusted basis (end) = 1,071.60 − 8.57 = 1,063.03
Repeat these calculations each period. Over many periods the amortization amounts will gradually reduce the adjusted basis toward $1,000. At maturity (if held all the way and no calls/sales), the adjusted basis should equal the par value
Tax reporting and practical implications
– Effect on reported interest. If you elect to amortize bond premium, the amortization reduces the interest income you report for tax purposes. In practice, with the constant-yield method the taxable interest for each period equals the “interest-by-yield” calculation used in the amortization schedule (beginning adjusted basis × periodic yield). Using the numbers from the previous schedule:
– Period 1 taxable interest = interest-by-yield = 1,080.00 × 0.02 = 21.60
– Period 2 taxable interest = interest-by-yield = 1,071.60 × 0.02 = 21.43
Thus your reported interest is lower than the coupon cash received because part of each coupon is treated as a return of capital (amortization of premium), not taxable interest.
– Tax-exempt (municipal) bonds. The same arithmetic can be used for tax-exempt municipal bonds, but the tax effect differs: amortizing premium on a tax-exempt bond reduces the amount of tax-exempt interest you report. You cannot use amortization to create a tax deduction for individuals; it merely reduces tax-exempt income.
– Basis and capital gain/loss. Amortization reduces the bond’s adjusted basis each period. If you hold to maturity, the adjusted basis reaches par and there is no capital gain or loss on principal repayment. If you sell or the bond is called before maturity, the difference between your adjusted basis at disposition and the sale/call price produces a capital gain or loss.
– Bonds with embedded special rules. If a bond has original issue discount (OID) or other special tax features, different rules (and ordering) may apply. Market discount, OID, premium, and acquisition premium rules can interact. Consult the IRS guidance or a tax advisor when multiple features are present.
How to build an amortization schedule (step-by-step checklist)
1. Gather inputs:
– Purchase price (adjusted basis at start).
– Coupon per period (cash coupon received each period).
– Par value