What an amortization schedule is
– An amortization schedule is a table showing how the remaining balance of a loan or the carrying amount of an intangible asset declines over time.
– For loans it breaks each payment into the interest portion (the cost of borrowing) and the principal portion (the reduction of the outstanding balance).
– For intangible assets (patents, trademarks, etc.) it shows how the asset’s cost is allocated across its useful life.
Key definitions
– Principal: the unpaid balance of the loan, excluding interest and fees.
– Interest: the charge the lender applies for borrowing the principal, usually expressed as an annual percentage rate (APR).
– Amortization (loan context): the process of repaying a loan through regular payments that include both interest and principal.
– Straight-line amortization (accounting): allocating an intangible asset’s cost evenly over its useful life.
How a loan amortization schedule works (step-by-step)
1. Inputs you need: loan amount, annual interest rate, payment frequency (monthly is common), and total number of payments (loan term × payments per year).
2. Convert the annual interest rate to the periodic rate: i = annual rate / 12 (for monthly).
3. Compute the fixed periodic payment using the annuity formula (if the loan is level-payment):
Payment = LoanAmount × [ i × (1 + i)^n ] / [ (1 + i)^n − 1 ]
where i = periodic rate, n = total number of payments.
4. For each payment period:
– Interest for the period = OutstandingBalance × i
– Principal portion = Payment − Interest
– New outstanding balance = OutstandingBalance − Principal portion
5. Repeat until outstanding balance is zero (for a fully amortizing loan).
Formulas (compact)
– Periodic rate: i = annual_rate / 12
– Payment (level-payment loan): Payment = L × [ i(1+i)^n ] / [ (1+i)^n − 1 ]
where L = loan amount, n = number of payments.
– Principal in a period: PrincipalPayment = Payment − (OutstandingBalance × i)
Worked numeric example (car loan)
Inputs:
– Loan amount = $30,000
– Annual interest rate = 3% = 0.03
– Term = 4 years → n = 4 × 12 = 48 monthly payments
– Monthly rate i = 0.03 / 12 = 0.0025
Compute the monthly payment:
– Payment = 30,000 × [0.0025 × (1 + 0.0025)^48] / [(1 + 0.0025)^48 − 1]
– That evaluates to about $664.03 per month.
First-month breakdown:
– Interest (month 1) = 30,000 × 0.0025 = $75.00
– Principal (month 1) = 664.03 − 75.00 = $589.03
– New balance after payment = 30,000 − 589.03 = $29,410.97
Notes about the example:
– The total payment ($664.03) stays the same each month. Over time the interest portion gets smaller and the principal portion larger, because interest is charged on a shrinking outstanding balance.
Loan amortization schedule vs. loan term
– Amortization schedule: the payment plan used to calculate periodic payments (for example, payments calculated as if the loan will be repaid over 30 years).
– Loan term: the period before the loan obligor must satisfy the loan (for example, a 10-year term). If the term is shorter than the amortization schedule, a remaining balance may be due at term end (a balloon payment).
Amortization for intangible assets (accounting)
– Businesses commonly use straight-line amort
-line amortization for intangible assets with finite useful lives. Below I continue the topic, focusing on accounting mechanics, examples, tax differences, impairment, and presentation.
Straight-line amortization (accounting)
– Formula: Amortization expense = (Cost − Residual value) / Useful life.
– Cost: cash or cash-equivalent paid to acquire the intangible, plus any directly attributable costs to prepare it for use (e.g., legal fees for a patent).
– Residual value: the estimated amount the asset will be worth at the end of its useful life; for many intangibles this is zero.
– Useful life: period over which the asset is expected to contribute to cash flows; measured in years (or months).
Worked example (patent)
1. Company buys a patent for $120,000. Expected useful life = 10 years. Residual value = $0.
2. Annual amortization = (120,000 − 0) / 10 = $12,000.
3. Journal entry each year (straight-line):
– Debit Amortization Expense $12,000
– Credit Accumulated Amortization—Patent $12,000
4. Balance-sheet effect after year 1:
– Patent (cost) = $120,000
– Less: Accumulated Amortization = $12,000
– Carrying amount (net book value) = $108,000
5. Cash-flow impact:
– Amortization is a non-cash expense. Under the indirect method, add back $12,000 to operating cash flows.
Partial-period example
– If the patent is placed in service on April 1 and the fiscal year ends Dec. 31 (9 months), prorate the first-year expense:
– First-year amortization = $12,000 × (9/12) = $9,000.
Methods other than straight-line
– Straight-line is the common method for intangibles with predictable benefits.
– If benefits vary with use, a units-of-production method (expense per unit × units used) may better match expense to economic benefit.
– Declining-balance methods are unusual for intangibles and more common for tangible assets.
Accumulated amortization
– Accumulated amortization is a contra‑asset account that offsets the intangible asset on the balance sheet.
– It accumulates prior amortization charges and reduces the carrying amount to show remaining unamortized cost.
Indefinite-lived intangibles (and goodwill)
– Intangibles with indefinite useful lives (for example, certain trademarks expected to generate cash flows indefinitely) are not amortized.
– Instead, they are tested for impairment at least annually (or more often if indicators arise).
– Goodwill acquired in a business combination is not amortized under U.S. GAAP; it is tested for impairment. IFRS similarly requires impairment testing for indefinite-lived intangibles and goodwill.
Impairment (brief how-to)
– When events or changes in circumstances indicate the carrying amount may not be recoverable, perform an impairment assessment for finite-lived intangibles:
1. Estimate future undiscounted cash flows attributable to the asset.
2. If undiscounted cash flows < carrying amount, compute impairment loss = carrying amount − fair value.