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Depreciation (MACRS)

Depreciation schedules of a business asset by every common method: straight line, 150 % and 200 % declining balance with the switch to straight line, sum-of-years digits, units of production, and the United States tax methods of IRS Publication 946, MACRS GDS with the half-year, mid-quarter and mid-month conventions from Tables A-1 to A-7a and ADS straight line from Table A-8, with Section 179 expensing, the special (bonus) allowance and the convention rules for a disposal before the recovery period ends. The page shows the schedule of the chosen method, every method side by side with its book-value curve, the present value of each method's tax shield at the after-tax discount rate, the after-tax cash flow and NPV of the asset with the entered annual saving, the recapture or gain on disposal, and the book-against-tax difference with the deferred tax. The default case is a 100,000 seven-year property placed in service in August, whose MACRS percentages are Publication 946's own 7-year example (14.29, 24.49, 17.49, 12.49, 8.93, 8.92, 8.93, 4.46 %).

  • Straight line, 150 % and 200 % declining balance with the switch, sum-of-years digits, units of production

  • MACRS GDS Tables A-1 to A-7a (half-year, mid-quarter, mid-month) and ADS Table A-8, shown to follow from DB with the switch

  • Section 179, bonus allowance, disposal-year conventions, recapture and capital gain, deferred tax

  • Present value of the tax shield of every method, after-tax cash flow and NPV of the asset

Depreciation

Unit System: /

Asset (money in one currency, no unit attached; years as plain numbers)






Method







Expensing and Disposal (0 for none)






After-Tax Analysis (rates in percent)






Book Methods, MACRS Tables and Conventions, Tax Shield | Method page
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Depreciation (MACRS)

Book Methods, MACRS Tables and Conventions, Tax Shield

What depreciation does

An asset bought for a business is not written off in the year of purchase; its cost is spread over the years it is used. The yearly charge is the depreciation Dt, the cost less the depreciation taken so far is the book value BVt, and the methods differ only in how the depreciable amount is distributed over the years. For the accounts (book depreciation) a company picks a method that matches the asset's use; for the United States income-tax return it must use the methods and recovery periods of the Internal Revenue Code, set out in IRS Publication 946 as the Modified Accelerated Cost Recovery System (MACRS). Because depreciation is deducted from taxable income, each year's deduction saves T Dt of tax (T the tax rate): the tax shield. The total shield is the same for every method that writes off the same amount, so the value of an accelerated method lies in taking the shield sooner, measured by its present value at the firm's after-tax rate of return.

Book methods

With cost B, salvage value S and life n years (Blank and Tarquin, chapter 16):

  • Straight line: Dt = (B − S)/n every year; BVt = B − t D.
  • Declining balance: a fixed rate d = f/n (f = 1.5 for 150 %, 2 for 200 % or double declining balance) applied to the book value at the start of the year, Dt = d BVt−1, so BVt = B (1 − d)t and the amounts fall geometrically. The salvage value is not in the formula; the tool stops depreciating when the book value would fall below S. Since pure DB never reaches zero, practice switches to straight line on the remaining depreciable value, (BVt−1 − S)/(n − t + 1), in the first year that gives the larger amount; this is the rule MACRS itself is built on.
  • Sum-of-years digits: Dt = (n − t + 1)/SUM × (B − S) with SUM = n(n + 1)/2, so the first year takes n/SUM of the depreciable value and the last 1/SUM.
  • Units of production: Dt = (B − S) ut/U, the year's output ut over the lifetime output U, for assets whose wear follows use (hours, miles, pieces).

The tool takes the book methods over whole years from the start of year 1 and, when a disposal year is entered, keeps the whole amount of that year; the partial-year conventions below belong to the tax methods.

MACRS GDS

Under the General Depreciation System each asset falls in a property class with a recovery period: 3-, 5-, 7- and 10-year property is depreciated by 200 % declining balance, 15- and 20-year property by 150 % declining balance, both switching to straight line, and residential rental (27.5 years) and nonresidential real property (39 years; 31.5 years for property placed in service before 13 May 1993) by straight line. Salvage value is ignored: the whole basis is recovered. Publication 946 prints the resulting percentages of the unadjusted basis in Appendix A, and the deduction of a year is simply the basis times that year's percentage. The tool carries Tables A-1 (half-year), A-2 to A-5 (mid-quarter by the quarter placed in service), A-6 (27.5-year), A-7 (31.5-year), A-7a (39-year) and A-8 (ADS straight line, half-year, 2.5 to 50 years), transcribed from the 2025 edition with every column checked to sum to 100 %.

The tables are not arbitrary: the "Where the Table Comes From" section recomputes them. The declining-balance rate is f/n (40 % for 5-year, 28.571 % for 7-year, 10 % for 15-year property), the first year takes the convention's fraction of a full year, each later year applies the rate to the remaining basis, and the method switches to straight line, 1 over the years remaining (the first-year fraction counted), in the first year that gives an equal or greater deduction: the fourth year for 5-year property, the fifth for 7-year, the seventh for 10- and 15-year, the ninth for 20-year. Publication 946's own example (5-year property of 1,000: 200, 320, 192, 115, 115, 58) is reproduced, and the computed percentages agree with the printed tables to the rounding of the last digit (the tables are rounded so that each column sums to exactly 100).

Conventions

  • Half-year: every asset is treated as placed in service in the middle of the year: half a year's depreciation in year 1 and the other half in the year after the recovery period, so a 7-year schedule runs eight tax years.
  • Mid-quarter: required when more than 40 % of the bases placed in service in the year came in the last three months (land and real property excluded); then every item takes the fraction of the quarter it was placed in service: 87.5, 62.5, 37.5 or 12.5 % of a full year for the first to fourth quarter. The tool reads the quarter from the month entered; the 40 % test itself needs the year's whole asset list and is left to the user.
  • Mid-month: real property: the first year takes (full months in service + ½)/12 of a full year; a building placed in service in August is in service 4.5 months, 0.375 of the year.

Disposal before the end of the recovery period takes part of that year's full amount: one half under the half-year convention, 12.5 / 37.5 / 62.5 / 87.5 % by the quarter of disposal under the mid-quarter convention, and (months of use including the half month of disposal)/12 under the mid-month convention. Publication 946's examples, 5-year property placed in service in December 2022 and sold in April 2025 (1,368 × 37.5 % = 513) and a rental sold in March (3,636 × 2.5/12 = 757.50), are checks of the tool. An asset placed in service and disposed of in the same year earns no deduction.

Section 179 and the special allowance

Two elections take part of the cost in year 1 before the percentages apply (Pub 946 chapter 2 and 3; the MACRS Worksheet of chapter 4): the Section 179 expense, limited by the year's dollar ceiling and the business's taxable income, comes off the cost first; the special depreciation allowance (bonus depreciation) is a percentage of what is left; the MACRS percentages are applied to the remainder. The tool takes both as entered values and does not ship the yearly limits, which change with the law: enter the amount and the percentage that apply to the tax year.

ADS

The Alternative Depreciation System is straight line over longer recovery periods (Appendix B of Pub 946 lists the ADS life of each asset class), required for some property (used outside the United States, tax-exempt use, farming with certain elections) and available by election. Table A-8 prints the half-year percentages; the tool uses them where the period is listed and computes the straight-line schedule with the convention otherwise.

Tax shield, after-tax cash flow and NPV

Each year's deduction saves T Dt; the present value of the tax shield is Σ T Dt/(1 + i)t at the after-tax discount rate i. The comparison table gives it for every method, so the gain from MACRS over straight line, or from an ADS election, is a single number. The after-tax cash flow table follows Blank and Tarquin chapter 17: with an annual pre-tax saving A, taxable income is TIt = A − Dt, taxes are T TIt (a negative TI is a saving against the firm's other income), the after-tax flow is A − taxes, and the NPV discounts these flows against the cost at year 0. A positive NPV means the asset earns more than the required rate after tax.

Disposal: recapture, gain and loss

When the asset is sold the tax book value is compared with the price. The excess of the price over the book value, up to the original cost, is depreciation recapture (Section 1245 for personal property), taxed as ordinary income because it undoes deductions already taken; a price above the original cost adds a capital gain (taxed at the entered capital-gain rate, the ordinary rate for corporations); a price below the book value is a loss that reduces taxable income. The net proceeds after that tax enter the cash flow of the disposal year. Real property has its own recapture rules (Section 1250, unrecaptured gain at 25 % for individuals), which the tool does not model.

Book against tax: deferred tax

A company that uses straight line in its accounts and MACRS on its return deducts more for tax than it expenses in the early years, so it pays less tax now than its book income implies. The difference T (Dtax − Dbook) is the deferred tax expense of the year and its running total the deferred tax liability (FASB ASC 740); the liability unwinds in the later years when the book amounts overtake the tax amounts, and a salvage value kept on the books leaves T × S outstanding until the asset is retired.

Limits

Calendar tax years; one asset at a time (the 40 % mid-quarter test over a year's purchases is not performed); the yearly Section 179 and bonus limits, the listed-property and passenger-automobile caps, the income limitation and the alternative minimum tax are not shipped; Section 1250 recapture, state taxes and inflation are not modelled; the book methods use whole years. Values are in one currency with no unit attached.



References

Internal Revenue Service (2026). How to Depreciate Property. Publication 946 (2025), U.S. Department of the Treasury, Washington, DC.

Blank, L. T., and Tarquin, A. J. (2012). Engineering Economy, 7th ed. McGraw-Hill, New York.

Park, C. S. (2016). Contemporary Engineering Economics, 6th ed. Pearson, Hoboken, NJ.

Newnan, D. G., Eschenbach, T. G., and Lavelle, J. P. (2012). Engineering Economic Analysis, 11th ed. Oxford University Press, New York.

Financial Accounting Standards Board (2009). Accounting Standards Codification Topic 740, Income Taxes. FASB, Norwalk, CT.

Worked Examples

Published examples this tool reproduces; each page lists the inputs to enter and the printed answers.

All worked examples

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