Depreciation methods

Straight-line, declining-balance, double-declining, sum-of-years'-digits, sinking-fund and units-of-production depreciation, with book values and the salvage floor.

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Why it matters

Machines, tools and buildings lose value as they wear out or become obsolete. Depreciation spreads that loss over the asset's life so that product costs carry a fair share of capital cost, books show a realistic asset value, and the firm saves tax because depreciation is a deductible expense. The method chosen changes the yearly charge, the book value and the timing of tax savings.

Key ideas

Depreciation is the systematic allocation of an asset's depreciable amount (first cost minus estimated salvage value) over its useful life. It is a non-cash expense: no money leaves the firm when it is charged, but it lowers taxable income.

Causes: physical wear and tear, deterioration with time (corrosion, ageing), obsolescence (a better machine appears), and inadequacy (the machine can no longer meet demand).

Terms.

  • First cost C (or P): purchase price plus installation and commissioning.
  • Salvage value S: estimated net resale or scrap value at the end of life.
  • Useful life n: the period over which the asset is expected to serve economically.
  • Book value Bₜ: first cost minus accumulated depreciation at the end of year t.
  • Market value: what the asset would actually fetch; it can differ widely from book value.

Methods.

  • Straight-line (SL): equal charge every year. Simple; book value falls linearly.
  • Declining balance (DB): a fixed percentage of the start-of-year book value. Double declining balance (DDB) uses twice the SL rate, 2/n. Salvage is not used in computing the charge, so book value never reaches zero; in practice, depreciation is stopped (or the method switched to SL) so that book value does not fall below the salvage value.
  • Fixed-percentage (Matheson) method: a DB rate chosen so the book value equals S exactly at year n.
  • Sum-of-the-years'-digits (SOYD): a falling fraction of (C − S); year 1 uses n / SOY, year 2 uses (n − 1) / SOY, and so on.
  • Sinking fund: an equal amount is deposited each year into a fund earning interest i so that the fund equals (C − S) at year n. Depreciation in year t is the deposit plus interest earned, so the charge increases with time — the opposite of accelerated methods.
  • Units of production / machine-hour: depreciation in proportion to output or hours used, suitable where wear depends on use rather than time.

DB, DDB and SOYD are accelerated methods: larger charges early, which bring tax savings forward and so have a higher present worth of tax shield. In India, the Companies Act and the Income Tax Act prescribe their own methods and rates (written-down value is common for tax); take actual rates from those schedules.

Formulas

  • Straight-line: Dₜ = (C − S) / n, Bₜ = C − t·(C − S) / n
  • Declining balance with rate R: Dₜ = R·Bₜ₋₁, Bₜ = C(1 − R)ᵗ
  • Double declining balance: R = 2 / n
  • Fixed-percentage (Matheson) rate: R = 1 − (S / C)^(1/n)
  • Sum of years' digits: SOY = n(n + 1) / 2, Dₜ = (n − t + 1)(C − S) / SOY
  • SOYD book value: Bₜ = C − (C − S)·[t(n − t/2 + 1/2)] / SOY
  • Sinking fund deposit: A = (C − S)·(A/F, i, n) = (C − S)·i / [(1 + i)ⁿ − 1]
  • Sinking fund depreciation in year t: Dₜ = A(1 + i)^(t−1); book value Bₜ = C − A(F/A, i, t)
  • Units of production: D = (C − S) × (units in period / total lifetime units)

Symbols: C = first cost (₹); S = salvage value (₹); n = useful life (years); t = year number; Dₜ = depreciation charge in year t (₹); Bₜ = book value at end of year t (₹); R = DB rate (decimal per year); i = interest rate earned by the sinking fund (decimal per year).

Worked examples

Example 1 (standard). A CNC lathe costs ₹5,00,000, has a salvage value of ₹50,000 and a life of 5 years. Find the year-1 charge and book value after year 2 by SL, DDB and SOYD.

  1. SL: D = (5,00,000 − 50,000) / 5 = ₹90,000 per year. B₂ = 5,00,000 − 2 × 90,000 = ₹3,20,000.
  2. DDB: R = 2/5 = 0.4. D₁ = 0.4 × 5,00,000 = ₹2,00,000; B₁ = ₹3,00,000. D₂ = 0.4 × 3,00,000 = ₹1,20,000; B₂ = ₹1,80,000.
  3. SOYD: SOY = 5 × 6 / 2 = 15. D₁ = (5/15) × 4,50,000 = ₹1,50,000; D₂ = (4/15) × 4,50,000 = ₹1,20,000. B₂ = 5,00,000 − 2,70,000 = ₹2,30,000.

Year-1 charges: SL ₹90,000, DDB ₹2,00,000, SOYD ₹1,50,000.

Note on DDB: continuing, B₃ = ₹1,08,000 and B₄ = ₹64,800. A full 40% charge in year 5 (₹25,920) would take B₅ to ₹38,880, below the salvage value, so the year-5 charge is limited to 64,800 − 50,000 = ₹14,800.

Example 2 (GATE level) — sinking fund. Same lathe, with the sinking fund earning 10% per year. Find the annual deposit, the depreciation charged in year 3 and the book value at the end of year 3.

  1. (A/F, 10%, 5) = 0.10 / [(1.1)⁵ − 1] = 0.10 / 0.61051 = 0.163797.
  2. A = 4,50,000 × 0.163797 = ₹73,708.9 per year.
  3. D₃ = A(1.1)² = 73,708.9 × 1.21 = ₹89,187.7.
  4. (F/A, 10%, 3) = [(1.1)³ − 1] / 0.1 = 3.31. Fund after 3 years = 73,708.9 × 3.31 = ₹2,43,976.4.
  5. B₃ = 5,00,000 − 2,43,976.4 = ₹2,56,023.6.

Compare with SOYD after 3 years: B₃ = 5,00,000 − (5 + 4 + 3)/15 × 4,50,000 = ₹1,40,000. The sinking fund method writes the asset down most slowly.

Common mistakes

  • Subtracting salvage before applying a declining-balance rate. In DB the rate is applied to the full book value; salvage enters only as a floor.
  • Taking the DDB rate as 2 / (n + 1) or applying it to the first cost every year instead of the reducing book value.
  • In SOYD, using t / SOY instead of (n − t + 1) / SOY, which reverses the order of charges.
  • Treating the sinking-fund deposit as the depreciation for every year; the charge also includes interest earned on the fund.
  • Thinking depreciation is a cash outflow. It is not; it affects cash flow only through income tax.
  • Confusing book value with market value when deciding to sell or replace.

For GATE PI

Expect short numericals: annual depreciation or book value after t years by SL, DB/DDB, SOYD or sinking fund, and the depreciation rate that brings book value to salvage. Conceptual questions ask which methods are accelerated, which give an increasing charge, and why depreciation reduces tax. Practise building a small year-by-year table quickly, since GATE often asks for a specific year rather than year 1.

Quick check

  1. A ₹2,00,000 machine with ₹20,000 salvage and 6-year life: SL charge per year?
  2. With DDB for a 10-year life, what is the rate?
  3. Which method gives a depreciation charge that increases each year?
  4. For n = 4 years, what fraction of (C − S) is charged in year 2 under SOYD?

Answers: 1. ₹30,000; 2. 20% of book value; 3. sinking fund method; 4. 3/10.

Interview questions

All Engineering Economics and Product Design interview questions

Try answering each one aloud before you open it.

  1. 1.What is depreciation in the context of engineering economics?Concept

    Depreciation is the process of allocating the cost of a tangible asset over its useful life. In engineering economics, it reflects the decrease in value of an asset due to wear and tear, age, or obsolescence. This allocation helps in understanding the true cost of using an asset over time.

  2. 2.Explain the straight-line method of depreciation.Concept

    The straight-line method charges the same amount every year: D = (C − S)/n, where C is first cost, S salvage value and n useful life. Book value therefore falls linearly from C to S. It is simple and suits assets that lose value evenly with time, but it ignores the fact that many machines lose more value in their early years.

  3. 3.What is the declining balance method of depreciation, and how does it differ from the straight-line method?Concept

    The declining balance method is an accelerated depreciation technique where the asset loses value at a higher rate in the earlier years. Unlike the straight-line method, which spreads the cost evenly, the declining balance method applies a constant depreciation rate to the reducing book value of the asset each year, resulting in higher depreciation expenses initially.

  4. 4.Why might a company choose to use the sum-of-the-years-digits method for depreciation?Application

    A company might choose the sum-of-the-years-digits method to accelerate depreciation, which can be beneficial for tax purposes. This method results in higher depreciation expenses in the early years of an asset's life, which can reduce taxable income when the asset is most productive and generating higher revenue.

  5. 5.How does depreciation affect a company's financial statements?Application

    Depreciation affects a company's financial statements by reducing the book value of assets on the balance sheet and increasing expenses on the income statement. This, in turn, reduces net income. Depreciation does not directly affect cash flow, but it provides a tax shield by reducing taxable income.

  6. 6.What happens if a company underestimates the useful life of an asset?Application

    If a company underestimates the useful life of an asset, it will depreciate the asset too quickly, resulting in higher depreciation expenses in the short term. This can lead to lower net income and potentially higher taxes in later years when the depreciation expense is lower. It may also misrepresent the asset's value on the balance sheet.

  7. 7.Explain how the units of production method of depreciation works.Concept

    The units of production method calculates depreciation based on the actual usage of the asset. It is determined by dividing the total cost minus salvage value by the total estimated production capacity, then multiplying by the actual units produced in a period. This method aligns depreciation with the asset's productivity.

  8. 8.Why is it important to consider salvage value when calculating depreciation?Application

    Salvage value is important because it represents the estimated residual value of an asset at the end of its useful life. It is subtracted from the asset's initial cost to determine the total amount to be depreciated. Ignoring salvage value can lead to over-depreciation and misrepresentation of an asset's value.

  9. 9.Calculate the annual straight-line depreciation for an asset with a first cost of ₹1,00,000, a salvage value of ₹10,000 and a useful life of 10 years.Numerical

    D = (C − S) / n = (1,00,000 − 10,000) / 10 = ₹9,000 per year. The book value falls by ₹9,000 each year and reaches the ₹10,000 salvage value at the end of year 10.

  10. 10.An asset has a book value of ₹50,000 at the beginning of the year and is depreciated by the double-declining-balance method on a 10-year life. What is the depreciation for the year?Numerical

    The DDB rate is 2/n = 2/10 = 20% of the opening book value, so D = 0.20 × 50,000 = ₹10,000 and the closing book value is ₹40,000. Salvage value is not used in the calculation, except that depreciation stops once book value reaches salvage.

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