Depreciation methods

Straight-line, declining-balance, sum-of-the-years-digits, sinking-fund and units-of-production depreciation, book value, and why accelerated depreciation raises present worth.

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Why it matters

Equipment wears out, corrodes and becomes obsolete, so part of its cost must be charged against each year's production. Depreciation is that charge. It is not a cash payment, but because it is deducted from profit before tax it lowers income tax and so raises cash flow; the method chosen changes when the tax saving arrives and therefore the project's present worth.

Key ideas

What depreciation is. Depreciation is the systematic allocation of the depreciable cost of an asset over its service life. The depreciable amount is the original cost V minus the estimated salvage (scrap or resale) value S at the end of the service life n. Land is not depreciated, and working capital is not depreciated.

Causes of loss of value. Physical depreciation (wear, corrosion, fouling) and functional depreciation (obsolescence: a newer process or more efficient equipment makes the old one uneconomic, or demand changes).

Book value is the original cost minus all depreciation charged so far. It is an accounting value and usually differs from market value.

Methods.

  • Straight-line — equal charge every year. Simple, widely used for company accounts.
  • Declining-balance (fixed-percentage) — a constant fraction f of the book value at the start of each year. Charges are high early and fall each year. The fraction that brings the book value exactly to S after n years is given by Matheson's formula. Double-declining balance uses f = 2/n and ignores salvage in the rate (the book value must not be taken below S).
  • Sum-of-the-years-digits (SYD) — the depreciable amount is multiplied each year by (remaining life at the start of the year)/(1 + 2 + … + n). Also accelerated, but reaches S exactly.
  • Sinking-fund — the annual charge is the deposit A that, invested at rate i, would accumulate to V − S in n years. Depreciation in year k is the deposit plus the interest earned on the fund, so charges rise with time (a decelerated method).
  • Units-of-production — depreciation proportional to output or operating hours; suits equipment whose wear depends on use (e.g. catalysts, crushers).

Accelerated versus straight-line. Over the whole life every method charges the same total, V − S. Accelerated methods (declining-balance, SYD) charge more in early years, so taxable income and tax are lower early and higher later. Because money now is worth more than money later, the present worth of the tax savings is higher: accelerated depreciation improves NPV and IRR even though total tax paid is unchanged.

Practice in India. For income tax, depreciation is charged on the written-down value of blocks of assets at rates prescribed in the tax rules; company accounts use useful lives prescribed under company law, usually straight-line. These rates change — take current values from the rules, not from memory. In examinations, use the method and rate given.

Formulas

Straight-line: d = (V − S) / n, B_k = V − k·d Declining-balance: d_k = f·B_(k−1), B_k = V·(1 − f)^k Matheson rate to reach S: f = 1 − (S / V)^(1/n) Double-declining balance: f = 2 / n Sum-of-the-years-digits: d_k = (V − S)·(n − k + 1) / [n(n + 1)/2] Sinking-fund: annual deposit A = (V − S)·i / [(1 + i)ⁿ − 1]; depreciation in year k d_k = A·(1 + i)^(k−1); book value B_k = V − A·[(1 + i)^k − 1] / i Units-of-production: d = (V − S)·(units in period / total lifetime units)

Symbols: V original (installed) cost (₹), S salvage value (₹), n service life (years), k year number (1 to n), d or d_k depreciation charge in a year (₹/yr), B_k book value at end of year k (₹), f fixed fraction (–), i interest rate for the sinking fund (decimal).

Worked examples

Example 1 (standard). V = ₹20 lakh, S = ₹2 lakh, n = 6 years. Find the year-3 charge and book value after 3 years by straight-line, SYD and double-declining balance.

  1. Straight-line: d = 18/6 = ₹3 lakh/yr; B₃ = 20 − 9 = ₹11 lakh.
  2. SYD: sum of digits = 6 × 7/2 = 21. Year-3 fraction = 4/21; d₃ = 18 × 4/21 = ₹3.43 lakh. Charges in years 1–3 = 18 × (6 + 5 + 4)/21 = 12.86, so B₃ = ₹7.14 lakh.
  3. DDB: f = 2/6 = 1/3. B₃ = 20 × (2/3)³ = ₹5.93 lakh; d₃ = f·B₂ = (1/3) × 20 × (2/3)² = ₹2.96 lakh.
  4. Year-3 charge: SL ₹3.00 lakh, SYD ₹3.43 lakh, DDB ₹2.96 lakh. Book value after 3 years: ₹11.0, ₹7.14 and ₹5.93 lakh. The accelerated methods have written off much more of the cost by year 3.

Example 2 (GATE level). For the same equipment (V = ₹20 lakh, S = ₹2 lakh, n = 6), find (a) the fixed percentage that reaches S exactly at 6 years and the book value after 3 years, and (b) the book value after 3 years by the sinking-fund method at 8%.

  1. (a) f = 1 − (S/V)^(1/n) = 1 − (0.1)^(1/6) = 1 − 0.6813 = 0.3187.
  2. B₃ = V·(1 − f)³ = 20 × 0.6813³ = ₹6.32 lakh (equivalently 20 × √0.1).
  3. (b) A = (V − S)·i/[(1 + i)ⁿ − 1] = 18 × 0.08/(1.08⁶ − 1) = 1.44/0.5869 = ₹2.454 lakh/yr.
  4. Fund after 3 years = A·[(1 + i)³ − 1]/i = 2.454 × 0.2597/0.08 = ₹7.97 lakh.
  5. B₃ = 20 − 7.97 = ₹12.03 lakh.
  6. (a) f = 31.9%, B₃ = ₹6.32 lakh; (b) B₃ = ₹12.03 lakh — higher than straight-line (₹11 lakh) because sinking-fund charges start low and grow.

Common mistakes

  • Subtracting salvage before applying a declining-balance rate (the rate acts on the full book value; salvage enters only through Matheson's f or as a floor).
  • In SYD, using the year number instead of the remaining life in the numerator.
  • Depreciating land or working capital.
  • Treating depreciation as a cash outflow in cash-flow calculations.
  • Forgetting that every method writes off the same total, V − S.
  • Confusing the sinking-fund deposit with the sinking-fund depreciation in a later year (which includes interest).

For GATE CH

Expect direct numericals: annual charge or book value after k years by straight-line, declining-balance, SYD or sinking-fund; the fixed percentage from V, S and n; and conceptual questions on why accelerated depreciation increases present worth. Practise the book-value formulas so you need not tabulate every year.

Quick check

  1. V = ₹10 lakh, S = ₹1 lakh, n = 9. Straight-line charge?
  2. Same asset, SYD charge in year 1?
  3. Declining balance at 20%, V = ₹5 lakh. Book value after 2 years?
  4. Does accelerated depreciation change the total tax paid over the life? Why is it still preferred?

Answers: 1. 9/9 = ₹1 lakh/yr. 2. 9 × 9/45 = ₹1.8 lakh. 3. 5 × 0.8² = ₹3.2 lakh. 4. No (at a constant tax rate); it moves tax savings earlier, which raises their present worth.

Interview questions

All Plant Design and Economics interview questions

Try answering each one aloud before you open it.

  1. 1.What is depreciation in the context of plant design and economics?Concept

    Depreciation is the process of allocating the cost of a tangible asset over its useful life. In plant design and economics, it represents the reduction in value of plant equipment and facilities over time due to wear and tear, obsolescence, or other factors. This allocation helps in determining the true cost of production and is important for financial reporting and tax calculations.

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

    The straight-line method of depreciation spreads the cost of an asset evenly over its useful life. It is calculated by subtracting the salvage value of the asset from its initial cost and then dividing by the number of years of its useful life. This method is simple and provides a consistent expense amount each year.

  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 of depreciation is an accelerated depreciation method where the asset loses value at a higher rate in the initial years of its life. 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 in the early years and lower expenses later.

  4. 4.Why might a company choose the declining-balance method over the straight-line method?Application

    Declining-balance charges more depreciation in the early years, so taxable profit and income tax are lower early and higher later. Total depreciation and total tax over the life are the same, but the tax savings arrive sooner, so their present worth is higher and NPV and IRR improve. It also matches assets that lose value or efficiency fastest when new, such as equipment exposed to rapid obsolescence. For tax purposes, though, the method and rate are those allowed by the tax rules.

  5. 5.What happens if a company does not account for depreciation in its financial statements?Application

    If a company does not account for depreciation, it may overstate its profits, as the reduction in asset value is not reflected in the expenses. This can lead to inaccurate financial reporting and mislead stakeholders about the company's financial health. Additionally, it may result in higher tax liabilities since depreciation is a deductible expense.

  6. 6.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 of the asset minus its salvage value by the total estimated production units over its life. The depreciation expense for each period is then calculated by multiplying the per-unit depreciation by the number of units produced in that period.

  7. 7.In what scenarios is the units of production method most appropriate?Application

    The units of production method is most appropriate for assets whose wear and tear is more closely related to usage rather than time. Examples include machinery used in manufacturing where the depreciation is better matched to the actual output, providing a more accurate reflection of the asset's consumption and remaining value.

  8. 8.Calculate the annual straight-line depreciation for equipment costing ₹10 lakh with a salvage value of ₹1 lakh and a useful life of 10 years.Numerical

    Straight-line depreciation d = (V − S)/n = (10 − 1)/10 = ₹0.9 lakh, i.e. ₹90,000 per year. The book value falls by ₹90,000 every year and reaches the ₹1 lakh salvage value at the end of year 10.

  9. 9.Using the declining-balance method at 20% per year, find the first- and second-year depreciation for equipment costing ₹5 lakh.Numerical

    Year 1: d₁ = f × V = 0.20 × 5,00,000 = ₹1,00,000, leaving a book value of ₹4,00,000. Year 2: d₂ = 0.20 × 4,00,000 = ₹80,000. The rate applies to the book value at the start of each year, so the charge falls every year; salvage is not subtracted before applying the rate.

  10. 10.How does the choice of depreciation method impact a company's financial statements and tax liabilities?Application

    The choice of depreciation method affects the timing of expense recognition on the financial statements. Accelerated methods like declining balance result in higher expenses in the early years, reducing taxable income and tax liabilities initially. Conversely, the straight-line method spreads expenses evenly, leading to consistent tax liabilities over time. The method chosen can influence cash flow, profit reporting, and strategic financial planning.

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