Short note: methods of calculating depreciation

Depreciation is the decrease in the value of a physical asset with time and use. In accounting it is the systematic allocation of the cost of an asset (less salvage value) over its useful life. Common methods:

1. Straight-line (SL) method

Equal charge each year: D = (P − S) / N, where P = cost, S = salvage value, N = life. Book value falls linearly. It is the simplest method.

2. Declining-balance (DB) method

A fixed percentage of the opening book value is charged each year: D_k = R × BV_{k−1}. The charge is large in early years. The double declining balance (DDB) method uses R = 2/N. A fixed rate that brings book value exactly to S is R = 1 − (S/P)^(1/N).

3. Sum-of-the-years'-digits (SOYD) method

D_k = (P − S) × (N − k + 1) / [N(N + 1)/2]. It is also an accelerated method: the fraction is largest in year 1.

4. Sinking-fund method

A fund that grows at interest rate i is assumed to replace the asset. The yearly deposit is (P − S)(A/F, i, N) and depreciation in year k is the deposit × (F/P, i, k − 1). The charge is small early and larger later.

5. Unit-of-production (service output) method

D = (P − S) × (units produced in the year / total expected units). It is suitable for machinery whose wear depends on use.

6. MACRS (tax depreciation)

Property is placed in a class (3, 5, 7, 10 … year) and a fixed percentage table is used; it ignores salvage value.

Accelerated methods (DB, SOYD, MACRS) give larger deductions early, which reduce early taxes and raise present worth of after-tax cash flows.