Depreciation
Learning Objectives
- Distinguish first cost, depreciable basis, book value, market value, and salvage value.
- Compute depreciation schedules using straight-line, declining-balance, and sum-of-years'-digits methods.
- Prevent book value from being confused with market value or cash balance.
- Explain why depreciation is not itself a cash outflow but can affect after-tax cash flow through taxable income.
- Select and state the assumed depreciation method without presenting jurisdiction-specific tax rules as universal.
Depreciation
Depreciation is the systematic allocation of an asset's depreciable basis over its accounting or economic life under a specified method. It is an accounting measure, not a physical measurement of deterioration or an annual cash payment.
Basis
Basis is the amount assigned to the asset for depreciation purposes under the assumptions of the analysis. In simple engineering-economy problems it is often the installed first cost, but actual tax basis rules are jurisdiction-specific.
Book Value
Book value is the remaining undepreciated basis at a stated date according to the chosen depreciation schedule.
Market Value
Market value is the amount the asset could be sold for in the relevant market at a stated date. Market value and book value are conceptually different and need not be equal.
Salvage Value
Salvage value is the estimated value retained at the end of the modeled life. In depreciation schedules it may act as a book-value floor when the assumed method requires one.
Straight-Line Depreciation
Allocates the depreciable amount uniformly over n years.
Variables
| Symbol | Description | Unit |
|---|---|---|
| Annual straight-line depreciation | - | |
| Depreciation basis | - | |
| Assumed salvage value | - | |
| Depreciation life in years | - |
Straight-Line Book Value after t Years
Remaining basis after t equal depreciation charges.
Variables
| Symbol | Description | Unit |
|---|---|---|
| Book value after t years | - | |
| Initial basis | - | |
| Annual straight-line depreciation | - | |
| Elapsed depreciation years | - |
Declining-Balance Depreciation
Declining-balance depreciation applies a constant percentage to the beginning book value each year, producing larger depreciation charges early in the life and smaller charges later.
Declining-Balance Book Value
Book value after t periods before any explicit salvage-floor adjustment.
Variables
| Symbol | Description | Unit |
|---|---|---|
| Book value after t periods | - | |
| Initial basis | - | |
| Declining-balance rate per period | - | |
| Elapsed periods | - |
Double-Declining Balance (DDB)
DDB is a declining-balance method that commonly uses a rate equal to twice the straight-line rate , subject to the depreciation convention and salvage constraints adopted in the analysis. In a generic one-year teaching schedule, a declining-balance rate cannot exceed 100%, so the effective generic rate must be capped or another stated convention must be used.
Pure DDB Does Not Automatically End at Salvage
Applying a fixed declining-balance percentage year after year can leave ending book value above the assumed salvage floor at the end of the modeled life. A switch from DDB to straight-line, a final-year adjustment, or another tax/accounting convention is a separate rule and must be stated explicitly; it should not be silently inserted into the method.
Sum-of-Years'-Digits (SYD)
SYD is an accelerated depreciation method that allocates the depreciable amount using fractions whose numerators decrease from to and whose denominator is .
SYD Depreciation in Year t
Accelerated annual allocation of the depreciable amount B-S.
Variables
| Symbol | Description | Unit |
|---|---|---|
| Depreciation in year t | - | |
| Basis | - | |
| Salvage value | - | |
| Life in years | - | |
| Year number, 1 through n | - |
Interactive Depreciation Schedule
Compare straight-line, DDB, and SYD schedules and observe how annual depreciation and book value change. The simulator shows the DDB rate and makes the salvage-floor assumption visible rather than silently forcing all methods to finish at the same book value.
| Year | Beginning BV | Depreciation | Ending BV |
|---|---|---|---|
| 1 | ₱2,500,000 | ₱275,000 | ₱2,225,000 |
| 2 | ₱2,225,000 | ₱275,000 | ₱1,950,000 |
| 3 | ₱1,950,000 | ₱275,000 | ₱1,675,000 |
| 4 | ₱1,675,000 | ₱275,000 | ₱1,400,000 |
| 5 | ₱1,400,000 | ₱275,000 | ₱1,125,000 |
| 6 | ₱1,125,000 | ₱275,000 | ₱850,000 |
| 7 | ₱850,000 | ₱275,000 | ₱575,000 |
| 8 | ₱575,000 | ₱275,000 | ₱300,000 |
Straight-line and SYD allocate the stated depreciable amount across the modeled life. Pure declining-balance methods can finish above a salvage floor unless a switch or final adjustment is separately specified. Depreciation is accounting allocation; it is not itself an annual cash payment.
| Year | Depreciation | Ending BV | Taxable income | Tax | Operating ATCF | Terminal sale | Total CF |
|---|---|---|---|---|---|---|---|
| 1 | ₱437,500 | ₱3,562,500 | ₱512,500 | ₱128,125 | ₱821,875 | ₱0 | ₱821,875 |
| 2 | ₱437,500 | ₱3,125,000 | ₱512,500 | ₱128,125 | ₱821,875 | ₱0 | ₱821,875 |
| 3 | ₱437,500 | ₱2,687,500 | ₱512,500 | ₱128,125 | ₱821,875 | ₱0 | ₱821,875 |
| 4 | ₱437,500 | ₱2,250,000 | ₱512,500 | ₱128,125 | ₱821,875 | ₱0 | ₱821,875 |
| 5 | ₱437,500 | ₱1,812,500 | ₱512,500 | ₱128,125 | ₱821,875 | ₱0 | ₱821,875 |
| 6 | ₱437,500 | ₱1,375,000 | ₱512,500 | ₱128,125 | ₱821,875 | ₱0 | ₱821,875 |
| 7 | ₱437,500 | ₱937,500 | ₱512,500 | ₱128,125 | ₱821,875 | ₱0 | ₱821,875 |
| 8 | ₱437,500 | ₱500,000 | ₱512,500 | ₱128,125 | ₱821,875 | ₱612,500 | ₱1,434,375 |
This is a generic educational model, not a jurisdiction-specific tax calculator. Actual basis rules, allowable depreciation, tax rates, loss utilization, recapture, gain classification, incentives, and disposal treatment must be verified from current authoritative rules for the applicable jurisdiction, entity, and analysis date.
Depreciation and Cash Flow
Depreciation does not consume cash in the year it is recorded. In an after-tax model, it can reduce modeled taxable income and therefore alter tax cash flow. The actual tax effect depends on the governing tax rules and the ability to use deductions or losses.
Book Value Is Not Market Value
Do not use book value as an automatic estimate of resale value. Book value comes from an accounting schedule; market value comes from the asset's actual or estimated market conditions.
Tax Depreciation Rules Are Jurisdiction-Specific
Permitted methods, useful lives, conventions, basis adjustments, and recapture/gain treatment vary by jurisdiction and date. Course examples use explicitly stated generic assumptions unless an authoritative rule is cited and dated.
Depreciation-Schedule Workflow
- Establish the modeled basis , salvage , life , and method.
- Compute each year's depreciation using the stated method and rate convention.
- Subtract depreciation from beginning book value to obtain ending book value.
- Enforce any stated salvage or book-value floor consistently.
- Do not force a declining-balance schedule to end exactly at salvage unless a switch or final-adjustment rule is part of the stated method.
- Verify cumulative depreciation against the method's modeled allocation and floor.
- Keep market value as a separate estimate.
- Use depreciation in an after-tax model only under explicit tax assumptions.
- Depreciation allocates basis; it is not an annual cash payment.
- Book value is schedule-derived and is not automatically market value.
- Straight-line allocates evenly; DDB and SYD accelerate depreciation toward earlier years.
- A pure declining-balance schedule can end above salvage unless an additional switch or adjustment convention is specified.
- Salvage assumptions must be handled consistently with the selected method.
- Depreciation affects after-tax analysis through taxable income, subject to tax rules.
- Jurisdiction-specific tax depreciation should never be presented as a timeless universal formula.