Depreciation

Depreciation

Learning Objectives

Define depreciation and understand its purpose as a non-cash expense and tax shield.
Differentiate between basis, book value, salvage value, and useful life.
Calculate depreciation using Straight-Line, Declining Balance, and Sum-of-the-Years-Digits methods.
Understand the characteristics and applications of the MACRS system.
Calculate cost depletion for natural resources.

The decrease in value of physical property with the passage of time. It is an accounting concept used to systematically allocate the cost of a tangible asset over its useful life.

Depreciation is a non-cash expense. While no actual cash leaves the company when depreciation is recorded, it serves a vital economic purpose: it reduces taxable income, thus providing a "tax shield" that lowers the company's tax burden and improves after-tax cash flow. It represents the "using up" of an asset's utility.

Key Terminology

Key Terminology

Basis (B) or First Cost (P): The total initial cost of acquiring the asset, including purchase price, taxes, delivery, installation, and testing fees to get it ready for use.
Book Value ( $BV_t$ ): The initial cost (Basis) minus all accumulated depreciation up to year $t$ . It represents the remaining unallocated accounting value of the asset.
Salvage Value (SV): The estimated market value or trade-in value of the asset at the end of its useful life.
Useful Life (n): The expected service life or recovery period of the asset in years.

Depreciation Methods

Interactive Simulation

Use the interactive simulation below to compare how the book value of an asset decreases over time using Straight-Line, Declining Balance, and Sum-of-the-Years-Digits depreciation methods.

Depreciation Methods Comparison

First Cost (P)10,000 $

Initial cost of the asset including installation.

Salvage Value (SV)1,000 $

Estimated value at the end of useful life.

Useful Life (n)5 years

Formula & Details

Straight Line depreciates uniformly.

D_t = \frac{P - SV}{n}

Book Value & Depreciation Schedule

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1. Straight-Line Method (SL)

The simplest and most common method. The asset loses value uniformly (by the same dollar amount) over its entire life.

Straight-Line Depreciation

Calculates the uniform annual depreciation and book value for an asset.

D_t = \frac{B - SV}{n}

BV_t = B - t \cdot D_t

Variables

Symbol	Description	Unit
$D_t$	Annual Depreciation amount for year t	-
$B$	Basis or First Cost	-
$SV$	Salvage Value	-
$n$	Useful Life in years	-
$BV_t$	Book Value at year t	-
$t$	Current year	-

2. Declining Balance Method (DB)

Also known as the constant percentage method. A fixed percentage ( $R$ ) is applied to the declining book value each year. Because the percentage is taken against a shrinking book value, the depreciation amount is highest in the first year and decreases every year thereafter. This is an accelerated depreciation method.

Declining Balance Depreciation

Calculates the depreciation rate, annual depreciation, and book value.

R = 1 - \left( \frac{SV}{B} \right)^{\frac{1}{n}}

D_t = R \cdot BV_{t-1}

BV_t = B(1 - R)^t

Variables

Symbol	Description	Unit
$R$	Depreciation Rate	-
$SV$	Salvage Value	-
$B$	Basis or First Cost	-
$n$	Useful Life in years	-
$D_t$	Annual Depreciation amount for year t	-
$BV_{t-1}$	Book Value at year t-1	-
$BV_t$	Book Value at year t	-

Double Declining Balance (DDB): A very common variation dictated by tax codes where the rate is fixed at exactly twice the straight-line rate: $R = 2/n$ .

Crucial Rule for DDB: Unlike standard DB, salvage value is not used to calculate the annual depreciation amount ( $D_t = \frac{2}{n} \times BV_{t-1}$ ), but the book value is never allowed to fall below the salvage value. In the final years, the depreciation amount must be manually adjusted (lowered) to ensure $BV_n = SV$ .

3. Sum-of-the-Years' Digits Method (SYD)

Another accelerated depreciation method. It applies a declining fraction to the total depreciable basis ( $B - SV$ ). It front-loads depreciation but drops to zero smoothly at year $n$ .

Sum-of-the-Years' Digits Depreciation

Calculates the sum of years and annual depreciation amount.

S = \frac{n(n+1)}{2}

D_t = \frac{n - t + 1}{S} (B - SV)

Variables

Symbol	Description	Unit
$S$	Sum of the years' digits	-
$n$	Useful Life in years	-
$D_t$	Annual Depreciation amount for year t	-
$t$	Current year	-
$B$	Basis or First Cost	-
$SV$	Salvage Value	-

4. Modified Accelerated Cost Recovery System (MACRS)

MACRS is the current standard tax depreciation system used in the United States. It dictates the specific recovery periods (property classes like 3-year, 5-year, 7-year) and the depreciation percentages applied to the asset's basis each year.

MACRS Characteristics

Half-Year Convention: MACRS implicitly assumes the asset is placed in service halfway through the first year. Therefore, a "5-year" asset actually takes 6 years to fully depreciate.
No Salvage Value: Under MACRS, salvage value is always assumed to be zero ( $SV = 0$ ) for the purpose of calculating depreciation percentages. The asset is depreciated entirely to $BV = 0$ .
Method Switching: MACRS tables usually employ the Double Declining Balance (DDB) method, automatically switching to the Straight-Line (SL) method in the year when SL yields a higher deduction.

5. Depletion (For Natural Resources)

Depletion

While depreciation applies to tangible manufactured assets, depletion applies to natural resources (timber, oil, mining) being extracted or exhausted.

Cost Depletion

Allocates the cost of a resource based on the physical amount extracted in a given year.

p_t = \frac{\text{Initial Cost}}{\text{Total Estimated Units}}

Depletion_t = p_t \times \text{Units Extracted in Year } t

Variables

Symbol	Description	Unit
$p_t$	Depletion unit cost for year t	-
$Depletion_t$	Depletion amount for year t	-

Interactive Calculator

Interactive Simulation

Use the calculator below to compare how the Straight Line, Sum-of-Years-Digits, and Double Declining Balance methods reduce the book value of an asset over time.

Equipment Depreciation Comparison

Initial Cost ($)

Salvage Value ($)

Useful Life (Years)

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Straight Line: Constant depreciation amount each year.

Sum of Years Digits: Accelerated depreciation (higher in early years).

Double Declining Balance: Most aggressive early depreciation, often used for tax benefits.

Key Takeaways

Non-Cash Expense: Depreciation is an accounting mechanism, not an actual cash outflow.
Tax Shield: It reduces taxable income, which indirectly generates actual cash savings by lowering the tax bill.
Basis ( $B$ ): The total installed cost of the asset, ready for use.
Book Value ( $BV_t$ ): The accounting value of the asset at the end of year $t$ . It must never fall below the estimated salvage value.
Straight Line: Depreciates an equal amount every year. Easiest to calculate.
Declining Balance / DDB: Accelerated methods that write off more value in the early years. DDB uses a rate of $2/n$ . SV is initially ignored in the calculation but serves as a hard floor for BV.
SYD: Accelerated method based on a declining fraction of the total depreciable amount ( $B - SV$ ).
MACRS: The primary system for US taxes. Uses DDB switching to SL, assumes a half-year convention, and ignores salvage value ( $SV=0$ ).

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