ECE 192 WINTER 2025
CHAPTER 3.1: DEPRECIATION
1/26/2025
Presented by: Dario Peralta,
ECE Department
University of Waterloo
Outline
▪ Depreciation:
▪ Definitions
▪ Depreciation Methods:
▪ Straight-line
▪ Declining-balance
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Definition
▪ Depreciation can be defined as the gradual decrease in utility of fixed assets with
use and time:
▪ With pass of time, assets lose value or depreciate.
▪ Estimation of the loss in value and remaining value of their assets.
▪ Planning replacements of aging assets.
▪ Types of depreciation:
▪ Economic Depreciation:
▪ Use-related physical loss, time-related physical loss, functional loss.
▪ Accounting Depreciation:
▪ Book depreciation and tax depreciation.
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Definition
▪ Accounting Depreciation:
Unlike costs such as maintenance, material, and labour, the costs of fixed
assets are not treated simply as expenses to be accounted for in the year that
they are acquired.
Rather, these assets are ‘capitalized’, i.e., their costs are distributed by
subtracting them as expenses from gross income.
The systematic allocation of the initial cost of an asset in parts, over time,
known as the asset’s depreciable life, is accounting deprecation or asset
depreciation.
Cost Basis
Useful life
Salvage value (Residual and scrap)
Book Value
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Definition
▪ Cost Basis: represents the total cost that is claimed as an expense
over an asset’s life.
▪ Includes the actual cost of an asset and all other incidental expenses.
▪ Useful life: is an estimate of the duration over which the asset is
expected to fulfill its intended purpose.
▪ Salvage value (Residual and scrap): is an asset’s value at the end of
its life
▪ The amount recovered through sale, trade-in, and can sometimes be
negative if there are costs incurred for disposal.
▪ Book value: is the depreciated value of an asset for accounting
purposes, as calculated with a depreciation model.
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Depreciation Methods
Straight-line depreciation
Declining Balance (DB) Method
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Depreciation: Straight-line method
Assumes that the rate of loss
in value (or depreciation
charge) 𝐷𝐷𝑛𝑛 of an asset is
constant over its useful life:
𝑃𝑃 − 𝑆𝑆 𝑃𝑃
𝐷𝐷𝑛𝑛 = 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 𝐷𝐷1 = 𝐷𝐷2 … = 𝐷𝐷𝑛𝑛 𝐷𝐷1
Book Value ($)
𝑁𝑁
𝐷𝐷2
Then the Book value 𝐵𝐵𝐵𝐵𝑛𝑛 after n
years is:
𝑃𝑃 − 𝑆𝑆
𝐵𝐵𝐵𝐵𝑛𝑛 = 𝑃𝑃 − 𝑛𝑛 𝑆𝑆
𝑁𝑁
P: Purchase price of asset 0 1 2 𝑛𝑛 𝑁𝑁
S: Salvage value after N periods
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Declining-balance method
Assumes that the loss in value of an
asset over a period is a constant
fraction of the asset’s book value at the
end of the last period.
The depreciation cost in every period is
a constant proportion (depreciation
rate) of the closing book value from the 𝑃𝑃
previous period: 𝐷𝐷1
Book Value ($)
𝐷𝐷𝑛𝑛 = 𝐵𝐵𝐵𝐵𝑛𝑛−1 𝑑𝑑
𝑛𝑛
𝐵𝐵𝐵𝐵𝑛𝑛 = 𝑃𝑃 1 − 𝑑𝑑
𝑛𝑛−1
𝐷𝐷𝑛𝑛 = 𝑃𝑃𝑃𝑃 1 − 𝑑𝑑
Where:
𝐵𝐵𝑉𝑉N
𝐷𝐷𝑛𝑛 : depreciation charge at period n
𝐵𝐵𝐵𝐵𝑛𝑛 : book value at end of period n 1 𝑛𝑛 𝑁𝑁
𝑃𝑃: purchase price of asset
d: depreciation rate
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Comparison
Depreciation using different methods
DB (25%)
DB (10%)
Book Value ($)
SL
𝑆𝑆
𝑁𝑁 ∗ 𝑁𝑁
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Example
Consider the following automobile data:
Data Value
Cost basis of the asset, P $10,000
Useful life, N 5 years
Estimated salvage value, S $2,000
Compute the annual depreciation allowances and the book value
each year of the automobile using the straight-line depreciation
method
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Solution:
Annual depreciation charge
𝑃𝑃 − 𝑆𝑆 10,000 − 2,000
𝐷𝐷𝑛𝑛 = = = 1,600
𝑁𝑁 5
Book Value
𝑃𝑃 − 𝑆𝑆 10,000 − 2,000
𝐵𝐵𝐵𝐵1 = 𝑃𝑃 − 𝑛𝑛 = 10,000 − = 8,400
𝑁𝑁 5
10,000 − 2,000
𝐵𝐵𝐵𝐵2 = 10,000 − 2 = 6,800
5
10,000 − 2,000
𝐵𝐵𝐵𝐵3 = 10,000 − 3 = 5,200
5
10,000 − 2,000
𝐵𝐵𝐵𝐵4 = 10,000 − 4 = 3,600
5
10,000 − 2,000
𝐵𝐵𝐵𝐵5 = 10,000 − 5 = 2,000
5
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Example-2
Sarah wants to estimate the salvage value of a coffee shop 20
years after purchase.
She feels that the depreciation is best represented using the
declining-balance method, but she doesn't know what
depreciation rate to use.
She observes that the purchase price of the coffee shop was
$245,000 three years ago, and an estimate of its current salvage
value (Book value) is $180,000.
What is a good estimate of the value of the coffee shop after 20
years?
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Solution
From this equation we can obtain the depreciation rate d for n=3
𝑛𝑛
𝑛𝑛 𝐵𝐵𝐵𝐵𝑛𝑛
𝐵𝐵𝐵𝐵𝑛𝑛 = 𝑃𝑃 1 − 𝑑𝑑 → 𝑑𝑑 = 1 −
𝑃𝑃
180,000
𝑑𝑑 = 1 − 3 = 0.097663
245,000
Then the estimated Salvage value of the coffee shop is:
𝐵𝐵𝐵𝐵20 = 𝑆𝑆 = 𝑃𝑃 1 − 𝑑𝑑 𝑛𝑛 = 245,000 1 − 0.097663 20 = $31,372
An estimate of the salvage value of the coffee shop after 20 years using
the declining-balance method of depreciation is $ 31,372
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