DEPRECIATION

DEPRECIATION
• Depreciation is the decrease in the value of physical property with
the passage of time

• Definitions of Value
• Value, in a commercial sense, is the present worth of all future profits that
are to be received through ownership of a particular property.
• The market value of a property is the amount which a willing buyer will
pay to a willing seller for the property where each has equal advantage and
is under no compulsion to buy or sell.
• The utility or use value of a property is what the property is worth to the
owner as an operating unit.
• Fair value is the value which is usually determined by a disinterested third
party in order to establish a price that is fair to both seller and buyer
 • Book value, sometimes called depreciated book value, is the
worth of a property as shown on the accounting records of the
enterprise.
• Salvage value, or resale, is the price that can be obtained
from the sale of a property after it has been used.
• Scrap value, is the amount the property would sell for if
disposed off as a junk.

• PURPOSES OF DEPRECIATION
• 1. To provide for the recovery of capital which has been
invested in physical property
• 2. To enable the cost of depreciation to be charged to the cost
of producing products or services that results from the use of
property.
TYPES OF DEPRECIATION
• 1. Normal Depreciation
• A. Physical Depreciation, is due to the lessening of the physical ability of a
property to produce results. Its common cause is wear or deterioration.
• B. Functional Depreciation, is due to the lessening in the demand for the
function which the property is designed to render. Its common causes are
inadequacy, changes in styles, population centers shift, saturation of
markets or more efficient machines are produced.
• 2. Depreciation due to the changes in price levels, is almost
impossible to predict and therefore is not considered in economy
studies.
• 3. Depletion, refers to the decrease in the value of a property due
to the gradual extraction of its contents
• PHYSICAL AND ECONOMIC LIFE
• ❖ Physical life of a property, is the length of time during which
it is capable of performing the functions for which it is
designed and manufactured.
• ❖ Economic life, is the length of time during which the
property may be operated at a profit.

• REQUIREMENTS OF A DEPRECIATION METHOD

• 1. It should be simple.
• 2. It should recover capital
• 3. The book value will be reasonably close to the market value
at any time.
• 4. The method should be accepted by the Bureau of Internal
Revenue
METHODS IN SOLVING
DEPRECIATION
• TIME INDEPENDENT • TIME DEPENDENT

1. Working Hours Method • Uniform Methods

2. Unit Production Method 1. Straight Line Depreciation
2. Sinking Fund Method

• Non-Uniform Methods
1. Declining Balance Method
2. Sum of Years Digit Method
3. MACRS Method
STRAIGHT LINE DEPRECIATION
• This method assumes that the loss in value is directly
proportional to the age of the property.

FC−SV
• D= annual depreciation =
n
• Dm = total depreciation after m years
• Where
• BVm = book value after m years = FC- Dm • FC= first value
D • SV= Salvage Value
• Depreciation rate=
FC • N = life of the property
SV or equipment
• Salvage Rate =
FC
• Sunk Cost = Book Value – actual resale value
EXAMPLE 1
• A machine has an initial cost of P50,000 and a
salvage value of P10,000 after 10 years. What is
the book value after five years using straight line
depreciation?
SINKING FUND METHOD
• This method assumes that a sinking fund is established in which
funds will accumulate for replacement. The total depreciation
that has taken place up to any given time is assumed to be equal
to the accumulated amount in the sinking fund at that time.
FC−SV i
• d= annual depreciation =
(1+i)n −1
(1+i)m −1
• Dm = total depreciation after m years = d[ ]
i
• BVm = book value after m years = FC- Dm
• Sunk Cost = Book Value – actual resale value
EXAMPLE 2
• A unit welding machine costs P45,000 with an
estimated life of 5 years. Its salvage is P2,500.
Find the book value after 3 years using sinking
fund method with 8.5 % interest.
EXAMPLE 3
• A machine, initially costing Php 155,000, is set to
depreciate Php20,000 every year using Sinking Fund
Method. How much must be invested every year to
replace the asset with a better but more expensive
machine costing Php250,000 after 5 years at an annual
rate of 5%?
METHODS IN SOLVING
DEPRECIATION
• TIME INDEPENDENT • TIME DEPENDENT

1. Working Hours Method • Uniform Methods

2. Unit Production Method ✓ Straight Line Depreciation
✓ Sinking Fund Method

• Non-Uniform Methods
1. Declining Balance Method
2. Sum of Years Digit Method
3. MACRS Method
DECLINING BALANCE METHOD
• In this method, sometimes called the constant percentage
method or the Matheson Formula, it is assumed that the annual
cost of depreciation is a fixed percentage of the salvage value at
the beginning of the year.
• The ratio of the depreciation in any year to the book value at the
beginning of that year is constant throughout the life of the
property and is designated by k, the rate of depreciation
 DECLINING BALANCE METHOD
n SV
• K = constant ratio = 1-
FC
• Annual depreciation
Depreciation for the first five years:
D1 = k(FC)(1 − k)0
D2 = k(FC)(1 − k)1
D3 = k(FC)(1 − k)2
D4 = k(FC)(1 − k)3
D5 = k(FC)(1 − k)4
DECLINING BALANCE METHOD
• Therefore, annual depreciation for any year is:

• dn = k(FC)(1 − k)n−1

• Total depreciation after 5 years

• DT5 = D1 + D2 + D3 + D4 + D5
• BVm = book value after 5 years = FC- DT5
• BVm = book value after m years = (FC)(1 − k)m
EXAMPLE 4
• A company decided to acquire a state-of-the- art
production machine that will cost Php 2,500,000. It
will also require another Php 50,000 for shipping
and Php 65,000 for installation. Using standard
Declining Balance Method at 8% annual rate, find:
• a) the depreciation cost for its 3rd year of use.
• b) the accumulated depreciation after 6 years.
• c) the salvage value if it is expected to last for 15
years.
EXAMPLE 5
• A construction company bought a concrete mixer truck
at Php 1,700,000 and is expected to last for 10 years.
Using the double declining balance method find the
salvage value of the mixer truck.
 SUM OF THE YEARS DIGIT
METHOD (SOYD)
𝑅𝑒𝑚𝑎𝑖𝑛𝑖𝑛𝑔 𝑈𝑠𝑒𝑓𝑢𝑙 𝐿𝑖𝑓𝑒
• 𝑑𝑟 = 𝑥 𝐷𝑛
𝑠𝑢𝑚 𝑜𝑓 𝑦𝑒𝑎𝑟𝑠 𝑑𝑖𝑔𝑖𝑡 (𝑆𝑌𝐷)

• For 8 years (n=8) Depreciation for the first 5 years:

• SYD = 1+2+3…..+8 = 36 d1=(FC−SV)(8/36)
𝑛 d2=(FC−SV)(7/36)
• Using the SYD Formula: SYD = (1 + 𝑛) d3=(FC−SV)(6/36)
2
d4=(FC−SV)(5/36)
d5=(FC−SV)(4/36)
• Remaining Useful Life = (𝑛 − 𝑟 + 1)
SUM OF THE YEARS DIGIT
METHOD (SOYD)
• DT5 = total depreciation after 5 years:

• DT5 = d1 + d2 + d3 + d4 + d5

• Or

𝑟(1+2𝑛−𝑟)
• 𝐷𝑟 = 𝐷𝑛
𝑛(1+𝑛)

• BVm = book value after 5 years = FC- DT5

EXAMPLE 6
• What is the book value of equipment purchased
4 years ago for $15,000 if it depreciated using the
sum of the year’s digit (SOYD) method? The
expected life is 6 years.
MODIFIED ACCELERATED COST
RECOVERY SYSTEM (MACRS)
• Depreciation charge for the first 5 years:
d1 = FC/n
2
d2 = [ FC − d1 ]
n
2
d3 = [ FC − (𝑑1 +d2 ]
n
2
d4 = [ FC − (𝑑1 +d2 + d3 ]
n
2
d5 = [ FC − (𝑑1 +d2 + d3 + d4 ]
n

• BV5 = [ FC − (𝑑1 +d2 + d3 + d4 + d5 ]

EXAMPLE 7
• A machine initially costing $25,000 will have a
salvage value of $6,000 after five years. Using
MACRS depreciation, what will its book value be
after the third year?