DEPRECIATION
BES 314- ENGINEERING ECONOMY
Depreciation (D) – the reduction in value of physical properties with the passage of time. It
establishes an annual deduction against before-tax income such that the effect of time on
an asset’s value can be reflected in the firm’s financial statements. It is a non-cash cost that
affects income taxes.
A property is depreciable if:
• It is used in business or held for the production of income
• It has a determinable life that is longer than 1 year
• It is something that wears out, decays, gets used up, becomes obsolete, or loses value
from natural causes
Depreciation
• Salvage (SV) or residual value (RV) – the price that can be obtained from the sale of a
property after it has been used. If used in depreciation calculations, it is referred to as
estimated salvage (ES), representing an asset’s terminal value.
• Book value (BV) – the worth of a property as shown on the accounting records of a
company; it means the original cost of the property less all amounts that have been
charged as depreciation expenses. In equation form, 𝐵𝑉𝑘 = 𝐵 − 𝑑𝑘
• Cost basis (B) is the initial cost of acquiring an asset (purchase price) and all other
normal costs of making the asset serviceable, such as freight, site preparation, and
installation. Cost basis is also referred to as basis or unadjusted cost.
Depreciation
• Value is the present worth (PW) of all the future profits that are to be received through
ownership of a particular property.
• Market value (MV) is what will be paid by a willing buyer to a willing seller for a
property where each has equal advantage and is under no compulsion to buy or sell.
• Useful life (N) is the period of time an asset is kept in productive use in a trade or
business.
Depreciation Methods
Straight-line Method
This method assumes that a constant amount is depreciated each year over the useful life
of the asset.
Sample Problem
Sample Problem
Declining Balance Method
The declining balance method is sometimes called the constant percentage
method or the Matheson formula, and assumes that the annual cost of
depreciation is a fixed percentage of the book value at the beginning of the
year, 𝐵𝑉𝐾−1. The ratio (also known as depreciation rate, R) of the
depreciation in any one year to the BV at the beginning of the year is constant
throughout the life of the asset. In this method, R = 2/N when a 200%
declining balance or double declining balance is being used, and N equals the
depreciable (useful) life of an asset. If the 150% DB method is specified, then R
= 1.5/N. As N increases, R decreases, thereby resulting to high depreciation
deductions during the early years of the asset.
Sample Problem
Sample Problem
Sum-of-the-years-Digits (SYD) Method
With the sum-of-the-years-digits (SYD) method, the value of the property decreases
at a decreasing rate. This method provides very rapid depreciation during the early
years of life of the property, and therefore enables faster recovery of capital.
Procedure:
1) List the digits corresponding to the number for each permissible year of life in
reverse order.
2) Determine the sum of these digits.
3) For any year, the depreciation factor is the number from the reversed-order
listing for that year divided by the sum of the digits.
4) The depreciation deduction for any year is the product of the SYD depreciation
factor that year and the difference between the cost basis and the salvage value.
Sample Problem
An asset is purchased for ₱9,000.00. Its estimated life is 10 years, after
which it will be sold for ₱1,000.00. Find the book value during the third year
if the sum-of the-year’s digit (SOYD) depreciation is used.
Sample Problem
A telephone company purchased a microwave radio equipment for ₱6M.
Freight and installment charges amounted to 3% of the purchased price. If
the equipment shall be depreciated over a period of 8 years with a salvage
value of 5%. Determine the depreciation charge during the 5th year using
SYOD method.
Sample Problem
ABC Corporation makes its policy that for every new equipment purchased,
the annual depreciation cost should not exceed 20% of the first cost at any
time without salvage value. Determine the length of service if the
depreciation used is the SYOD method.
Sample Problem
ABC Corporation makes its policy that for every new equipment purchased,
the annual depreciation cost should not exceed 20% of the first cost at any
time without salvage value. Determine the length of service if the
depreciation used is the SYOD method.
Sinking Fund Method
The sinking fund method depreciates an asset as if the firm were to make a
series of equal deposits whose value at the end of the asset’s useful life just
equaled the cost of replacing the asset. All amounts in the sinking fund earn
interest.
If
A' = sinking fund deposit
C = purchase price of replacement asset – net salvage value of current asset
n = useful life of current asset
i = annual interest rate
Then A’ = C(A/F, i%, n).
Sample Problem
A unit of welding machine cost ₱45,000 with an estimated life of 5 years. Its
salvage value is ₱2,500 find its depreciation rate of sinking fund method.
Assuming that will deposit the money to a bank giving 8.5%. Solve for the
depreciation.
Sample Problem
A ₱110,000 chemical plant had an estimated life of 6 years and a projected
scrap value of ₱10,000. After 3 years of operation an explosion made it a
total loss. How much money would have to be raised to put up a new plant
costing ₱150,000, if a depreciation reserved have been maintained during its
3 years of operation by sinking fund method at 6%?
Service-Output Method
The service-output method or units-of-production method assumes that the
total depreciation that has taken place is directly proportional to the quantity
of output of the property up to that time. This method has the advantage of
making the unit cost of depreciation constant and gives low depreciation
expense during periods of low production.
Let TQ = total units of output up to the end of the useful life of the asset
QK = total units of output during year k
Assignment
Assignment
A milling machine was invoiced from Japan CIF (cost, insurance,
freight) Manila at P 250,000. Brokerage, bank, customs duties,
permits etc. total at P 120,000. It is believed that the machine can
be sold for p 50,000 at the end of its 10-year service life. Prepare a
depreciation schedule for each of the following methods: (a) straight
line method and (b) SYD method.
