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DEPRECIATION

Is the decrease in the value of physical property with the passage of time
o VALUE
 In a commercial sense, is the present worth of all future profits that are to
be received through ownership of a particular property
a. MARKET VALUE
 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
b. USE VALUE
 What the property is worth to the owner as an operating unit
c. FAIR VALUE
 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
d. BOOK VALUE
 Sometimes called depreciated book value
 The worth of a property as shown on the accounting records of an
enterprise
e. SALVAGE VALUE
 Also called resale value
 The price that can be obtained from the sale of the property after it
has been used
 Salvage year is the time when the scrap value is equal to the book
value
f. SCRAP VALUE
 The amount of the property would sell for if disposed off as a junk
o PURPOSES OF DEPRECIATION
1. To provide for the recovery of capital which has been invested in physical
property
2. To enable the cost of depreciate to be charged to the cost of producing
products or services that results from the use of the property.
o TYPES OF DEPRECIATION
1. Normal depreciation
a. Physical
 Is due to the lessening of the physical ability of a property to
produce results
 Common causes are wear and deterioration
b. Functional
 Due to the lessening in the demand for the function which the property
was designed to render
 Common causes are inadequacy, changes in styles, saturation of
markets or more efficient machines are produced
2. Depreciation due to changes in price levels
 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.
o PHYSICAL LIFE
 The length of time during which it is capable of performing the function for
which it was designed and manufactured
o ECONOMIC LIFE
 The length of time during which the property may be operated at a profit
o REQUIREMENTS OF A DEPRECIATION METHOD
1.
2.
3.
4.
It should be simple
It should recover capital
The book value will be reasonably close to the market value at any time
The method should be accepted by the Bureau of Internal Revenue
o DEPRECIATION METHODS
We shall use of the following symbols for the different depreciation methods
L
Co
CL
=
=
=
d
Cn
Dn
=
=
=
useful life of the property in years
the original cost
the value at the end of life, the scrap value
(including gain or loss due to removal)
the annual cost of depreciation
the book value at the end of n years
depreciation up to age n years
a. STRAIGHT LINE METHOD
 This method assume that the loss in value is directly
proportional to the age of the property
d=
V O −V s
n
D a=
a( V O−V s)
L
V n=V O −Da
Example:
a. An electronic balance costs P90,000 and has an estimated salvage value
of P8,000 at the end of its 10 years lifetime. What would be the book value
after three years, using straight line method in solving for the
depreciation?
Ans. P65,400
b. Prepare a depreciation table for an asset which was brought at 15,000
and estimated to be useful for a period of 4 years. Estimated salvage
value is 10% of its original cost.
Ans: d=3375
year
Beginning book
value
15,000
11,625
8,250
4,875
1
2
3
4
Depreciation
Book value
3375
3375
3375
3375
11,625
8,250
4,875
1,500
b. SINKING FUND FORMULA
 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
d=
CO −C L
F
Da=d
, i ,n Cn =CO −D a
F
A
,i , L
A
(
)
Example:
A firm bought an equipment fee for P56,000. Other expenses including
installation amounted to P4,000. The equipment is expected to have a life of 16
years with a salvage value of 10% of the original cost. Determine the book value at
the end of 12 years by straight line methods and sinking fund methods at 12%
interest.
Ans: P19,500;P29,520
a. Prepare a depreciation table for an asset which was brought at 15,000
and estimated to be useful for a period of 3 years. Estimated salvage
value is 10% of its original cost. Money is worth 10% compounded
annually
initial
book
value
yr
1
2
3
15000
10468.
74
5484.5
64
ending
depreciati
book
on
total dep value
10468.
4531.26
4531.26
74
5484.5
4531.26 9515.436
64
14998.13
4531.26
96 1.8604
c. DECLINING BALANCE METHOD
 Sometimes called the constant percentage method of 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
 This method does not apply if the salvage value is zero,
because k will be equal to one and d will be equal to Co.
1−k
¿
¿
1−k
¿
¿
d a=C o ¿
1−k
¿
¿
C a=C o ¿
Example:
A certain type of machine loses 10% of its value each year. The machine
costs P2,000 originally. Make out a schedule showing the yearly depreciation, the
total depreciation and the book value at the end of each year for 3 years.
Ans:
endin
initial
g
book
depreciati total
book
value
on
dep
value
1
2,000
200
200 1,800
2
1800
180
380
1620
3
1620
162
542
1458
yr
c. A machine worth 800,000 is brought from china, freight charges amount
to 200,000. If the scrap value of the machine is 50,000 that occurs at the
end of 17 years. (a) compute the depreciation at the end of the year11 (b)
Compute the book value at the end of 11 years .
d. DOUBLE DECLINING BALANCE METHOD
 This method is very similar to declining balance method except that the rate of
depreciation k is replaced by 2/L.
 The salvage value should not be subtracted from the first cost when calculating
the depreciation charge.
1−
¿
¿
1−
¿
¿
1−
2
L
2
L
2
L
¿
¿
d n=C o ¿
Example:
Determine the rate of depreciation, the total depreciation up to end of the
8 year and the book value at the end of 8 years for an asset that costs P15,000
new and has an estimated scrap value of P2,000 at the end of 10 years by double
declining balance method.
Ans: 20%, P12, 483
th
e. SUM – OF-THE-YEARS (SYD) METHOD
Let
dn = depreciation charge during the nth year
reverse digit
(C −C )
=
∑ of digits o L
Sum of the years= n(n+1)/2
Example:
A structure costs P12,000 new. It is estimated to have a new life of 5 years
with a salvage value at the end of life of P1,000. Determine the book value at the
end of each year of life.
Ans: P8,333 ; P5,400; P 3,200; P 1,733; P 1,000
f. SERVICE-OUTPUT METHOD
 This 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.
 Has the advantage of making the unit cost depreciation constant
and giving low depreciation expense during periods of low
production.
Let
T
Qn
= total units of output up to the end of life
= total number of units of output during the nth year
C o−C L
Depreciation per unit of output =
T
Co −C L
dn
=
Qn
T
(
)
Example:
A Television Company purchased machinery for P100,000 on July 1,
1979. It is estimated that it will have a useful life of 10 years; scrap value of P4,000,
production of P400,000 units and working hours of P120,000. The company uses
the machinery for 14,000 hours in 1979 and 18,000 hours in 1980. The machinery
produces 36,000 in 1979 and 44,000 units in 1980. Compute the depreciation in
1980 using service-output method.
Ans: P10,560
Hour/ output method
D= h/H (C-Cl) ; Cn = Co- Dn
H=total hours of economic life
h=hours the asset has been used
an electric bulb bought for 100 is guaranteed to be useful for 50 hours, the certain
company uses the said bulb 10 hrs a day. If there is no scrap value, compute for the
daily depreciation . determine the book value on the 4 th day.
d=20/a day
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