ENGINEERING ECONOMY 2.

The Sinking Fund Method: States that a

sinking funds will accumulate for
DEPRECIATION – it is the decrease in the value of
replacement purposes and will bear interest.
a property due to the passage of time.
The total depreciation which has occurred up
TYPES to any given time is assumed to equal the
accumulated value of the sinking fund at that
1. Physical Depreciation – due to the deterioration time.
caused by various chemical and mechanical
factors on the materials composing the property
such as rusting of metal parts of a machine or
equipment.

2. Functional Depreciation – due to the decrease in

the demand for the equipment for which it was
designed such as obsolescence of the
equipment.
CAUSES
1. Wear and tear
2. Obsolescence
3. Decrease in capacity
4. Change in technology
5. Out-modeled
6. Deterioration
Depletion – it is the decrease in the value of a
property with the passage of time due to the
consumption of each resource.
3. Declining Balance Method (Matheson Formula) /
METHODS OF DETERMINING DEPRECIATION Fixed Percentage method : this method considers
that the annual cost of depreciation is a fixed
1. The Straight Line Method : States that the loss in percentage or constant percentage of the book
value is considered to be directly proportional to value or salvage value at the beginning of the
the age of the assets. No interest is assumed to year. The annual depreciation charges, different
be paid on the amounts set aside in the each year, decrease from year to year, greatest
depreciation fund. It is simple and is more widely during the first year and least in the last year of
used than any other method. It also gives a life of the property. It should be noted that in this
uniform annual charge, in truth it is acceptable to method, a property can never depreciate to zero
the Bureau of Internal Revenue (BIR). value.
4. The Sum of the Year’s Digit Method (SYD):
provides very rapid depreciation during the early
EXERCISES:
years of life of the property, and therefore
enables faster recovery of capital. It is easier to 1. The cost of equipment is P500,000 and the cost
use than the Matheson Formula. The properties of installation is P30,000. If the salvage value at
can be depreciated to zero value. the end of 5 years is 10% of the cost of
equipment, determine the book value at the end
of the 4th year. Use straight line method.
2. An engineer bought an equipment for P500,000.
He spent an additional amount of P30,000 for
installation and other expenses. The salvage
value is 10% of the first cost. If the book value at
the end of 5 years will be P291,500 using
straight line method of depreciation, compute the
useful life of the equipment in years.
3. The initial cost of a paint sand mill, including its
installation, is P800,00. The BIR approved life of
the machine is 10 years for depreciation. The
estimated salvage value of the mill is P50,000
and the cost of dismantling is estimated to be
P15,000. Using straight line depreciation, what is
the annual depreciation charge and what is the
book value of the machine at the end of 6 years?
For example : N = 8 years 4. A certain machinery costs P50,000 last 12 years
with a salvage value of P5,000. Money is worth
Sum = (8+1)(8/2) = 36 5%. If the owner decides to sell it after using it
for 5 years, what should his price be so that he
Sum = 1+2+3+4+5+6+7+8 = 36
will not lose or gain financially in the transaction?
Year Depreciation Use sinking fund method of depreciation.
8
5. A machine costs P80,000 and has an estimated
1 (𝐹𝐶 − 𝑆𝑉) salvage value of P20,000 at the end of 20 years
36
7 useful life. Compute the book value at the end of
2 (𝐹𝐶 − 𝑆𝑉)
36
6 2nd year using sinking fund method of
3 (𝐹𝐶 − 𝑆𝑉) depreciation based on 8% interest rate.
36
5
4 (𝐹𝐶 − 𝑆𝑉) 6. A certain equipment has a first cost of P20,000
36
4 and salvage value of P1,000 at the end of 10
5 (𝐹𝐶 − 𝑆𝑉) years. Determine its book value at the end of 6
36
3
6 (𝐹𝐶 − 𝑆𝑉) years using declining balance method.
36
2 7. A radio service panel truck initially cost
7 (𝐹𝐶 − 𝑆𝑉)
36 P56,000.00. Its resale value at the end of the 5th
1
8 (𝐹𝐶 − 𝑆𝑉) year of the useful life is estimated at P15,000.00.
36
By means of the declining balance method,
Book value after 4th year: determine the depreciation charge for the 2nd
8+7+6+5 year.
BV4 = FC –(𝐹𝐶 − 𝑆𝑉)
36 8. A machine costs P80,000 and has an estimated
salvage value of P20,000 at the end of 20 years
First Cost – the sum of the initial expenditures
useful life. Compute the book value of the
involved in capitalizing a property or building a
machine after two years using SYD method.
project; includes items such as transportation,
9. ABC Corporation makes its policy that for every
preparation for service, as well as other related
new equipment purchased, the annual
costs.
depreciation cost should not exceed 20% of the
Salvage Value – second-hand value, or it is the sum first cost at any time without salvage value.
of money which the machine will bring when sold to Determine the length of service if the
some other company or second hand dealer. depreciation used is SYD method.
10. A telephone company purchased a microwave
Book value – it is the worth of the property which is
radio equipment for P6M. Freight and installation
equal to the original cost less the amount which has
charges amounted to 3% of the purchased price.
been charged to depreciation.
If the equipment shall be depreciated over a
Scrap value – the amount that the property would period of 8 years with a salvage value of 5%.
bring if sold for junk. Determine the depreciation charge during the 5 th
year using the SYD method.
Obsolescence – refers to changes in conditions
external to the equipment under consideration.
SAMPLE PROBLEMS: 4. A P110,000 chemical plant had an estimated life
of 6 years and a projected scrap value of P10,000.
1. A machine has an initial cost of P50,000.00 and a
After 3 years of operation, an explosion made it a
salvage value of P10,000.00 after 10 years. What
total loss. How much money would have to be
is the book value after five years using straight
raised to put up a new plant costing P150,000, if a
line depreciation?
depreciation reserved have been maintained during
Solution: Annual Depreciation its 3 years of operation by sinking fund method at
6%.
FC−SV
D=
N Solution: Sinking fund method:
50,000 − 10,000 (FC−SV)𝑖
= Annual depreciation =
10 (1+𝑖)𝑛 −1

D = 4,000 (110,000−10,000) 0.06

Annual depreciation =
(1.06)6 −1
Book Value after 5 years:
Annual depreciation = P14,336.26
BV5 = FC – nD
Total depreciation (F) after 3 years:
= 50,000 – 5(4,000)
(1+𝑖)𝑛 −1
BV5 = 30,000.00 F= A
𝑖

(1+0.06)3 −1
F = 14,336 = P45,640.92
0.06
2. An asset is purchased for P500,000.00. The
salvage value in 25 years is P100,000.00. What are Amount to be raised:
the depreciations in the first three years using
= P150,000 – P45,640.92
straight line method?
= P140,359.08
Solution: Annual Depreciation
FC−SV 5. A machine costing P720,000 is estimated to have
D= a life of 10 years. If the annual rate of depreciation is
N
25%, determine the total depreciation using a
500,000 − 100,000 constant percentage of the declining balance
=
25 method.
D = 16,000 Solution:
Total Depreciation for 3 years: 𝑛 SV
k=1− √
Total Dep = nD FC

SV
= 3(16,000) = (1 − 𝑘)𝑛
FC
Total Dep = P48,000 SV = FC(1 − 𝑘)𝑛

SV = 720,000 (1 − 0.25)10
SV = P40,545.73
3. A unit of welding machine cost P45,000 with an Depreciation = FC – SV
estimated life of 5 years. Its salvage value is P2,500,
find its depreciation rate of sinking fund method. = 720,000 – 40,545.73
Assuming that will deposit the money to a bank
Depreciation = P679,454.27
giving 8.5%. Solve for the depreciation.
6. The cost of a certain asset is P3000, its life is 6
Solution: i = 0.085
years and scrap value is P500. Find the annual rate
(FC−SV)𝑖 of depreciation under a constant percentage method
Depreciation =
(1+𝑖)𝑛 −1 and construct a depreciation table.

= Solution:
(45000−2500) 0.085
(1+0.085)5 −1
FC = P3000 , SC = 500 n =6

D = P7,172.54 Using constant percentage method:

𝑛 SV
k=1− √ =
FC

6 500
k= 1− √ k = 0.25816
3000
Depreciation table:
Year Depreciation, FC(k) Book Value (FC – Dep)
1 3000(.25816) = 774.48 3000 - 774.48 = 2225.52
2 2225.52(.25816) = 574.54 2225.52 – 574.54 = 1650.98
3 1650.98(.25816) = 426.22 1650.98 – 426.22 = 1224.76
4 1224.76(.25816) = 316.18 1224.76 – 316.18 = 908.58
5 908.58 (.25816) = 234.56 908.58 – 234.56 = 674.02
6 674.02 (.25816) = 174.02 674.02 – 174.02 = 500.00

7. An asset is purchased for P9,000. Its estimated

life is 10 years, after which it will be sold for
P1,000.00. find the book value during the third year
if the sum-of-the-year’s digit depreciation is used.
Solution:
SYD = 1+2+3+4+5+6+7+8+9+10 = 55
SYD = (10 + 1) (10/2) = 55
Year Depreciation (FC – SV)
1 (9000 – 1000) (10/55) = P1,454.54
2 (9000 – 1000) (9/55) = P1,309.10
3 (9000 – 1000) (8/55) = P1,163.63
Total for 3 years = P3,927.28
BV3 = 9000 – 3,927.28
BV3 = P5,072.72

8. An equipment costs P7,000 has a life of 8 years

and salvage value of “x” after 8 years. If the book
value of the equipment at the 4th year is equal to
P2197.22 , compute the salvage value “x” using the
SYD method.

Solution:

SYD = (1+8) (8/2) = 36

Book value = First Cost – Total Depreciation (4th yr)
BV4 = FC - ΣD
2197.22 = 7000 – ΣD
ΣD = 4802.78
Depreciation @ 4th year
(8+7+6+5)
D= (𝐹𝐶 − 𝑆𝑉)
36
26
4802.78 = (7000 − 𝑆𝑉)
36

6650 = 7000 – SV
SV = 350
x = 350 (salvage value)