### Economics

```Section 3
Dr.Hoda’s part
Depreciation
Eng. Reda Zein
Depreciation

 A noncash expense that reduces the value of an asset as
a result of wear and tear, age, or obsolescence. Most assets
lose their value over time (in other words, they depreciate),
and must be replaced once the end of their useful life is
reached.
 There are several accounting method that are used in order
to calculate an assets depreciation costs over the period of its
useful life..
Depreciation methods
1- Straight line method:

−
=

Where: d: depreciation charge, Vo: orignal value, Vs:
salvage value, n: service life
( −  ): is the total depreciated value.
2- Use or production method:
()  ℎ
=
∗ ( −  ) ≠ const

Depreciation methods

3- Double declining balance method:
1
=2∗
∗ remaining cost
n
4- Sum of years digits method:
=
Useful service life remaining

=1
∗ ( −  )
Where: n: Total service life, Useful life remaining= years
remaining of service life at the beginning of year considered

=1  : Arithmetic sum of digits of years
Let’s begin our sheet

2) A reactor of special design is the major item of equipment
in a small chemical plant. The initial cost of the completely
installed reactor is \$60,000 and salvage value at the end of
the useful life is estimated to be \$10,000. Excluding
depreciation costs for the reactor, the total annual expenses
for the plant are \$100,000. How many years of useful life
should be estimated for the reactor if 12% of the total annual
expenses for the plant are due to the cost of reactor
depreciation? The straight line method for determining
depreciation should be used.
(Ans.=3.7 year)
3)
Apiece of equipment originally costing \$40,000 was put
into use 12years ago. At the time the equipment was put into
use, the service life was estimated to be 20 years and the
salvage and the scrap value at the end of the service life were
assumed to be zero. On this basis, straight line depreciation
fund was set up. The equipment can now be sold for \$10,000
and a more advanced model can be installed for \$55,000.
Assuming the depreciation fund is available for use, how
much new capital must be supplied to make the purchase?
(Ans. =\$21,000)
4) A piece of equipment having a negligible salvage value is
estimated to have a service life of 10 years. The original cost of
equipment was \$40,000. Determine the following:
a- The depreciation charge during the 5th year if straight line
depreciation is used.
b- The depreciation charge during the 5th year if sum–of-yearsdigits depreciation is used.
c- The percent of original investment paid off in the first half of
the service life using sum–of-years- digits method.
d- The percent of original investment paid off in the first half of
the service life using the double declining balance method.
(Ans.:a-\$4,000, b- \$4363.6, c-72.7%, d- 67.2%)
5) The original investment for an asset was \$10,000 and the asset
was assumed to have a service life of 12 years with \$2,000 salvage
value at the end of service life. After the asset has been in use for 5
years, the remaining service life and final salvage value are reestimated at 10 years and \$1,000 , respectively. Under these
conditions, what is the depreciation cost during the sixth year of
the total life if straight line depreciation is used ?
(Ans.:\$566.7)
7) In order to make it worth while to purchase a new piece of
equipment, the annual depreciation costs for the equipment
cannot exceed \$3,000 at any time. The original cost of equipment
is \$30,000 and it has zero salvage and scrap value. Determine the
length of service life necessary if the equipment is depreciated by
(a) The straight-line method and (b) The sum–of-years- digits
method.
(Ans.: (a) 10 years (b) 19 year )
Any questions? 

```