21.5 DEPRECIATION

Depreciation is the amount by which the value of an item decreases over time.
The new reduced value of an item is known as its
book value.
Once the item has reached the stage where it can no longer be used profitably by a company, it is sold off. The price that the item is sold for is known as
scrap value.

There are three main methods used to determine the depreciated value of an item. These are:
• Unit Cost depreciation
• Flat Rate depreciation
• Reducing Balance depreciation

Sometimes items of equipment are valued according to the amount of use they have had rather than their age.
For example 2 cars may have the same age but vary significantly in relation to the kilometres travelled
(mileage). The value of the 2 cars may be different as a result.

The process of depreciating an item on the basis of the amount of use; that is, according to the number of units it has produced, is called unit cost
depreciation.
To calculate unit cost we use the general rule:
Unit Cost = purchase price – scrap value total production

To calculate the depreciation, and hence the book value of the item:
Depreciation and Book Value
Depreciation (D) = unit cost x n
Book value (V) = purchase price – unit cost x n
Where n = the number of units produced
V = the book value after the production of n units

To determine the length of time the item will be in use:
Length of time in use
Length of time in use (t) = purchase price – scrap value average depreciation per year
Refer to Example 14 page 574

Flat rate depreciation is when the value of an item is reduced by the same percentage of the purchase price, or amount, for each year it is in use.
It is equivalent to simple interest.
Flat rate depreciation
D = purchase price x interest rate (p.a) x length of time
100
D = Prt_
100

To determine the book value of an item ($V), which has a purchase price of $P, and which is depreciating at a flat rate of r% per annum annually for a period of time:
Book Value (flat rate depreciation)
V = purchase price – depreciation
V = P - Prt_
100

As is the case of simple interest, the relationship between book value and age for flat rate depreciation is linear.
For this reason, this form of depreciation is also known as straight line depreciation.
Refer to Example 15 page 576

Determining flat rate depreciation and book value using the TI-Nspire CAS calculator:
Refer to page 577 and work through the example.

Reducing balance depreciation is when the value of an item is reduced by a constant percentage for each year it is in use.
It is the equivalent, but opposite, situation to
compound interest, and the amount of the depreciation is given by:
D = P – V

The book value of an item:
V = P x ( 1 - r_ ) t
100
Note that the sign is now negative because the value of the item is decreasing.
This relationship for reducing balance depreciation is non-linear.
Refer to Example 16 page 579

Determining reducing balance depreciation and book value using the TI-Nspire CAS calculator:
Refer to page 580 and work through the example.