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HP 12c Financial Calculator  Depreciation
Depreciation
Depreciation (Latin 'Depretium': 'decline in price' or 'value') is an accounting term that may be defined as the permanent
and continuing diminution in the quality, quantity or the value of an asset over time. This is due to many reasons, from
deterioration and obsolescence to impending retirement. It applies particularly to physical assets like equipment and
structures. In industry, for accounting purposes, depreciation is also a method of deducting the cost of business property
related to capital assets as they wear out, lose value, or become obsolete in order to recover their cost as a business
expense. A capital asset can be a piece of equipment, a building or a vehicle expected to be used for several years. The
purchase price of the asset on the purchase date is called book value.
Depreciation on the HP 12c
There are mathematical tools that calculate the depreciation of assets, and the HP 12c has functions that allow three
different approaches: straightline depreciation (), depreciation using declining balance () and depreciation
using sum of the years digits (). These functions can be used to directly calculate depreciation or as part of a
program or more complex calculations. The expressions used by the HP 12c to calculate depreciation with these
functions are:
Figure : Expressions for calculating depreciation
Where:
Term

Description

L

Asset's useful life expectancy

SBV

Starting book value

SAL

Salvage value

FACT

Declining balance factor expressed as a percentage

j

Period number

DPN_{j}

Depreciation expense during period j

RDV_{j}

Remaining depreciable value at the end of period j;
RDV_{j} = RDV_{j1} − DPN_{j}
where RDV_{0}= SBV − SAL

RBV_{j}

Remaining book value;
RBV_{j} = RBV_{j1} − DPN_{j}
where RBV_{0} = SBV

Y_{1}

Number of months in the partial first year.

The HP 12c calculates depreciation with either of these three methods by using TVM registers , , and to
hold the necessary data, as shown below:
Register

Contents


Salvage value of the asset


Original cost of the asset


Expected useful life of the asset (years)


Decliningbalance factor ( only).

To calculate the depreciation after entering these values, key in the number of the year for which the depreciation is to
be calculated and press , or . The amount of depreciation is calculated and shown in the
display. To see the remaining depreciable value (book value minus salvage value) press .
Practice solving depreciation problems
Example 1
The R&D department of a crystal refinement company spent $28,000 for new equipment for the digital
spectrometer lab. The expected life for this equipment is 12 years, and the salvage value is $2,500.
Calculate the declining balance depreciation for the fifth and eighth years and compare the values to the
straightline fixed depreciation. Use the DB method with a 2× weight (200%) related to the SL.
Solution
Load the TVM registers with the relevant values and calculate the depreciation for the fifth and eighth years
using the DB method:
Keystroke

Display


Figure : Calculating depreciation for the fifth year


Figure : Calculating depreciation for the eighth year

Keep the TVM registers with previous values and calculate the depreciation using the SL method. As the
straightline method returns the same depreciation amount for each valid period, it is enough to calculate it
for the first year.
Keystroke

Display


Figure : Calculating depreciation for the first year

Answer
The amount of depreciation with 2× weighted DB method for the 5^{th} year is $2,250.52 and $1,302.38 for
the 8^{th} year. With the same figures, the annual amount of depreciation calculated with the SL method is
$2,125.
Example 2
Professional video equipment bought for $15,000 has a useful life of 8 years with a salvage value of
$1,100. Using the SOYD method, find the amount of depreciation for the fourth year.
Solution
Load the TVM registers with the relevant values and calculate the SOYD depreciation for the fourth year:
Keystroke

Display


Figure : Calculating depreciation for the fourth year

Answer
The amount of depreciation for the fourth year is $1,930.56.
Practice solving partialyear depreciation problems
In most cases, the acquisition date of an asset does not coincide with the start of the fiscal or tax year. In these cases,
the amounts of the first and last year's depreciation are computed as fractions of a full year's depreciation. Consider the
example shown in Figure 6.
Figure : Calculating the amount of depreciation as fractions
When using the straightline method, calculating partialyear depreciation is a matter of calculating depreciation fractions
related to the calendar year, because the amount of depreciation for each depreciation year is constant. In the diagram
shown in Figure 3, the amount of depreciation calculated with SL for the first calendar year is 2/3 of the amount of
depreciation for a full year, and for the fourth calendar year it is just 1/3 of it.
When using either DB or SOYD depreciation method, the depreciation fractions are the ones reflected by the fractions of
the depreciation years. The relationship between the calendar year and the depreciation year in the example shown in
Figure 6 for DB and SOYD depreciation methods is shown in the table below:
Figure : Relationship between calendar year and depreciation year
Example 3
Using the same video equipment from the previous example, calculate the amount of depreciation of the
fourth year using SOYD, but now assume that the equipment was bought in February.
Figure : Calculating partial depreciation
Solution
The diagram in Figure 8 helps building the solution. The fourth year is calculated by adding 1/12 of the third
depreciation year to 11/12 of the fourth depreciation year. If data from previous example has not been
changed yet, the following keystroke sequence can be used:
Keystroke

Display


Figure : Calculating depreciation amount for 1/12 of the third year

This is the depreciation amount for 1/12 of the 3^{rd} year, and it is stored in R_{0}. Now calculate 11/12 of the
fourth depreciation year, add it to R_{0} and retrieve the accumulated value:
Keystroke

Display


Figure : Calculating the amount of depreciation for the fourth year

Answer
The amount of depreciation for the fourth year is $1,962.74 given that the first depreciation year was only
11 months long.
Additional information
The HP 12c Owner's Handbook and Problem Solving Guide , Part III Section 13, under Investment Analysis, has
many examples on how to use programs with depreciation functions in more complex depreciation situations.
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