Depreciation

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Depreciation is a group of methods used in project economics that allows for the CAPEX to be spread out over the useful life of the capital. In many cases such as mills and processing plants, the useful life of capital parallels the life of the project. By spreading this expenditure out, future revenue streams are depreciated by subtracting a portion of these capital expenses. The benefits of this can manifest themselves in both tax and accounting purposes.

When analyzing the cash flows and reported results from an operation, including depreciation in the balance sheet can give a better perspective to what the costs/benefits of production actually are instead of lumping all CAPEX to the beginning of a project. The method used varies from company to company and thus careful attention must be paid to each individual balance sheet and income statement.

For taxation purposes, depreciating can reduce the taxable income at an operation as it is subtracted from gross revenue alongside operating expenses. When dealing with taxation however, the maximum depreciation rate for a specific class of asset is prescribed (at least in Canada) by the government. Most machinery at a mining operation will fall under Class 38 with a rate of 30%, and most buildings will fall under Class 1 with a rate of 6%.[1]

Contents

Methods

Simple syntax used in the depreciation methods is defined as such:

IC represents the initial cost of capital
DCi represents the depreciation charge in year i
BVi represents the book value of the asset in year i
n represents the estimated number of periods in the assets’ useful life
r represents the depreciation rate as a decimal

Straight-line depreciation

Straight-line depreciation is the simplest of methods and is commonly used because of this. In this method, the capital cost of the asset is spread evenly over each year of its useful life according to the prescribed (or selected) depreciation rate.[2]

DC = \left( {IC - SV} \right)r
n = \frac{1}{r}

This depreciation charge is constant for each year and thus only needs to be calculated once. Since n and r are inversely related, typically a useful life is estimated for an asset and then the depreciation rate follows. A haul truck with an initial cost of $750,000 and a salvage value of $10,000 exhibits the following characteristics over a 5 year useful life (depreciation rate of 20%) if straight-line is used.

Year Book Value Depreciation Charge
0 $750,000 $0
1 $602,000 $148,000
2 $454,000 $148,000
3 $306,000 $148,000
4 $158,000 $148,000
5 $10,000 $148,000

Declining balance depreciation

Declining Balance Depreciation (also known as DBD) methods allocates higher depreciation charges to the beginning of the project. This method is used in scenarios in which the asset is more productive in its earlier years and will generate more revenue and thus will have a higher depreciation charge associated with it in these years. This is accomplished by determining the depreciation charge for the year as a product of the previous book value and current depreciation rate.[2]

B{V_i} = IC{\left( {1 - r} \right)^i}

Thus every year, the book value becomes a fraction (1 − r) of the previous year’s value.

D{C_i} = IC{\left( {1 - r} \right)^{i - 1}}r

For example, a haul truck with a capital cost of $750,000 and a depreciation rate of 20% would exhibit the following behaviour over a life of 5 years if DBD is used.

Year Book Value Depreciation Charge
0 $750,000 $0
1 $600,000 $150,000
2 $480,000 $120,000
3 $384,000 $96,000
4 $307,200 $76,800
5 $245,760 $61,440

If a salvage value can be estimated with reasonable certainty, the depreciation rate can be adjusted to meet this salvage value at the end of useful life.

r = 1 - \sqrt[n]{{\frac{{B{V_n}}}{{IC}}}}

Where BVn is synonymous with the salvage value.

Sum-of-the-years’-digits depreciation

This method (SOYDD) allocates higher depreciation charges to earlier years, much like DBD, to account for the fact that most assets are more productive when they are new. To achieve this a variable depreciation rate is used which decreased over time while the depreciation charge is independent of the book value.[2]

{r_i} = \frac{{\left( {n - \left( {i - 1} \right)} \right)}}{{\mathop \sum_{j = 1}^n j}}
D{C_i} = \left( {IC - SV} \right){r_i}
B{V_i} = IC - \left( {IC - SV} \right)\mathop \sum_{j = 1}^i {r_j}

The sum operators represent the sum-of-the-years from which the method is named. A haul truck with an initial cost of $750,000 and a salvage value of $10,000 exhibits the following characteristics over a 5 year useful life if SOYDD is used.

Year r Depreciation Charge Book Value
0 0 $0 $750,000
1 0.333 $246,667 $503,333
2 0.267 $197,333 $306,000
3 0.2 $148,000 $158,000
4 0.133 $98,667 $59,333
5 0.067 $49,333 $10,000

Unit of production depreciation

UPD is unique in the fact that the depreciation charge is based on the usage of the asset in the period of interest. High output periods will induce a high depreciation charge whereas idle periods will be associated with a charge of zero. For this method one is required to estimate the total production capacity over the assets\’ useful life instead of the length of its useful life.[2]

r = \frac{{IC - SV}}{{{\rm{Total Production}}}}
D{C_i} = Productio{n_i} * \mathop r
B{V_i} = IC - \mathop \sum_{j = 1}^i Productio{n_j}*r

A haul truck with an initial cost of $750,000, salvage value of $10,000 and a total production of 1,000,000 tonnes can be depreciated using UPD in the following manner.

Year Production r Depreciation Charge Book Value
0 0 0 $0.00 $750,000
1 25000 0.74 $18,500 $731,500
2 50000 0.74 $37,000 $694,500
3 100000 0.74 $74,000 $620,500
4 200000 0.74 $148,000 $472,500
5 400000 0.74 $296,000 $176,500

References

  1. http://www.cra-arc.gc.ca/tx/bsnss/tpcs/slprtnr/rprtng/cptl/dprcbl-eng.html
  2. 2.0 2.1 2.2 2.3 http://accountinginfo.com/study/dep/depreciation-01.htm
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