# Depreciation

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]

## 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.

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