# Depreciation and Depreciation Methods

The term depreciation(link is external) usually refers to the process of losing value over the time for a property, like wear and tear. When a machine is purchased to produce and generate income, it won’t be as good when it becomes older. It happens because the machine gets exhausted or production becomes obsolete. Therefore the machine loses its value over time and can’t be sold for high value. Tax law allows the company to deduct the depreciated value of the asset from the generated income. There are permitted methods (will be explained later in this lesson) to calculate the depreciated value, which might be different from how the asset depreciates in reality. For example, the asset might be still functional while it is already fully depreciated in tax calculations. In this text by the term annual depreciation deduction we refer to tax allowance.

A depreciable property:

1) Must be used (or be ready to be replaced) for producing income
2) Must have a determinable lifetime longer than one year
3) Must lose its value over time
4) Must be used or be ready to be used

For example land is an asset that is not permitted for depreciation. More information about depreciation can be found at the Internal Revenue Service (IRS) website(link is external). Depreciation is usually applied to the tangible(link is external) property while amortization is for intangible(link is external) property.

### Depreciation Methods

This section explains four major depreciation methods including:

1. Straight Line
2. Declining Balance
3. Declining Balance Switching to Straight Line
4. Modified Accelerated Cost Recovery Systems (MACRS)

#### 1. Straight Line Depreciation

This method is the simplest way of calculating the depreciation. In this method, depreciation is constant and equally distributed over the allowable life time of the property as:

Straight Line Depreciation per year = (Cost of the asset- Salvage value)/ Allowable life time

Equation 7-3

The biggest problem in this method is straight line depreciation is very slow and capital cost is recovered slowly. The faster costs are recovered the lower tax is paid in early years and it enhances the economics of the project.

Straight line depreciation is the method that used to calculate the non-cash capital cost deduction in example 7-3.

Example 7-4: Following the example 7-3, assume the investor buys a piece of land for $25000 at time zero that can be sold at year 10 for$35,000.

Note that investment for land is not depreciable. The land resale value of $35,000 should be added to the income of 10th year. But the initial value of land is deductible as “Write-off”. Because just the profit ($35,000 - $25,000 =$10,000) made on selling the land is taxable.
After-Tax Cash Flow will be determined as:

 Year 0 1 2 3 4 5 6 7 8 9 10 Revenue $28,000$28,000 $28,000$28,000 $28,000$28,000 $28,000$28,000 $28,000$28,000 +Land resale $35,000 - Operating cost -$12,000 -$12,000 -$12,000 -$12,000 -$12,000 -$12,000 -$12,000 -$12,000 -$12,000 -$12,000 - Depreciation -$10,000 -$10,000 -$10,000 -$10,000 -$10,000 -$10,000 -$10,000 -$10,000 -$10,000 -$10,000 - Write-off -$25,000 Taxable income $6,000$6,000 $6,000$6,000 $6,000$6,000 $6,000$6,000 $6,000$16,000 - Income tax $1,500$1,500 $1,500$1,500 $1,500$1,500 $1,500$1,500 $1,500$4000 Net Income $4,500$4,500 $4,500$4,500 $4,500$4,500 $4,500$4,500 $4,500$12,000 + Depreciation $10,000$10,000 $10,000$10,000 $10,000$10,000 $10,000$10,000 $10,000$10,000 + Write-off $25,000 - Capital cost -$100,000 - Land -$25,000 ATCF -$125,000 $14,500$14,500 $14,500$14,500 $14,500$14,500 $14,500$14,500 $14,500$47,000

ROR for After-Tax Cash Flow will be 6%.

#### 2. Declining Balance Depreciation

This method is also called “exponential depreciation” and calculates the depreciation based on constant rate (instead of constant amount as the case for straight line depreciation). This method is not allowed in United States, but in some other countries companies can use it. In this method, a constant declining rate is multiplied by Adjusted Basis to calculate each year’s depreciation. And the Adjusted Basis equals residual book value of the asset (cost - cumulative depreciation previously taken).

Declining Balance Depreciation Per Year = (Declining Rate) * (Adjusted Basis)

While for any depreciation method,

Adjusted Basis = Cost or Other Basis - Cumulative Depreciation Previously Taken

Equation 7-4

For example if the declining rate is 0.25 and the asset is purchased at $100. First year deprecation = 0.25*$100 = $25 Second year adjusted basis would be$100-$25=$75 and deprecation = 0.25*$75 =$18.75
Third year adjusted basis would be $75-$18.75 =$56.25 and deprecation = 0.25*$56.25 = $14.06 Fourth year adjusted basis would be$56.25-$14.06 =$42.19 and deprecation = 0.25*($42.2) = *($10.55)

Some governments announce the declining balance rate as a percentage that needs to be multiplied by 1/n (n is the depreciation life) to give the declining rate. For example, if an asset has the depreciation life of 5 years and the government announces 150% declining balance rate, then the declining curve would be 1.5/5= 0.3.

Example 7-5: Calculate the depreciation in example 7-3, assuming declining balance depreciation method and declining balance rate of 150%.

Since depreciation life is considered 10 year, then declining rate equals 150%/10 = 0.15 so depreciation can be calculated as:

 Year Adjusted Basis Declining Balance Depreciation 1 $100,000 0.15*$100,000=$15,000 2$100,000-$15,000=$85,000 0.15*$80,000=$12,750 3 $85,000-$12,750=$72,250 0.15*$72,250=$10,837.5 4$72,250-$10,837.5=$61,412.5 0.15*$61,412.5=$9,211.9 5 $61,412.5-$9211.9=$52,200.6 0.15*$52,200.6=$7,830.1 6$52,200.6-$7,830.1=$44,370.5 0.15*$44,370.5=$6,655.6 7 $44,370.5-$6,655.6=$37714.9 0.15*$37714.9=$5,657.2 8$37714.9-$5,657.2=$32,057.7 0.15*$32,057.7=$4,808.7 9 $32,057.7-$3,355.4=$27,249.1 0.15*$27,249.1=$4,087.4 10$27,249.1-$2,684.4=$23,161.7 0.15*$23,161.7=$3,474.3

#### 3. Declining Balance Switching to Straight Line

In this method, depreciation is calculated using declining balance for early years and then switches to the straight line method. It is desirable to switch to straight line from declining balance in the year when you will get an equal or larger deduction by switching. This occurs when the straight line rate equals or exceeds the declining balance rate, because when you switch, the remaining basis is depreciated by straight line method over the remaining years of depreciation life.

Example 7-6: Calculate the depreciation in example 7-3, applying declining balance depreciation switching to straight line method for declining balance rate of 150%.

Here, it’s more economically desirable to switch to the straight line method after the fourth year, because the annual depreciation will be higher when switching from declining balance to straight line.

 Year Method Adjusted Basis Declining Balance Depreciation 1 DB $100,000 0.15*$100,000=$15,000 2 DB$100,000-$15,000=$85,000 0.15*$80,000=$12,750 3 DB $85,000-$12,750=$72,250 0.15*$72,250=$10,837.5 4 DB$72,250-$10,837.5=$61,412.5 0.15*$61,412.5=$9,211.9 5 SL $61,412.5-$9211.9=$52,200.6$52,200.6/6=$8700.1 6 SL$52,200.6 $8700.1 7 SL$52,200.6 $8700.1 8 SL$52,200.6 $8700.1 9 SL$52,200.6 $8700.1 10 SL$52,200.6 $8700.1 To find out which year is better to switch, we can draw a table that includes straight line calculations for each year and compare it with declining balance. The year that has the higher depreciation for straight line than declining balance is the best year to switch. The grey row in following table indicates this year.  Year Adjusted Basis Declining Balance Depreciation Straight Line Depreciation 1$100,000 0.15*$100,000=$15,000 $100,000/10=$10,000 2 $100,000-$15,000=$85,000 0.15*$80,000=$12,750$85,000/9=$9,444.4 3$85,000-$12,750=$72,250 0.15*$72,250=$10,837.5 $72,250/8=$9,031.3 4 $72,250-$10,837.5=$61,412.5 0.15*$61,412.5=$9,211.9$61,412.5/7=$8,773.2 5$61,412.5-$9211.9=$52,200.6 0.15*$52,200.6=$7,830.1 $52,200.6/6=$8700.1 6 $52,200.6-$7,830.1=$44,370.5 0.15*$44,370.5=$6,655.6$44,370.5/5=$8,874.1 7$44,370.5-$6,655.6=$37714.9 0.15*$37714.9=$5,657.2 $37714.9/4=$9,428.7 8 $37714.9-$5,657.2=$32,057.7 0.15*$32,057.7=$4,808.7$32,057.7/3=$10,685.9 9$32,057.7-$3,355.4=$27,249.1 0.15*$27,249.1=$4,087.4 $27,249.1/2=$13,624.5 10 $27,249.1-$2,684.4=$23,161.7 0.15*$23,161.7= $3,474.3$23,161.7/1=\$23,161.7

#### 4. Modified Accelerated Cost Recovery Systems (MACRS)

This is a popular method in United States to recover the cost of most intangible depreciable assets. MACRS depreciation methods for personal property include 200% and 150% declining balance switching to straight line. U.S. Internal Revenue Service (IRS) publishes tables that indicate the deprecation allowance for different depreciation lifetime and different property types.