## Depreciation and Depreciation Methods

### Depreciation and Depreciation Methods

As explained before, depreciation is a method to capitalize and recover business costs over a specified period of time or over the useful life of the investment.

The term depreciation 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. Depreciation is usually applied to the tangible property while amortization is for intangible 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)

Please watch the following video (4:20): After Tax Cash Flow: Expensing Versus Capitalizing Investment Costs.

After Tax Cash Flow: Expensing Versus Capitalizing Investment Costs

#### 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 depreciation 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 allowable depreciation life time is 5 years, starting from year 1. Also assume the investor buys a piece of land for $25000 at time zero that can be sold at year 10 for$35,000.

Straight Line Depreciation=( 100,000 )/5=  $20,000 per year from year 1 to year 5 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$38,000 $38,000$38,000 $38,000$38,000 $38,000$38,000 $38,000$38,000 $38,000 +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 -$20,000 -$20,000 -$20,000 -$20,000 -$20,000 - Write-off -$25,000 Taxable income $6,000$6,000 $6,000$6,000 $6,000$26,000 $26,000$26,000 $26,000$36,000 - Income tax $1,500$1,500 $1,500$1,500 $1,500$6,500 $6,500$6,500 $6,500$9000 Net Income $4,500$4,500 $4,500$4,500 $4,500$19,500 $19,500$19,500 $19,500$27,000 + Depreciation $20,000$20,000 $20,000$20,000 $20,000 + Write-off$25,000 - Capital cost -$100,000 - Land -$25,000 ATCF -$125,000$24,500 $24,500$24,500 $24,500$24,500 $19,500$19,500 $19,500$19,500 $52,000 ROR for After-Tax Cash Flow will be 14.5%. #### Half-year convention Under half-year convention properties are assumed to be placed in service in the middle of the year. Consequently, half of the first year normal depreciation has to be applied to the year that the property is placed in service. For example, if half-year convention is applied to the first year in example 7-4 to calculate the depreciation using Straight Line method, then the calculated depreciation would be: Half-year convention straight line depreciation by year Year Half-year convention straight line Depreciation 1 ($100,000 )( 1/5 )( 1/2 )=$10,000 2 ($100,000 )( 1/5 )=$20,000 3 ($100,000 )( 1/5 )=$20,000 4 ($100,000 )( 1/5 )=$20,000 5 ($100,000 )( 1/5 )=$20,000 6 ($100,000 )( 1/5 )( 1/2 )=$10,000 Total$100,000

Note that because we applied half-year convention to the strait line depreciation method we considered half of the first year normal depreciation for year 1, thus we needed to add the rest (other half) to the year 6; consequently there will be 6 years of depreciation periods.

Please watch the following video (23:32): Straight Line Depreciation Method.

Straight Line Depreciation Method

#### 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 depreciation=0.25*$100=$25 Second year adjusted basis would be$100−$25=$75 and depreciation=0.25*$75=$18.75 Third year adjusted basis would be $75−$18.75=$56.25 and depreciation=0.25*$56.25=$14.06 Fourth year adjusted basis would be$56.25−$14.06=$42.19 and depreciation=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, declining balance rate of 150%, and depreciation life of 5 years.

Since depreciation life is considered 5 years, then declining rate equals 150%/5 = 0.3 so depreciation can be calculated as:

Adjusted basis and declining balance depreciation by year
Year Adjusted Basis Declining Balance Depreciation
1 $100,000 0.3*$100,000=$30,000 2$100,000−$30,000=$70,000 0.3*$70,000=$21,000
3 $70,000−$21,000=$49,000 0.3*$49,000=$14,700 4$49,000−$14,700=$34,300 0.3*$34,300=$10,290
5 $34,300−$10,290=$24,010 0.3*$24,010=$7,203 Total 83,193 As you can see, the last row shows that total of$83,193 is less than the capital spent on the property ($100,000). Thus in this method asset will not be fully depreciated. Please watch the following video (15:34): Declining Balance Depreciation Method. Declining Balance Depreciation Method #### 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% and depreciation life of 10 years. Depreciation life is considered 10 year, then declining rate equals 150%/10 = 0.15. 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. Adjusted basis and declining balance depreciation by method and year 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*$80,000=$12,750
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.

Adjusted Basis and Declining Balance Depreciation with Straight Line Depreciation by 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

Please watch the following video (20:50): Declining Balance Switching to Straight Line Depreciation Method.

Declining Balance Switching to Straight Line Depreciation Method

#### 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 depreciation allowance for different depreciation lifetime and different property types.

#### Example 7-7:

Calculate the depreciation in Example 7-3, Modified Accelerated Cost Recovery Systems (MACRS) for 5-year half-year convention, starting from year 1.

In order to calculate the depreciation for each year, depreciation rate can be read from table A-1 and then multiplied by the investment cost of $100,000: Depreciation rates by year Year MACRS 5-year half-year Depreciation Rate Declining Balance Depreciation 1 20% 0.2*$100,000=$20,000 2 32% 0.32*$100,000=$32,000 3 19.2% 0.192*$100,000=$19,200 4 11.52% 0.1152*$100,000=$11,520 5 11.52% 0.1152*$100,000=$11,520 6 5.76% 0.0576*$100,000=$5,760 Total =$100,000

Note that, since question and table are for half-year convention, the depreciation is distributed over 6 years.

Please watch the following video (6:37): Modified Accelerated Cost Recovery Systems (MACRS) Depreciation Method.

Modified Accelerated Cost Recovery System

Source: Farid Tayari and Kuangyuan Zhang, https://www.e-education.psu.edu/eme460/node/649