In this lesson, we focus on depreciation, depreciation methods, and After-Tax Cash Flow. An investor is allowed to utilize these methods to recover some types of capital cost. This lesson will explain how these techniques can be used to calculate the taxable income and income tax. To calculate the income tax, taxable income needs to be determined properly.
At the successful completion of this lesson, students should:
This lesson will take us one week to complete. Please refer to the Course Syllabus for specific time frames and due dates. Specific directions for the assignment below can be found within this lesson.
Reading | Read Chapter 7 of the textbook and following pages in this lesson in the website. |
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Assignment | None. |
If you have any questions, please post them to our discussion forum, located under the Modules tab in Canvas. I will check that discussion forum daily to respond. While you are there, feel free to post your own responses if you, too, are able to help out a classmate.
After revenue and costs are determined, taxable income and income tax need to be calculated. Tax calculations can be very complicated, but here we just address the basics. Usually, in a specified time period, total costs deducted from total revenue gives the taxable income. Before-Tax and After-Tax Cash Flow can be calculated as:
Revenue
− Operating Costs
− Capital Cost
————————————————
Before-Tax Cash Flow (BTCF)
− Income Tax
————————————————
After-Tax Cash Flow (ATCF)
Operating and Capital Costs deducted from Revenue gives the Before-Tax Cash Flow. And After-Tax Cash Flow equals Before-Tax Cash Flow minus Income Tax.
Assume a project that has the estimated gross revenue of $28,000 dollars, operating cost of $12,000, and capital cost of $10,000 next year with the income tax of $1,500. Then, next year After-Tax Cash flow can be calculated as:
From a tax view point, there are two types of investments. According to US tax law, for the purpose of tax calculations, an investor is allowed to recover some specified types of investments, meaning that the investor can take some amounts of money from the generated revenue as tax deductions. Types of property that may be recovered over their useful lifetime are including (but not limited to) building, machinery, equipment, and trucks. Simply, most of the property types that lose their value over the time (have zero or low salvage value) may be allowed to be recovered. On the other side, there are investments that can’t be deducted from income for tax purposes. Investing in a bank account or buying land are the examples of this type.
Assume an investor deposits $100,000 in a bank account for 10 years with annual interest of 16% and will take the $100,000 in the end of 10th year. Calculate Before-Tax Cash Flow and After-Tax Cash Flow in this investment considering the income tax of 25%.
The annual income will be .
Since tax deduction is not allowed for investments such as bank account and bond, the annual revenue is fully taxable.
Year | 0 | 1 | 2 | 3 | ... | 9 | 10 |
|
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Revenue | $16,000 | $16,000 | $16,000 | ... | $16,000 | $16,000 | |
- Cost | -$100,000 | ||||||
+ Salvage | $100,000 | ||||||
|
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BTCF | -$100,000 | $16,000 | $16,000 | $16,000 | ... | $16,000 | $116,000 |
In order to determine After-Tax Cash Flow, we need to determine the taxable income and deduct the tax from Before-Tax Cash Flow.
Year | 0 | 1 | 2 | 3 | ... | 9 | 10 |
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Revenue | $16,000 | $16,000 | $16,000 | ... | $16,000 | $16,000 | |
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Taxable Income | $16,000 | $16,000 | $16,000 | ... | $16,000 | $16,000 | |
- Income Tax of 25% | -$4,000 | -$4,000 | -$4,000 | ... | -$4,000 | -$4,000 | |
|
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Net Income | $12,000 | $12,000 | $12,000 | ... | $12,000 | $12,000 | |
- Cost | -$100,000 | ||||||
+ Salvage | $100,000 | ||||||
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ATCF | -$100,000 | $12,000 | $12,000 | $12,000 | ... | $12,000 | $112,000 |
By trial and error, the ROR=12% is calculated for this After-Tax Cash Flow.
Now, assume the investor pays 100,000 dollars for a machine at time zero, and the machine can start producing goods and generating annual revenue of $38,000 with operating cost of $12,000 from first to 10th year, and the salvage value will be zero with income tax of 25%.
The Before-Tax Cash Flow here can be determined as:
Year | 0 | 1 | 2 | 3 | ... | 9 | 10 |
|
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Revenue | $38,000 | $38,000 | $38,000 | ... | $38,000 | $38,000 | |
- Operating cost | -$12,000 | -$12,000 | -$12,000 | ... | -$12,000 | -$12,000 | |
- Capital cost | -$100,000 | ||||||
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BTCF | -$100,000 | $26,000 | $26,000 | $26,000 | ... | $26,000 | $26,000 |
By trial and error, ROR=22.6% for Before-Tax Cash Flow.
In this hypothetical case, the investor is allowed by tax law to recover the out of pocket cash “capital cost” and gradually deduct it from taxable income. One way to calculate the taxable income for each year is to distribute the capital cost of $100,000 equally over the allowable depreciation life time of 10 years. And After-Tax Cash Flow will be determined as:
Year | 0 | 1 | 2 | 3 | ... | 9 | 10 |
|
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Revenue | $38,000 | $38,000 | $38,000 | ... | $38,000 | $38,000 | |
- Operating cost | -$12,000 | -$12,000 | -$12,000 | ... | -$12,000 | -$12,000 | |
- non-cash capital cost deduction | -$10,000 | -$10,000 | -$10,000 | ... | -$10,000 | -$10,000 | |
|
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Taxable income | $16,000 | $16,000 | $16,000 | ... | $16,000 | $16,000 | |
- Income tax | $4,000 | $4,000 | $4,000 | ... | $4,000 | $4,000 | |
|
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Net Income | $12,000 | $12,000 | $12,000 | ... | $12,000 | $12,000 | |
+ non-cash capital cost | $10,000 | $10,000 | $10,000 | ... | $10,000 | $10,000 | |
- Capital cost | -$100,000 | ||||||
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ATCF | -$100,000 | $22,000 | $22,000 | $22,000 | ... | $22,000 | $22,000 |
This way, the taxable income for each year would be 16,000 dollars, which gives the tax of . Note that, in reality, no annual cash is transferred and the annual sum of $10,000 (non-cash capital cost deduction) is applied just for the purpose of tax calculations. This annual sum is called non-cash capital cost to adjust and recover the the capital cost of $100,000 at time zero. And when tax is calculated, $10,000 has to be returned to cash flow to give the After-Tax Cash Flow.
ROR for After-Tax Cash Flow is 17.7%.
Applying tax deductions to recover the investment causes lower taxable incomes and consequently lower taxes and can only be used for specified types of properties. Investments that are allowed to be recovered by tax law are divided into two categories.
1)Investments that can be expensed: These investments are allowed to be deducted from revenue in full amount in the year of occurrence for tax calculation.
2) Capital costs: These investments are allowed to be deducted gradually (cost needs to be distributed over more than one year) from the revenue for tax calculation.
Depreciation, depletion, and amortization are methods that can be utilized to calculate the distribution of capital costs deductions over the time.
Acquisition costs and lease bonus costs paid for mineral rights for natural resources such as oil and gas are examples of investment property costs that may be recovered by depletion. Numerous other business costs such as the cost of acquiring a business lease, research and development costs such as expenses, trademark expenses, and pollution control equipment costs may be recovered by amortization. Depreciation, depletion, and amortization all achieve essentially the same thing—recovery of the cost or other basis of investments in before-tax dollars through allowable tax deductions over a specified period of time or over the useful life of the investment. If depreciable property is sold, all or a portion of any extra depreciation claimed in prior years may have to be recaptured as taxable income. These methods will be explained in this lesson.
Please watch the following video (4:34): After Tax Cash Flow.
In general, After-Tax Cash Flow requires the following calculations:
Revenue
- Operating Costs
- Depreciation
- Depletion
- Amortization
- Write-offs
————————————————
Taxable Income
- Income Tax
————————————————
Net Income
+ Depreciation
+ Depletion
+ Amortization
+ Write-offs
- Capital Expenditures
————————————————
After-Tax Cash Flow (ATCF)
Where, Depreciation, Depletion, Amortization, and Write-offs are called Non-cash capital cost deductions. ATCF can be written in form of equation as:
Or
As explained in Example 7-2 and 7-3, depending on the characteristics of investment, Before-Tax Cash Flow and After-Tax Cash Flow calculations might be different and may give different economic results.
Italicized sections are from Stermole, F.J., Stermole, J.M. (2014) Economic Evaluation and Investment Decision Methods, 14th edition. Lakewood, Colorado: Investment Evaluations Co.
As explained on the previous page, there are two types of investments that are allowed to be recovered and deducted from revenue for tax calculation. These two types include: the investments that can be expensed (deducted in full amount on the year occurred) and capital costs that have to be deducted (“capitalized”) over more than one year.
It’s obvious that the faster an investor can deduct the recoverable investments from the revenue, the better economic benefits will be for the project. For example, if there is no limitation, the investor is better off if deducting all the investments in full amount in the year of occurrence and paying lower tax in early years than later years. (We learned in this course that money is worth more on closer future). But tax law doesn’t allow all the investments to be expensed, and there are strict regulations for different types of investments.
Operating costs that may be expensed include costs for direct labor, indirect labor, materials, parts, and supplies used for product produced and sold. Only costs associated with product actually sold may be deducted. Some other common costs in the operating expense category include utilities, freight and containers, borrowed money interest paid, royalties, severance taxes, sales taxes, ad valorem taxes, and certain excise taxes. Note that costs such as spare parts inventory, accounts receivable, required cash on hand, etc., are not deductible for tax purposes until such items are actually used up or sold. These costs are called working capital.
Research and experimental costs including labor, supplies, etc., are considered to be the equivalent of operating costs and may be expensed in the year incurred.
Mining exploration costs are expenditures required to delineate the extent and quality of an ore body and may include core drilling, assaying, engineering fees, geological fees, exploratory shafts, pits, drifts, etc. Exploration costs may be either capitalized into the cost depletion basis or expensed in the full amount in the year incurred by individual taxpayers.
Mining development costs are defined as expenditures incurred after the determination has been made that an ore body is economically viable and the decision has been made to develop the property. Development costs may include exploration type costs after the decision has been made to develop a mine. Mining development costs typically include costs for overburden stripping, underground shafts, drifts, tunnels, raises, audits, etc. Development expenditures end when a mine reaches a level of full production. Then, costs that previously were mine development costs are treated as operating expenses from the time forward.
Petroleum Intangible Drilling Costs (IDC's) are defined as the cost of drilling oil and gas wells to the point of completion and may include:
Similar to mining development costs, intangible drilling costs may either be capitalized into the cost depletion basis or expensed in full amount in the year incurred.
Italicized sections are from Stermole, F.J., Stermole, J.M. (2014) Economic Evaluation and Investment Decision Methods, 14th edition. Lakewood, Colorado: Investment Evaluations Co.
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 [1] 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:
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 [2]. Depreciation is usually applied to the tangible [3] property while amortization is for intangible [4] property.
This section explains four major depreciation methods including:
Please watch the following video (4:20): After Tax Cash Flow: Expensing Versus Capitalizing Investment Costs.
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:
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.
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.
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 |
|
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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 | ||||||||||
|
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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 | |
|
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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 | ||||||||||
|
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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%.
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:
Year | Half-year convention straight line Depreciation |
---|---|
1 | |
2 | |
3 | |
4 | |
5 | |
6 | |
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.
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).
While for any depreciation method,
For example, if the declining rate is 0.25 and the asset is purchased at $100.
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.
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:
Year | Adjusted Basis | Declining Balance Depreciation |
---|---|---|
1 | $100,000 | |
2 | ||
3 | ||
4 | ||
5 | ||
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.
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.
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.
Year | Method | Adjusted Basis | Declining Balance Depreciation |
---|---|---|---|
1 | DB | $100,000 | |
2 | DB | ||
3 | DB | ||
4 | DB | ||
5 | SL | ||
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 | ||
2 | |||
3 | |||
4 | |||
5 | |||
6 | |||
7 | |||
8 | |||
9 | |||
10 |
Please watch the following video (20:50): Declining Balance Switching to Straight Line Depreciation Method.
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 [5] that indicate the depreciation allowance for different depreciation lifetime and different property types.
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 [6] and then multiplied by the investment cost of $100,000:
Year | MACRS 5-year half-year Depreciation Rate | Declining Balance Depreciation |
---|---|---|
1 | 20% | |
2 | 32% | |
3 | 19.2% | |
4 | 11.52% | |
5 | 11.52% | |
6 | 5.76% | |
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.
Italicized sections are from Stermole, F.J., Stermole, J.M. (2014) Economic Evaluation and Investment Decision Methods, 14 edition. Lakewood, Colorado: Investment Evaluations Co.
The owner of an economic interest in mineral deposits, oil and gas wells, or standing timber may recover his or her cost through federal tax deductions for depletion over the economic life of the property. Oil, gas, and mineral depletion is computed by two methods: 1) cost depletion and 2) percentage depletion. Only cost depletion applies to timber. For petroleum and mining, both cost and percentage depletion must be computed each year. The result that gives the largest allowable tax deduction, accounting for the 50% or 100% percentage depletion limits applicable to mining and petroleum producers, is used later as described. One can switch methods from year to year with the exception that integrated oil and gas producers may only take cost depletion on oil and gas properties. More information about depletion can be found at IRS website [7].
It is permissible for a business to deduct each year as amortization [8]a proportionate part of certain capital expenditures. Amortization permits the recovery of these expenditures in a manner similar to straight line depreciation over five years, or a different specified life. As a general rule, amortization relates to intangible asset costs while depreciation relates to tangible asset costs. However, only certain specified expenditures may be amortized for federal income tax purposes. You can find more detailed information about amortization at IRS website [9].
Italicized sections are from Stermole, F.J., Stermole, J.M. (2014) Economic Evaluation and Investment Decision Methods, 14 edition. Lakewood, Colorado: Investment Evaluations Co.
In this lesson, we've learned how to calculate Before-Tax Cash Flow and After-Tax Cash Flow. Also, we learned about investments that can be expensed in the year of occurrence in full amount or capitalized over more than one year.
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 and tax allowance. The most common methods include Straight Line, Declining Balance, Declining Balance Switching to Straight Line, and Accelerated Cost Recovery System (ACRS).
The Straight Line Depreciation method is the simplest way of calculating depreciation. In this method, depreciation is constant and equally distributed over the allowable lifetime of the property. But the biggest problem with this method is that Straight Line depreciation is very slow, and capital cost is recovered slowly.
The Declining Balance Depreciation method calculates depreciation based on constant rate. 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).
Modified Accelerated Cost Recovery Systems (MACRS) is a popular method in the 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.
You have reached the end of Lesson 7! Double-check the to-do list on the Lesson 7 Overview page [10] to make sure you have completed all of the activities listed there before you begin Lesson 8.
Links
[1] http://www.investopedia.com/terms/d/depreciation.asp
[2] https://www.irs.gov/publications/p946/index.html
[3] http://www.investopedia.com/terms/t/tangibleasset.asp
[4] http://www.investopedia.com/terms/i/intangibleasset.asp
[5] http://www.irs.gov/publications/p946/ar02.html
[6] https://www.irs.gov/publications/p946/ar02.html
[7] http://www.irs.gov/publications/p535/ch09.html
[8] http://www.investopedia.com/terms/a/amortization.asp
[9] http://www.irs.gov/publications/p535/ch08.html
[10] https://www.e-education.psu.edu/eme460/node/744