T = the depreciation life of an asset
UDC = The Un-depreciated cost of the asset
n= the nth year of the assets life
A= 2 if T = 3, 5, or 7
A= 1.5 if T = 15, or 20
The MACRS rate for the nth year of the assets life is:
If n = 1:
MACRS Rate = 1/T
If n > 1:
MACRS Rate = A / T * ( 1 - 1 / T ) * ( 1 - A / T ) ^ ( n - 2 )
If MACRS Rate < Straight Line Method Rate:
start using straight line
DISCLAIMER:
1) This does not match exactly with the IRS Publication946
If you read that publication, they indicate that the actual formula does not match their MACRS tables. I suspect that their tables are built to control round off errors.
The method below, differs from the IRS tables by no more than 0.01%.
2) There is not an actual formula, but I have this as a sub-routine in my computer written in C++. If you want, I could translate it into something a bit more generic such as BASIC. If there is requests, I can post the actual code.
To Calculate MACRS
Using UDA = UnDepreciated Amount
The Basic MACRS = UDA / Number of years to Depreciate
But, the Second and subsequent years are DOUBLED.
So for an item of $1000, 5 year depreciation ( 60 months ), Bought sometime in 2001
Year 2001, the MACRS = 1000/5 = $200.00 -- UDA is now $1000-$200 = $800
Year 2002, the MACRS = 2*800/5 = $320.00 -- UDA is now $800 - $320 = $480
Year 2003, the MACRS = 2*480/5 = $192.00 -- UDA is now $480 - $192 = $288
Year 2004, the MACRS = 2*280/5 = $115.20 -- UDA is now $288 - $115.20 = $172.80
For you math majors, you might see that this is a log decay curve and goes on forever, never to end. But, the IRS has a neat solution. When the UDA is less than the first years depreciation ( In this case, $200.00 ) you use a straight line method. So...
Year 2005, the MACRS = $115.20 -- UDA is now $172.80 - $115.20 = $57.60
Year 2006, the MACRS = $57.60 ( You are DONE )
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NOTE: You must consider the Salvage Value of the property
Therefore: UDA at the start is = The Cost of the Item - Salvage Value
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Reference:
MACR Table: http://www.studyfinance.com/lectures/depreciation/macrs.mv
IRS Pub 946: http://www.irs.gov/publications/p946/ch04.html
The Modified Accelerated Cost Recovery System (MACRS) is used by the US tax system.
Following are different methods of depreciation: 1 - Straight line method 2 - Diminishing balance method 3 - Double declining method 4 - Sum of years method 5 - MACRS
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MACRS allows you to move up your deductions to the current year instead of pushing them off into the future
MACRS is better because it allows you to take bigger deductions in the early years of the project which is a time value benefit.
MACRS is pronounced as "mak-ers." It stands for Modified Accelerated Cost Recovery System, which is a method used in the United States to calculate depreciation for tax purposes.
MACRS (Modified Accelerated Cost Recovery System) is based on the principle of assigning a shorter recovery period to assets that are typically used at a higher rate in the early years of their useful life. It also takes into account the time value of money by allowing greater depreciation deductions in the earlier years of an asset's life. MACRS uses specific depreciation tables and formulas provided by the IRS to determine the depreciation expense for different types of assets over their useful life.
The Modified Accelerated Cost Recovery System (MACRS) is used by the US tax system.
Following are different methods of depreciation: 1 - Straight line method 2 - Diminishing balance method 3 - Double declining method 4 - Sum of years method 5 - MACRS
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For the necessary tables to find the depreciation deduction, go to www.irs.gov/formspubs for Publication 946: How to Depreciate Property. MACRS is Modified Accelerated Cost Recovery System. Under MACRS, residential rental property uses the General Depreciation System (GDS) depreciation with the Mid-Month Convention and Straight Line Method. Under Mid-Month Convention, all property placed in service is treated as though it had been placed in service at the mid-point (halfway through) the month. In the Publication 946 Appendix, go to Table A-6: Residential Rental Property Mid-Month Convention Straight Line - 27.5 Years. The percentage in the first year for property placed in service in August is 1.364 percent. The deduction for the first year is $500,000 multiplied by 1.364 percent and then multiplied by 4.5 (number of months in service: 4 months plus 1/2 of August) and divided by 12 (total months of the year). The deduction is $2558.
A formula unit is an empirical formula.
The formula AF(p -> Xp) is such a formula. It's simple to see that the formula is a LTL formula and judging by its syntax, it's not a CTL formula. The proof that there is no equivalent CTL formula is a bit more complicated.