Both Declining Balance and Double Declining Balance can lead to arguments with the IRS regarding the value of n. So in 1981 these methods were superseded by a simpler procedure called :
ACRS : Accelerated Cost Recovery System.
This was modified later in 1986 as :MACRS : Modified ACRS.

IRS has guidelines for what n can be dependent based upon the type of property.
(See also Table 12.1 on Page 321 of the text)

Depreciation is based on a declining balance using either : 
      DB% = 2(1/n). This is the General Depreciation System (GDS) which is the standard or 
      DB% = 1.5(1/n). This is the Alternative Depreciation System (ADS) which is elective  and allows a longer n.

Either method switches from DB to SL (of remaining balance) at approximately t = (n+1)/2.

The mid-year convention is in effect which allows only 50% of the first year DB depreciation to be taken in the first year.

Fortunately, tables have been developed for MACRS Depreciation rates.
(See Table 12.2 on Page 321 of the Text. Note that Table12.2 only shows the MACRS-GDS rates)

There is no salvage. MACRS depreciates the entire asset.

Explanation of MACRS Table

Remember that : SL      d_t = 1/n applied to B
                         DB      d_t = 1/n to 2/n applied to BV_t-1
Thus, as MACRS begins with DDB and the half-year convention, the tabled factors have been converted to apply to B (The first cost).

In order to understand the MACRS rates and how they work, let's look at a $100 asset in a 5 year class.

Year 1: Use 1/2 of DDB rate for 5 years.
            DDB rate = 2(1/n) = 2/5 = 0.40(1/2) = 0.20 = 20% (MACRS rates in Table 12.2)

Year 2: Use DDB rate on BV₁
            P= [100-(0.20)100](0.40) = $32
           d_t = 32/100 = 0.32 = 32% (This is % applied to B.)

Year 3: Again use DDB rate on BV2
            BV₂ = 100-20-32 = $48                       SL- 3.5 years remain. (Years 3-5 + 1/2 year of 6)
               D = (48)(0.4) = $19.20                        d = 1/n = 1/3.5 = 0.2857
               d_t = 19.20/100 = 0.1920 = 19.2%       D = 48(d) = $13.71 or d_t = 13.71% (Use DDB)

Year 4: BV₃ = 48-19.20=28.80                       SL- 2.5 years remain (Years 4&5 + 1/2 year of 6)
                D = (28.80)(0.4) = $11.52                 d = 1/n = 1/2.5 = 0.400
                d_t = 11.52/100 = 0.1152  = 11.52%   D = 11.52d_t = 0.1152 = 11.52%(Switch to SL)

Year 5: BV4 = 28.80-11.52 = 17.28                 SL-1.5 years remain (Year 5 & 1/2 year of 6)
                D = (17.28)(0.40) = $6.91                   d = 1/n = 0.6667
                                                                            D = 11.52d_t= 0.1152 = 11.52% (Use SL)

Year 6 : D =100-(D₁+D₂+D₃+D₄+D₅+D₆) = 100- 94.24 = $5.76 of $100 = 5.76%

This exercise has shown that MACRS rates are a product of DDB and SL methods, but require you only to use the tabled MACRS rates against the first cost (B) to obtain D_t for any year.

Example: Determine the amount of depreciation and book value for each year for a $35,000 tractor using MACRS-GDS.

First, from Table 13.4  n = 3 years

Year N         MACRS Rate           D_t               BVt 

   0                       -                         -              35,000
   1                    0.3333               11,665        23,335
   2                    0.4445               15,557          7,778
   3                    0.1481                 5,184          2,594
   4                    0.0741                 2,594                 0

BV_n = B - B(Sum of MACRS rates from 1 to n) = B(1- Sum of MACRS rate)
BV₃ = 35000(1-[0.3333+0.4445+0.1481] ) = 35000(1-0.9259) =$2594

If SV= $3000@ year 4, how much depreciation is allowed in years 3 and 4?

D₃ = 7778-3000=$4778
D₄ = $0  since BV₃<SV₄

Capital Gains

Income obtained due to the selling of assets.

Capital Gains (CG) = Selling Price-Purchase Price (assuming that SP>PP)

If not, then Capital Loss (CL) = Selling Price-Purchase Price (which will be negative).

However, if an asset is being depreciated, the book value at the time of disposal is used as the cost basis instead of the purchase price.

Several cases exist:

Thus, as we progress towards determining Taxable Income(TI) and taxes we have:
TI = GI - E - D + DR + CG - CL  (For CG grater than CL)
   and
Taxes = (TI)T

Example: A company has the following transactions. Determine the total Net Capital Gain/Loss and DR for the year. Purchase of all assets occurred 3 years earlier.

                                                         MACRS
   Asset           Purchase Price      Recovery Period        Sale Price 

 Land                 $100,000                    -                       $105,000
Machine 1            $50,500                   5                        $17,500
Machine 2            $10,000                   3                        $11,000
Machine 3            $30,000                   7                        $10,000

 Asset         D3               BV3               DR         CG/CL

 Land               0       $100,000            -           $5,000 (Remember land is not depreciable)
   M1     $35,956        $14,544        $2956           -       (Sold for more than BV₃ , thus DR)
   M2       $9,259             $741        $9259        $1,000 (Sold for more than DP, thus DR & CG)
   M3     $16,881        $13,119            -             $3,119 (Sold for less than BV₃, thus CL)
 Total                                            $12,215        $2881

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