Income Tax Basics

Gross Income (GI) : The total of all income from revenue producing sources.

Operating Expenses (E) : All the costs incurred by a corporation in transaction of its 
                                           business.

Taxable Income (TI) : The amount upon which taxes are calculated.

               TI = GI - E -Depreciation

Tax Rate : A % of TI owed in taxes.

                    Corporate                                                             Personal
GI = Business Revenue + Other Income              GI=Salaries & wages + Interest &  dividends                                                                                                                  + Other Income
TI = Gross Income-Operating Expenses              TI = Gross Income-Personal Exemption-
                             -Depreciation                                    Standard Itemized Deductions
Tax = TI (Tax Rate)                                             Tax = TI (Tax Rate)

We are concerned with corporate tax ramifications in this class. The higher the operating expenses and depreciation, the lower the corporate taxes.

So, what is depreciation?

Depreciation

The accounting for a reduction in value of an asset due to age, wear and obsolescence.

Over its life

• Use government approved rules, rates & formulas.
• Depreciation Charge: D_t(For any year t)

• First Cost (Unadjusted Basis)(B): Cost of the asset including purchase, delivery and installation
• Book value (BV_t): The remaining, undepreciated investment on the books after total depreciation to date has been subtracted from basis.
• Recovery Period (n): The depreciable life of an asset for depreciation and tax purposes.
• Market value: Estimated amount if asset is sold on open market. It may be more or less than BV. 
• Depreciation Rate (Recovery Rate)(d_t): Fraction of first cost removed by depreciation each year.
• Salvage Value (S): Market value at end of useful life of an asset.
• Personal Property : Income producing, tangible possessions of a corporation used to conduct business.
  Examples: Vehicles, machinery, computers, office furniture, etc.
• Real Property : Real estate and improvements (buildings)
                            Land is real property but not depreciable.
• Half-year convention: Assumes assets are placed into service or disposed of in mid-year regardless of when they really occurred.

Several Depreciation Methods

• Straight line method (SL)
  
  D_t = (B-S_v)d
  Since the book value decreases linearly over time, d = 1/n. Any year 1/n^th of the value will "elapse".
  Hence D_t = (B-S_v)d or (B-S_v)/n and the book value at any year is BV_t = B-tD_t
  
  Example: An asset with a first cost of $80,000 has a salvage value of $20,000 after 6 years. What is the depreciation each year and BV after each year?
  
  B=$80,000       S=$20,000     n = 6
           d = 1/6 = 0.1667
  D_t = (B-S)d = (80,000-20,000)0.1667 = $10,000/yr
  
  Year         Dt                 BVt
     0             -                80,000 (B)
     1         10,000          70,000
     2         10,000          60,000
     3         10,000          50,000
     4         10,000          40,000
     5         10,000          30,000
     6         10,000          20,000   Many conflicts between owner and IRS on what is really S .
  
  D_t = Amount deductible from GI.
  As a check: BV₃ = B-tD_t = $80,000 - 3(10,000) = $50,000
  
• Declining Balance (DB)
  
  
  d = Fixed Percentage of BV at beginning of each year.
  The maximum rate allowed is twice the SL rate.
  No salvage value is used.
  Thus, if n = 10 years, then d = 1/n = 1/10 = 0.10
  If the maximum is used then d = 2(0.10%) = 0.20
  
  
• Double Declining Balance (DDB)
  When twice d is used it is called the Double Declining Balance.
  Since in DB or DDB, d is applied at beginning of each year                                                                                     d_t = d(1-d)^t-1  --- Relative to 1st cost (B)
  and the depreciation for any year is : D_t = dBV_t-1= (d)B(1-d)^t-1
  The book value for any year is : BV_t = B(1-d)^t = BV_t-1-D_t = BV_t-1-d(BV_t-1)
  Note that BV does not decline to 0. An implied salvage value exists after n years of time.
  
  Implied S = BVn = B(1-d)n.
  And with an implied S, an implied d can be found.
  Implied d = 1- (Implied S / B)^1/n
  
  Example: Again 1st cost = $80,000, SV = $20,000, N = 6years. Using DOB method, find :
  1)Depreciation and book value after 2 years.
  2)Implied SV₆ usind DDB.
  
  First find the DDB rate: d = 2(1/n) = 2/6 = 1/3 = 0.333/year.
  
  D₂= dB(1-d)^t-1= 0.333(80,000)(1-0.333)¹= $17,778
  BV₂ = B(1-d)^t = 80,000(1-0.333)² = $35,556
  
  Implied SV = BV_n = B(1-d)ⁿ = 80,000(1-0.333)⁶ = $7,023
  
  But, SV = $20,000 @ 6 years.
  
  BV_n is not equal to SV      BV_n is the amount of worth due to loss of value and 
                                           SV is the amount for which the item can actually be sold for.
  
  If BV_n < SV, then no depreciation can be allowed after BV_t goes less than SV.

Here is what would happen in our example when the depreciation schedule is calculated.

t            BVt                 Dt              Depreciation Allowed 
0        80,000                 -                             -
1        53,333            26,667                    26,667
2        35,555            17,777                    17,777
3        23,703            11,852                    11,852
4        15,802              7,901          23,703-20,000 = $3,703
5        10,535              5,267                            0
6          7,023              3,512                            0

It is rare that the SV is known for the end of an asset's life. We will see what happens for the usual case in the next lesson.

Added to the Web: May 20, 2002. Last updated: April 26, 2002. Web page design by Dan Solarek.	http://cset.sp.utoledo.edu/engt3600/