Transcript Place of Engineering Economics in the World

Taxes and Depreciation
If you make some money, the government
takes part of it
Who gets it? Who pays it? What is it used
for?
TAXES
Fe de ral
State
Local
Income TAX
Prope rty TAX
Sale s TAX
Excise TAX
Inhe re tance TAX
Import TAX
Value Adde d TAX
… TAX
GOVERNMENT
Fe de ral
State
Local
Military
Social Se rvice s
Environme nt
Schools
Roads
Prisons
Scie ntific Re se arch
Industrial Support
…
Taxable Income
•
We pay taxes as individuals on our taxable income.
PERS ONAL TAXES
Wages
+ Interest Income
+ Dividends
+ Capital Gains
+ Other Income
Gross Income
– Adjustments
– Exemptions
– Deductions
Taxable Income
Computation of Personal Income Taxes
•
The tax rate is graduated to tax the rich more than the
poor. In 2000, the tax rates for a single individual
were:
Marginal
Tax
Rate
15%
28%
31%
36%
3 9 .6%
Taxable
Income
Income Tax
$ 0 - $ 2 6,2 5 0
$ 2 6,2 5 1 - $ 63 ,55 0
$ 6 3,5 5 1 - $ 13 2 ,6 0 0
$ 1 32, 6 01 - $2 8 8, 3 50
$ 2 88, 3 50 - in fin it y
1 5 % o f t he am o u nt ov e r $0
$ 3 ,93 7 .5 0 + 2 8% o f th e am oun t o ve r $ 2 6,2 5 0
$ 1 4,3 8 1. 5 0 + 31% o f t he a m o u n t o ver $ 63, 5 50
$ 3 5,7 8 7 + 36 % o f t he a m o u n t ov e r $1 3 2,6 0 0
$91,857 + 39.6% of the amount over $288,350
Corporation’s Taxable Income
•
A corporation pays taxes on its Before Tax
Income
CO RPO RATE TAXES
Sale s
– Cost of Goods Sold
Gross Margin
– De preciation
– O ther Expenses
+ Dividend and Interest Income
– Inte re st Expe nse
Income Be fore Taxe s
Computation of a Corporation’s Taxes
•
The corporate rate is also graduated. In 1996:
Taxable
Income
Tax
Rate
$0 - $50,000
$50,001 - $75,000
$75,001 - $100,000
$100,001 - $335,000
$335,001 - $10,000 ,000
$10,000 ,001 - $15,000 ,000
$15,000 ,001 - $18,333 ,333
$18,333 ,334 a nd up
15%
25%
34%
39%
34%
35%
38%
35%
Income Tax
1 5 % of t h e amo u n t ov e r $ 0
$ 7 ,5 0 0 + 2 5 % o f t h e amo u n t ov e r $ 5 0,0 00
$ 1 3,7 50 + 3 4 % o f t h e amo u n t ov e r $ 7 5,0 00
$ 2 2,2 50 + 3 9 % o f t h e a mou nt ov e r $ 1 00 ,00 0
$ 1 13 ,99 0 +
$ 3 ,4 0 0,0 00
$ 5 ,1 5 0,0 00
$ 6 ,4 1 6,6 66
3 4 % o f t h e amo u n t ov e r $ 3 35 ,00 0
+ 3 5 % o f t h e amo u n t ov e r $ 1 0,0 00 ,00 0
+ 3 8 % o f t h e amo u n t ov e r $ 1 5,0 00 ,00 0
+ 3 5 %$ o f t h e amo u n t ov e r $ 1 8,3 33 ,33 3
Taxes on Profit
•
The owners of a company are taxed twice on its
profits
– Dividends come from the company’s after tax income
– Stock holders must pay personal income tax on
dividend receipts as ordinary income
– Stock holders must pay the tax on profits made because
of growth in stock price as capital gains
Economic Analysis considering Taxes
•
How do we do an economic analysis considering
the effects of taxes?
Use After Tax Cash Flows for Analys is
After Tax Cash Flow
= Before Tax Cash Flow – Income Taxes
Income Taxes
= (Before Tax Cash Flow – Depreciation)*(Tax Rate)
Analyze with MARR after taxes
Example 1: Should we invest?
•
New Machine:
–
–
–
–
–
–
–
Investment = $11,000
Tax Life (N) and Actual Life (n) = 5 years
Tax Salvage(SV) and Actual Salvage (MV) = $1,000
Income = $4,000 per year
Operating Expenses = $1,000 per year
40% Tax Rate
After Tax MARR = 9%
Method 1: Straight Line Depreciation
•
•
•
•
•
•
•
P is the investment,
N is the tax life, and
SV is the tax salvage
The depreciation amount is the same each year.
The depreciation in year k is: (P - SV)/N.
The book value at year N is to be equal to SV.
The book value decreases linearly.
For the Straight Line Method
Straight Line Depreciation
12000
10000
8000
6000
4000
2000
0
0
1
2
3
4
5
Example 1: After Tax Analysis
Periods
Before Tax
Cash Flow
Depreciat ion
Taxable
Income
Tax
Aft er Tax
Cash Flow
0
-11 00 0
1
30 00
20 00
1 0 00
400
26 00
2
30 00
20 00
1 0 00
400
26 00
3
30 00
20 00
1 0 00
400
26 00
4
30 00
20 00
1 0 00
400
26 00
5
30 00
20 00
1 0 00
400
26 00
5
Salvage
10 00
10 00
0
0
10 00
-11 00 0
Example 1: ROR
•
After-tax NPW
= -11000 + 2600 (P/A, 0.09, 5) + 1000 (P/F, 0.09, 5)
= -236
•
•
Before-tax ROR = 13.34%
After-tax ROR = 8.20%
What is Depreciation?
•
•
•
•
•
Decline in value to the owner.
Decline in resale value.
Decline in value due to wear and tear
(deterioration).
Decline in value due to obsolescence.
An amount deducted from income before
computing taxes
Why do we compute depreciation?
•
•
•
Reduces net profit before taxes
Decreases taxes
Increases the cash flow after taxes
ATCF = Depreciation + Net Income after taxes
•
To maximize net present worth of cash flows,
we would like to make depreciation as large as
possible!
How do you compute Depreciation?
•
•
•
•
•
It is computed separately for each asset
It depends on the age of the asset
It depends on the Initial Cost of the asset (P)
It depends (sometimes) on the Tax Salvage of
the Asset (SV)
It depends on the Tax Life of the asset (N)
Definitions of Depreciation and Book
Value
•
•
The Depreciation in year k is Dk
The Book Value is the Initial Cost (P) minus the
Accumulated Depreciation
– BVk = P - (D1 + D2 + … + Dk)
Different Depreciation Methods
•
So-called historical or classical methods
– Straight Line
– Sum of the Years Digits
– Declining Balance
•
Current method mandated by the government
– Modified Accelerated Capital Recovery System
(MACRS) - GDS and ADS
Method 2: SYD
•
The Sum of Years Digits (SYD) method is d
based on
SYD = 1 + 2 + … + N = (N)(N+1)/2
•
The depreciation in year k is
(N - k + 1)/SYD multiplied by (P - S)
•
This is an accelerated depreciation method.
SYD Method
Sum-of-Years Digits Depreciation
11000
10000
9000
8000
7000
6000
5000
4000
3000
2000
1000
0
0
1
2
3
4
5
Example 1 with SYD Depreciation
Periods
Before Tax
Cash Flow
Depreciat ion
Taxable
Income
Tax
Aft er Tax
Cash Flow
0
-11 00 0
1
30 00
3 3 33. 3 3
-3 3 3.3 3
-13 3.3 3
31 33. 3 3
2
30 00
2 6 66. 6 7
33 3.3 3
13 3.3 3
28 66. 6 7
3
30 00
2 0 00. 0 0
10 00. 0 0
40 0.0 0
26 00. 0 0
4
30 00
1 3 33. 3 3
16 66. 6 7
66 6.6 7
23 33. 3 3
5
30 00
66 6.6 7
23 33. 3 3
93 3.3 3
20 66. 6 7
5
Salvage
10 00
1 0 00. 0 0
0. 0 0
0. 0 0
10 00. 0 0
-11 00 0
Economic Analysis for SYD Depreciation
•
After-tax NPW
= -11000 + 3133 (P/A, 0.09, 5) – 266.67 (P/G, 0.09, 5)
+ 1000 (P/F, 0.09, 5)
= -58.77
•
•
Before-tax ROR = 13.34%
After-tax ROR = 8.79%
Method 3: The Declining Balance method
•
•
•
•
•
A rate (a fraction) must be specified
The depreciation in year k is rate*(book value at
beginning of that year)
Double Declining Balance (DDB) means the rate
of depreciation is two times the straight-line
rate.
In other words, for the DDB, the rate = 2(1/N)
This is an accelerated depreciation method.
For the Declining Balance method
Double Declining Balance Depreciation
11000
10000
9000
8000
7000
6000
5000
4000
3000
2000
1000
0
0
1
2
3
4
5
Example 1 DDB Depreciation
Periods
Book Value
0
Before
Tax
Cash
Flow
-1 100 0
Depreciat ion
Taxable
Income
Tax
1
3 000 .00
6 600
4 400 .00
-1 400 .00
-5 60. 00
3 560 .00
2
3 000 .00
3 960
2 640 .00
3 60. 00
1 44. 00
2 856 .00
3
3 000 .00
2 376
1 584 .00
1 416 .00
5 66. 40
2 433 .60
4
3 000 .00
1 425 .6
9 50. 40
2 049 .60
8 19. 84
2 180 .16
5
3 000 .00
8 55. 36
5 70. 24
2 429 .76
9 71. 90
2 028 .10
5
Salvage
1 000 .00
1 44. 64
5 7.8 6
9 42. 14
1 100 0
Aft er Tax
Cash Flow
-1 100 0
This type of income is called “Gain on disposal”
This type of tax is called “Recapture”
Economic Analysis for DDB Depreciation
•
After tax NPW
= -11000 + 3560(P/F, 0.09, 1) + 2856(P/F, .09, 2) +
… + 942(P/F, .09, 5)
= 24.01
•
•
Before-tax ROR = 13.34%
After-tax ROR = 9.09%
Example 1 Comparison
Purchase (Yr. 0)
Yr. 1 Operations
Yr. 2 Operations
Yr. 3 Operations
Yr. 4 Operations
Yr. 5 Operations
Yr. 5 Salvage
ROR
Straight Line
-11000
2600
2600
2600
2600
2600
1000
8.20%
SYD
-11000
3133
2867
2600
2333
2067
1000
8.79%
DDB
-11000
3560
2856
2434
2180
2028
942
9.09%
Switching from the Declining Balance
method to the Straight Line method
•
One can switch to the straight line method
– to reduce the Book Value to zero
– or to reach some specified salvage value
•
The best place to switch is when the straight line depreciation is
greater than the declining balance depreciation
12000
10000
8000
6000
4000
2000
0
0
1
2
3
4
5
6
7
8
9
10
Conclusions
•
•
•
•
All previous analysis methods described work
with tax considerations
Use after tax cash flows and after tax MARR for
analysis
Depreciation of investments is required in
analysis
The method of depreciation may affect the
decision