# After Tax Analysis

After-Tax Economic Analysis
Gross Income (GI) – total income realized from all
revenue-producing sources, including items such
as the sales of assets, royalties, license fees, etc…
Income Tax – amount of taxes based on gross income.
Corporate taxes are typically paid quarterly, and
are actual cash flows.
Operating Expenses (E) – all corporate costs incurred
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After-Tax Economic Analysis
Taxable Income (TI) – the amount upon which taxes
are based.
TI = ______________
Where D is depreciation defined in previous lecture.
Tax Rate (T) – percentage of TI owed in taxes. This
rate is graduated, based on TI. (See table 17-1)
Net Profit after taxes (NPAT) – amount remaining each
year when income taxes are subtracted from
taxable income.
NPAT = _____________
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After-Tax Economic Analysis
Corporate Federal Income Tax Rate Schedule (2003)
TI Limits
\$1-\$50,000
TI Range
Tax Rate T
Maximum Tax for
TI Range
Maximum Tax
Incurred
\$50,000
0.15
\$7,500
\$7,500
\$50,001-\$75,000
25,000
0.25
6,250
13,750
\$75,001-\$100,000
25,000
0.34
8,500
22,250
\$100,001-\$335,000
235,000
0.39
91,650
113,900
\$335,001-\$10 mil
9.665 mil
0.34
3.2861 mil
3.4 mil
over \$10 - \$15 mil
5 mil
0.35
1.75 mil
5.15 mil
3.33 mil
0.38
1.267 mil
6.417 mil
unlimited
0.35
unlimited
unlimited
over \$15 - \$18.33 mil
over \$18.33 mil
Graduated tax rate schedule (table 17-1, pg. 571)
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After-Tax Economic Analysis
Average Tax Rate – because the marginal tax rate
varies as TI varies, the average tax rate is
calculate as:
Ave tax rate = total taxes / TI
Effective Tax Rate (Te) – the total rate paid by
corporations, including federal, state and local
taxes. Note state taxes can be deducted from
federal taxes. So:
Te = state rate + (1-state rate)( federal rate)
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Example: Problem 17.5
a) Average Tax Rate
Taxes on \$300,000 = ____________________
Ave tax rate = _______________________
Effective Tax Rate (assume state tax = 7%
Te = ______________________________
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CFBT – vs – CFAT
•
Cash flow before tax (CFBT) – all cash flows
throughout the year without considering taxes. Note,
all our PW, FW, AW analysis to this point have been
CBFT cash flows.
CFBT = GI – E – P + S
where P is initial investments and S is salvage.
•
Cash flow after tax (CFAT) – includes the cash flow
impact of taxes.
CFAT = CFBT - taxes
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CFBT – vs – CFAT
•
Knowing CFAT = CFBT – taxes …
•
Taxes are calculated taking depreciation (D) into
account, however depreciation is not a cash flow,
but taxes are.
Taxes = TI(Te)
TI = GI – E – D
CFAT = GI – E – P + S – (GI – E – D)(Te)
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After-Tax Economic Analysis
Example 17.3 from Book
Cash Flow Before Taxes
Year
GI
E
0
P and S
CFBT
(\$550,000)
(\$550,000)
1
\$200,000
(\$90,000)
\$110,000
2
\$200,000
(\$90,000)
\$110,000
3
\$200,000
(\$90,000)
\$110,000
4
\$200,000
(\$90,000)
\$110,000
5
\$200,000
(\$90,000)
\$110,000
6
\$200,000
(\$90,000)
\$150,000
Total
\$260,000
\$260,000
Cash Flow After Taxes
Year
GI
E
0
P and S
D
TI
Taxes
CFAT
(\$550,000)
(\$550,000)
1
\$200,000
(\$90,000)
\$110,000
\$0
\$0
\$110,000
2
\$200,000
(\$90,000)
\$176,000
(\$66,000)
(\$23,100)
\$133,100
3
\$200,000
(\$90,000)
\$105,600
\$4,400
\$1,540
\$108,460
4
\$200,000
(\$90,000)
\$63,360
\$46,640
\$16,324
\$93,676
5
\$200,000
(\$90,000)
\$63,360
\$46,640
\$16,324
\$93,676
6
\$200,000
(\$90,000)
\$31,680
\$78,320
\$27,412
\$232,588
Total
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\$150,000
\$550,000
\$221,500
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Definitions
Capital Gains (CG): Occurs when selling price is greater than first cost.
Capital gain = selling price – first cost
CG = SP – P
Depreciation Recovery (DR): Occurs when a depreciable asset is sold
for more than the current book value.
Depreciation recapture = selling price – book value
DR = SP – BVt
Capital Loss (CL): Occurs when a depreciable asset is disposed of for
less than its current book value.
CL = BVt - SP
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After-Tax Economic Analysis
DR
\$0
BV
CG
P
SP
When selling price exceeds first cost then both a capital
gain and a depreciation recovery occur.
DR
\$0
BV
SP
P
When selling price exceeds book value but is less than
he first cost then a depreciation recovery occurs.
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After-Tax Economic Analysis
CL
\$0
SP
BV
P
When selling price is below book value a capital
loss occurs.
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After-Tax Economic Analysis
Considering capital gains, depreciation recovery and
capital losses,
TI = gross income – expenses – depreciation
+ depreciation recapture + capital gains
– capital loss
TI = GI – E – D + DR + CG - CL
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After-Tax PW and AW Analysis
• Relationship between before-tax MARR and aftertax MARR:
Before-tax MARR = After-tax MARR
1 - Te
Te for corporations is often between 30 and 50%.
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After-Tax PW and AW Analysis
• Approach 1: Find the PW or AW of an alternative
using the CFAT and the After-tax MARR. That
alternative with the largest PW (AW) is chosen.
Note, PW must use LCM (least common multiple of
years.)
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After-Tax Economic Analysis
Using cash flows from Example 17.3, and an after-tax
MARR of 7%, the PW of this alternative is:
Year
PW = - \$550,000
+ \$110,000(P/F, 7%, 1)
+ \$133,100(P/F, 7%, 2)
+ \$108,460(P/F, 7%, 3)
+ \$ 93,676(P/F, 7%, 4)
+ \$ 93,676(P/F, 7%, 5)
+ \$232,588(P/F, 7%, 6)
CFAT
0
(\$550,000)
1
\$110,000
2
\$133,100
3
\$108,460
4
\$93,676
5
\$93,676
6
\$232,588
Total
\$221,500
= ______________
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