# After-Tax Economic Analysis

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```					               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)

Maximum Tax for    Maximum Tax
TI Limits             TI Range      Tax Rate T          TI Range          Incurred

\$1-\$50,000                        \$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

over \$15 - \$18.33 mil              3.33 mil           0.38          1.267 mil       6.417 mil

over \$18.33 mil                   unlimited           0.35          unlimited       unlimited

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              P and S     CFBT
0                                     (\$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      \$260,000
Total                                                   \$260,000

Cash Flow After Taxes
Year          GI          E             P and S            D         TI         Taxes        CFAT
0                                    (\$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)         \$150,000        \$31,680      \$78,320     \$27,412      \$232,588
Total                                                   \$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     CG

\$0           BV         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 after-
tax 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     CFAT
PW = - \$550,000                           0      (\$550,000)
+ \$110,000(P/F, 7%, 1)               1        \$110,000
+ \$133,100(P/F, 7%, 2)               2       \$133,100
+ \$108,460(P/F, 7%, 3)               3       \$108,460
+ \$ 93,676(P/F, 7%, 4)               4        \$93,676
+ \$ 93,676(P/F, 7%, 5)               5        \$93,676
+ \$232,588(P/F, 7%, 6)               6       \$232,588
Total       \$221,500
= ______________
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