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
in the transaction of business.
After-Tax Economic Analysis
Taxable Income (TI) – the amount upon which taxes
are based.
TI = GI – E – D
Where D is depreciation defined in previous lecture.
Tax Rate (T) – percentage of TI owed in taxes. This
rate is graduated, based on TI.
Net Profit after taxes (NPAT) – amount remaining each
year when income taxes are subtracted from
taxable income.
NPAT = TI – TI(T)
After-Tax Economic Analysis
Corporate Federal Income Tax Rate Schedule (2000)
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
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)
After-Tax Economic Analysis
CFBT – vs – CFAT
Cash flow before tax (CBFT) – all cash flows
throughout the year without considering taxes.
Note, all our PW, FW, AW analysis to this point
have been CBFT cash flows.
CBFT = 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
After-Tax Economic Analysis
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)
After-Tax Economic Analysis
Example 17.3 from Book
Cash Flow Before Taxes
Year
GI
R
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
R
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
$150,000
$550,000
$221,500
After-Tax Economic Analysis
Capital Gains (CG)
Occurs when selling price is greater than first cost:
Capital gain = selling price – first cost
CG = SP – P
Depreciation Recovery (DR)
Occurs when a depreciable asset is sold for more than the current
book value.
Depreciation recapture = selling price – book value
DR = SP – BVt
Capital Loss (CL)
Occurs when a depreciable asset is disposed of for less than its
current book value.
CL = BVt - SP
After-Tax Economic Analysis
DR
0$
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.
After-Tax Economic Analysis
CL
0$
SP
BV
P
When selling price is below book value a capital
loss occurs.
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
After-Tax Economic Analysis
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%.
After-Tax Economic Analysis
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).
After-Tax Economic Analysis
Using cash flows from Example 17.3, and an
after-tax MARR of 7%, the PW
Year
Of this alternative is:
PW = - $500,000
+ $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