Taxes
Before we look at after tax flow calculations, we need to see how taxes are
calculated. Federal tax rates are graduated.
Higher taxes are paid for larger T I
's.
Average tax rate (federal) = Total taxes paid / Total TI
Additionally state taxes are usually not graduated and are deductible (not counted) from
federal TI.
Hence, Effective Tax Rate = Te = State Rate + (1-
State Rate) Federal Rate
Example: Total Federal taxes paid = $32,390. TI = $126,000. State rate = 4.6%. What is Te?
Average Federal tax rate = $32,390 / $126,000 = 25.71%
Te = 0.046 +
(1-0.046)(0.2571) = 29.12%
Net Cash Flow (NCF)
Let's now see how taxes affect an economic alternative.
NCF = -Capital expense + Gross income - Operating expenses + Salvage value -
Taxes
= -P + GI - E + SV -
(TI)T
Before Tax Cash Flow = BTCF = NCF without taxes included.
After Tax Cash Flow = ATCF = NCF
Correct economic analyses are performed using the ATCF (NCF).
Other items that can affect NCF and TI is the question of how the capital expense is funded. Namely, how taxes are affected by debt payments.
Type of Cash
Flow
Tax
Effect on
debt
involved
Treatment
NCF
Loan
Receive
P None
+
Loan Pay
interest
Deduct
-
Loan
Repay
Principle Not
Deduct -
Bond
Receive face
value None
+
Bond Pay
dividend
Deduct
-
Bond Repay
face value Not
Deduct
-
Let's investigate how the analysis of an option using its NCF proceeds.
Example: Find PW of NCF of a depreciable asset for a $45,000 testing machine (without loan). Use MACRS without salvage value for N = 5 years. Annual income = $23,000, MARR = 10%, Annual O&M = $7300, Te = 40%. Is the purchase a profitable investment?
First determine the NCF for each year.
Capital
MACRS
Year
GI
E
Expenses d
D
TI
Tax
NCF
0
-
-
$45,000
-
-
-
- -$45,000
1 23,000
7300
- 0.20
9000 6700
2680 13020
2 23,000
7300
- 0.32
14400 1300
520 15180
3 23,000
7300
-
0.192 8640 7060
2824 12876
4
23,000 7300
-
0.1152 5184 10516
4206 11494
5 23,000
7300
-
0.1152 5184
10516 4206 11494
6 23,000
7300
-
0.0576 2592
13108 5243
10457
Determine the Present Worth of the NCF.
PW = -$45,000 + 13,020
(P/F,10,1)
+ 15,180
(P/F,10,2)
+ 12,876
(P/F,10,3)
+ 11,494 [(P/F,10,4) +
(P/F,10,5)]
+ 10,457 (P/F,10,6)
= -$45,000 + 13,020
(0.90909)
+ 15,180
(0.82645)
+ 12,876
(0.75131)
+ 11,494 [(0.68301) +
(0.62092)]
+ 10,457 (0.56447)
= $9,946 > 0 -- Hence a good
investment
Or if we had found
the rate of return, then i* =
17.63% > 10% MARR--Again a good investment.
Let's look at some variations to the original cash flow.
Note that in each scenario below, only the affected year is shown.
What if after 6
years the machine had been sold for $3000?
Capital
MACRS
Year
GI
E Expenses
d
D
TI
Tax
NCF
6 23,000 +
3,000 7,300
-
0.0576 2592 16,108
6443 12257
PW = $10,962 > 0 , i*
=18.24%
Additionally, what if a $17,500 overhaul is required at the end of year
3?
Capital
MACRS
Year
GI
E
Expenses
d
D
TI
Tax
NCF
3 23,000
7,300+17,500
-
0.192 8640
-10,490 -4176
2376
Note that a negative tax is a
refund!!
PW = $3073 , i* = 12.37%
Additionally, what if an
investment tax credit of 5% of the initial cost, is to be taken in year
1?
Capital
MACRS
Tax
Year GI
E Expenses d
D
TI Tax
Credit NCF
1 23,000
7,300
- 0.20
9000 6,700
2680 2250
15270
PW = $5119, i* = 14.03%
Each additional change to the proposal affected the
final PW and i* results, but in each case the proposal is acceptable.
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20, 2002. Last updated: April 26, 2002. Web page design by Dan Solarek. |
 http://cset.sp.utoledo.edu/engt3600/ |