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Engineering Economy, 8th edition
Leland Blank and Anthony Tarquin
Chapter 17
After-Tax Economic Analysis
Terminology and Basic Tax Computations
17.1 NOI = Net Operating Income; GI = Gross Income; Te = Effective Tax Rate: NOPAT = Net
17.2 (a) From Table 17.1, marginal tax rate = 39%
(b) Taxes = 0.15(50,000) + 0.25(75,000 – 50,000) + 0.34(100,000 - 75,000) +
17.3 (a) Net operating profit after taxes; (b) Taxable income; (c) Depreciation;
17.4 (a) In $1 million units,
(b) EBIT = NOI
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72,000 = 22,250 + 0.39(TI – 100,000)
0.39TI = 88,750
TI = $227,564
(b) Average tax rate = T = 72,000/227,564 = 0.316 (31.6%)
17.8 (a) TI = GI – OE – depreciation
(b) Use the TI relation with varying OE amounts to plot taxes. It is linear.
17.9 (a) Te = 9.8 + (1 – 0.098)(31%) = 37.76%
17.10 (a) Company ABC:
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= $236,000
Taxes = 22,250 + 0.39(236,000 – 100,000)
= $75,290
(b) ABC: (213,860/1,500,000)*100% = 14.26%
(c) ABC:
Taxes = (TI)(Te) = 629,000(0.34) = $213,860
XYZ:
17.11 (a) Te = 0.076 + (1 – 0.076)(0.34) = 0.3902
(b) NOPAT = TI(1-Te) = 2,400,000(0.6098) = $1,463,520
17.12 (a) Federal taxes = 13,750 + 0.34(5000) = $15,450 (using Table 17-1 rates)
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Federal: 80,000[0.1931(1 – 0.06)] = 80,000(0.1815)
= $14,520
17.13 (a) Te = 0.06 + (1 – 0.06)(0.23)
(c) Since Te = 22% is lower than the current federal rate of 23%, no provincial tax could
17.14 IRS Publication 17 for 2015 is used for this solution.
17.15 Tax rates for 2015 from IRS Publication 17 are below. Your tax amounts and plot will
vary when the current tax rates are applied. The percentage of GI spent on taxes has varied
widely as shown in the plot.
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CFBT and CFAT
17.16 CFBT does not include life of asset, depreciation, and tax rate
17.17 NOPAT = GI – OE – D – Taxes
17.18 Use TI = GI – OE – D and CFBT = GI – OE = TI + D
17.19 CFBT = [750,000 – 400,000(0.36)]/(1 – 0.36)
17.20 Solve for GI
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= $3,973,913
17.21 By hand: Missing values are shown in bold.
CFBT2 = 950 – 150 = $800
Spreadsheet: Missing values are shown in bold. Functions for year 4 are detailed.
17.22 By hand: CFAT = GI – OE – P + S – (GI – OE –D)Te
(a) P & S = 0
(b) S = $20,000
(c) S = $20,000 D = 0
= $50,000
Year
GI
E
P and S
CFBT
D
TI
Taxes
CFAT
Spreadsheet: MACRS d4 = 0.0741 SL d4 = 0
Same answers as above using Table 17-2 template
17.23 All monetary units are in $1 million
(a) CFAT = GI – OE – TI(Te )
(c) NOPAT = TI(1 - Te ) = 11.8(1 - 0.39225)
GI – E = CFAT + (GI – E – D)(Te)
Solve for GI to obtain a general relation for each year t:
GIt = [CFAT + E(1- Te) - DTe]/ (1- Te)
Year 1: GI1 = [2.5 million + 650,000(0.736) – 650,000(0.264)]/0.736
Year 3: GI3 = [2.5 million + 1,150,000(0.736) – 1,150,000(0.264)]/0.736
17.25 By hand:
Method A: Years 1-5, Depreciation = (100,000 – 10,000)/5 = $18,000
Method B: Years 1-5, Depreciation = (150,000 – 20,000)/5 = $26,000
Spreadsheet: Select Method B.
Depreciation Effects on Taxes
17.26 Depreciation is a 100% deduction from TI when corporate taxes are calculated. Thus, one
17.28 (a) Spreadsheet shows tax curves. There is no depreciation allowed after n = 6 for SL and
17.29 Did you guess correctly that SL with n = 4 years will be slightly lower in PW of taxes?
The shorter recovery period overrides the accelerated write-off in this case.
17.30 (a) Recovery over 3 years. SL depreciation is 60,000/3 = $20,000 per year
Year 4-6: Taxes = (GI - OE)( Te )
PWtax = 620(P/A,12%,3) + 6820(P/A,12%,3)(P/F,12%,3)
Recovery over 6 years. SL depreciation is 60,000/6 = $10,000 per year
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= $3720
Total taxes = 6(3720) = $22,320
PWtax = 3720(P/A,12%,6)
(b) Spreadsheet: Solution follows with only the functions shown.
(c) Spreadsheet functions:
Function for 3-year recovery: = -PV(12%,3,620) + PV(12%,3,,PV(12%,3,6820))
17.31 (a) In $1000 units for monetary values.
SL: D = (20 – 0)/3 = $6.667 Te = 0.40
Year GI P OE D TI Taxes CFAT
(b) In $1000 units for monetary values.
MACRS rates Te = 0.40
Year GI P OE D TI Taxes CFAT
17.32 Find the difference between PW of CFBT and CFAT at Te = 0.40 and i = 10%
Year CFBT, $ d Depr., $ TI, $ Taxes, $ CFAT, $
17.33 All monetary terms are in $1000 units
Scenario 1: Uniform write-off
Sample for year 2: CFAT = 15 – 4 – [(15 – 4 - 6)(0.32)] = 9.40
NOPAT = 5 – 1.6 = 3.40
Year GI OE P D TI Taxes CFAT NOPAT
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(a) Total NOPAT = $4.76 ($4760)
(b) PWtax = 1.6(P/F,6%,2) + 0.96(P/F,6%,3) - 0.32(P/F,6%.4)
= $1.9765 ($1977)
Scenario 2: Accelerated write-off
Year GI OE P D TI Taxes CFAT NOPAT
Total 4.205
Conclusion: A larger NOPAT and lower PWtax are better economically. Scenario 1
(accelerated depreciation) is the choice for the PWtax criterion.
Depreciation Recapture and Capital Gains (Losses)
17.34 It is important in an after-tax replacement analysis, because a ‘sacrifice’ trade-in value
17.35 BV2 = 120,000 – 120,000(0.3333 + 0.4445) = $26,664
17.36 TI will increase by DR, since MACRS BV5 = 0
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Te = 0.065 + (1 - 0.065)(0.35) = 0.39225
Tax increase = 100,000(0.39225) = $39,225
17.37 (a) Land is not depreciable.
(b) SP = $10,000
(c) SP = 0.2(150,000) = $30,000
17.38 Total MACRS depreciation: 20% + 32% + 19.2% = 71.2%
Selling price of $80,000 < BV3. There is a capital loss
17.39 (a) CG = 285,000 – 240,000
(b) Taxes are shown in column I. TI for year 3 must include CG and DR as fully taxable.
17.40 Land: CG = $45,000
17.41 (a) BV2 = 28,500 – 28,500(0.3333 + 0.4445) = $6333
(b) Capital losses can only be used to offset capital gains. This will reduce taxes on the
17.42 Thomas omitted the $100,000 DR in year 4. If included, in $1000 units, the CFAT is
After-Tax Economic Evaluation
17.43 (a) Before-tax ROR: 0 = -750,000 + 260,000(P/A,i*,3) + 187,500(P/F,i*,3)
(b) Approximate after-tax ROR = (before-tax ROR) (1-Te)
17.44 Effective tax rate = 0.06 + (1 – 0.06)(0.35) = 0.38
17.45 0.08 = 0.12(1 - Te)
17.46 After-tax ROR = 24(1- 0.35) = 15.6%
17.47 Calculate taxes using Table 17-1 rates; the average tax rate Te; then after-tax ROR
17.48 (a) Develop two tables similar to those shown.
(b) Plot of CFAT values shows they track closely.
17.49 System A: Depreciation = 150,000/3 = $50,000
Years 1 to 3: TI = 60,000 – 50,000 = $10,000
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System B: Depreciation = 85,000/5 = $17,000
For year 5 only, when B is sold for 10% of first cost:
Select system A
17.50 For a 12% after-tax return, find n in a PW relation.
Keep the equipment for 8.85 (or 9 rounded off) years
17.51 (a) By hand: Alternative X
Year
P and S
GI - OE
D
TI
Taxes
CFAT
0
-8000
-
-
-
-
-8000
1
3500
2666
834
333
3167
2
3500
3556
-56
-22
3522
3
3500
1185
2315
926
2574
4
0
0
593
-593
-237
237
PWX = -8000 + 3167(P/F,8%,1) + 3522(P/F,8%,2) + 2574(P/F,8%,3) + 237(P/F,8%,4)
= $169
