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Measures of profitability
(Problem solving)
1 Material used in this lecture is sourced from "Plant Design and Economics for Chem. Engineers", 5th ed. McGraw Hill, © 2003 , by Peters, et
al., and also from Engineering Economics 4N04 class notes, McMaster University © 2001-2007.
Dr. A. Alim
Example from Peters:
Example 8-3, p. 331(modified)
2 Material used in this lecture is sourced from "Plant Design and Economics for Chem. Engineers", 5th ed. McGraw Hill, © 2003 , by Peters, et al.,
and also from Engineering Economics 4N04 class notes, McMaster University © 2001-2007.
3 investments. Need to evaluate profitability of each.
Use ROI, PBP, NPV, and DCFRR.
Assume straight line depreciation.
Tax rate is 35%
MARR is 15%
Use MARR as interest rate for time value of money.
Both salvage value and working capital are recovered in last year.
3 Material used in this lecture is sourced from "Plant Design and Economics for Chem. Engineers", 5th ed. McGraw Hill, © 2003 , by Peters, et al., and also from Engineering Economics 4N04 class notes, McMaster University © 2001-2007.
Investment #
Fixed capital
$
Working capital
$
Salvage value
$
Service life, years
GI – E
$
1 100,000 10,000 10,000 5 See yearly tabulation
2 170,000 10,000 15,000 7 64,615
(constant)
3 210,000 15,000 20,000 8 73,846
(constant)
For investment # 1:
Year 1 2 3 4 5
GI – E
$
46,154 47,692 55,385 61,539 66,154
4 Material used in this lecture is sourced from "Plant Design and Economics for Chem. Engineers", 5th ed. McGraw Hill, © 2003 , by Peters, et
al., and also from Engineering Economics 4N04 class notes, McMaster University © 2001-2007.
ROI calculation:
ROI = (NPAT)AV / Total capital
(NPAT)AV = (1/N) Σ (NPAT)n for n = 1 to N
(NPAT)n = (GI – E – D)n (1-Te)
PBP calculation:
PBP = Fixed capital / (CFAT)AV
(CFAT)AV = (1/N) Σ (CFAT)n for n = 1 to N
(CFAT)n = (NPAT + D)n
R = Fixed capital / Total capital
PBP (ref) = R/(MARR + R/N)
5 Material used in this lecture is sourced from "Plant Design and Economics for Chem. Engineers", 5th ed. McGraw Hill, © 2003 , by Peters, et al.,
and also from Engineering Economics 4N04 class notes, McMaster University © 2001-2007.
NPV calculation:
NPV = -(total capital) + Σ (CFAT)n (1+i) – n for n = 1 to N
For NPV calculations, we use CFAT = CFBT - taxes
DCFRR (IRR) calculation:
DCFRR is the interest rate obtained by setting NPV = zero
NPV = 0 = -(total capital) + Σ (CFAT)n (1+IRR) – n for n = 1 to N
Excel function IRR is often used instead of the trial and error approach.
6 Material used in this lecture is sourced from "Plant Design and Economics for Chem. Engineers", 5th ed. McGraw Hill, © 2003 , by Peters, et al.,
and also from Engineering Economics 4N04 class notes, McMaster University © 2001-2007.
For investment # 1: Depreciation D = (100,000 – 10,000) / 5 = $18,000 per year NPAT = (GI – E – D)*(1 – Te) = 0.65(GI – E – 18,000)
Year 1 2 3 4 5
GI – E
D
NPAT
46,154
18,000
18,300
47,692
18,000
19,300
55,385
18,000
24,3000
61,539
18,000
28,300
66,154
18,000
31,300
(NPAT)AV = 121,500 / 5 = $24,300 ROI = (NPAT)AV / total capital = 24,300/110,000 = 22.1% which is > MARR Acceptable
Total = $121,500
1. Return on Invested Capital (ROI)
7 Material used in this lecture is sourced from "Plant Design and Economics for Chem. Engineers", 5th ed. McGraw Hill, © 2003 , by Peters, et al.,
and also from Engineering Economics 4N04 class notes, McMaster University © 2001-2007.
For investment # 2: Depreciation D = (170,000 – 15,000) / 7 = $22,143 per year
(NPAT)AV = (64,615 – 22,143) (1 – 0.35) = $27,607 ROI = (NPAT)AV / total capital = 27,607/180,000 = 15.3% which is > MARR Acceptable
1. Return on Invested Capital (ROI)
8 Material used in this lecture is sourced from "Plant Design and Economics for Chem. Engineers", 5th ed. McGraw Hill, © 2003 , by Peters, et al.,
and also from Engineering Economics 4N04 class notes, McMaster University © 2001-2007.
For investment # 3: Depreciation D = (210,000 – 20,000) / 8 = $23,750 per year
(NPAT)AV = (73,846 – 23,750) (1 – 0.35) = $32,562 ROI = (NPAT)AV / total capital = 32,562/225,000 = 14.5% which is < MARR Unacceptable
1. Return on Invested Capital (ROI)
9 Material used in this lecture is sourced from "Plant Design and Economics for Chem. Engineers", 5th ed. McGraw Hill, © 2003 , by Peters, et al.,
and also from Engineering Economics 4N04 class notes, McMaster University © 2001-2007.
For investment # 1: R = 100/110 = 0.91 PBPRef = 0.91 / (0.15 + (0.91/5)) = 2.74 years PBP = 100,000 / (24,300 + 18,000) = 2.36 years PBP < PBPRef → Acceptable
2. Payback period (PBP)
10 Material used in this lecture is sourced from "Plant Design and Economics for Chem. Engineers", 5th ed. McGraw Hill, © 2003 , by Peters, et al.,
and also from Engineering Economics 4N04 class notes, McMaster University © 2001-2007.
For investment # 2: R = 170/180 = 0.94 PBPRef = 0.94 / (0.15 + (0.94/7)) = 3.31 years PBP = 170,000 / (27,607 + 22,143) = 3.41 years PBP > PBPRef → Unacceptable
2. Payback period (PBP)
11 Material used in this lecture is sourced from "Plant Design and Economics for Chem. Engineers", 5th ed. McGraw Hill, © 2003 , by Peters, et al.,
and also from Engineering Economics 4N04 class notes, McMaster University © 2001-2007.
For investment # 3: R = 210/225 = 0.93 PBPRef = 0.93 / (0.15 + (0.93/8)) = 3.49 years PBP = 210,000 / (32,562 + 23,750) = 3.72 years PBP > PBPRef → Unacceptable
2. Payback period (PBP)
12 Material used in this lecture is sourced from "Plant Design and Economics for Chem. Engineers", 5th ed. McGraw Hill, © 2003 , by Peters, et al.,
and also from Engineering Economics 4N04 class notes, McMaster University © 2001-2007.
INVESTMENT # 1 :
Fixed Cap. = $100,000 MARR = 0.15
Working Cap. = $10,000 Tax Rate = 0.35
Salvage Value = $10,000
Service Life = 5
Year GI - E P/S/W Dep. CFBT TI Taxes NPAT NPAT + D CFAT (CFBT - Taxes)
0 -$110,000 -$110,000 -$110,000
1 $46,154 $18,000 $46,154 $28,154 $9,854 $18,300 $36,300 $36,300
2 $47,692 $18,000 $47,692 $29,692 $10,392 $19,300 $37,300 $37,300
3 $55,385 $18,000 $55,385 $37,385 $13,085 $24,300 $42,300 $42,300
4 $61,539 $18,000 $61,539 $43,539 $15,239 $28,300 $46,300 $46,300
5 $66,154 $20,000 $18,000 $86,154 $48,154 $16,854 $31,300 $49,300 $69,300
Years 1 to 5 average $18,000 $24,300 $42,300 ROI = 22.1 % Acceptabe More than MARR
PBP (ref) = 2.74 Years
PBP = 2.36 Years Acceptable Less than PBP (ref)
NPV = $38,509 Acceptable Positive
DCFRR 27% Acceptabe More than MARR
13 Material used in this lecture is sourced from "Plant Design and Economics for Chem. Engineers", 5th ed. McGraw Hill, © 2003 , by Peters, et al.,
and also from Engineering Economics 4N04 class notes, McMaster University © 2001-2007.
INVESTMENT # 2 :
Fixed Cap. = $170,000 MARR = 0.15
Working Cap. = $10,000 Tax Rate = 0.35
Salvage Value = $15,000
Service Life = 7
Year GI - E P/S/W Dep. CFBT TI Taxes NPAT NPAT + D CFAT (CFBT-Taxes)
0 -$180,000 -$180,000 -$180,000
1 $64,615 $22,143 $64,615 $42,472 $14,865 $27,607 $49,750 $49,750
2 $64,615 $22,143 $64,615 $42,472 $14,865 $27,607 $49,750 $49,750
3 $64,615 $22,143 $64,615 $42,472 $14,865 $27,607 $49,750 $49,750
4 $64,615 $22,143 $64,615 $42,472 $14,865 $27,607 $49,750 $49,750
5 $64,615 $22,143 $64,615 $42,472 $14,865 $27,607 $49,750 $49,750
6 $64,615 $22,143 $64,615 $42,472 $14,865 $27,607 $49,750 $49,750
7 $64,615 $25,000 $22,143 $89,615 $42,472 $14,865 $27,607 $49,750 $74,750
Years 1 to 7 average $22,143 $27,607 $49,750 ROI = 15.3 % Acceptabe More than MARR
PBP (ref) = 3.31 Years
PBP = 3.42 Years Unacceptable Longer than PBP (ref)
NPV = $36,378 Acceptable Positive
DCFRR 21% Acceptabe More than MARR
14 Material used in this lecture is sourced from "Plant Design and Economics for Chem. Engineers", 5th ed. McGraw Hill, © 2003 , by Peters, et al., and also from Engineering Economics 4N04 class notes, McMaster University © 2001-2007.
INVESTMENT #3 :
Fixed Cap. = $210,000 MARR = 0.15
Working Cap. = $15,000 Tax Rate = 0.35
Salvage Value = $20,000
Service Life = 8
Year GI - E P/S/W Dep. CFBT TI Taxes NPAT NPAT + D CFAT (CFBT-Taxes)
0 -$225,000 -$225,000 -$225,000
1 $73,846 $23,750 $73,846 $50,096 $17,534 $32,562 $56,312 $56,312
2 $73,846 $23,750 $73,846 $50,096 $17,534 $32,562 $56,312 $56,312
3 $73,846 $23,750 $73,846 $50,096 $17,534 $32,562 $56,312 $56,312
4 $73,846 $23,750 $73,846 $50,096 $17,534 $32,562 $56,312 $56,312
5 $73,846 $23,750 $73,846 $50,096 $17,534 $32,562 $56,312 $56,312
6 $73,846 $23,750 $73,846 $50,096 $17,534 $32,562 $56,312 $56,312
7 $73,846 $23,750 $73,846 $50,096 $17,534 $32,562 $56,312 $56,312
8 $73,846 $35,000 $23,750 $108,846 $50,096 $17,534 $32,562 $56,312 $91,312
Years 1 to 8 average $23,750 $32,562 $56,312 ROI = 14.5 % Unacceptabe Less than MARR
PBP (ref) = 3.50 Years
PBP = 3.73 Years Unacceptable Longer than PBP (ref)
NPV = $39,133 Acceptable Positive
DCFRR 20% Acceptabe More than MARR
15 Material used in this lecture is sourced from "Plant Design and Economics for Chem. Engineers", 5th ed. McGraw Hill, © 2003 , by Peters, et al., and also from Engineering Economics 4N04 class notes, McMaster University © 2001-2007.
16 Material used in this lecture is sourced from "Plant Design and Economics for Chem. Engineers", 5th ed. McGraw Hill, © 2003 , by Peters, et al., and also from Engineering Economics 4N04 class notes, McMaster University © 2001-2007.
Peters, example 8.1, page 325 Peters, example 8.2, page 328
17 Material used in this lecture is sourced from "Plant Design and Economics for Chem. Engineers", 5th ed. McGraw Hill, © 2003 , by Peters, et al., and also from Engineering Economics 4N04 class notes, McMaster University © 2001-2007.
18 Material used in this lecture is sourced from "Plant Design and Economics for Chem. Engineers", 5th ed. McGraw Hill, © 2003 , by Peters, et al., and also from Engineering Economics 4N04 class notes, McMaster University © 2001-2007.
MACRS, 5 years, Fixed Capital = $ 24 million
Year d % D ($ 106 / year)
1 20 4.8
2 32 7.7
3 19.2 4.6
4 11.52 2.8
5 11.52 2.7
6 5.76 1.4
Total 100 24
19 Material used in this lecture is sourced from "Plant Design and Economics for Chem. Engineers", 5th ed. McGraw Hill, © 2003 , by Peters, et al., and also from Engineering Economics 4N04 class notes, McMaster University © 2001-2007.
20 Material used in this lecture is sourced from "Plant Design and Economics for Chem. Engineers", 5th ed. McGraw Hill, © 2003 , by Peters, et al., and also from Engineering Economics 4N04 class notes, McMaster University © 2001-2007.
21 Material used in this lecture is sourced from "Plant Design and Economics for Chem. Engineers", 5th ed. McGraw Hill, © 2003 , by Peters, et al., and also from Engineering Economics 4N04 class notes, McMaster University © 2001-2007.
22 Material used in this lecture is sourced from "Plant Design and Economics for Chem. Engineers", 5th ed. McGraw Hill, © 2003 , by Peters, et al., and also from Engineering Economics 4N04 class notes, McMaster University © 2001-2007.
23 Material used in this lecture is sourced from "Plant Design and Economics for Chem. Engineers", 5th ed. McGraw Hill, © 2003 , by Peters, et al., and also from Engineering Economics 4N04 class notes, McMaster University © 2001-2007.
24
Material used in this lecture is sourced from "Plant Design and Economics for Chem. Engineers", 5th ed. McGraw Hill, © 2003 , by Peters, et al., and also from Engineering Economics 4N04 class notes, McMaster University © 2001-2007.
25 Material used in this lecture is sourced from "Plant Design and Economics for Chem. Engineers", 5th ed. McGraw Hill, © 2003 , by Peters, et al., and also from Engineering Economics 4N04 class notes, McMaster University © 2001-2007.
MEASURES OF PROFITABILITY
We have learned four measures of profitability
• Payback time Not recommended
• ROI Not recommended
• NPV Recommended
• DCFRR Recommended
26 Material used in this lecture is sourced from "Plant Design and Economics for Chem. Engineers", 5th ed. McGraw Hill, © 2003 , by Peters, et al., and also from Engineering Economics 4N04 class notes, McMaster University © 2001-2007.
Material used in this lecture is sourced from "Plant Design and Economics for Chem. Engineers", 5th ed. McGraw Hill, © 2003 , by Peters, et al., and also from Engineering Economics 4N04 class notes, McMaster University © 2001-2007. 27
CHEE 5369 / 6369 Homework # 5
Thursday, February 27, 2014 The following problems from Peters, Timmerhaus, and West (fifth edition): In all problems, unless specified, assume tax rate is 35 % Problem 8.2 page 353 Problem 8.8 page 354 Problem 8.9 page 355 Problem 8.10 page 355
Material used in this lecture is sourced from "Plant Design and Economics for Chem. Engineers", 5th ed. McGraw Hill, © 2003 , by Peters, et al., and also from Engineering Economics 4N04 class notes, McMaster University © 2001-2007. 28
SOLUTIONS
8-2: Assume total capital is F: F = working capital + fixed capital = 0.25 F + 10 x 106 Hence F = $ 13.33 x 106 ROI = NPAT / F = 3 x 106 / 13.33 x 106 = 0.225 or 22.5 % PBP = Fixed capital / (NPAT + D) = 10 x 106 / (3 x 106 + 1 x 106 ) = 2.5 years
Material used in this lecture is sourced from "Plant Design and Economics for Chem. Engineers", 5th ed. McGraw Hill, © 2003 , by Peters, et al., and also from Engineering Economics 4N04 class notes, McMaster University © 2001-2007. 29
8-8: GI = $ 8,000,000 E = $ 2,000,000 D = $ 9,000,000 / 10 = $ 900,000 per year NPAT = (GI – E – D)( 1-Te ) = (8,000,000 – 2,000,000 – 900,000) (1-0.35) = $ 3,315,000 ROI = NPAT / F = $ 3,315,000 / $ 10,000,000 = 0.3315 or 33.15 % CFAT = NPAT + D = $ 3,315,000 + $ 900,000 = $ 4,215,000 PBP = Fixed capital / CFAT = $ 9,000,000 / $ 4,215,000 = 2.14 years
Material used in this lecture is sourced from "Plant Design and Economics for Chem. Engineers", 5th ed. McGraw Hill, © 2003 , by Peters, et al., and also from Engineering Economics 4N04 class notes, McMaster University © 2001-2007. 30
8-9: Compare total costs over the 20 years period: Total cost without sprinklers = total insurance cost Total cost with sprinklers = total insurance cost + Installation + Maintenance Insurance without sprinklers = 20 (0.011) (500,000) + (0.0095) (400,000) = $186,000 Insurance with sprinklers = (0.75) 20 (0.011) (520,000) + (0.0095) (400,000) = $143,000 Total cost with sprinklers = $143,000 + $20,000 + 20(300) = $169,000 Savings in 20 years with sprinklers = $186,000 - $169,000 = $17,000 Average annual savings = $17,000/20 = $850 ROI = annual savings / total capital = 850 / 20,000 = 0.0425 or 4.25 % Note that since the savings are the objective here, we can use annual savings instead of NPAT to estimate ROI. The current operation yields a return of 8% which is higher than the return with the sprinklers. Economically, the sprinklers do not make financial sense. However, for safety reasons and risk point of view, installing the sprinklers would probably be advisable.
Material used in this lecture is sourced from "Plant Design and Economics for Chem. Engineers", 5th ed. McGraw Hill, © 2003 , by Peters, et al., and also from Engineering Economics 4N04 class notes, McMaster University © 2001-2007. 31
8-10:
CFAT = CFBT - taxes = (GI-E-P+S) - (GI-E-D)(t)
Interest rate = 0.15
Tax rate = 0.35
Note that P is the total capital invested, i.e. $ 57.5 million
Note also that D is based only on fixed capital, since the working capital is not depreciated.
All entries are in $ million
YEAR GI E P/S MACRS rate % D CFAT
0 -57.5 -57.50
1 7.0 4.0 20.00 10 5.45
2 10.0 5.6 32.00 16 8.46
3 15.0 6.8 19.20 9.6 8.69
4 20.0 7.8 11.52 5.76 9.95
5 22.5 8.8 11.52 5.76 10.92
6 24.0 9.6 5.76 2.88 10.37
7 25.0 10.0 9.75
NPV = ($21.39)
DCFRR = 2.4%
Clearly, this project must be rejected.