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.