Lecture # 11 measures of profitability i

Lecture # 11
Measures of profitability
1 Dr. A. Alim

MEASURES OF PROFITABILITY
• We need a systematic method for comparing
expenses and incomes at different times
• We need to compare the project profitability with a
norm or minimum acceptable performance
• Many measures are in use; we’ll look at four.
- Two include time value of money. These are
almost always used.
- Two do not include time value of money. These
are only used for initial screening, but are not
recommended for final decision making.
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

Key Relationships
For any year:
CFBT = GI – E – P + S
= GI – E For years 1 to (n-1)
Taxable income TI = GI – E – D
Taxes = TI (te)
Net Profit after taxes = Np = TI (1-te)
CFAT = A = Np + D only for years 1 to (n-1)
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,
5
Important reminder:
Taxable income (TI) does not include P, S, or W
…just (GI-E-D)!

1. RETURN ON ORIGINAL INVESTMENT(ROI)
• Simple calculation
• Defined as: ROI = NP, av. / F
= (average annual profit)/(fixed capital + working
capital)
• Expressed in units of %/yr
• For acceptable investment ROI >MARR >Cost of
capital
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Example, ROI calculation:
Interest in converting trucks fueled by Diesel to run on compressed natural gas
(CNG) has been increasing in recent years. Studies have shown that 25%
savings in fuel cost/mile are achievable.
The following information is available for a certain truck being considered for
such conversion. Calculate the expected ROI for this project:
Annual miles driven = 30,000 miles/year
Truck diesel fuel economy = 8 miles per gallon (MPG)
Cost of diesel fuel = $ 4 per gallon
Conversion hardware cost (tanks, valves, etc…) = $15,000
Solution:
Diesel fuel cost per year = [(30,000 miles/year) / (8 miles/gallon)] x (4
$/gallon) = 15,000 $/year
Annual fuel cost savings with CNG = 0.25 x 15,000 = $3750
Therefore ROI = 3750/15,000 = 25 % per year
In addition to cost savings, there are also environmental benefits.

2. PAYBACK PERIOD (PBP)
• This measure is often used as a “quick and dirty” measure of
profitability. Also called Payback Time
• Defined in units of time (months or years):
- The time for the cumulative cash flow (CFAT) from operation to
recover the fixed capital.
Usually , payback period does not consider time value of money.
However, time value of money could be considered if discounted CFAT
are used.
• The CFAT used in PBP calculation is the cash flow from operation only.
It does not include the initial investment in year 0, or the recovery of
salvage value or working capital in the last year of operation.
• Therefore, for PBP calculation we should use the equation:
CFAT = NPAT + D (and not CFAT = CFBT – taxes) .
. It is therefore recommended to use CFAT = NPAT + D for all years
from 1 to n.
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PAYBACK PERIOD (PBP)
• PBP = Fixed capital / Average annual cash flow after tax
= Fixed capital / A av.
• Aav is average annual cash flow after tax for years 1 to n.
• It is recommended to use “ CFAT = NPAT + D” for all years from 1 to
n.
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Example: PBP*
Period Cash Flow (k$)
0 -1000
1 475
2 400
3 330
4 270
5 200
• A project with initial investment of k$ 1000
(all fixed) has the following series of CFAT.
What is the PBP of this project?
* Jelen’s cost and optimization engineering, third edition, McGraw Hill
1991. Page 104
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• The average annual cash flow is:
(475 + 400 + 330 + 270 + 200) / 5 = 335
Hence: Payback Time = 1000/335  3
years
• Note:
- No time value of money
12

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PAYBACK PERIOD (PBP)
• PBP = Fixed capital cost / Average annual cash flow after tax
• For acceptable investment PBP should be ≤ PBP ref
• PBP ref is defined as PBP when ROI = MARR
• Since fixed capital is usually 0.85 F; where F is the total capital invested:
PBP = 0.85F/A av. = 0.85F / ( Np+ D ) av.
• ROI = Np / F or NP = ROI * F
• When ROI = MARR → NP(at MARR) = MARR*F
PBP ref = 0.85F/{(MARR)*F) + (0.85F/n)} = 0.85/(MARR +(0.85/n))
this is Np this is D
Generally, if R = Fixed capital / Total capital, then:
PBP ref = R / (MARR + R /n)
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Limitations of PAYBACK PERIOD method:
1) It neglects any required return, since the time value of money is
omitted.
2) It also neglects all net cash flows after the PBP, including
positive cash flows that may contribute to the return on the
investment.
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3. NET PRESENT WORTH or VALUE (NPW) or (NPV)
• Explicitly considers time value of money
• Defined as present value of all after-tax cash flows
• Must be positive for acceptable investment.
• For n compounding periods in the life of the project, with
net cash flow at each period = An
• NPV is calculated at interest rate = MARR
FiANPV
N
n
n
n  

1
)1(
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Period Cash Flow
(k$)
0 -1000
1 475
2 400
3 330
4 270
5 200
• Calculate the NPV for this project at 10%
Class Exercise: Net Present Value
(NPV)
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• Calculate the NPV for this project at 10%
NPV = -1000 + 475/(1.1) + 400/(1.1)2 + …. =
Note - Considers time value of money explicitly
Class Exercise: Net Present Value
(NPV)
і = 0.1
n 0 1 2 3 4 5
C -1000 475 400 330 270 200
PV -1000 431.82 330.58 247.93 184.41 124.18 sum = 318.93
Alternatively, we can use Excel NPV function:
NPV = NPV(0.10,A1:A5) + A0
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4. DISCOUNTED CASH FLOW RATE OF RETURN (DCFRR)
Also called, Discounted Cash Flow (DCF) or
Internal Rate of Return (IRR)
Defined as the interest rate that results in a NPV value of 0.0
DFCRR must be ≥ MARR for acceptable investment.
0)1(
1
 

FiANPV
N
n
n
n
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Period Cash Flow
(k$)
0 -1000
1 475
2 400
3 330
4 270
5 200
• Calculate the DCFRR for this project
Class Exercise: Discounted cash
flow rate of return (DCFRR)
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• Calculate the DCFRR for this project
NPV = -1000 + 475/(1+i) + 400/(1+i)2 + …. = 0
DCFRR = i = .2393 or 23.93% (By trial and error)
• Note - Considers time value of money explicitly
і = 0.2393
n 0 1 2 3 4 5
C -1000 475 400 330 270 200 23.93%
PV -1000 383.2809 260.4396 173.3742 114.4611 68.41444 sum = -0.02968
Alternatively we can use the Excel IRR function:
DCFRR = IRR(A0:A5)
21Material used in this lecture is sourced from "Plant Design and Economics for Chem. Engineers", 5th

Profitability vs. Cash Flow
• Assume Companies A & B make the same product, in
same quantities and have the same gross income
(revenues) GI of $100,000 per year
• Annual expenses are $50,000/yr for both
• A produces products on a machine worth $200,000 and
has a life of 5 years
• B's machine also costs $200,000, but has a useful life
of 10 years
• MARR is 5% for both companies.
Cash flow before taxes (CFBT)
For A = $100,000 - $50,000 = $50,000/yr
For B = $100,000 - $50,000 = $50,000/yr
NO DIFFERENCE!
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Net Profit after Taxes (NPAT)
•Taxable Income (GI – E – D):
A = $100,000 - $50,000 - (200,000/5) = $10,000/yr
B = $100,000 - $50,000 - (200,000/10) = $30,000/yr
• Taxes @ (50%)
A = 0.50($10,000) = $5,000/yr
B = 0.50($30,000) = $15,000/yr
• NPAT
(Taxable income) - (Taxes)
A = 10,000 - 5000 = $5,000
B = 30,000 - 15,000 = $15,000
• CFAT = [CFBT - Taxes]
A = $50,000 - $5,000 = $45,000
B = $50,000 - $15,000 = $35,000
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Which company is better?
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A B
F (total = fixed) $200,000 $200,000
MARR 5% 5%
CFAT $45,000 $35,000
NPAT $5,000 $15,000
n 5 10
D $40,000 $20,000
Profitability analysis assuming MARR = 5%
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A Acceptable
?
B Acceptable
?
ROI
%
5,000/200,000
= 2.5%
NO 15,000/200,000
= 7.5%
YES
PBPref
years
1/(0.05 + 1/5)
= 4.00
1/(0.05 + 1/10)
= 6.67
PBP
years
200,000 / 45,000
= 4.44
NO 200,000 / 35,000
= 5.71
YES
NPV
$
-$5,173
EXCEL
NO $70,261
EXCEL
YES
IRR
%
4%
EXCEL
NO 12%
EXCEL
YES
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n CFAT n CFAT
0 -200000 0 -200000
1 45000 1 35000
2 45000 2 35000
3 45000 3 35000
4 45000 4 35000
5 45000 5 35000
6 35000
7 35000
8 35000
9 35000
10 35000
NPV = ($5,173.55) NPV = $70,260.72
IRR = 4% IRR = 12%
Company A Company B
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Which company is better?
• Company B is better as shown by profitability analysis
• Higher cash flow is not necessarily better. Profitability
analysis should be used to select the better alternative.
• A has “turned” more of its assets into cash, but is using its
assets less efficiently (shorter useful life!)
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Lecture # 11 measures of profitability i

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