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.

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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.

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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)

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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. 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

6 Material used in this lecture is sourced from "Plant Design and Economics for Chem. Engineers", 5th ed.



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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.





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




• 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




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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

FiANPVN

n

n

n

1

)1(

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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

18 Material used in this lecture is sourced from "Plant Design and Economics for Chem. Engineers", 5th



MEASURES OF PROFITABILITY 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

FiANPVN

n

n

n

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Material used in this lecture is sourced from "Plant Design and Economics for Chem. Engineers", 5th





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)





• 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)




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




Which company is better?




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%




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




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




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!)




Lecture # 11 measures of profitability i

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Transcript of Lecture # 11 measures of profitability i