11 Profitability Parameters

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Cash flow diagram Cash flow Revenue Operation

Cash operating expenses

Operating income Depreciation Depletion

Gross profit

Net profit Income tax

Profitability 

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The word profitability is used as the general term for the measure of the amount of profit that can be obtained from a given situation. Total profit alone cannot be used as the deciding profitability factor in determining if an investment should be made. The profit goal of a company is to maximize income above the cost of the capital which must be invested to generate the income.

Profitability Evaluation Rate of return on investment 2. Payout period 3. Net present worth 4. Discounted cash flow based on full-life performance 1.

Rate of return on investment  ROI    ROI  

annual   profit  total capital  investment  annual   profit   FC  WC 

100%

100%



 A proposed manufacturing plant requires an initial fixed-capital investment of $900,000 and $100,000 of working capital. It is estimated that the annual income will be $800,000 and the annual expenses including depreciation will be $520,000 before income taxes. A minimum annual return of 15 percent before income taxes is required before the investment will be worthwhile. Income taxes amount to 34 percent of all pre-tax profits.

Example 1 Determination of rate of return on investment-consideration of income-tax effects 

Determine the following: (a) The annual percent return on the total initial investment before income taxes. (b) The annual percent return on the total initial investment after income taxes. (c) The annual percent return on the total initial investment before income taxes based on capital recovery with minimum profit. (d) The annual percent return on the average investment before income taxes assuming straight-line depreciation and zero salvage value.

Example 1 Determination of rate of return on investment-consideration of income-tax effects (a) Annual profit before income taxes = $800,000 $520,000 = $280,000.  Annual percent return on the total initial investment before income taxes = [280,000/(900,000 + 100,000)].(100) = 28 percent. (b) Annual profit after income taxes = ($280,000)(0.66) = $184,800.  Annual percent return on the total initial investment after income taxes = [184,800/(900,000 + 100,000)].(100) = 18.5 percent.

Example 1 Determination of rate of return on investment-consideration of income-tax effects (c) Minimum profit required per year before income taxes = ($900,000 + $100,000).(0.15) = $150,000. Fictitious expenses based on capital recovery with minimum profit = $520,000 + $150,000 = $670,000/year.  Annual percent return on the total investment based on capital recovery with minimum annual rate of return of 15 percent before income taxes = [($800,000 670,000)/(900,000 + 100,000)].(100) = 13 percent. (d) Average investment assuming straight-line depreciation and zero salvage value = $900,000/2 + $100,000 = $550,000.  Annual percent return on average investment before income taxes = (280,000/550,000).(100) = 51 percent.

Payout period Other equivalent names are payback period, payback time, payoff period, payoff time, and cash recovery period

Example 2. POT 

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Use the data in example 1. In addition, it is estimated that the salvage value at end of service life is $100,000. Use straight line depreciation. Determine the minimum pay-out-time without interest charge. Solution: Depreciable fixed-capital investment = FC  – SV = $900,000 - $100,000 = $800,000 Depreciation = $800,000 / 5 = $160,000 Profit before tax = $800,000 - $520,000 = $280,000 Profit after tax = ($280,000)(0.66) = $184,800 POT before tax = $800,000 / ($280,000 + $160,000) = 1.8 years POT after tax = $800,000 / ($184,800 + $160,000) = 2.3

Net Present Worth (NPW)

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The calculations may be made using discrete or continuous interest.

Rate of Return Based on Discounted Cash Flow 

Common names of methods of return calculations related to the discounted-cash-flow approach are profitability index, interest rate of return, true rate of return, and investor’s rate of return.

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In principle, the technique is similar to the NPW method.  

NPW calculation uses interest rate set by the company. IRR is the calculated interest rate that will produce NPW equal to zero.

Example 3: DCFRR & NPW 

Consider the case of a proposed project for which the following data apply:    

Initial fixed-capital investment = $100,000 Working-capital investment = $10,000 Service life = 5 years Salvage value at end of service life = $10,000

Example 3: DCFRR & NPW  Year

Predicted after-tax cash flow to project based on total income minus all costs except depreciation, $ (expressed as end-of-year situation)

0

- 110,000

1

30,000

2

31,000

3

36,000

4

40,000

5

43,000

Example 3: DCFRR & NPW 

Determine: a. Net Present worth if the value of capital to

the company is at an interest rate of 15 percent b. Discounted-cash-flow rate of return with discrete interest c. Discounted-cash-flow rate of return with continuous interest

a. Computation of net present worth Year

Estimated cash i = 0.15 flow, $ Discount factor: 1 Present value, $

1  i 

n

0

- 110,000

1

30,000

0.8696

26.100

2

31,000

0.7561

23,400

3

36,000

0.6575

23,300

4

40,000

0.5718

22,900

5

43,000 + 20,000

0.4971

31,300

Total

NPW = $127,000 – $110,000 = $17,000

127,000

b. Computation of discounted-cash-flow rate of return with discrete interest Year

Estimated cash Trial i = 0.15 flow, $ Discount factor: 1 Present value, $

1  i 

n

0

- 110,000

1

30,000

0.8696

26.100

2

31,000

0.7561

23,400

3

36,000

0.6575

23,300

4

40,000

0.5718

22,900

5

43,000 + 20,000

0.4971

31,300 127,000

 Ratio

total  present  value 

total investment 

Trial i, to get ratio = 1

1,155

b. Computation of discounted-cash-flow rate of return with discrete interest Year

Estimated cash Trial i = 0.1763 flow, $ Discount factor: 1 Present value, $

1  i 

n

0

- 110,000

1

30,000

0.8501

24852

2

31,000

0.7227

21273

3

36,000

0.6143

20465

4

40,000

0.5222

18837

5

43,000 + 20,000

0.4440

24577 110005

 Ratio

total  present  value 

total investment 

DCFRR with discrete interest = 17.63%

1,0000

c. Cash flow for computation of discounted-cashflow rate of return with continuous interest Year

Predicted after-tax cash flow to project based on total income minus all costs except depreciation with cash flow occurring continuously, S (total of  continuous cash flow for year indicated)

1

30,000

2

31,000

3

36,000

4

40,000

5

43,000

c. Computation of discounted-cash-flow rate of return with continuous interest Year

Estimated cash flow, $

Trial i = 0.2249 Discount factor: Fb

Present value, $

Fa

0

- 110,000

0 – 1

30,000

0.8955

26,866

1 – 2

31,000

0.7152

22,170

2 – 3

36,000

0.5711

20,561

3 – 4

40,000

0.4561

18,244

4 – 5

43,000

0.3642

15,663

5

+ 20,000

0.3248 Total

6,496 110,000

Trial i, to get total PW = 110,000

DCFRR with continuous interest = 22.49%

c. Computation of discounted-cash-flow rate of return with continuous interest 

Fa = Discount factor to give present worth for cash flows which occur in an instant at a point in time after the reference point.

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Fb = Discount factor to give present worth for cash flows which occur uniformly over one-year periods after the reference point. (S is the total cash flow for the nth year.)

References Peters, M.S., Timmerhaus, K.D., Plant Design and Economics for Chemical Engineers, 4th ed., McGraw Hill, New York, 1991  Couper, J.R., Process Engineering Economics, Marcel Dekker, Inc., New York, 2003 