11 Profitability Parameters

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Cash flow diagram

Cash flow diagram

Operation

Operation

Revenue

Revenue Cash operatingCash operating_{expensesexpenses}

Operating income Operating income Depreciation Depreciation Depletion Depletion Gross profit Gross profit Net profit Net profit Income tax Income tax Cash flow Cash flow

Profitability



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

1.

Rate of return on investment

Payout period

3.

Net present worth

4.

Discounted cash flow based on full-life

Rate of return on investment

WC 

 FC 

 profit 

annual 

 ROI 

investment 

capital 

total 

 profit 

annual 

 ROI 

  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 o

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

 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

Net Present Worth (NPW)

 The calculations may be made using discrete or

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.

 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

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

a. Computation of net present worth

Year Estimated cash flow, $

i = 0.15

Discount factor: Present value, $

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 127,000





NPW = $127,000

$110,000 = $17,000

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

Year Estimated cash flow, $

Trial i = 0.15

Discount factor: Present value, $

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 1,155





Year Estimated cash flow, $

Trial i = 0.1763

Discount factor: Present value, $

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 1,0000





DCFRR with discrete interest = 17.63%

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

c. Cash flow for computation of discounted-cash-flow 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

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

Year Estimated cash flow,

$

Trial i = 0.2249

Discount factor: Present value, $

Fb 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 6,496 Total 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.

 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, 4

_{ed., McGraw Hill, New}

York, 1991



Couper, J.R., Process Engineering

Economics, Marcel Dekker, Inc., New

York, 2003