Term used to measure the amount of profit from a certain investment
Total Profit cannot be used as means of comparing investments.
Example:
Investment Profit
$ 100,000 10,000$/yr
$ 1,000,000 25,000$/yr
The second investment has a larger profit. However, when the profit is compared to the investment, the first investment looks better.

1) RATE OF RETURN (ROI)
ROI=
Pr ofit After Taxes ( PAT )
TCI
(If Depreciation is not included in PAT, use CASH
FLOW instead)
Since equipment depreciate, it is better to use average values over the life of the project .
Averaged Annual Pr ofit
ROI=
Averaged TCI
Averaged TCI = FCI -Salvage Value + Working Capital

Incorporate a certain Minimum Profit desired as a fictitious expense
ROI=
Income

Expense

Min . Pr ofit
TCI
Return calculated in this manner gives the
RISK EARNING RATE
Caution: It is better to use CASH FLOW instead of INCOME-EXPENSE
Return of Investment is a point value.
Calculations are done for a particular or average year.
* No time value of money is included

Assume
1) A loan at interest i is used to finance
the project.
2) The cash flow of the project is used
to pay principal and interest.
Then ROI = i
EXAMPLE:
FCI = $100,000 Year CF
WC = $ 10,000 1 $ 30,000
V
S
= $ 10,000 2 $ 31,000
n = 5 years 3 $ 36,000
4 $ 40,000
5 $ 43,000
We calculate the future worth of the proceeds at the end of the 5 years (or the cash flow of the project, compounded on the basis of end-of-year income)
S = 30,000 (1+ i ) 4 + 31,000(1+ i ) 3 + 36,000 (1+ i ) 2 +
+ 40,000 (1+ i ) + 43,000
S= n 
CF a
(1+ i ) n-a

CF a
: predicted cash flow for year a
We calculate now the amount of money needed to pay the loan :
V= 110,000 (1+ i ) 5 = TCI(1+ i ) n
Therefore, the future worth of proceeds corrected for salvage value and working capital (recovered at the end) should be equal to V
V=S+V
S
+WC
110,000 (1+ i) 5 = 30,000 (1+ i) 4 + 31,000 (1+ i) 3 +
+36,000 (1+ i) 2 +40,000(1+ i)
+43,000+10,000+10,000
TCI(1+i) n = n 
CF a
(1+i) n-a +V
S
+WC
This is a polynomial of degree n. Solve it, i.e. find the root.
For the example i =0.207 ROI=20.7%
Note : i corresponds to zero future value of proceeds as compared to the FCI.

Present Value of Investment =
Present Value of Cash Flows
TCI = n 
CF a
(1+i) -a +(V
S
+WC)(1+i) -n
So, if the cash flow is equal for all years
(the simplest situation possible), then
TCI =CF n 
(1+i) -a +(V
S
+WC)(1+i) -n

Present value of annual cash flows - initial investment.
EXAMPLE : Same data as before.
Assume the capital of the company is normally put at 15% interest.
Year Cash Flow Present Value
1 $ 30,000 $ 26,087 (
=30,000/(1+i)
)
2 $ 31,000 $ 23,440 (
=31,000/(1+i) 2
)
3 $ 36,000 $ 23,670
4 $ 40,000 $ 22,870
5 $ 43,000
+ $ 20,000 $ 31,332
TOTAL = 127,399
NET PRESENT WORTH = $127,399+
- $110,000 =
$17,399

NPW= a

1 n 

1
CF a +
CF n

V
S

WC
- TCI

Useful for comparing alternatives within a single project. (Recall the stainless steel vs. Mild steel reactor example)
BASIC EQUATION :
K = C
V
+
( 1

C
R i ) n

1
But C
V
= C
R
+V
S.
Then
K = C
R
( 1
( 1
 i ) i ) n
 n

1
+ V
S
( 1
( 1
 i ) i n
) n
 
1
: Capitalized Cost factor.
K is the amount of money needed initially to purchase equipment and perpetually replace it.

Extension to include Operating Costs
Consider operating costs as a piece of equipment that lasts for one year and has zero scrap value.
Calculate the present value of each year’s cost
(as in net present worth method) and then calculate the capitalized cost of these annual cash expenses. (K
O
).
EXAMPLE : Assume i =15% and the following Operating Costs.
Year Op. Costs Present Value
1 $ 30,000 $ 26,087
2 $ 30,000 $ 22,684
3 $ 30,000 $ 19,725
4 $ 30,000 $ 17,153
5 $ 30,000 $ 14,915
TOTAL = $ 100,565
K
O
= $ 100,565
5
( . ) 5

1
= $ 200,000

Therefore :
Net present worth of annual Op. Costs: a


1
C a 
1
( 1 i ) a
Capitalized Cost of annual Op. costs
K
O
=
( 1
( 1
 i ) i n
) n
 
1 a


1
C a 
1
( 1 i ) a
If C a
is equal for all years, then :
K
O
=
( 1
( 1
 i ) i n
) n
 
1
C
1
1 i
General formula
Cap. Cost = K + K
O
+ Working Capital

Minimum length of time needed to recover the investment in a form of cash flow.
Payout =
FCI
Average Cash Flow
Other names are : Payback, Payoff, Cash
Recovery period.
Inclusion of Interest
Payout =
FCI

Interest on TCI
Average Cash Flow
Interest on TCI is calculated as annual cash flows discounted at interest rate I to get an average annual value.

Need to compare with other investments and their risks
Investment Return Risk
Government 5-7% Almost
Bonds none
Preferred Stock 7-9 % Some
Common Stock >9 % Higher

EXAMPLE
Investment Profit ROI
$ 1,200,000 $ 240,000 20 %
$ 2,000,000 $ 300,000 15%
Assume your minimum profitability is 10%
If amount of investment is not the issue, we are faced with two options:
1) Invest 1,200,000 and put
$800,000 in some other place
2) Invest $2,000,000
INCREMENTAL INVESTMENT
Incremental investment =$800,000
Incremental profit =$ 60,000.
This corresponds to a ROI of 7.5%.
Bad deal !! Put the $800,000 in some other investment.

EXAMPLE : Consider a heat exchanger installation to recover energy. Assume there are
4 alternatives.
ALT. FCI OPER. VALUE OF
COST HEAT SAVED
1 $10,000 $100 $4,100
2 $16,000 $100 $6,000
3 $20,000 $100 $6,900
4 $26,000 $100 $8,850
Assume a depreciation of 20%/yr and a minimum ROI of 10
% Then
Savings=Value-depreciation-Operating costs
ALT. SAVINGS ROI INCREMENTAL
(over ALT 1)
1 $2,000 20 % -
2 $2,700 16.9% 11.7%
3 $2,800 14 % 2.5%
4 $3,550 13.6 % 8.5%
Pick Alternative 2