- The document discusses various methods for evaluating the profitability and desirability of potential investment ventures, including net present value (NPV), internal rate of return (IRR), payback period, and discounted cash flow rate of return (DCFROR). - It provides examples of calculating these metrics for projects with cash flows over multiple time periods, including determining the IRR through trial-and-error calculations. - Present value profiles, which plot NPV against discount rates, can help compare projects and identify the IRR at which a project's NPV equals zero.

1. ECONOMIC STUDIES

2. OUTLINE
➢ NET CASH FLOW (NCF)
CALCULATIONS
➢ DEPRECIATION
➢ DEPLETION
➢ AMORTIZATION
➢ TIME VALUE OF MONEY
➢ PROFITABILITY OF A VENTURE

3. PROFITABILITY OF A VENTURE
❖ This is the yardstick for measuring the
productivity of individual investment. Companies
usually consider the possible benefits they may
derive from ventures before investing money.
❖ The financial benefits, expressed by the
profitability of the investments are measured by
profitability criteria, profit indicators or
economic yardsticks.

4. PROFITABILITY OF A VENTURE
There are two kinds of yardsticks:
Screening – which ventures meet the minimum
qualifications to be considered for investment.
Ranking – which of two or more mutually exclusive
ventures is the most desirable.
NOTE: No single criterion tells us everything about profitability.
So we normally choose the criterion that gives the management the
maximum amount of information about economic factors.

5. PROFITABILITY OF A VENTURE
PAYOUT (PAYBACK) PERIOD
This is the time required for the cumulative net earning to equal the initial
investment. It measures the speed with which invested funds are returned to the
business.
The shorter the period, the better and the higher the project is rated.
PROJECT A B
Investment 250,000 250,000
Annual Income 50,000 75,000
Payout 250,000/50,000 250,000/75,000
= 5.00 years = 3.33 years
Project B, with a shorter payout period would be the better investment proposal.

6. DISCOUNTED PROFIT-TO-INVESTMENT
RATIO (DPR)
It is defined as the ratio of total net profit to the
investment.
i = minimum acceptable ROR
➢ It is used when money is limited but you have
several investments options.
STRATEGY
> Maximize DPR

7. NET PRESENT VALUE (NPV)
The net present value (NPV) or net present worth profit is
the algebraic sum of all net cash flows when discounted to
time zero using a single discounting rate.
STRATEGY FOR SELECTION
1)Accept projects that maximize NPV profit and reject all
project having negative NPV profit (except to meet
certain objectives – pollution control to meet standards)
2)The greater the positive NPV for a project, the more
economically attractive it is.
PROFITABILITY OF A VENTURE

8. WORKED EXAMPLE
The cost of putting a well on stream is $1,500,000. The after tax cash flows
generated by the investment for six years are:
The end of year convention is used. Annual compounding is also used. Using an
average reinvestment rate of 15%, calculate the net present profit of the cash
flow.
Year Cash Flow (Revenue)
($)
1 1,000,000
2 800,000
3 600,000
4 400,000
5 200,000
6 100,000
Total 3,100,000

9. SOLUTION
Year Net cash flow Discount Factor Discounted C-Flow
($) i= 0.15 ($)
0 -1,500,000 1.0000 -1,500,000
1 1,000,000 0.8696 869,960
2 800,000 0.7561 604,880
3 600,000 0.6575 394,500
4 400,000 0.5718 228,720
5 200,000 0.4972 99,440
6 100,000 0.4323 43,230
NPV i=0.15 740,730
CONCLUSION
The NPV discounted at 15% is positive. This means that the six years
cash revenues are preferred to our initial investment of $1,500,000 if
the discount rate is 15%. If we invest the $1,500,000 we would make
a 15% rate of return plus increase our net worth by $740,730 over 6
yrs.

10. NET PRESENT VALUE (NPV)
•The NPV takes account of all earnings throughout the
expected life of the asset. When comparing alternatives
with different expected lives, assumption is made in the
evaluation of the future rates that a company’s fund can
earn.
•For this criterion, it remains a problem to determine the
minimum acceptable rate of return that projects are
expected to earn to justify investment of the business’s
funds.
•The rate of return should be above the cost of capital to
the firm. If not, no need to invest.

11. NET PRESENT VALUE (NPV)
The minimum acceptable rate of return to use in the NPV calculation is usually
set by top management after consideration of at least some of the following
factors:
1. Future investment opportunities and their anticipated
rate of earnings.
2. If investment capital borrowed, i* must at least exceed
the interest rate of the loan, or should at least exceed
the average cost of capital.
3. Corporate growth objectives (the rate at which
management has set for annual growth rate of
treasury) should be taken into account.

12. MID-YEAR PAYMENT

13. EXAMPLE (MID-YEAR PAYMENT)
The capital cost of natural gas treatment plant is $31,000 and the earning life
of the plant will be 6years. The net incomes in these 6 years will be $5,000;
$12,000; $13,000; $12,000, $12,000, and $8,000 respectively. Calculate the
undiscounted per cent profit and payout time, the discounted values using a
discount rate of 10% and the rate of return. Assume that income is paid as a
lump sum at the midpoint of the year.
SOLUTION
Year Undis- Cumu Un- Undis- Discount Factor Dis- Cumu Discounted
discounted discounted discounted counted Discounted profit
net income net income profit net income net income
1 5,000 5,000 (26,000) 1/(1.1)1/2
= 0.9535 4,768 4,768 (26,232)
2 12,000 17,000 (14,000) 1/(1.1)3/2
= 0.8668 10,402 15,170 (15,830)
3 13,000 30,000 (1,000) 1/(1.1)5/2
= 0.788 10,244 25,414 (5,586)
4 12,000 42,000 11,000 1/(1.1)7/2
= 0.716 8,592 34,006 3,006
5 12,000 54,000 23,000 1/(1.1)9/2
= 0.651 7,812 41,818 10,818
6 8,000 62,000 31,000 1/(1.1)
11/2
= 0.592 4,736 46,554 15,554

14. From the Table: Undiscounted Profit = $62,000 - $31,000 = $31,000
Undiscounted % Profit = $31,000/$31,000 x 100 = 100%
Similarly: Discounted Profit = $46,554 - $31,000 = $15,554
Discounted % Profit = $15,554/$31,000 x 100 = 50.2%
-40000
-30000
-20000
-10000
0
10000
20000
30000
40000
0 2 4 6 8
Cumulative
Profit
Time (Year)
Cumulative Profit vs Time plot
Undiscounted
Discounted at 10%

15. From the graph of Cumulative profit versus time:
Undiscounted Payout time = 3.15 years
Discounted Payout time = 3.65 years
Plotting the Cumulative discounted net income against various discount rates gives
the project ROR as 27.6%
-
10,000
20,000
30,000
40,000
50,000
60,000
70,000
0 5 10 15 20 25 30 35
Cumulative
discounted
net
income
Discount Rate (%)
ROR
Capital cost of project

16. DISCOUNTED CASH FLOW RATE OF RETURN
(DCFROR)
It is defined as the discount rate that makes the NPV of a project
equal to zero. It is also known as internal rate of return (IRR), rate of
return (ROR). It is expressed as:
Or in the continuous form as:

17. PROCEDURE TO CALCULATE DCFROR
It is calculated by a trial-and-error series of calculations
•List the annual cash flow.
• Select a discount rate and list the discount factors.
• Calculate the present value of each annual cash flow and
add the discounted values to obtain the NPV of the cash
flow.
• If the NPV is positive, select a higher discount rate. If
negative, select a lower discount rate.
• After several trials and the zero NPV is bracketed,
interpolate to find the DCFROR.

18. WORKED EXAMPLE
The cost of putting a well on stream is $1,500,000. The after tax cash flows
generated by the investment for six years are:
The end of year convention is used. Annual compounding is also used. Calculate
the DCFROR for the cash flow.
Year Cash Flow (Revenue)
($)
1 1,000,000
2 800,000
3 600,000
4 400,000
5 200,000
6 100,000
Total 3,100,000

19. SOLUTION
This involves trial and error computation. The final stages
of the computation are as follows:
Yr NCF DFactor DCF DFactor DCF
($) i= 0.35 ($) i= 0.45 ($)
0 -1,500,000 1.0000 -1,500,000 1.0000 -1,500,000
1 1,000,000 0.7407 740,740 0.6897 689,655
2 800,000 0.5487 438,957 0.4756 380,499
3 600,000 0.4064 243,865 0.3280 196,810
4 400,000 0.3011 120,427 0.2262 90,487
5 200,000 0.2230 44,603 0.1560 31,203
6 100,000 0.1652 16,520 0.1076 10,759
NPV i=0.35 105,112 NPV i=0.45 -100,587

20. SOLUTION
Interpolating between 0.35 and 0.45:
DCFROR = 0.35 + {105,112/(105,112 + 100,587)} (0.10)
= 40.11%
Hence investing $1,500,000 to buy the future series
of six annual revenues is equivalent to investing
$1,500,000 in a project that pays 40.11%
compound annual interest.

21. PRESENT VALUE PROFILE
Much of the confusion that results from the use of profitability criteria can
be eliminated by plotting the present value profit versus the discount rate.
This curve is called the present value profile.
The present value profile for the prospect considered in the last worked
example is as shown below.

22. PRESENT VALUE PROFILE
0 1600000
15 740730
35 105112
45 -100587
-200000
0
200000
400000
600000
800000
1000000
1200000
1400000
1600000
1800000
0 10 20 30 40 50
NPV
Discount Rate
PRESENTVALUE PROFILE

23. PRESENT VALUE PROFILE
The point where the profile crosses the discount
axis is the ROR of about 40%.
For discount rates less than 40% , NPV is positive
hence accept if the cost of capital is less than 40%.
For discount rates greater than 40%, NPV is
negative, hence reject the prospect.
Changes in the initial investment simply shift the
profile in the vertical direction by the amount of
this change.

24. PROFITABILITY OF TWO PROPOSALS
Compare the profitability of the following two
investment proposals:
• Proposal A: An investment of $100,000 today to
receive $120,000 continuously in one year.
• Proposal B: An investment of $100,000 today to
receive $200,000 continuously in seven years.
Use continuous compounding method.

25. Rate NPV of NPV of
(j) A B
0 20000 100000
5 17049 68750
10 14195 45833
15 11434 23821
20 8762 7629
25 6176 -5574
30 3673 -16424
35 1250 -25412
40 -1096 -32915
45 -3368 -39229
50 -5567 -44583
Data for preparation of the present value profile are shown
below using the continuous compounding relationship.
Profitability of two investments proposals

26. Rate A B
0 20000 100000
5 17049 68750
10 14195 45833
15 11434 23821
20 8762 7629
25 6176 -5574
30 3673 -16424
35 1250 -25412
40 -1096 -32915
45 -3368 -39229
50 -5567 -44583
-60000
-40000
-20000
0
20000
40000
60000
80000
100000
120000
0 20 40 60
NPV
Discount Rate
PV Profiles for ProposalsA & B
Proposal A
Proposal B
Profitability of two investments proposals
The present value profiles for proposals A and B are shown
below

27. Profitability of two investments proposals
Proposal A has a discounted cash flow rate of
return of 37.5% and a net profit of $20,000 while
Proposal B has a discounted cash flow rate of
return of 22.8% and a net profit of $100,000.
Using the profit-to-investment ratio, B is a better
option than A. However, P/I does not reflect the
time-rate pattern of income from the prospects.
This is one of the weakness of the P/I ratio.

28. Profitability of two investments proposals
The discounted cash flow rate of return indicates A to be
better proposal, while the NPV at 15% indicates B to be
the better proposal.
The present value profiles give the whole picture. The
profile intersect at a discount rate of 19.5%. This is the
break-even point.
NOTE:
B/w: 0-19.5: B is good At 19.5: Both are good
B/w: 19.5-40.11: A is good > 40.11: Both are not good

29. CONFLICT BETWEEN PROFIT INDICATORS
> Determine (Y-X)
> Handle by PV indicator
For PV @ 10%: Project Y is better than X
DCF : Project X is better than Y
Which ONE do we choose?
Determine the PV of (Y-X); if positive then Y is better.
Hence: Y is better than X
Yr X Y Y-X
0 -85 -87 -2
1 100 38 -62
2 38 38
3 38 38
Total 15 27 12
DCF 38% 21% 12%
PV@10% 10 13 3

30. INCREMENTAL CASH FLOW
Note
Primary production is better since it has lower PBP and higher P/I at
i of 20%.
If i =20%, and (Y-X) is 28%, then we can do waterflooding (optional).
If i = 30%, and (Y-X) is 28%, then do not waterflood.
Yr X-Primary Y-Flooding Y-X
0 -20 -260 -240
1 100 70 -30
2 90 200 110
3 80 400 320
4 70 100 30
5 60 70 10
Total 380 580 200
PBP 0.2 yrs 2 2.5
P/$ 19 2.23 0.83
DCF > 100% 74% 28%