2. What is Project Selection?
• Project Selection is the process of choosing a project rationally in the
light of objectives and inherent constraints on the basis of appraisal.
• Identification of a new project is a complex problem. The project
selection process starts with the generation of project ideas. In order
to select the most promising project, the entrepreneur needs to
generate a few ideas about the possible project one can undertake.
4. Project Selection Process
• Pre-Screening
• Individual Project Evaluation
• Screening
• Portfolio Selection
• Portfolio Balancing and Adjustment
• Model Selection and Development
5. Project Selection Methods
• Payback period
• Average Rate of Return (ARR)
• Net present value Method
• Internal Rate of Return Method
• Profitability index
6. Payback Period
• Payback period can be defined as period of time required to recover its
initial cost and expenses and cost of investment done for project to reach at
time where there is no loss no profit i.e. breakeven point..
• Formula
For even cash flow
Payback Period =
Initial Investment
Net Cash Flow per Period
For uneven cash flow
Payback Period =
A +
B
C
Where,
A is the last period number with a negative cumulative cash flow;
B is the absolute value (i.e. value without negative sign) of cumulative net cash flow at the end of
the period A; and
C is the total cash inflow during the period following period A
Cumulative net cash flow is the sum of inflows to date, minus the initial outflow.
7. Examples
Example 1: Even Cash Flows
• Company C is planning to undertake a project requiring initial
investment of $105 million. The project is expected to generate $25
million per year in net cash flows for 7 years. Calculate the payback
period of the project.
• Solution
• Payback Period
Formula = Initial Investment ÷ Annual Cash Flow
= $105M ÷ $25M
= 4.2 years
8. Example 2: Uneven Cash Flows
• Company C is planning to undertake another project requiring initial
investment of $50 million and is expected to generate $10 million net cash
flow in Year 1, $13 million in Year 2, $16 million in year 3, $19 million in
Year 4 and $22 million in Year 5.
• REQUIREMENT
• Calculate the payback value of the project.
•
Cumulative net cash flow is the sum of inflows to date, minus
the initial outflow.
9. Step 1. Calculate Cumulative Cash Flows
Year
(cash flows in millions)
Annual
Cash Flow
Cumulative
Cash Flow
0 (50) (50)
1 10
2 13
3 16
4 19
5 22
As our investment is cash outflow, so, we denote it as a negative value. Then, we need to add yearly cash inflow. After that, using these
values, we will create the cumulative cash flows column. Follow the steps.
10. Step 2: Calculate Negative Cash Flow Years
Year
(cash flows in millions)
Annual
Cash Flow
Cumulative
Cash Flow
0 (50) (50)
1 10 (40)
2 13 (27)
3 16 (11)
4 19 8
5 22 30
Then, we want to calculate the number of years in which we have negative cash flows. Where
cumulative cash flows are in excess of the primary investment, this is referred to as the break-even
point.
12. Step 4: Estimate Cash Flow for Next Year
Year
(cash flows in millions)
Annual
Cash Flow
Cumulative
Cash Flow
0 (50) (50)
1 10 (40)
2 13 (27)
3 16 (11)
4 19 8
5 22 30
13. Step 5: Calculate Pay back Period
Year
(cash flows in millions)
Annual
Cash Flow
Cumulative
Cash Flow
0 (50) (50)
1 10 (40)
2 13 (27)
3 16 (11)
4 19 8
5 22 30
Payback Period = 3 + 11/19 = 3 + 0.58 ≈ 3.58 years
14. Decision Rule
• The longer the payback period of a project, the higher the risk.
Between mutually exclusive projects having similar return, the
decision should be to invest in the project having the shortest
payback period.
15. Average Rate of Return (ARR)
• The average rate of return is the average return which is
expected out of an investment in its life. It is basically the
amount of cash flows which is getting generated during the
investment period.
• ARR for Even Cash Flow
• Formula= Average Rate of Return = Average Annual
Profit / Initial Investment* 100
16. Examples
• Consider a retail company X which has invested $1 million in a project
which has a life of 4 years. During the project, year wise profit which
the X has earned is given below:
REQUIREMENT:-
COMPUTE= AVERAGE RATE OF RETURN
17. solution
• Formula:- Average Annual Profit= sum of years profit/n
=($76,000 + $45,000 + $89,000 + $67,000) / 4
• Average Annual Profit = $69,250
• Formula for Average Rate of Return
• Formula= ARR= Average Annual Profit / Initial Investment* 100
• Average Rate of Return = $69,250 / $1,000,000* 100
• Average Rate of Return = 6.925%
18. Decision Rule
• When a company is presented with the option of multiple projects to
invest in, the decision rule states that a company should accept the
project with the highest accounting rate of return as long as the
return is at least equal to the cost of capital.
20. Solution:
• Step 1 – Computation of annual depreciation expenses:
• Formula+ (Cost – salvage value)/life of the asset
= ($650,000 – $20,000)/6
= $10,5000
21. • = $97,000
Formula= IAI= Cash inflow-depreciation
Average Income= Sum of NOI/life of the asset
Average income = (45,000 + 115,000 + 195,000 + 145,000 + 75,000 + 7,000)/6
22. Step 3 – Computation of accounting rate of return
(ARR):
• If initial investment is used as denominator:
• Accounting rate of return = Incremental accounting income/Initial
investment
= $97,000/$650,000
= 14.92%
23. Net present value Method
• The net present value formula calculates NPV, which is the difference
between the present value of cash inflows and the present value of cash
outflows, over a period of time.
• Net present value (NPV) determines the total current value of all cash
flows generated, including the initial capital investment, by a project
• Formula=
NPV=Cash flow/ (1+i)t−initial investment
where: i= Required return or discount rate
t= Number of time periods
24. Example
• To begin with, assume a project that requires an investment of Rs
20,000. Rate of return is 8%. The following paragraph lists future cash
flows of the project.
• First year Rs 5,000
• Second year 6,000
• Third year 8,000
• Fourth year 7,000
• Fifth year 4,000
• From the above available information, calculate the NPV.
25. Step 1. Arrange Future Cash Flows
Future cash flow
1st Year 2nd year 3rd year 4th Year 5th year
5000 6000 8000 7000 4000
26. Step 2. Calculate present value of each future
cash flow
Formula for Present Value
Where; FV= future value; k = discounting factor / interest rate and N = Number of time periods
First Year Second Year Third Year Fourth Year Fifth Yea
Future Cash
Flow
5000 6000 8000 7000 4000
Present Value
(PV)
5000 /
(1+0.08)^1
5000 / 1.08
6000 /
(1+0.08)^2
6000 / 1.1664
8000 /
(1+0.08)^3
8000 /
1.259712
7000 /
(1+0.08)^4
7000 / 1.3605
4000 /
(1+0.08)^5
4000 / 1.46953
PV 4630 5144 6351 5145 2722
27. Step 3 Calculation of Net Present Value NPV
• Formula of NPV
• NPV= Sum of Present value- Subtract investment value (cash outflow)
from Sum of Present Value (PV) of all future cash flows
Sum of Present Value
(4630+5144+6351+5145+2722= 23,992
Investment Value 20,000
Net Present Value (NPV) 23,992 – 20,000 = 3,992
28. Step 3. Make a Decision
• In order to arrive at the project selection decision the following
criteria is followed.
• Accept the project if NPV is greater than zero. (NPV > 0 Accept).
• Reject the project is NPV is less than zero. (NPV < 0 Reject).
• While comparing two projects always select the project with a higher NPV.
• In this case since the calculated NPV value is greater than zero
(3,992) hence select this project
29. INTERNAL RATE OF RETURN (IRR)
• The Internal Rate of Return (IRR) is the discount rate that makes
the net present value (NPV) of a project zero. In other words, it is the
expected compound annual rate of return that will be earned on a
project or investment.
• Formula and Calculation for IRR
30. In this formula:
•NPV is set to zero.
•Cash flows are the sums of money spent and earned on the investment for a
given period of time (e.g., monthly or annually).
•1, 2, and n are the periods of time, with n being the number of time intervals.
•IRR is the internal rate of return.
•Initial investment is how much the investment costs upfront.
32. Example
• The DEF Group wants to diversify its business and plan to take up a
new project that requires an initial investment of $400000. They will
pay it off in 4 years. It will generate $40000 in the first year, $80000 in
the second year, $1600000 in the third year, and $259600 in the
fourth year. Find out the feasibility of this investment project if the
discount rate is 8%.
33. Step 1. calculate NPV
NPV = $23,451.06
If it is positive proceed further
As you can see, our ending NPV is not equal to zero. Since it’s a positive
number, we need to increase the estimated internal rate. Let’s increase
it to 10 percent and recalculate
34. Step 2. calculate IRR
NPV = 0
Thus, if the IRR is 10%, the project will be at a break-even point. This
project generates a positive NPV, and the discount rate is lower than
the IRR. In other words, the IRR is more than the project’s required
rate of return; therefore, it is a profitable investment.
35. PROFITABILITY INDEX
• The profitability index (PI), alternatively referred to as value
investment ratio (VIR) or profit investment ratio (PIR), describes an
index that represents the relationship between the costs and benefits
of a proposed project.
• The profitability index is calculated as the ratio between the present
value of future expected cash flows and the initial amount invested in
the project.
• A higher PI means that a project will be considered more attractive.
37. Example of the Profitability Index
• Imagine that a company is considering two potential projects:
building a new factory, or expanding an existing one.
• The factory expansion project is expected to cost $1 million and
generate cash flows of $200,000 per year for the next 5 years, with a
discount rate of 10%.
• The new factory project is expected to cost $2 million and generate
cash flows of $300,000 per year for the next 5 years, also with a
discount rate of 10%.
38. Step 1. calculate PV for future cash flow for
factory expansion project
• Formula= PV = CF1 / (1 + r)^1 + CF2 / (1 + r)^2 + ... +
CFn / (1 + r)^n
• Where
• PV is the present value
• CF is the cash flow in a given year
• r is the discount rate
• n is the number of years.
• PV = $200,000 / (1 + 0.10)^1 + $200,000 / (1 + 0.10)^2 + ... +
$200,000 / (1 + 0.10)^5
• PV = $750,319
40. Step 1. calculate PV for future cash flow for
new factory project
• Formula= PV = CF1 / (1 + r)^1 + CF2 / (1 + r)^2 + ... +
CFn / (1 + r)^n
• Where
• PV is the present value
• CF is the cash flow in a given year
• r is the discount rate
• n is the number of years.
• PV = $300,000 / (1 + 0.10)^1 + $300,000 / (1 + 0.10)^2 + ... +
$300,000 / (1 + 0.10)^5
• PV = $1,125,479
41. Step 2. calculate profitability index
Formula= PI = PV / Initial Investment
•PI = $1,125,479/ $2,000,000
•PI = 0.56
42. DECISION
• In this example, the factory expansion project has a higher
profitability index, meaning it is a more attractive investment. The
company might decide to pursue this project instead of the new
factory project because it is expected to generate more value per unit
of investment.
