This document discusses two key measures for evaluating projects: net present value (NPV) and internal rate of return (IRR). It defines NPV as the difference between the present value of future cash flows from an investment and the initial investment amount. IRR is defined as the discount rate that results in an NPV of zero. The document provides examples of calculating NPV and IRR for projects and outlines the decision rules for accepting or rejecting projects based on whether their NPV is positive or negative and whether their IRR exceeds the cost of capital. It notes that while NPV and IRR typically provide the same decision, there are some exceptions like projects with non-conventional cash flows or mutually exclusive projects.

1.  Net Present Value Decision Rules
 IRR (Internal Rate of Return)
 in Project Management
The two most-used measures for evaluating projects are
the net present value and the internal rate of return!

2. Agenda
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3. Net Present Value
•
The difference between the present value of the future cash flows from
an investment and the amount of investment. Present value of the
expected cash flows is computed by discounting them at the required rate
of return.
Where,
N=total number of periods
T= the time of the cash flow
i= the discount rate (the rate of return that could be earned on an
investment)
Rt = the net cash flow i.e. cash inflow – cash outflow at time t (R0: it is
subtracted from the whole as any initial investments during first year is
not discounted for NPV purpose)
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4. The NPV Decision Rules
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5. Example
An Investment of $1,000 in year 1
 The discount rate is 10%
 In Year 2, we receive $110 in year 2
 You expect to receive $1,200 in year 3
1
2
3
Investment
($ 1,000)
Cash Inflows
$0
$ 110
$ 1200
Discounting
Factor
1
1.10
1.21
Discounted
Cash Inflow
0
$ 100
$ 991.74
Therefore, NPV= ($ 1,000) + $ 100 + $ 991.74= $ 91.74
Hence, we can do this investment.
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6. Internal Rate of Return
• The internal rate of return of a project is
known as the rate of return where the
particular project’s net present value
equals to zero.
• Formula:
– CF: Cash Flow
– r: Internal Rate of Return
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7. Internal Rate of Return Rules
In IRR decisions, if we have only one project, most
of the time we need the basic rule «independent
project»:
IRR > Cost of capital (should be accepted)
IRR = Cost of capital (provides the minimum return)
IRR < Cost of capital (shouldn’t be accepted)
In addition, we need to take other situations into
account too. Especially, eventhough NPV and IRR
will generally give us the same decision, there are
some exceptions:
•Nonconventional cash flows – cash flow signs
change more than once
•Mutually exclusive projects
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8. Example: Independent Project
If we want to decide on to accept the project or not, we
should consider the comparison of IRR & cost of capital
for an individual project.
In this example;
•when the cost of capital is 15%, then the NPV is
-227,53 (don’t accept)
• Alternative: IRR < Cost of capital
•when the cost of capital is 10%, then the NPV is 34,27
(accept)
• Alternative: IRR > Cost of capital
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9. Example: Mutual Projects
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10. Key differences:
NPV versus IRR
• NPV Method is preferred over other methods since it calculates additional wealth and
the IRR Method does not
• The IRR Method is more used in evaluating short-term projects and NPV is more used
in evaluating long-term projects.
• one significant advantage of IRR -- managers tend to better understand the concept of
returns stated in percentages and find it easy to compare to the required cost of capital
• Applying NPV using different discount rates will result in different recommendations.
The IRR method always gives the same recommendation.
Project A
Invest
compare two mutually
exclusive projects
Project B
-10.000
-25.000
Return
+25.000
+50.000
IRR
IRR 150%
IRR 100%
NPV by i=8%
13.148
21.296
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11. Link to Project Management
NPV and IRR in the decision taking process
Methods to evaluate a project
 estimate the value of the project
 choosing which project gets priority
By applying
 NPV as time value of money (money figure)
 IRR calculate the investments profitability as an interest rate
(percentage figure)
included in a business case prepared by the
controlling department
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12. Contact
Ujjwal Kumar Joshi
ujjwaljoshi1990@gmail.com
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