Methods of Evaluation of Investment Projects: NPV, IRR, Payback Period, Discounted Payback Period, PI

This article discusses the various methods of evaluating investment projects, including NPV, IRR, Payback Period, Discounted Payback Period, and PI. It also explains the problems faced in mutually exclusive projects and how to choose the most profitable one. The article provides examples and formulas to help readers understand the concepts better.

There are many methods of evaluation profitability of investment projects. All of these
methods have their own merits and demerits. Some of the methods which are used for
evaluation of investment projects are:
1. NPV (Net Present Value)
2. IRR (Internal Rate of Return)
3. Payback period
4. Discounted payback period
5. PI (Profitability Index)
NPV (Net Present Value)
NPV (Net present value) is present value of all cash flows (whether inflow or outflow).
Present value of cash flows is calculated at a predetermined rate (cost of capital).
Formula for NPV is given below:
NPV = Present value of cash inflows – Present value of cash outflows
IRR (Internal Rate of Return)
IRR (Internal rate of return) calculates the rate at which NPV is equal to zero. In other
words, rate at which present value of all cash flows (inflows and outflows) is equal to zero
is call Internal Rate of Return.
Mutually Exclusive Projects
In case of mutually exclusive projects, IRR and NPV may give different results. It means
IRR and NPV will prefer different projects. In this case, it become difficult to choose the
most profitable one. There are three kinds of problems faced when considering mutually
exclusive projects:
a. Size disparity problem
b. Time disparity problem
c. Unequal life span problem
Size disparity problem – It refers to the situation when the projects are of different
investment amount. For example, one project requires $100 whereas another project
requires $2000. In such situations, NPV and IRR both may give different results.
Let us understand using example:
Particulars Project A Project B
Initial investment $100 $2,000
Cash flow (at the
end of year 1)
$128 $2,500
NPV @ 10% $16.36 $272.73
IRR 28% 25%

As you can see, as per NPV, project B should be selected whereas as per IRR, project A
should be selected.
Time disparity problem – It refers to the situation when the cash flow patterns are very
different over the life of the project. Consider below example,
Particular
s
Project A Project B
Investment $1,000 $1,000
1 $200 $1,000
2 $500 $800
3 $900 $400
4 $1,100 $100
NPV @ 10% $1,022.54 $939.08
IRR 40.62% 65.27%
In this example, cash inflows of Project A are increasing over the life whereas in case
Project B, cash flows are decreasing. In this case, as per NPV, Project A should be
selected whereas as per IRR, Project B should be selected.
Unequal life span problem – It refers to the situation when the both projects have
unequal life. For example, Project A has life of 6 years and Project B has life of 4 years.
For example,
Particular
s
Project A Project B
Investment $1,000 $1,000
1 $400 $500
2 $400 $500
3 $400 $500
4 $400 $500
5 $400
6 $400
NPV @ 10% $742.10 $584.93
IRR 32.66% 34.90%
In this case also, both NPV and IRR are giving different results.
So, what should we do in such cases?
In case of first two issues (size and time disparity), NPV is preferred over IRR subject to
the availability of sufficient capital as IRR assumes investment and borrowings are being
done as same rate which is not the case in real world.
In case of unequal life span problem, first of all NPV should be calculated for both the
projects. Then, it should be divided by the PVAF (present value of annuity factor) at given
cost of capital and their respective period to calculate EAA (Equivalent Annual Annuities).
The project with highest EAA should be selected.