1) Traditional criteria (techniques)
a) Payback Period:
This is one of the widely used methods for evaluating the investment proposals. Under this
method the focus is on the recovery of original investment at the earliest possible. It determines
the number of years to recoup the original cash out flow, disregarding the salvage value and
interest. This method does not take into account the cash inflows that are received after the
payback period. There are two methods in use to calculate the payback period
1) Where annual cash flows are not consistent vary from year to year.
2) Where the annual cash flow are uniform.
1. Unequal cash flows
B
P=E+
C
Where, P stands for payback period.
E stands for number of years immediately preceding the year of final recovery.
B stands for the balance amount still to be recovered.
C stands for cash flow during the year of final recovery.
Example: The following is the information related to a company
Project A Project B
Year Cash flow $ Year Cash flow $
0 -700 0 -700
1 100 1 400
2 200 2 300
3 300 3 200
4 400 4 100
5 500 5 0
Calculate Payback Period
Project A Cumulative Project B Cumulative
Year Cash flow cash flow Year Cash flow Cash flow
0 -700 -700 0 -700 -700
1 100 -600 1 400 -300
2 200 -400 2 300 0
3 300 -100 3 200 200
4 400 300 4 100 300
5 500 800 5 0 -
B
P=E+
C
100
=3+
400
= 3.25 year
B
P=E+
C
=2+0
= 2 years
The Net Present Value (NPV)
Year Project A Project B
0 (80,000) (100,000)
1 20,000 25,000
2 25,000 20,000
3 25,000 30,000
4 30,000 35,000
5 20,000 40,000
The required rate of return on both projects is 12%. Then, evaluate these projects using the Net
Present Value Method.
The Net Present Value (NPV) for Project A is:
Year Cash Flows Discounting Factor (12%) Present Values
1 20,000 0.893 17,860
2 25,000 0.797 19,925
3 25,000 0.712 17,800
4 30,000 0.636 19,080
5 20,000 0.567 11,340
PV of cash inflows (sum) 86,005
PV of cash outflows 80,000
Net Present Value (NPV) 6,005 birr
The Net Present Value (NPV) for Project B is:
Year Cash Flows Discounting Factor (12%) Present Values
1 25,000 0.893 22,325
2 20,000 0.797 15,940
3 30,000 0.712 21,360
4 35,000 0.636 22,260
5 40,000 0.567 22,680
PV of cash inflows (sum) 104,565
PV of cash outflows 100,000
Net Present Value (NPV) 4,565 birr
Since the two projects are mutually exclusive, the one with the higher NPV has to be accepted.
Thus, project A is selected as its NPV is higher than that of project B. Had the two projects been
independent of one another, both of them would be accepted because both projects have positive
net present values (NPVs).
Unit 4 Activity 1
ABC PLC is considering an investment in a cement project. It has on hand $180, 000. It is
expected that the project may work for seven years and likely to generate the following annual
cash flows.
Year Cash Flows
1 30,000
2 50,000
3 60,000
4 65,000
5 40,000
6 30,000
7 16,000
The cost of capital is 8%
Required: - Calculate the Net Present Value.
a) Profitability Index Method / Benefit Cost Ratio
Profitability index method is the relationship between the present values of net cash inflows and
the present value of cash outflows. It can be worked out either in unitary or in percentage terms.
The formula is
Present va lue of cash inflows
Profitability Index =
Pr esent value of cash outflows
PI > 1 Accept
PI = 1 indifference
PI < 1 reject
Higher the profitability index more is the project preferred.
From the above example we can calculate the profitability index as below
Present value of cash out flows $ 180, 000
Present value of cash inflows $ 221, 513
221,513
: - PI =
180,000
b) The Internal Rate of Return
The IRR is the discount rate at which the NPV for a project equals zero. This rate means that the
present value of the cash inflows for the project would equal the present value of its outflows.
Suppose you were looking at an investment with investment costs $100,000 and net cash flow as
given below. The Required Rate of Return is 20%.
Year Description Cash Flow
0 Initial Investment (100,000)
1 Net Cash Flow 35,000
2 Net Cash Flow 40,000
3 Net Cash Flow 45,000
4 Net Cash Flow 70,000
What’s the IRR? If we require a 20 percent return, should we take this investment?
We can set the NPV equal to zero and solve for the discount rate:
Unfortunately, the only way to find the IRR in general is by trial and error, either by hand or by
calculator.
At 10%,
NPV = (100,000) + 146496
= 46,496
At 30 %,
NPV = (100,000) + 96266
= -3,734
The NPV appears to be zero with a discount rate between 10 percent and 30 percent, so the IRR
is somewhere in that range.
With a little more effort, we can find the IRR using the following formula
Where
• L = Lower discount rate L = Low
• H = Highest discount rate H = High
• NPVL = The NPV results for the lower discount rate
• NPVH = The NPV results for the higher discount rate
IRR = 10% + 18.5%
IRR = 28.5%
So, if our required return were less than 28.5 percent, we would take this investment. If our
required return exceeded 28.5 percent, we would reject it.
In our example, the NPV rule and the IRR rule lead to identical accept-reject decisions.
