The document discusses various capital budgeting techniques for investment decision making including net present value (NPV), benefit-cost ratio (BCR), internal rate of return (IRR), payback period, and accounting rate of return (ARR). Examples are provided to illustrate how to use the techniques to evaluate potential projects. The key criteria are NPV (accept if greater than 0), BCR (accept if greater than 1), IRR (accept if greater than required rate of return), and payback period (accept if less than cutoff period).

1. FIN 2732 - Fundamental of Financial
Management
Unit 2 –Investment Decisions
1

2. Coverage
11.1 Capital Budgeting process
11.3 Investment Criteria
11.4 Net Present Value (NPV)
11.5 Benefit-cost ratio (BCR or PI)
11.6 Internal rate of return (IRR)
11.8 Payback Period (PBP)
11.9 Accounting Rate of Return (ARR)
Reference: Chapter 11 (Financial Management Prasanna Chandra 8e)
2

3. Financial decisions of the firm
• Financing decisions
• Dividend decisions
• Investment decisions
– Short term investment / working capital
– Long term investment / capital expenditure –
examples: investment in a new plant, a commercial
bank is planning to computerization etc.
3

4. 4
Importance of Investment Decision
1. influence the firm’s growth in the long run.
2. have an impact on the risk of the firm.
3. involve outflow of large amount of funds
4. irreversible in nature
5. complex in nature

5. 5
11.1 Capital Budgeting process
• Identification of potential investment opportunities
– Market characteristics
– Product profile
– Export-import
– Social and economic trend
• Preliminary screening
• Feasibility study / appraisal
– Market Appraisal
– Technical Appraisal
– Financial Appraisal
– Economic Appraisal
• Project implementation
• Performance review

6. 6
11.3 Investment Criteria
Discounting criteria
• Net Present Value
• Benefit-Cost Ratio
• Internal Rate of Return
Non discounting criteria
• Pay back Period
• Accounting Rate of Return

7. 7
11.4 Net Present Value (NPV)
NPV is the difference between present value of cash inflows and
initial investment.
NPV = PV of cash inflows – initial investment
Acceptance Rule: Accept the project if NPV > 0
Limitations
1. Gives inconsistent results while comparing projects with unequal
lives.
2. Difficult to determine the precise discount rate.
3. gives absolute figure

8. 8
Example: X Ltd. is planning to buy machinery costing Rs. 50,400.
Following are the cash flows associated with the project over its life
period of 5 years.
Year Cash Flow After Tax
1
2
3
4
5
Rs. 10,000
Rs. 14,000
Rs. 14,000
Rs. 12,500
Rs. 9,800
Based on the NPV criterion, determine whether the new machine
should be bought or not, assuming discount rate to be 12%?

9. 9
Solution: Net Present Value = Present value of inflows – outflows
• Present value of inflows =
= 8,928.57 + 11,160.71 + 9,964.92 + 7,943.98 + 5,560.78
= Rs. 43,558.96.
NPV = 43,558.96 – 50,400 = - Rs 6,841.04
The company should not go in for the machinery as the NPV is
negative, in other words the benefits associated with the machinery
are less than the costs associated with it.
5
)
12
.
0
1
(
800
,
9
4
)
12
.
0
1
(
500
,
12
3
)
12
.
0
1
(
000
,
14
2
)
12
.
0
1
(
000
,
14
)
12
.
0
1
(
000
,
10










10. NPV with time-varying discount rate
• The discount rate may change due to
– level of interest rate
– Risk characteristics of project
– Financing mix of project
10

11. 11
Example: X Ltd. is planning to buy machinery costing Rs. 50,400.
Following are the cash flows associated with the project over its life
period of 5 years. Considering the forecasted interest rate, discount
rates are taken.
Year Cash Flow After Tax Discount rate
1
2
3
4
5
Rs. 10,000
Rs. 14,000
Rs. 14,000
Rs. 12,500
Rs. 9,800
12
10
10
8
6
Based on the NPV criterion, determine whether the new machine
should be bought or not?

12. Example: The cash flows associated with a project are given below:
Year 0 1 2 3 4 5
Cash flows -2200 900 850 700 650 500
Find out the Net present value of the project assuming discount rate as 10%.
12

13. 13
11.5 Benefit-Cost Ratio (BCR) / Profitability Index
BCR or PI is the ratio of present value of cash inflows at the required
rate of return and the initial cash outflow of the investment.
NBCR
Acceptance Rule: Accept the project if BCR > 1
Limitations:
1. Does not give valid results when cash outlay is spread over a
number of years.
2. Is not useful when multiple projects are acceptable but budget
constraint exists.
3. gives same result as NPV regarding accepting and rejecting project
investment
Initial
inflows
cash
of
lue
Present va
PI 

14. 14
Example: X Ltd. is planning to buy machinery costing Rs. 50,400.
Following are the cash flows associated with the project over its life
period of 5 years.
Year Cash Flow After Tax
1
2
3
4
5
Rs. 10,000
Rs. 14,000
Rs. 14,000
Rs. 12,500
Rs. 9,800
Based on the PI criterion, determine whether the new machine should
be bought or not, assuming discount rate to be 12%?

15. 15
Solution: PI =
= 0.8643
Since the profitability index is less than one, we should not buy the
machinery.
investment
Initial
inflows
cash
of
lue
Present va
50,400
43,558

16. Example: The net cash flows associated with two mutually exclusive
projects are given below:
Year 0 1 2 3 4 5 6 7
Project X -2500 1200 1200 1200
Project Y -2500 650 650 650 650 650 650 650
Calculate the Net Present Value (NPV) and profitability index of project X
and project Y assuming a cost of capital is 12%.
Which project would you choose and why?
16

17. Answer:
• NPVx = 382.4
• NPVy = 466.6
• BCRx = 1.153
• BCRy = 1.187
17

18. Example: Cash flow from a project is estimated as follow
Year 0 1 2 3
Cash flow -160 60 80 116
Calculate the benefit cost ratio, assuming cost of capital as 12%
18

19. • 199.19 / 160 = 1.2449
19

20. Example: The initial investment in a project under evaluation is
Rs.4.5 million. The expected annual cash inflows from the
project will be Rs.1 million. If the project’s duration is 6 years
and the required rate of return is 10%, should the project be
accepted on the basis of profitability index technique of
appraisal of capital budgeting?
20

21. 21
11.6 Internal Rate of Return (IRR)
Rate that equates the present value of cash inflows to cash outflows.
In other words IRR is the rate at which NPV is zero
Acceptance Rule: Accept the project if IRR > required rate of return
Limitations: It gives multiple values while dealing with projects
having one or more cash outflows interspersed with cash inflows.

22. 22
Example: S Ltd. wants to expand its business by investing either in
project A or in project B. Both the projects involve an outlay of Rs.
10,000 and have a life-span of three years. The cash flows after tax
associated with projects A and B are as follows:
Year Project A (Amount in Rs.) Project B
1
2
3
2000
4000
6000
4000
4000
4000
Based on the IRR criterion, determine which project should the
company invest in?

23. 23
Solution: Project A
Let r represent the IRR of project A:
10,000 = 3
2
)
1
(
6000
)
1
(
4000
)
1
(
2000
r
r
r 




Taking r as 9%
Value of the right hand side of the equation is = Rs. 9,834.
We want value of right hand side to be 10,000 so reduce the value of ‘r’
Taking r as 8%
Value of the right hand side of the equation is = Rs. 10,044.
Hence, r will lie between 8% and 9%.
Interpolation formula: lower rate + (difference in rate)
Interpolating these two values = 8 + (9 - 8)
)
(
)
(
lowervalue
e
highervalu
ue
desiredval
e
Highervalu


= 8.21%
)
9834
10044
(
)
10000
10044
(



24. 24
Project B
Let s represent the IRR of project B:
10,000 = 3
2
)
1
(
4000
)
1
(
4000
)
1
(
4000
r
r
r 




s = 8 + (10-8) = 9.71%
Hence, the company should invest in project B as the IRR for project B is greater
than the IRR for project A.
Taking r as 10%
Value of the right hand side of the equation is = Rs. 9947
We want value of right hand side to be 10,000 so reduce the value of ‘r’
Taking r as 8%
Value of the right hand side of the equation is = Rs. 10308
Hence, r will lie between 8% and 10%.
Interpolating these two values we get,
)
9947
10308
(
)
10000
10308
(



25. Example: A Ltd is planning for a capital investment at a cost of
Rs.100 where the projected cast flows are
Year 1 2 3 4
Cash flows 25 30 40 48
Calculate internal rate of return of the project.
25

26. • 14.2%
26

27. Example: The cash flows associated with a project are given below:
Year 0 1 2 3 4 5
Cash flows -2200 900 850 700 650 500
Find out the approximate IRR earned by the project
Answer: 21.36%
27

28. Example: Cash flow from a project is estimated as follow
Year 0 1 2 3
Cash flow -160 60 80 116
Calculate the IRR of the project
28

29. 29
11.8 Payback Period
Length of time required to recover the initial outlay of the project.
• If annual cash flow is constant =
• If annual cash flow is uneven (not constant) =
Cumulative Cash Flow = 0
Acceptance rule: If Payback period ≤ Cut-off period: Accept
inflow
cash
Annual
investment
Initial

30. Example: From the following data, calculate payback period for
projects X and Y
30
Year Project X Project Y
Cash Flow Cash Flow
0 -40,000 -40,000
1 14,000 10,000
2 16,000 15,000
3 5,000 15,000
4 5,000 5,000
5 10,000 2,000
6 10,000 3,000
7 5,000 NIL

31. Calculation of cumulative cash-flows for projects X and Y
31
Year Project X Project Y
Cash flow Cumulative Cash Flow Cumulative
0 -40,000 -40,000 -40,000 -40,000
1 14,000 -26,000 10,000 -30,000
2 16,000 -10,000 15,000 -15,000
3 5,000 -5,000 15,000 0
4 5,000 0 5,000 5,000
5 10,000 10,000 2,000 7,000
6 10,000 20,000 3,000 10,000
7 5,000 25,000 NIL 10,000

32. 32
30 80
Payback = 2 + /
= full years + (amount to be recovered / cash flow of next year)
= 2 + 0.375 years
Cash flows
Cumulative
0 1 2 3
-30
Project Payback Calculation
-100 50
-90
80
-100 60
10

33. Example: A company invests INR 40,000 in a new project with
expected useful life of 6 years. The cash flows after tax are
given for years 1 through 6 in the following table. Calculate
pay back period.
33
Year Cash flow after tax
1 10,000
2 11,000
3 15,000
4 10,000
5 12,000
6 11,000

34. Usage:
• Comparison purpose,
• Supplementary technique
Limitations:
• Does not consider time value of money
• ignores cash flow beyond payback period
34

35. 35
11.9 Accounting Rate of Return (ARR)
ARR measures the rate of return on the project using accounting
information.
• It is computed as:
Acceptance Rule: Accept the project if ARR > Required rate of return
Limitations:
-Ignores time value of money
-Uses accounting profits and not cash flows in evaluating the project
investment
of
value
Average
after tax
Profit
Average

36. 36
Year Value of investment Profit After Tax (in Rs.)
0
1
2
3
4
55,000
10,800
9,830
4,230
3,320
Example: A Ltd. is planning to invest in a project. The initial
investment required is Rs.55,000. The profit after tax associated with
the project, for a period of four years is given below:
Should the firm accept this project, if the minimum accounting rate of
return required by the company is 22.34%?

37. 37
Solution:
Accounting Rate of Return =
Average profit after tax = (10800 + 9830 + 4230 + 3320)/ 4 =Rs.7045
Average value of investment = Rs. 27,500.
Accounting Rate of Return = 0.2562 or 25.62%.
The company can accept this project, as its ARR is greater than the
minimum or standard ARR.
investment
of
value
Average
after tax
Profit
Average

38. Example: The expected cash flows of a project are as follows
Year Cash flow
0 -10,000
1. 2,000
2. 3,000
3. 4,000
4. 5,000
5. 3,000
The cost of capital is 12%. Calculate the following
1. Net present value
2. Benefit cost ratio / PI
3. Internal rate of return
4. Payback period
38

39. Year 0 1 2 3 4 5 6
Cash flow (Rs. ‘000) -2500 750 800 650 600 550 450
AB Ltd is a leading manufacturer of automotive components. It supplies to original
equipment manufacturers as well as the replacement market.
You have recently joined this firm as a financial analyst reporting to the CFO of the
company. He has given you the following table having cash flow associates with a
project which the firm is going to launch. With the help of your colleague you found
out the cost of capital which is 12%.
You are required to appraise the project using the techniques stated below:
•Net present value
•Profitability index
•Internal rate of return
•Payback period

40. Theory questions:1 to 21
Numerical: solved and unsolved Problem -
chapter end
40