Okay, here are the NPV calculations for Projects A and B with a discount rate of 8%: Project A: CF0 = -120,000 CF1 = 40,000 / (1.08) = 37,037 CF2 = 25,000 / (1.08)2 = 22,222 CF3 = 70,000 / (1.08)3 = 58,333 CF4 = 130,000 / (1.08)4 = 108,333 CF5 = 80,000 / (1.08)5 = 66,667 NPV = -120,000 + 37,037 + 22,222 + 58,333 + 108,333 + 66

1. 1
Project Mnagement
BY: Banbul Sh (Assistant Professor of Financial Management).
Email: shewaj12@gmail.com
Chapter 6

2. 2
Chapter 6:
project appraisal (project
evaluation techniques)

3. Capital Budgeting
 A capital budgeting decisions is defined as the firm’s
decision to invest its current funds most efficiently in
the long-term assets in anticipation of an expected
flow of benefits over a series of years.
 In other words, “capital budgeting is used to evaluate
the expenditure decisions such as acquisition of fixed
assets, changes in old assets and their replacement.”
3

4. Capital Budgeting….
 Is the process of figuring out which projects are
financially worth an investing.
 Firms should invest in projects that are only
worth more than they cost when the NPV is
positive.
 Importance of capital budgeting
Long term investment involves risk
Huge investment and irreversible one
Helps to appropriately plan longrun in
business
4

5. Significance of capital budgeting
 Essential tool in financial mgt-for evaluating
project
 Helps to see the risk & uncertainty of the
project
 Helps to keeping check an over or under
investment -controlling
5

6. Project Evaluation Techniques
There are two types of measures of project appraisal
techniques: undiscounted and discounted.
 Non-discounting Methods
 Ranking by inspection
 The payback period
 Proceeds per unit of outlay
 Discounting methods of project selection
 The Net present Value (NPV)
 The internal rate of return of a project (IRR)
 Modified Internal Rate of Return
6

7. Introduction
 The basic underlying difference between these two lies in
the consideration of time value of money in the project
investment.
 Undiscounted measures do not take into account the
time value of money, while discounted measures do.
7

8. Introduction
 Many economic decisions involve benefits and
costs that are expected to occur at future
time period.
 (for example: fish production)
 The construction of pond, and fish tank, for example,
requires immediate cash outlay, which with the
production and sale of fish, will result in future cash
inflows or returns
In order to determine whether the future cash
inflows justify present Initial investment, we must
compare money spent today with the money
received in the future.
8

9. Introduction
 The time value of money influences many
production decisions. Everyone prefers money today
to money in the future.
 The preference for the Birr now instead of a Birr in the
future arises from three basic reasons:
Uncertainty - Influences preferences because one is
never sure what will take place tomorrow.
Reinvestment-The sooner you get the dollar back,
the sooner you can reinvest it and earn a positive return;
Inflation - affects the purchasing power of the money.
Consumption Preference
9

10. Undiscounted methods
1. Inspection by ranking
2. Payback period
3. Proceeds per unit of outlay
10

11. Ranking by inspection
 By this, the assessor will be interested in the
 Investment cost of the project
 Cash flow patterns
 EX: Cash flows of hypothetical investments
 The deficiency of this method:
 It does not take into account the timing of the proceeds
11
Investment Initial cost (Birr) Net cash proceeds per year (Birr)
Year 1 Year 2
A 10,000 10,000 -
B 10,000 10,000 1,100
C 10,000 3,762 7,762
D 10,000 5,762 5,762

12. Ranking by inspection
1. Two investments have identical cash flows
 investment B is better than investment A, because all
factors are equal except that B continues to earn proceeds
after A has been retired.
2. Two investments have the same initial outlay & the
same earning life & earn the same total proceeds.
 Thus, investment D is more desirable than investment C
 The deficiency of this method:
 It does not take into account the timing of the proceeds
12

13. 2. Payback period:
 the length of time required to recover the initial
investment
 using project cash flows, PBP answers 'How long
will it take to pay back its cost?'
 Among alternative projects, the one with the
shortest payback period is more desirable .
Decision Rules:
 • If payback < acceptable time limit, accept project
• If payback >acceptable time limit, reject project
13

14. For a project with equal annual receipts
Years 0 1 2 3 4 5
Project A 1,000,000 250,000 250,000 250,000 250,000 250,000
For a project with equal annual receipts:
Payback period= Initial investment/Annual cash
flow
PBP= 1,000,000/250,000= 4 years.
14

15. If the cash flows of a project are not uniform, the payback period is
calculated by accumulating a series of cash flows until the
amount reaches the initial investment. i.e. The progressive sum of the cash
flows after the initial outlay:
Years 0 1 2 3 4
Project B - 10,000 5,000 2,500 4,000 1,000
15

16. Years 0 1 2 3 4
Project B - 10,000 5,000 2,500 4,000 1,000
Cumulative
incremental flow
- 10,000 -5,000 -2,500 1,500 2,500
• Payback period lies between year 2 and year 3.
• At the end of year 2, the remaining amount to be collected= 2,500.
• This means (2500/4000)=0.625 or 62.5 % of the time is required
to gain a financial return equal to the original investments.
= 2.625 years or 2 years
and (.625 * 12 months)= 2 years and 8 months
16

17. 8-17
Example: Computing Payback for the Project
 Do we accept or reject the project?
Capital Budgeting Project
Year CF Cum. CFs
0 (165,000)
$ (165,000)
$
1 63,120
$ (101,880)
$
2 70,800
$ (31,080)
$
3 91,080
$ 60,000
$
Payback = year 2 +
+ (31080/91080)
Payback = 2.34 years

18. Advantages of Payback
• It is simple to calculate.
• It is helpful in weeding out risky projects
 The pay back period is sometimes used by investors
who are in short of cash and need to reinvest all cash
flows that occur in early stages of the projects.
18

19. Disadvantages of Payback
• It ignores the time value of money.
• It may divert attention from profitability
 There is no objective measure of what constitutes an
acceptable payback period.
 It overlooks cash flows beyond the payback period.
19

20. Undiscounted method-cont’d
3. Proceeds per unit of outlay
 This is the ratio of the net value of production (proceeds)
to the total volume of the capital invested.
 The deficiency of this method:
 It does not take into account the timing of the proceeds
20
Ranking by proceeds per unit (a Birr)of outlay
Investment project
Total proceeds Investment
outlay
Proceeds per Birr of
outlay(P/B=TP/IO)
Ranking
A
10,000 10,000 1.0 4
B
11,100 10,000 1.11 3
C
11,524 10,000 1.15 2
D
11,800 10,000 1.18 1

21. Discounted methods
1. NPV
2. IRR
21

22. Time value of money
 The Discounted Cash Flow (DCF) method takes into
account the time value of money
 the value of money will change over time.
 All other things being equal, a dollar received soon is worth
more than a dollar expected to be received in the distant
future
 This is true for three different, yet related reasons:
 Risk/ uncertainty
 Reinvestment-The sooner you get the dollar back, the sooner you
can reinvest it and earn a positive return;
 Due to the forces of economic inflation, the dollar we receive
in the distant future will have proportionately less buying power
than it does today.
 In project management, the time value of money concept is
a foundational element to performing a financial analysis on
a project
22

23. Net present value (NPV)
 Net present value (NPV) is the difference between the
present value of cash inflows and the present value of
cash outflows over a period of time.
 NPV is used in capital budgeting to analyze the
profitability of a projected investment or project.
 The following is the formula for calculating NPV:
NPV= Cf1/(1+i)1 + cf2/(1+i)2 + cf3/(1+i)3 + …….Cfn/(1+i)n -I0
 In this equation: where
CFn = net cash inflow during the period n
Io = total initial investment costs
i = discount rate, and
n = number of time periods
23

24. Net present value (NPV)….
 Net present value is the sum of the present values of all
the positive cash flows minus the sum of the present
values of all the negative cash flows.
 Interpretation
 NPV measures the net contribution of the project
to firm wealth.
24
t = 0
t = 1 t = 2
t = 0
t = 2 t = 4
Initial Outlay0 NPV0 = ?
r = req’d return
t = 4
t = 3
t = 1
t = 3
CF1
CF2
–CF3
CF4

25. Discounting
 Discounting: The process of converting future
benefits and costs/Cash flows into today’s
dollars/Birr.
 the recognition that a future payoff amount is worth
something less than that amount today.
 Discount rate, the interest rate used in the
discounting process, reflecting the time value of
money.
• It is set by Central Authority (MOFED in Ethiopia)
• It has been estimated to be in the range of 9.96- 10.49
percent with an average percentage figure of 10.23.
25

26. NPV
 All future cash flows should be discounted into present
values. The discount factor is:
 Assume that a given project has a life of five years & a
discount rate (r) of 8% is used.
 For example, the discount factor for year 3 (i.e. t=3) is
calculated as follows:
26
FV = PV(1 + r)n…compounding

27. Net present value (NPV)
Consider Project A with the following cash flows:
The NPV for this project is…?
Decision?
Consider Project B with the following cash flows:
The NPV for this project is…?
Decision?
27
t = 0
t = 1 t = 2
–$100,000
r = 10%
t = 3
$20,000
$40,000
$45,000
$75,000
t = 4
t = 0
t = 1 t = 2
–$100,000
r = 10%
t = 3
$55,000
$45,000
$35,000
$25,000
t = 4

28. Net present value (NPV)
Consider Project A with the following cash flows:
The NPV for this project is $29,872.52.
Decision  Accept the project.
Consider Project B with the following cash flows:
The NPV for this project is $27,783.12.
Decision  Accept the project.
28
t = 0
t = 1 t = 2
–$100,000
r = 10%
t = 3
$20,000
$40,000
$45,000
$75,000
t = 4
t = 0
t = 1 t = 2
–$100,000
r = 10%
t = 3
$55,000
$45,000
$35,000
$25,000
t = 4

29. NPV calculations –example, r=8%
Question: Compute the NPV for project A & Project B:
29
year Cash flows for Project A Cash flows for Project B
0 (120,000) (75,000)
1 40,000 5,000
2 25,000 70,000
3 70,000 45,000
4 130,000 30,000
5 80,000 5,000

30. Solution
year Project A Discount factor Discounted cash flow
0 (120,000)
=
-120,000
1 40,000
37,037
2 25,000
21,433
3 70,000
55,568
4 130,000
95,554
5 80,000
54,447
Add them up NPV=
144,039
Project B
0 (75,000)
($75,000)
1 (5,000)
4,630)
2 70,000
60,014
3 45,000
35,723
4 30,000
22,051
5 5,000
3,403
Add them up NPV=
41,561

31. NPV-cont’d
 where regular cash flows are expected [these are
termed as annuities], the above expression can be
reduced to:
 Take-home Exercise: Compute the NPV for the
following three project alternatives at 3%, 5% & 8%
discount rates.
31
Projects X Y Z
Costs ($)-Initial investment 10,380 10,380 10,380
Project life span (years) 5 15 25
Annual Benefits ($) 2,397 1,000 736

32. NPV-Cont’d
 Net present value is expressed in terms of money, and it
represents the wealth that any single project is expected
to return to the company.
 This wealth typically comes in the form of either making
or saving money.
 In other words, a positive NPV project has the ability to
accomplish three things:
 cover its own financing costs /to service the debt required
to finance its execution/
 provide an attractive return to shareholders, and
 add to the accumulated wealth of the company.
32

33. 33
Rationale for the NPV Method
 NPV = PV inflows – PV Cost
 NPV = net gain in shareholder wealth
 NPV=0 → Project’s inflows are “exactly sufficient to
repay the invested capital and provide the
required rate of return”
Decision Rules:
If the NPV is positive, accept the project
If the NPV is negative, reject the project.
If the NPV is zero, be indifferent

34. Advantages of NPV
• time value of money
• The cash flows
• It focuses on the profitability of the project.
• useful for the comparison and selection from
among mutually exclusive projects or when
capital rationing is used.
• It discounts cash flows by the cost of capital
• the managers can understand it more easily
34

35. Disadvantages of NPV
• If the investments are different, deciding the desirability of the project
based on the NPV will be misleading.
 We have learnt that NPV tells us ‘how much birr is the net result of the project’ but
it does not tell us if this amount is the outcome of a big effort or a small one.
Example:
 For Project A:
NPV= 10; {B-C=110-100=10]
Big differences in investment amount
 For Project B:
NPV=15; [10,015-10,000=15]
• The cost of capital is assumed to remain constant throughout the life of
the project.
35

36. Internal Rate of Return (IRR)
Definition and Decision Rule
 IRR is also called DCF yield
 DCF return on investment
 IRR is the return to the capital invested or allocated or
investment in the project.
 It is the discount rate that makes the NPV of cash
inflows is equal to the present value of cash flows, i.e.,
NPV=0
36

37. IRR……
IRR is which makes NPV= 0,
 To get the IRR we will be looking for ‘r’ in the above
formula which makes NPV equals zero.
 However, the exact calculation of the IRR requires
some computation or trial and error process. For that
reason, an approximation is often favored.
 The approximation procedure is based on the principle
that an interpolation between a positive and negative
net present value approximately close to the condition
of a NPV of zero
37

38. 8-38
IRR ………
Definition:
 IRR = discount rate that makes the
NPV = 0
Decision Rules:
• If IRR > cost of capital, accept the project
• If IRR < cost of capital, reject the project
• If IRR = cost of capital, be indifferent.

39. Example
Calculate the IRR and NPV where the project cost is 10%
39
Project Year0 Year1 Year2 Year3 Year4 Year5 IRR(%) NPV
A (135) 10 40 70 80 50 20% 45.4
B (100) 40 40 50 40 - 25% 34.3

40. Use of interpolation formula
 IRR= ri + NPVri X (rh-ri)
NPVri- (NPVrh)
First compute the NPV with a given cost
NPV= cf/(1+i)n – I0
NPV A = 10/(1+0.1)1+….-Io
NPV B
40

41. Advantage and Disadvantage of IRR
Advantages of IRR
• the time value of money
• the total cash flows during the project life direct message
about the yield on the project.
Disadvantages of IRR
• It involves tedious work interpolation
• The IRR does not reflect the scale, or Birr/dollar size
• all proceeds are reinvested at the particular IRR,
• If there are non-conventional cash flows, it can produce
multiple rates.
41

42. Comparison of IRR & NPV
 IRR is easier to understand by a wider community, since it
states yield in terms of %.
 NPV directly measures the increase in value to the firm
 NPV approach requires a discount rate, which may not always
be possible.
 While NPV is a absolute measure IRR is a relative
measure.
 Whenever there is a conflict between NPV and IRR always
use NPV
42

43. Capital budgeting in practice
Firms should invest in projects that are worth more
than they cost. Investment projects are only worth
more than they cost when the net present value is
positive.
The net present value of a project is calculated by
discounting future cash flows, which are forecasted.
Thus, projects may appear to have positive NPV
because of errors in the forecasting.
To evaluate the influence of forecasting errors on the
estimated net present value of the projects several
tools exist:
43

44. Capital budgeting in practice …
1. Sensitivity Analysis
– Analysis of the effect on estimated NPV when
underlying assumptions change, e.g. market
size, market share or opportunity cost of capital.
– Sensitivity analysis uncovers how sensitive
NPV is to changes in key variables.
44

45. Capital budgeting in practice …
2. Scenario Analysis
Analyzes the impact on NPV of a particular combination
of assumptions.
Scenario analysis is particularly helpful if variables are
interrelated, e.g. if the economy enters a recession due
to high oil prices, both the firm’s cost structure, the
demand for the product and inflation might change.
45

46. Capital budgeting in practice …
Senario Analysis ……
Thus, rather than analyzing the effect on NPV of a
single variable (as sensitivity analysis) scenario
analysis considers the effect on NPV of a consistent
combination of variables.
– Scenario analysis calculates NPV in different states,
e.g. pessimistic, normal, and optimistic.
Pessimistic – what happen when the economy enter
into recession
Increase in oil price which leads to
 Inflation
 Change of demand for the product
 change of cost structure
46

47. Capital budgeting in practice …
3.Break Even Analysis
 Analysis of the level at which the company breaks even,
i.e. at which point the present value of revenues are
exactly equal to the present value of total costs.
 Thus, break-even analysis asks the question how much
should be sold before the production turns profitable.
47

48. Capital budgeting in practice …
4. Simulation Analysis – Monte Carlo simulation considers
all possible combinations of outcomes by modeling the project.
Monte Carlo simulation involves four steps:
1. Modeling the project by specifying the project's cash
flows as a function of revenues, costs, depreciation and
revenues and costs as a function of market size, market
shares, unit prices and costs.
2. Specifying probabilities for each of the underlying
variables, i.e. specifying a range for e.g. the expected
market share as well as all other variables in the model
3. Simulate cash flows using the model and probabilities
assumed above and calculate the net present value
48

49. Why Projects Have Positive NPV
In addition to performing a careful analysis of the
investment project's sensitivity to the underlying
assumptions, one should always strive to understand why
the project earns economic rent and whether the rents can
be sustained.
Economic rents are profits that are more than cover the
cost of capital.
Economic rents only occur if one has:
- Better product -
Lower costs
- Another competitive edge
49

50. Even with a competitive edge one should not assume
that other firms will watch passively. Rather one should
try to answer these questions:
- How long can the competitive edge be sustained?
- What will happen to profits when the edge
disappears?
- How will rivals react to my move in the meantime?
o Will they cut prices?
o Will they imitate the product?
Sooner or later competition is likely to
eliminate economic rents.
50

51. Comparison of IRR & NPV
 IRR is easier to understand by a wider community, since
it states yield in terms of %.
 NPV directly measures the increase in value to the firm
 NPV approach requires a discount rate, which may not
always be possible.
 While NPV is a absolute measure IRR is a relative
measure.
 Whenever there is a conflict between NPV and IRR always
use NPV
51

52. Advantages of IRR
• the time value of money
• the total cash flows during the project life direct
message about the yield on the project.
Disadvantages of IRR
• It involves tedious work interpolation
• The IRR does not reflect the scale, or Birr/dollar
size
• all proceeds are reinvested at the particular
IRR,
• If there are non-conventional cash flows, it
can produce multiple rates.
52

53. Discounted Payback Period
 This improves upon the payback period by taking
into account the time value of money.
 A project’s discounted payback period is the
number of years it takes for the net cash flows’
present values to pay back the net investment.
 Again, shorter paybacks are better than longer
paybacks.

54. Discounted Payback Period-Example:
 We will need a required rate of return for the
computation. Let’s use 10%.
Year CF (Birr)
0 -200,000
1 70,000
2 70,000
3 70,000
4 70,000
5 70,000

55. Discounted Payback Period
Year CF (Birr) PV of CF (Birr) Cumulative (Birr)
0 -200,000 -200,000 -200,000
1 70,000 63,636 -136,364
2 70,000 57,851 -78,513
3 70,000 52,592 -25,921
4 70,000 47,811
5 70,000 43,463
55

56. Discounted Payback Period
 The DPP will be 3 years plus whatever proportion of
year 4 is needed to pay back the final Birr 25,921.
 The discounted payback is 3.54 years.
 This project recovers its net investment in 3.54 years
when considering the time value of money.
54
.
3
47,811
25,921
3
DPP 



57. Discounted Payback Period
 The DPP is an improvement upon the payback period
in 2 ways:
 The DPP takes into account the time value of money.
 There is an objective criterion for an acceptable DPP if
a project has normal cash flows.
 Under these circumstances a project is acceptable if
the DPP is less than the economic life of the
project.

58. Discounted Payback Period-Exercise
 what is the discounted Payback period given that the
discount rate is 10%
58
Project Year Cash flow (in Birr)
0 -10000
1 5000
2 6000
3 8000
4 7000
5 6000

59. Discounted Payback Period- Exercise
 what is the discounted Payback period?
59
Project Year Cash flow PV of Birr
1 at 10%
PV of cash flow Cumulative cash
savings
0 -10000 1.000 -10000 -10000
1 5000 0.909 4545 -5455
2 6000 0.826 4956 -499
3 8000 0.751 6008 5509
4 7000 0.683 4781 10290
5 6000 0.621 3726 14016

60. 8-60
Summary _Project appraisal In Practice
 Consider all project appraisal criteria when making
decisions
 NPV and IRR are the most commonly used primary
investment criteria
 Payback is a commonly used secondary investment
criteria
 All provide valuable information

61. 8-61
NPV Summary
Net present value =
 Difference between market value (PV of
inflows) and cost
 Accept if NPV > 0
 No serious flaws
 Preferred decision criterion

62. 8-62
IRR Summary
Internal rate of return =
 Discount rate that makes NPV = 0
 Accept if IRR > required return
 Same decision as NPV with conventional
cash flows
 Unreliable with:
 Non-conventional cash flows
 Mutually exclusive projects

63. 8-63
Payback Summary
Payback period =Length of time until initial
investment is recovered
 Accept if payback < some specified target
 Doesn’t account for time value of money
 Ignores cash flows after payback
 Arbitrary cutoff period
 The best alternative: discounted payback
period