This document discusses various methods for financial analysis and project selection. It describes numeric models such as net present value (NPV), internal rate of return (IRR), payback period, accounting rate of return (ARR), and return on investment (ROI). It also discusses non-numeric models like sacred cow, operating necessity, and competitive necessity. The key techniques in numeric models are then explained in more detail, including discounting cash flows, calculating NPV, determining payback periods, and how to use these models to evaluate investment projects. Examples are provided to illustrate how to apply these financial analysis methods.
This pdf is only to learn payback, timevalue of money and IIr
and there example are also given by me to easy to lean there example if any doute then contact me...
Describes in detail the steps involved in the calculation of Internal Rate of Return. Useful to students of Under graduate, post graduate and professional course students pursuing course in finance
This pdf is only to learn payback, timevalue of money and IIr
and there example are also given by me to easy to lean there example if any doute then contact me...
Describes in detail the steps involved in the calculation of Internal Rate of Return. Useful to students of Under graduate, post graduate and professional course students pursuing course in finance
Meaning of financial statement
Objectives of financial statement
Characteristics of financial statement
Nature of financial statement
Balance sheet
Format of balance sheet
Illustrations
Exercises
Statement of profit & loss
Format of statement of profit & loss
Notes of statement of profit &loss
Illustrations
Exercises
Understanding Basics of Financial StatementsAnkita6745
Understanding the basic concepts and term used in the Financial Statements.Understanding the ratios used for analyzing the Financial Statements.Discussing factors that drive corporate valuations.
Projects may look attractive for two reasons:1) There are some errors in forecast 2)The company genuinely expects to earn excess profits.
So increase odds in your favor by moving in areas of competitive advantages.
Look at economic rents and where even advantage is absent or entry of competitors will push prices down or costs up, don’t enter .
When you have the market value of an asset use it..rather then over analysis…gold, real estate..airplanes etc…
PV calculations may vary and subject to error …that’s life!!!!!
Meaning of financial statement
Objectives of financial statement
Characteristics of financial statement
Nature of financial statement
Balance sheet
Format of balance sheet
Illustrations
Exercises
Statement of profit & loss
Format of statement of profit & loss
Notes of statement of profit &loss
Illustrations
Exercises
Understanding Basics of Financial StatementsAnkita6745
Understanding the basic concepts and term used in the Financial Statements.Understanding the ratios used for analyzing the Financial Statements.Discussing factors that drive corporate valuations.
Projects may look attractive for two reasons:1) There are some errors in forecast 2)The company genuinely expects to earn excess profits.
So increase odds in your favor by moving in areas of competitive advantages.
Look at economic rents and where even advantage is absent or entry of competitors will push prices down or costs up, don’t enter .
When you have the market value of an asset use it..rather then over analysis…gold, real estate..airplanes etc…
PV calculations may vary and subject to error …that’s life!!!!!
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Evgen Osmak: Methods of key project parameters estimation: from the shaman-in...
2.8 skill financial analysis
1. 2.8 FINANCIAL ANALYSIS
FINANCIAL ESTIMATES & PROJECTIONS (only
as a basis for additional readings )
• To judge a project from the financial angle, we
need information about the following
– Cost of project
– Means of financing
– Estimates of sales & production
– Cost of production
– Working capital requirement & its financing
– Estimates of working results profitability projections
– Break even point
– Projects cash flow statements
– Projected balance sheets
2. 2.8 FINANCIAL FEASIBILITY
• From the point of view of:-
The direct project beneficiaries
Project as a whole
Any financial intermediary
The government
• Values directly quantifiable Project inputs at market
prices
• Government policy measure effects can either be
cost or benefits
• Debt services are costs; &
• Presents an entity's point of view
3. PURPOSE OF FINANCIAL ANALYSIS
• Provide an adequate financing plan for the proposed
investment
• To determine the profitability of project from the point of view
of the financial agency (bankers), the owners or the projects
beneficiaries;
• To assist in planning the operation & control of the project by
providing management information to both internal & external
users;
• To illustrate the financial structure of a project entity, & its
existing & potential financial viability including the financial
efficiency & effectiveness of this operations;
• To advise on methods of improving the financial viability of a
project entity including the appropriateness of tariffs, prices &
cost recovery generally
4. METHODS OF FINANCIAL ANALYSIS
• Resources flow statements
• Cash flow statements
• Discounted cash flow
• Cost benefit analysis
Net present value
Internal rate of return
Benefit cost ratio
• Cost effectiveness analysis
• Sensitivity analysis
6. One birr received now is more than one birr received a year
later- because
• Pure time preference
• Opportunity cost of capital
• Inflationary period
• Risk & uncertainty
The concept of compounding
F=P(1+r)n
F = Future Value
P = Principal
R = Rate
N = The year
DISCOUNTING
7. Discounting – Reverse of compounding
P = F
(1+r)n The discount factor
Time preference & project appraisal
• To compare the true value of resources-absorbed & released
• Use a common denominator i.e. some way of treating on the same
basis costs & benefits that arise at different points in time
DISCOUNTING
8. TIME VALUE OF MONEY
Year 0 1 2 3 4
Cash flows -1000 250 250 250 250
• For example, assume that an intervention requires Birr 1,000 & the subsequent
inflows of Birr 250 in each of the next 4 years.
Table: Timeline of cash flows
• Compounding & discounting:
• Cash flows occur at different points of time
• So, for meaningful comparison, all these cash flows should be assessed at the same
point of time.
• Either
• the cash flow occurring today has to be converted into its equivalent at a
future date or
• the cash flow occurring later has to be converted back to today’s value.
9. COMPOUNDING
• With simple interest, the future value is determined by:
• Suppose you have won a lottery worth of Birr 1,000,000. If you
deposit it in Commercial Bank of Ethiopia with an interest rate of Birr
5% for 5 years, how much will the FV be in the 5th year?
• What about 1,000 Birr saved in Bank for 8 years with an interest of
10%?
t
t r
PV
FV )
1
(
t
FV
t
PV
Where = is future value at time n
= is the original sum invested or the principal value &
I =stands for annual rate of simple interest
10. TIME VALUE OF MONEY
• Simple Interest Rate:
• If no interest payment is reinvested to earn further interest in future
periods, we apply the following formula:
• For example, if Birr 1,000 is invested at 12% simple interest for 5
years, what will be the value at the end of the 5th year?
• Answer:
600
,
1
)
12
.
0
*
5
1
(
000
,
1
11. TIME VALUE OF MONEY
• Basis of Time Value
– The cash inflow & outflow usually occurs over a period of time.
– This leads us to consider time value of money.
– The value of money depends on when the cash flow occurs.
– Thus, Birr 100 at present is worth more than Birr 100 at a future date.
• Reasons:
– Interest or rent: money, like any other commodity, has a price. If you own it,
you can rent it or deposit it in a bank & earn interest.
• The interest or rent reflects the e time value of money.
• It comprises:
– Risk-free rate of return rewarding investors for foregoing immediate
consumption
– Compensation for risk & loss of purchasing power
11
12. TIME VALUE OF MONEY
• Uncertainty:
– Birr 100 now is more than Birr 100 at a future date
– This ‘bird-in-the-hand’ principle affects many aspects of financial management
– That is why individuals prefer current consumption to future consumption
• Inflation:
– Under inflationary conditions, the value of money, expressed in terms of its
purchasing power over goods & services, declines.
– Nominal or market interest rate = real interest or return + risk premiums +
expected rate of inflation.
• There are two methods of estimating time value of money:
• these are
– compounding &
– discounting.
12
13. THE NATURE OF PROJECT SELECTION MODELS
• There are two types of project selection models.
Non-numeric and models do not use numbers as inputs
Numeric But numeric models do
• What models should do for us:
Models do not make decisions;
people do-the manager,
not the model, bears responsibility for the decision.
All models, however sophisticated, are only partial
representations of the reality they are meant to reflect
• The non-numeric models are older & simpler.
14. TYPES OF PROJECT SELECTION MODELS NON-
NUMERIC MODELS
The subtypes of non-numeric models are the following:
a) The Sacred Cow: the project is suggested by a senior & powerful official.
The project is “sacred” in the sense that it will be maintained until
successfully concluded, or until the boss, personally, recognizes the idea
as a failure & terminates it.
b) The Operating Necessity: If a flood is threatening the plant, a project to
build a protective dike does not require much formal evaluation.
c) The Competitive Necessity: for example, companies may need to
modernize their work to remain competitive
d) The Product Line Extension: adding new products to the line making
sure that it strengths a weak link.
e) Comparative Benefit Model: selecting a project based on the benefits it
brings
15. TYPES OF PROJECT SELECTION MODELS- NUMERIC MODELS
Subtypes of Numeric Models
a) Ranking by Inspection
b) Return on investment (ROI)
c) Accounting Rate of Return (ARR)
d) Payback Period:
16. A) RANKING BY INSPECTION (RI)
• Basic question:
– Given alternative investments which one should be implemented & which one
should be discarded in a mutually exclusive investments?
• There may be an alternative as to build a factory or a business mall on the same
site.
• The investor might choose to start one with limited resources he/she has.
• RI consists of choosing the best investment by comparing the net proceeds of
alternative investments.
• The project having more cash proceeds will be preferred though are some
peculiarities on inspections.
• Comparing the net proceeds of A & B projects, we can find out which project has
shorter life period
• Compare the net proceeds of the short lived project with long lived one
• If the two have the same initial investment & proceeds throughout the period of
the short lived investment; & if the long lived investment continues to earn
income after the end of the short lived one, then the long lived one is more
desirable as the second project continues to earn proceeds while the first one has
ended
17. PROJECT SELECTION BASED ON RI
Project Investment Initial Cost Net Cash Proceeds in Years
1 2 Total
A 20,000 20,000 - 20,000
B 20,000 20,000 2,000 22,000
C 20,000 14,625 9,825 24,450
D 20,000 16,325 8,125 24,000
Then, which one is more desirable-taking into account the net proceeds?
Net Cash Flow of 4 Hypothetical Projects with Identical Initial Investment Outlays & Life Periods
Although the total net proceeds of C & D are identical, D earns more income earlier than C.
Thus D is more desirable than C
Project B is more desirable than A
Why????
19. B) RETURN ON INVESTMENT (ROI)
• Also called average income on cost
• Calculated by dividing the average income by the cost of investment
• Some planners prefer to take the ratio of the average income to the book value
(cost of investment after depreciation)
20. C) ACCOUNTING RATE OF RETURN (ARR)
• The accounting rate of return
(ARR), expresses the profit
forecast as a percentage of the
capital expenditure involved
• ARR is also known as accrual
accounting rate of return,
unadjusted rate of return model
& the book value model
• ARR is a measure of profitability in
accounting terms.
• This method aims to quantify the
profits expected from investment
projects under consideration
• There are different methods of
calculating the ARR
• ARR=Average Income after tax
Initial Investment
• ARR=Average Income after tax
Average Investment
• ARR= AIAT, but before Interest
Initial Investment
• ARR= AIAT, but before Interest
Average Investment
• ARR= Average Inc. b/r Int. &tax
Initial Investment
• ARR= Average Inc. b/r Int. &tax
Average Investment
21. ARR: Example
• A project requiring an average investment of ETB
1,000,000 & generating an average annual profit of ETB
150,000 would have an ARR of 15%.
22. D) PAYBACK PERIOD
• the initial fixed investment in the project divided by the estimated annual cash
inflows from the project.
• The ratio of these quantities is the number of years required for the project to
repay its initial fixed investment.
– For example, assume a project costs $100,000 to implement & has annual net cash inflows of
$25,000. Then Payback period = $100,000/$25,000= 4 years.
• This method ignores any cash inflows beyond the payback period
• The payback period is the length of time from the beginning of the project until
the sum of net incremental benefits of the project equal to total capital
investment.
• It is the amount of time it takes to recover the original/investment cost.
• The method is very simple.
• Moreover, it is a good measure when the project has problem of liquidity.
• The pay-back period is also a common, rough means of choosing among projects in
business enterprise, especially when the choice entails high degree of risk.
• Payback rule: If the calculated payback period is less than or equal to some pre-specified payback
period, then accept the project. Otherwise reject it.
23. TYPES OF PROJECT SELECTION MODELS
This method has two important weaknesses:
fails to consider the time & amount of net benefits after the payback period.
does not adequately take into account the time value of money even in the
payable periods.
24. Payback Period
Birr
+ve
- ve
Time
Payback period
Cumulative net
cash inflow)(CNCI)
Peak
cumulative
cash flow
Cash trough
Calculate annual net cash flow
Accumulate year on year
Plot on graph of CNCI against time
Total
profit
25. PAYBACK PERIOD
• If the expected cash inflow is a constant sum:
Pay Back period= Cash outlay (investment)
Net Annual cash inflows
If the expected cash inflow varies from period to period:
Pay Back period=Year before full recovery +
Unrecovered cost at the start of year
Cash flow during the year
But if the net cash inflow is the same across years, we use a
simple formula to get the payback period.
Example:
1. If Birr 2 million is invested to earn Birr 500,000 per annum
for 7 years, the pay back period is computed as follows:
Pay back period = Br 2million/500,000= 4yrs
26. EXERCISE 1
• Assume that a firm is considering two projects:
– Project A & project B,
– each requiring an investment of Br100 million.
– Below is the summary of expected net cash flows in millions.
• Then
– find the payback period for the two projects &
– indicate which project should be chosen. Initial Investment= 100 million
27. EXERCISE 2
Alternative
projects
Year Investment cost Net incremental
benefits
Cumulative net
incremental benefits
I 0
1
2
3
4
20000 -
2000
8000
12000
9000
31000
II 0
1
2
3
4
20000 -
2000
12000
8000
12000
34000
III 0
1
2
3
4
5
6
7
20000 -
1000
5000
6000
8000
10000
5000
2000
37000
28. EXERCISE 3
• Calculate the payback period for this project given the net cash
flows indicated in the table below
• Show the cash flow graphically
Time
(yrs)
0 1 2 3 4 5
Revenue 100 100 200 200 200
Costs (300) 20 20 20 20 20
Net Cash
flows
-300 80 80 180 180 180
29. ANSWER TO EXERCISE 4
PBP = 2.78 years
Time (yrs) 0 1 2 3 4 5
Revenue 100 100 200 200 200
Costs (300) 20 20 20 20 20
Net Cash flows -300 80 80 180 180 180
Cum cash flows -300 -220 -140 40 220 400
30. MERITS OF PAYBACK PERIOD AS AN
INVESTMENT APPRAISAL TECHNIQUE
• Simplicity
• Rapidly changing technology,
if new plant is likely to be
scrapped in a shorter period
because of obsolescence, a
quick payback is essential,
• Payback favors projects with a
quick return
• Rapid project payback leads to
rapid company growth
• Rapid payback minimizes risk
CRITICS OF PAYBACK PERIOD AS AN
INVESTMENT APPRAISAL TECHNIQUE
• Project return may be ignored-
in particular, cash flows arising
after the payback period are
ignored.
• Timing is ignored
• Lack of objectivity- what length
of time should be set as the
minimum payback period
• Project profitability is ignored
31. NUMERIC MODELS : DISCOUNTED MEASURES
• Net Present value (NPV)
• Internal rate of return (IRR)
• Benefit Cost ratio
32. NPV: as Investment Criteria
n
i
t
t
r
C
A
NPV
1
0
)
1
(
t
C
r
0
A
Where,
= the net cash flow in period t
= the required rate of return, &
= initial cash investment (because this is an outflow, it will be
negative).
NPV: it determines the net present value of all cash flows by
discounting them by the required rate of return.
32
33. THE NET PRESENT VALUE
• Simplest measure
• Measures aggregate surplus generated by the
project
• PV of Benefit – PV of Costs
Decision criteria
NPV > 0 Accept
NPV < 0 Reject
NPV = 0 Marginal case
34. NPV
Suppose that the project has the following data
• Initial Investment (I) = 300,000 Birr
• Annual costs of operation = 20,000 Birr
• Expected annual revenue =
100,000 Birr/year in the first 2 years &
200,000 Birr/year in the next 3 years
• Time horizon = 5 years
34
35. Gross cash flows
Time
(yrs)
0 1 2 3 4 5
Revenue 100 100 200 200 200
Costs (300) 20 20 20 20 20
Net cash
flows
-300 80 80 180 180 180
N.B: - All revenues & costs are in thousands of Birr
35
DF= 10%
39. Exercise
• Assume that the initial investment of a project is Birr
450,000. In the first & second years, the net benefits are
50,000 & 75,000 respectively. In the third, fourth & fifth
years, the net benefits stand at 100,000; 125,000 &
150,000. respectively. The discount rate is 10%.
Based on this information, find the NPV & show whether
the project should be accepted or rejected.
• Will your decision change if the discount factor is
increased to 15%?
39
40. solution
TiME 1 2 3 4 5
Benefits -450,000 50,000 75000 100,000 125,000 150,000
Discounte
d cash
flows 45454.55 61983.47 75131.48 85376.68 93138.2
commulati
ve
discounte
d cash
flow -404,545 -342,562 -267,431 -182,054 -88,915.6
r=10%
NPV<0
hence
reject
project
41. NPV
To include the impact of inflation where we have is the predicted
rate of inflation during period
n
i
t
t
t
p
r
C
A
NPV
1
0
)
1
(
t
p t
•Initial investment Birr 100,000.
•Net cash inflow Birr 25,000
• discount factor: 7%
•Inflation rate: 5%
•The life span of the project is 8 years
•Find the NPV & make a decision whether the project should be
accepted or not.
41
42. NPV (exercise)
Early in the life of a project, net cash flow is likely to be negative
The major outflow at this stage is the initial investment in the
project
The project is acceptable if the sum of the NPVs of all estimated
cash flows over the life of the project is positive.
Example, the investment is 100,000 with a net cash inflow of
25,000 per year for a period of eight years. The discount rate is
15%, an inflation rate is 3% per year. Calculate NPV.
Use the above formula.
The answer is = 1939.
The NPV of the inflows is greater than the NPV of the outflow-
i.e., the NPV is positive-the project is deemed acceptable.
42
44. NPV
44
Calculation & Answer:
NPVA = -5,000 + 500 + 1,000 + 1,000 + 1,500 + 2,500 + 1,000 = $469
(1.084)1 (1.084)2 (1.084)3 (1.084)4 (1.084)5 (1.084)6
NPVB = -2,000 + 500 + 1,500 + 1,500 + 1,500 + 1,500 + 1,500 = $3,929
(1.084)1 (1.084)2 (1.084)3 (1.084)4 (1.084)5 (1.084)6
Given that both machines have NPV > 0, both projects are acceptable. However, for
mutually exclusive projects, the decision rule is to choose the project with the
greatest NPV. Since the NPVB > NPVA, the company should choose the project for
Machine B.
45. 2. IRR
• Internal rate of return (IRR)
• The internal rate of return is defined as the rate of discount, which brings
about equality between the present value of future net benefits & initial
investment. It is the value of r in the following equation.
• I – investment cost
• Ct – Net benefit for year t
• r - IRR
• n - Life of the project
• Illustration: For project A in the above table can be formulated as follows:
45
n
t
t
t
r
C
I
1 1
IRR is PV(Benefits) = PV(Costs). Use algebra or a spreadsheet
46. IRR
Internal Rate of Return (IRR);- emerges from the cost-benefit data of the
project
It is the discount rate that reduces the NPV of a project to zero
IRR = Discount Rate, which makes the NPV zero
46
NPV
IRR
Discount Rate
NPV
47. IRR
• Calculation of IRR
• Year Cash flow
• 0 -100000
• 1 30000
• 2 30000
• 3 40000
• 4 45000
• The IRR is the value of r which satisfies the following equation:
4
3
2
1
0
)
1
(
000
,
45
)
1
(
000
,
40
)
1
(
000
,
30
)
1
(
000
,
30
)
1
(
000
,
1000
0
r
r
r
r
r
4
3
2
1
)
1
(
000
,
45
)
1
(
000
,
40
)
1
(
000
,
30
)
1
(
000
,
30
000
,
100
r
r
r
r
The calculation of r consists of a process of trial & error by assuming various values
of r say eg.14, 15, 16 & so on. The IRR % may fall anywhere between these % values.
47
48. IRR
• The calculation of r involves a process of trial & error. We try different values of “r”
till we find that the right-hand side of the above equation is equal to 100,000. Let us
try to use 15%. This makes the right-hand side to be:
48
4
3
2
1
1
000
,
45
1
000
,
40
1
000
,
30
1
000
,
30
000
,
100
r
r
r
r
Year 0 1 2 3 4
Cash flow (100,000) 30,000 30,000 40,000 45,000
IRR is the value of r which satisfies the following equation:
802
,
100
15
.
1
000
,
45
15
.
1
000
,
40
15
.
1
000
,
30
15
.
1
000
,
30
000
,
100 4
3
2
Since the value is slightly higher than our target value, which is 100,000, we
increase the value to 16%.
641
,
98
16
.
1
000
,
45
16
.
1
000
,
40
16
.
1
000
,
30
16
.
1
000
,
30
000
,
100 4
3
2
49. IRR
• Since this value is now less than 100,000, we conclude that the value of r
lies between 15 & 16%. For most of the purposes, this indication suffices.
• If a more refined estimate of r is needed, we use the following procedure:
1. Determine the NPV of the two closest rates of return
(NPV/15%) = 802
(NPV/16%) = 1,359
2. Find the sum of the absolute values of the NPVs obtained in Step 1
802+1,359 = 2,161
3. Calculate the ratio of the NPV of the smaller discount rate, identified in
Step 1, to the sum obtained in Step 2
802/2,161 = 0.37
4. Add the number obtained in Step 3 to the smallest discount rate
15+0.37 = 15.37
49
50. INTERNAL RATE OF RETURN
• Equates the PV of the costs and benefit streams
• NPV becomes zero
• Measure the efficiency of the use of capital
Decision criteria
• IRR > Test Discount Rate – Accept
• IRR < Test Discount Rate - Reject
• IRR = Test Discount Rate – Marginal
53. Self-check Exercise
Project A Project B
Year Net benefits Gross benefits Costs
1 7,500 7,000 2,000
2 7,000 5,500 2,000
3 5,500 7,500 2,500
4 6,250 8,500 2,500
5 6,500 9,500 2,000
53
Table 1. Cash flow for project A & B
Initial investment is Birr 20,000 each.
Discount factor: 10%
54. Exercise
54
Year Gross Benefits Costs
1 200,000 50,000
2 200,000 50,000
3 300,000 100,000
4 300,000 100,000
5 350,000 100,000
Initial Investment: Birr 700,000
Find the NPV & IRR of an environmental project from the following table
Consider different discount rates.
Hint: you may start from 10%
55. Conditions of Financial Viability of a Project
• The acceptance criterion for an investment is:
NPV positive,
IRR greater than the discounted rate; &
discounted benefits greater than discounted costs
55
56. BENEFIT- COST (B/C) RATIO
• Ratio of the PV of benefits to the PV of costs
• Measure of efficiency
B/C Ratio = PVB
PVC
Decision criteria
B/C Ratio > 1 Then NPV +ve Accept
B/C Ratio < 1 Then NPV -ve Reject
B/C Ratio = 1 Then NPV 0 Marginal
57. 3. Benefit-Cost Ratio (BCR) Computation
• BCR =
Or
Outflows
Cash
of
Value
esent
Inflows
Cash
of
Value
esent
BCR
Pr
Pr
57
58. BCR
T
t
t
t
t
T
t
t
t
t
r
Cost
r
Benefit
BCR
1
1
1
1
58
59. Find the BCR & decide whether to accept the project
59
Time Gross
Benefit
Cost
0 100 150
1 100 100
2 100 50
DF: 10%
60. Find the BCR
Time Benefit Cost Net Benefit
0 100 150 -50
1 100 100 0
2 100 50 50
What is your decision?
60
62. Exercise
• The details of a project which costs Birr. 25,000 as initial investment
are given below:
• Year Cash flow
• 0 (25,000)
• 1 5,000
• 2 7,000
• 3 13,000
• 4 16,000
• Calculate:
• a)Net present Value(NPV) at 20%:
• b) Internal Rate of Return(IRR):
• c) Payback Period:
• Use graphs to display your answers
62
66. Financial checklist
• Are the sources of financing clearly identified (equity, loan, grant)?
• Is the amount of money required to implement & operate the project
adequate & will it be timely available?
• What are the terms of financing the project?
• Is proper cost-benefit analysis being done for the project?
• Do the expected results bring about a reasonable return on the capital
invested?
• What is the financial rate of return (NPV, IRR, etc)?
• Is sensitivity analysis made for the project?
• What are the net effects on the government’s budget, allowing for any
loss of customs duty on imports, the cost of fiscal incentives & allowances,
& initial equity participation, & recurrent subsidy?