3. INTRODUCTION
Investment decision is one of the main roles
of the financial manager, others being
dividend and financing decisions.
It involves decisions on whether or not to
undertake a particular investment or a project
among alternatives.
It requires the estimation of relevant cash
flows and appropriate discount rates.
Discount rates can be monetary (including
inflation) or real (excluding inflation).
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4. INTRODUCTION
Investment decision is underpinned by the
Concept of Time Value of Money(TVM).
TVM is a central concept in financial
management. It applies to almost all financial
decisions in today’s business world.
It involves the timing of cash flows based on
the premises that, a shilling today is worth
more than a shilling tomorrow.
TVM is grounded by the Bird-In-Hand Theory
established by Myron Gordon in 1959.
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5. INTRODUCTION
The theory asserts that; a bird in hand is
more preferred to two birds in the bush.
The theory implies that contemporaneous
cash flows are known with certainty and
therefore safe while future cash flows are
uncertain because they are subject to risk
and inflation.
Thus, there are three elements of TMV;
namely; time value (time difference), risk and
inflation.
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6. INTRODUCTION
When appraising a capital project, it is important to
first determine which cost or revenue should be
included.
That is: not every cost or revenue is relevant for
capital budgeting decisions.
The capital budgeting decisions should be based
on after tax cash flows.
The decisions should also include cash flows NOT
accounting income.
Also, decisions should only consider the
incremental cash flows.
Net cash flows = Net income + Depreciation
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7. DETERMINING RELEVANT CASH FLOWS
When appraising a project, it is important to determine whether a cash
flow is relevant or irrelevant. This is due to the fact that, not every cash
flow is relevant for decision making.
1. Income or Profit
This is not relevant for capital budgeting decisions because it is not a
cash flow but rather an amount earned from business activity. To be
considered as a cash flow, income should be adjusted including adding
back depreciation (if any). Normally, after tax cash flows are used NOT
accounting profits.
2. Sunk Costs
A sunk cost is an outlay that already has been spent or committed or
occurred and can not be recovered regardless of whether the project is
accepted or rejected. For example, the feasibility study costs, the
development or demolition costs etc. These costs should be ignored in
cash flow projections.
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8. DETERMINING RELEVANT CASH FLOWS
3. Incremental Cash Flows
These are cash flows that are dependent on the project's implementation or
cash flows which result directly from the decision to accept the project and
they represent the changes in the firm's total cash flows. A fundamental
principle in appraising a project is to include all incremental cash flows. The
project cash flows are normally categorized into three parts;
a) Initial Investment Outlay: This is a cash flow that occurs at the beginning
of the projects life, time 0. This may include; purchase price of the new
project or capital equipment, shipping costs, installation costs, disposal of
the old machinery or building, and changes in the net working capital.
b) Incremental Operating Cash Flow: This is a cash flow that emanates
from the project's operations and occurs continuously throughout the
project's life.
c) The Terminal Cash Flow: This is the net cash flow that occurs only at the
end or the termination of the project. It may include; the final disposal of
the project, salvage or scrap value, and the reversal of any working capital
changes occurred at the beginning of the period.
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9. DETERMINING RELEVANT CASH FLOWS
4. Opportunity Costs
These are cash flows that could be generated from the assets
the firm already owns provided they are not used for the project
being appraised. For example, land that could be rented or sold
and generate income is an example of the opportunity costs.
Others may include; the loss of net cash flows from other
projects as a result of accepting the project. Thus, opportunity
costs are relevant for cash flow projections.
5. Externalities/ Incidental Effects: The effect of a project will
have on the cash flows of the other parts of the firm when
accepted e.g. increase or decrease in sales of other products of
the company.
6. Shipping and Installation Costs: These are relevant costs
and have to be added to the invoice price of the equipment when
the total cost of the project is being determined.
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10. DETERMINING RELEVANT CASH FLOWS
7. Working Capital
Normally, when a capital project is accepted, it
involves a huge amount of expenditures and
depreciable assets. However, additional investment
is required in terms of working capital which is the
difference between current assets and current
liabilities. The main short-term assets are cash,
stock (inventories) and debtors whilst the principal
short-term liabilities are creditors.
Thus, working capital = ∆Current Assets -∆Current
Liabilities.
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11. CAPITAL BUDGETING DECISIONS
UNDER CERTAINTY SITUATION
1. Introduction
These are capital budgeting decisions with possible single
outcomes known with certainty.
Capital budgeting is a planning decision process involving the
forecast of future cash flows and the commitment of current
resources in order to realize future stream of benefits.
Capital budgeting is concerned with long-term investment
decisions, thus the planning horizon has to be longer than one
year.
Expenditures in capital budgeting are irreversible; thus proper
planning is required to avoid loosing funds.
In evaluating the project, the following analysis may also be
included: market, technical, financial, economic and
ecological analyses.
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12. CAPITAL BUDGETING
TECHNIQUES
3. Capital Budgeting Techniques
1. Non-Discounted Cash Flow Techniques
These are capital budgeting techniques which do not take into
consideration the concept of Time Value of Money.
i. Payback Method (Payback Period)
This is the length of time before the cumulated stream of forecasted
cash flows equals the initial investment or It is the number of years
required to return the original investment from the net cash flows (i.e.
Net operating income after taxes plus depreciation).
The Decision Rule
If payback period > acceptable time limit reject the project
If the payback period ≤ acceptable time limit accept the project
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13. CAPITAL BUDGETING TECHNIQUES
Example
ABC Ltd is considering two projects; A and B. Each requires an
investment of $100 millions. The cost of capital is 10%. Below is the
summary of expected net cash flows in millions
Year Project A Project B
1 50 10
2 40 20
3 30 30
4 10 40
5 1 50
6 1 60
Which project should be accepted?
Note: The payback period for project A is 2 and 1/3 years whilst that of
B is 4 years. Thus, project A should be accepted. Normally, the firm
pre-determines the payback period.
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14. CAPITAL BUDGETING TECHNIQUES
Advantages of Payback Method
It is very easy to calculate but it can lead to wrong decision.
Put more emphasis to quick return of invested fund so that
they may be put to use in other places or in meeting their
needs.
Easy to apply
Disadvantages of Payback Method
Does not consider post-payback cash flows
Does not consider time value of money
Does not explicitly consider risk
The acceptable time period is arbitrary: The period is not
necessarily optimal payback period.
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15. CAPITAL BUDGETING TECHNIQUES
ii. Accounting Rate of Return (ARR)
This method is sometimes known as accrual
accounting rate of return. The accounting
rate of return is given by;
Or
%
100
Pr
x
ent
ualInvestm
AverageAnn
ofit
AverageNet
ARR
%
100
x
I
D
O
ARR
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16. CAPITAL BUDGETING TECHNIQUES
Where;
ARR= Average Accounting Rate of Return
O = Average Annual Investment and Inflow from operation.
D = The incremental average annual depreciations
NOTE: The project or investment is only accepted when ARR exceeds the minimum rate
of return (Hurdle rate) set by the firm.
Advantages
It is simple to calculate using accounting data
It is easy to understand
Earnings of each year are included in calculating the profitability of the project.
Disadvantages
It is inconsistent with wealth maximization as the objective of the firm.
It uses accounting profits instead of cash flows
It ignores the time value of money
It is based on the familiar accrual accounting.
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17. CAPITAL BUDGETING TECHNIQUES
Numerical Example
Assume that the firm has invested £800,000 in
machinery and its expected useful life is 4years. If
the estimated disposal or scrap value is zero and
the expected annual cash inflow from operations is
£260,000. Calculate the accounting rate of return.
Suggested Solution.
Annual depreciation = original investment/ useful lie
(Assuming straight-line method of depreciation).
= £ 800000/4 = 200,000
Thus, Accounting Rate of Return (ARR) =
%
5
.
7
000
,
800
000
,
200
000
,
260
£
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18. CAPITAL BUDGETING TECHNIQUES
2. Discounted Cash Flows Techniques
i. Discounted Payback Method
Unlike the normal payback method, this one
uses the discounted cash flows.
ii. Net Present Value
iii. IRR
o
n
n
I
k
F
k
F
k
F
NPV
)
1
(
.....
..........
)
1
(
)
1
( 2
2
1
1
o
n
n
I
F
F
F
.....
..........
0 2
2
1
1
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19. CAPITAL BUDGETING TECHNIQUES
iv. Profitability Index (PI)
This is sometimes called the Benefits Cost
Ratio or Present Value Index.
)
(
Pr
flow
InitialOut
Cost
lows
sofCashInf
esentValue
PI
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20. Discounted Payback Method
This method is similar to the normal pay
back period method in approach.
Future cash inflows are discounted first
Then, Cumulative cash inflows are
calculated
The length of time to cover the original
investment is thus determined.
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21. NPV
NPV Decision Rules
For independent projects: Accept all
projects where NPV≥ 0, reject otherwise.
For mutually exclusive projects; Rank
projects from highest to lowest NPV and
choose the project with the highest (positive)
NPV.
NPV Curve or Profile
This is a graphical plot of the inverse
relationship between the discount rate, k and a
project's NPV.
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23. NPV Profile
The implication is that, the higher the
discount rate, the lower the NPV and vice
versa.
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24. NPV
Advantages
Considers the Time Value of Money
It takes into account the scale (size) of
investment i.e. absolute amounts of wealth
change.
Disadvantages
It is relatively difficult to explain to non-
finance people.
Solution is in absolute amounts of money, not
percentage rates of return.
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25. IRR
IRR is the discount rate which when applied to the cash
flows of a project, results in zero net present value or is
the estimated rate of return given its incremental cash
flows.
IRR is obtained when, NPV = 0.
IRR Decision Rules
Independent Projects: Accept all as long as the IRR ≥
Hurdle rate
Mutually Exclusive Projects: Compute (IRR-Hurdle
rate) for each project, rank from highest to lowest and
accept the highest ranking project (Assuming the
computation, IRR-Hurdle rate > 0).
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26. IRR
Advantages
Considers time value of money
Considers all cash flows
Comparable with hurdle rate
Disadvantages
Does not show dollar improvement in value of firm if
project is accepted.
Possible existence of multiple IRRs (Multiple IRR
Problem) when cash flows are unconventional.
IRR can be affected by the scale (size) of the
investment (i.e. I0).
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27. IRR
The Relationship between IRR and the NPV Profile
1. When IRR = the firm's hurdle rate, NPV = 0.
2. When IRR ˂ the firm's hurdle rate, NPV ˂ 0.
3. When IRR ˃ the firm's hurdle rate, NPV ˃ 0.
NPV and IRR Methods : Possible Decision Conflicts
The decision conflict arises when one method gives a
different decision from the other one. For example when, NPV
suggests to accept the project, IRR suggests to reject it.
The conflict only arises for mutually exclusive projects.
The conflict arises due to timing and magnitude differences in
incremental cash flows.
When a conflict arises, the solution is to pick a the project with
the highest NPV.
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28. Estimating IRR When Two
Points are given
When two points of the discount rates and
Present Values are given say; P1(R1, N1)
and P2 (R2, N2), then we can estimate IRR
as follows;
IRR = R1± (R2 – R1)x N1
N2-N1
+ Is used when the present value of the lower
discount rate is positive while
- Is used when the present value of the lower
discount rate is negative.
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29. PROBLEMS WITH IRR
Multiple IRRs
– Conventional cash flows investments (those
with - + + +… pattern of cash flows) have
unique IRR
– Non conventional investments have other
pattern of cash flows and NPV can be found
to be equal to zero at more than one rate!
Hence Multiple IRRs.
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30. PROBLEMS WITH IRR
Multiple IRRs? Cont’d
– A possibility of multiple IRRs poses problems to the use of IRR
as investment criteria. Why?
The normal IRR decision rule do not always work
Project may be profitable only within a range of rates not acceptable
by IRR
– Hence a need to consider NPV rule in such situation
Example
Coal Mining Project with initial outlay of $22m and cash inflows of
$15m per year for the first 4 years and -$40m at the end of year 5
to reclaim the land. Cost of capital is 10%. Should the project be
undertaken using IRR criterion.
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31. PI
This is also known as Benefit Cost Ratio or Present
Value Index (PVI).
It is the ratio of Present Value of cash inflows to the
present value of cash outflows.
The decision rule is to accept the project when PI ≥
1.
Using this method, projects are ranked from the one
with highest PI to the one with the lowest PI and
then are selected in the order of ranking up to the
point where budget is exhausted. This is the case
when capital is insufficient and hence, capital
rationing takes place.
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33. TAXATION AND INVESTMENT
APPRAISAL
TAXATION AND INVESTMENT APPRAISAL
The investment appraisal usually uses
After-tax cash flows because they are
enhancing shareholders' wealth.
Thus, there are two rules to follow in
investment appraisal in a world with
taxation.
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34. TAXATION AND INVESTMENT
APPRAISAL
Rule 1
If acceptance of a project changes the tax
liabilities of the firm then incremental tax
effects need to be accommodated in
analysis
Rule 2
Get the timing right. Incorporate the cash out
flow of tax into the analysis at the right time.
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35. INFLATION AND INVESTMENT
APPRAISAL
INFLATION AND INVESTMENT APPRAISAL
Inflation (if any) needs to be adjusted appropriately
in investment appraisal
Two Common Methods for Adjusting Inflation
Method 1
Estimate the cash flows in monetary terms and use a
monetary discount rate
Method 2
Estimate the cash flows in real terms and use a real
discount rate
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36. CAPITAL BUDGETING UNDER
UNCERTAINTY SITUATION
If projected cash flows are uncertain due to risk
and other factors, the investment appraisal may
involve;
Sensitivity analysis ( What If analysis)
Assigning probabilities on projected future
cash flows
Carrying out Scenario Capital Budgeting
(Preparing different cash flow projections due
to different levels of economies
Discounting future cash flows using risk-
adjusted discount rates.
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37. EXAMPLE ON CAPITAL BUDGETING
TECHNIQUES
Example
ABC Ltd is considering two projects; A and B. Each requires an investment of $100 millions.
The cost of capital is 10%. Below is the summary of expected net cash flows in millions
Year Project A Project B
1 50 10
2 40 20
3 30 30
4 10 40
5 1 50
6 1 60
Questions
a) Calculate the discounted payback period for each project. Which project is likely to be
selected using this method?
b) Calculate the Net Present Value (NPV) for each project. Which project is likely to be
selected using this method?
c) Calculate the Internal Rate of Return (IRR)for each project. Which project is likely to be
selected using this method?
d) Calculate the Profitability Index (PI) for each project. Which project is likely to be selected
using this method?
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38. CAPITAL RATIONING
Capital Rationing
This is the process of placing restrictions or limits on the amount of new
investments or projects undertaken by a company.
This is accomplished by imposing a higher cost of capital for investment
consideration or by setting a ceiling on the specific sections of the budget.
It occurs when a company has a number of capital budgeting projects with
positive Net Present Values (NPV) than it has money to invest in them.
Thus, some projects that should be accepted are excluded because of the
financial constrains.
A firm may use capital rationing because it is fearful of too much growth or
is not willing to use external sources of financing.
Capital rationing involves ranking all projects according to their NPVs or
required rates of return and selecting only few projects depending on the
amount available.
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39. CAPITAL RATIONING
Types of Capital Rationing
a) Hard Capital Rationing: This happens when constraints are
externally determined and under imperfect markets.
b) Soft Capital Rationing : This happens when constraints are
internally determined e.g. when the management imposes
limits on investment expenditure.
Reasons for Capital Rationing
a) External Reasons: This happens when the firm is unable
to borrow from outside. This may be a result of financial
distress or tight credit conditions etc.
b) Internal Reasons: They include; ownership dilution,
divisional constraints, human resource limitations, debt
constraints etc.
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40. CAPITAL RATIONING
Example 1: Assume that the amount provided for
investment is limited to Tsh. 50,000,000. Which
projects will be selected under capital rationing?
Project Investment (Io-
Tsh.)
Total Investment NPV
A 20,000,000 4,000,000
B 20,000,000 3,800,000
C 10,000,000 50,000,000 1,500,000
D 10,000,000 1,000,000
E 8,000,000 68,000,000 400,000
F 8,000,000 (300,000)
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41. CAPITAL RATIONING
Example 2
Assuming that the cash available for capital
investment is TZS 1,100 million. Under capital
rationing, which projects among the following will
be selected, using PI?
Project I0 (Tsh. Mil) NPV (Tsh.
Mil)
PI Rank
A 500 110 0.22 1
B 150 -7.5 -0.05 6
C 350 70 0.20 2
D 450 81 0.15 4
E 200 38 0.19 3
F 400 20 0.05 5
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43. Seminar Questions
1. What do you understand by non-discounted and discounted project
evaluation?
2. What is the payback period? What advantages and disadvantages do the
payback method have?
3. XYZ company is analysing two projects i.e. Project 1 and 2. The cost of
each project is $ 500mil and the required rate of return for each project is
12%. The projects expected net cash inflows are as follows;
Year Project 1 ($Million) Project 2 ($ Million)
0 (500) (500)
1 325 175
2 150 175
3 150 175
4 50 175
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44. Seminar Questions
a) Calculate each of projects payback period, net present value (NPV), and Internal Rate of Return (IRR)
b) Which project or projects should be accepted if they are independent?
c) Which project should be accepted if they are mutually exclusive?
d) How might a change in the required rate of return produce a conflict between NPV and IRR rankings of
the projects?
4. ABC Ltd has £1 million allocated for capital expenditures. Which of the following projects should the
company accept to stay within £1million budget? How much does the budget limit cost the company in
terms of its market value? The opportunity cost of capital is 11% for each of the projects.
Project Investment ($ 000) NPV ($ 000) IRR (%)
1 300 66 17.2
2 200 -4 10.7
3 250 43 16.6
4 100 14 12.1
5 100 7 11.8
6 350 63 18.0
7 400 48 13.5
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45. Seminar Questions
5. Why should companies undertake capital rationing? What are the
important factors to consider in capital rationing?
6.What are the advantages and disadvantages of the Non
Discounting Methods of project evaluation?
7. What is the “Multiple IRR problem” and what condition is
necessary for its existence?
8. Explain what is meant by conventional and unconventional cash
flows and what problems they might cause in investment appraisal.
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46. Seminar Questions
9. Hekima Ltd is considering buying a new machine which would have
a useful economic life of five years, a cost of Tshs. 100 million and
scrap value of Tshs. 5 million. The machine would produce 50,000
units per annum of a new product with an estimated selling price of
Tshs. 3000 per unit. Direct costs would Tshs. 1750 per unit and annual
fixed costs, including depreciation calculated on a straight line basis,
would be Tshs. 40 million per annum. In years 1 and 2,special sales
promotion expenditure, not included in the above costs, would be
incurred, amounting to Tshs. 10 million and Tshs. 15 million
respectively. As a consequence of this particular project, investment by
the company in debtors and stocks would increase, during year 1, by
Tshs. 15 million and Tshs. 20million respectively, and creditors would
also increase by Tshs. 10 million. At the end of the machine's life,
debtors, stocks and creditors would revert to their previous levels.
Evaluate the project using the NPV method of investment appraisal,
assuming the company's cost of capital is 10%.
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47. Seminar Questions
10. BMT Ltd is considering which of two mutually exclusive projects
to accept, each with a five-year life. Project A requires an initial
expenditure of Tshs. 24,000,000 and it is forecasting to generate annual
cash flows before depreciation of Tshs. 9million.The equipment
purchased at time zero has an estimated residual value after five years
of Tshs. 3 million. Project B costs Tshs. 6,600,000 and has a residual
value of Tshs. 600,000 and cash inflows before depreciation of Tshs.
2500,000 per annum are anticipated. The company has a straight-line
depreciation policy and a cost of capital of 15%.
a) Calculate the accounting rate of return
b) Calculate the Net Present Value
c) Which project is worth undertaking using the two methods above?
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48. Seminar Questions
10. HPC Plc has two possible projects to consider. It can not do both-
they are mutually exclusive. The cash flows are:
Year Project A (£) Project B(£)
0 -420,000 -100000
1 150,000 75,000
2 150,000 75,000
3 150,000 0
4 150,000 0
HPCꞌs cost of capital is 12 per cent. Assume unlimited funds. These are the
only cash flows associated with the projects.
a) Calculate the internal rate of return (IRR) for each project.
b) Calculate the net present value (NPV) for each project.
c) Compare and explain the results in (a) and (b) and indicate which project
the company should undertake and why?
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49. Seminar Questions
11. Using a 13% discount rate find the NPV of the
project with the following cash flows?
Points in time (in years) 0 1 2 3
Cash flow (£) -300 +260 -200 +600
How many IRRs would you expect to find for this project? What
is the type of these cash flows?
12. Which are the common capital budgeting techniques in
practice? Why many firms are not applying these techniques
when evaluating their investments?
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50. Seminar Questions
13. Explain why it is possible to obtain an inaccurate result using
the trial and error method of IRR when a wide difference of two
discount rates is used for interpolation.
14. The Bird-In-Hand-Theory and the Finance Theory (CAPM)
are two sides of the same coin. Discuss this statement in
relationship to investment decisions.
15. (a) Why Time Value of Money is a central concept in finance
and particularly investment criteria?
(b) When appraising capital projects using NPV and IRR
methods, decision conflicts are likely to occur. What are the
decision conflicts and under what condition do they occur? What
is the solution in case they occur?
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