2. Chapter Outline
Capital Budgeting Concepts
Cash Flow Estimation
Types of Investment Appraisal Criteria
Risk Analysis in Investment Appraisal
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3. Introduction
The managers of all businesses will find themselves
faced, from time to time, by Capital Investment
decisions.
• Capital investment decisions have direct effect on
future profitability --- increase in efficiency and
reduction in costs.
• Proper evaluation of Capital expenditure projects is
important before taking ‘go ahead’ decision.
• Capital expenditures differ from revenue
expenditures as they involve bigger outlay of money
and benefit will accrue over a long period of time.
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4. Cont…
Investment appraisal (capital budgeting) - A means of
assessing whether an investment project is worthwhile
or not.
• Investment project could be the purchase of a new PC
for a small firm, a new piece of equipment in a
manufacturing plant, a whole new factory, etc.
• As investments involve large resources, wrong
investment decisions are very expensive to correct.
• Managers are responsible for comparing and evaluating
alternative projects so as to allocate limited resources
and maximize the firm’s wealth.
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5. Planning Steps for Capital Investment Decisions
Identification of investment opportunity.
Consideration of the alternatives to the project
being evaluated.
Acquiring relevant information --- form the basis for
informed decisions otherwise projects to be
abandoned at early stage.
Detailed planning is involved.
Taking the investment decisions.
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Cont…
6. Project Classifications
1. Replacement of equipment: Maintenance of
business
2. Replacement of equipment: Cost reduction
3. Expansion of existing products / markets
4. Expansion into new products / markets
5. Safety and other environmental projects
6. Research and development (R&D)
7. Long term contracts
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Cont…
7. (A) Accounting Rate of Return (ARR)
• A.K.A return on investment (ROI) method.
The accounting rate of return method of appraising a
capital project is to estimate the accounting rate of
return or return on investment that project should
yield.
If it exceeds a target rate of return, the project will
be undertaken.
Unfortunately, there are several different definitions of
“return on investment”. One of the most popular is as follows:
ARR = Estimated average profit X 100 %
Estimated average investment
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8. The others include:
ARR = Estimated total profits X 100 %
Estimated initial investment
ARR = Estimated average profits X 100 %
Estimated initial investment
There are arguments in favor of each these definitions.
The most important point is, however, that the method
selected should be used consistently.
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Cont…
9. Example:
A company has a target accounting rate of return of 20 %
and is now considering the following project:
Capital Cost of the Asset Br.80,000
Estimated life of the asset 4 years
Estimated profit before depreciation
Year 1 Br.20,000
Year 2 25,000
Year 3 35,000
Year 4 25,000
The capital asset would be depreciated by 25 % of its cost each year, and
will have no residual value.
Question: Should the project be undertaken?
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Cont…
10. Solution:
The annual profits after depreciation, and mid-year
net book value of the asset, would be as follows:
Profit after Mid-year net ARR in
Year depreciation book value the year %
1 0 70,000 0
2 5,000 50,000 10
3 15,000 30,000 50
4 5,000 10,000 50
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Cont…
11. As the table shows, the ARR is low in early stages of
the project, partly because of low profits in year 1
but mainly due to the net book value of the asset is
much higher in its life.
The project does not achieve the target 20 % in its
first 2 years, but exceeds it in years 3 and 4 . So it
should be under taken.
However when the ARR from a project varies from
year to year, it makes sense to take an overall or
average view of the project’s return. In this case we
should look at the return as a whole over the four
years period of time.
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Cont…
12. Total profit before depreciation over 4 years Br.105,000
Total profit after depreciation over four years 25,000
Average annual profit after depreciation 6,250
Original cost of investment 80,000
Average book value over the 4 years period (80,000+0)/2;
=Br 40,000
So, the average ARR = Br. 6250/Br. 40,000= 15.625%
The project would not be undertaken because it would
fail to yield the target return of 20 %.
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Cont…
13. The Draw Backs of ARR Method
The ARR method of capital investment has serious
draw back that it does not take account of timing of
the profits from an investment.
When ever capital is invested in a project, money
tied up in one project cannot be invested anywhere
else until the profits come in.
Management should be aware of the benefits of
early repayments from an investment, which will
provide the money for other investment.
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Cont…
14. (B) The Pay Back Method
The payback is defined as the time it takes the cash
inflow from a capital investment project to equal the
cash outflows, usually expressed in years.
The pay back period provides a rough measure of
liquidity and not profitability.
When deciding between two or more competing
projects, the usual decision is to accept the one with
the shortest payback (less capital tie-up and low
investment risk).
Pay back is commonly used as a first screening method.
Project should be rejected if its payback period is more
than the company’s target payback period.
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15. Consider this example:
Project P Project Q
Capital expenditure Br.60,000 Br.60,000
Cash Inflows:
Year 1 20,000 50,000
Year 2 30,000 20,000
Year 3 40,000 5,000
Year 4 50,000 5,000
Year 5 60,000 5,000
Cont…
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16. Solution:
Project P
Year 0 ( 60,000)
Year 1 20,000
Year 2 30,000
Year 3 40,000 only 10,000 more
required in 3rd year
There fore Project P’s pay back period is about one
quarter of the way through year 3 i.e., 2.25 years.
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Cont…
17. Project Q
Year 0 (60,000)
Year 1 50,000
Year 2 20,000 only 10,000 more
required in 2nd year
There fore Project Q’s pay back period is about Half
way through year 2 i.e., 1.5 years.
Using pay back period alone to judge the Capital
investment projects, project Q would be preferred.
But the returns from project P over its life are much
higher than the returns from project Q.
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Cont…
18. (C) Discounted Cash Flow
• The ARR method of project valuation ignores the
timing of cash flows and the opportunity cost of
capital tied up. Pay back considers the time it takes
to recover the original investment cost, but ignores
total profits over a project’s life.
• Discounted cash flow, or DCF for short, is an
investment appraisal technique which takes into
account both the time value of money and also the
profitability over a project’s life.
• DCF is therefore superior to both ARR and pay back
as method of investment appraisal.
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19. (i) Discounted Payback period
Some Companies use a variant of the regular
payback, the Discounted payback period, which
is similar to regular payback period except that
the expected cash flows are discounted by the
project’s cost of capital.
By Discounted pay back period we mean the
number of years required to recover the
Investment from discounted net cash flows.
Each cash inflow is divided by (1+r)t
Where t= year in which cash flow occurs
r = project’s cost of capital
Cont…
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20. Example: Discounted Payback
Project S: Year 0 1 2 3 4
Net Cash Flows -1000 500 400 300 100
Discounted NCF(@10%) -1000 455 331 225 68
Cumulative discounted NCF -1000 -545 -214 11 79
Pay back period S = 2.95 years
Project L: Year 0 1 2 3 4
Net Cash Flows -1000 100 300 400 600
Discounted NCF(@10%) -1000 91 248 301 410
Cumulative discounted NCF -1000 -909 -661 -360 50
Payback period L = 3.88 years
Cont…
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21. 4/25/2024 21
(ii) Net Present Value (NPV)
The NPV is the algebraic sum of the discounted
values of the incremental expected positive and
negative net cash flows over a project’s anticipated
lifetime.
What does net present value mean?
NPV- measures the change in wealth created by the
project.
Cont…
22. Procedure:
1. Find the present value of each cash flow, including
all inflows and outflows, discounted at the project’s
cost of capital.
2. Sum these discounted cash flows; this sum is
defined as the project’s NPV.
3. If the NPV is positive, the project should be
accepted, while if the NPV is negative, it should be
rejected. If two projects with positive NPV’s are
mutually exclusive, the one with higher NPV
should be chosen.
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Cont…
23. The Equation for NPV:
NPV= CF0+ CF1 + CF2 +…+ CFN
(1+r)1 (1+r)2 (1+r)N
Where:
CF1, 2…= Expected net cash flow at period 1, 2…,
respectively,
r = the project’s cost of capital, and
N = life of the project.
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Cont…
24. Example: NPV appraisal method
0 r=10% 1 2 3 4
Cash flows -1000 500 400 300 100
In Br. 454.55
330.58
225.39
68.30
NPV Br. 78.82
Note: Cash out flows are treated as negative cash flows. At
10% cost of capital, the above project’s NPV is Br. 78.82
{NPV = -1000 + 500/(1.10) + 400/(1.21) +300/(1.331)+100/(1.4641)=Br. 78.82}
Cont…
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25. NPV as a Decision Criterion
• Use NPV as a decision criterion to answer following:
a. When to reject projects?
b. Select project(s) under a budget constraint?
c. Compare mutually exclusive projects.
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Cont…
26. a. When to Reject Projects?
Rule: “Do not accept any project unless it generates a positive
net present value when discounted by the opportunity cost of
funds”
Example:
Project A: Present Value Costs $1 million, NPV + $70,000
Project B: Present Value Costs $5 million, NPV - $50,000
Project C: Present Value Costs $2 million, NPV + $100,000
Project D: Present Value Costs $3 million, NPV - $25,000
Result: Only projects A and C are acceptable. The firm is made
worse off if projects B and D are undertaken.
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Cont…
27. 4/25/2024 27
c. When You Need to Compare Mutually Exclusive Projects?
Rule: “In a situation where there is no budget constraint but a
project must be chosen from mutually exclusive alternatives, we
should always choose the alternative that generates the
largest net present value”
Example: Assume that we must make a choice between the
following three mutually exclusive projects:
Project I: PV costs $1.0 million, NPV $300,000
Project J: PV costs $4.0 million, NPV $700,000
Project K: PV costs $1.5 million, NPV $600,000
Result: Project J should be chosen because it has the largest
NPV.
Cont…
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(iii) Internal Rate of Return (IRR)
IRR is the discount rate (K) at which the present
value of benefits are just equal to the present value
of costs for the particular project.
PV(Inflows) = PV (Investment Costs)
OR: Bt - Ct
(1 + K)t = 0
t
i=0
Cont…
29. Example of IRR:
0 IRR? 1 2 3 4
Cash flows -1000 500 400 300 100
Sum of PV’s for CF 1-4 1000
NPV 0
IRR = 14.5 % , In case if the cost of capital is < 14.5 % then the project
should be accepted.
N:B You may apply the Interpolation Technique to determine the IRR.
Cont…
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30. Common uses of IRR:
(a) If the IRR is larger than the cost of funds, then
the project should be undertaken.
(b) Often the IRR is used to rank mutually exclusive
projects. The highest IRR project should be
chosen.
• An advantage of the IRR is that it only uses
information from the project.
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Cont…
31. (D) Benefit-cost Ratio or Profitability Index
As its name indicates, the benefit-cost ratio, R, or
what is sometimes referred to as the profitability
index, is the ratio of the PV of the net cash inflows
(or economic benefits) to the PV of the net cash
outflows (or economic costs):
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)
(
)
(
Costs
Economic
or
Outflows
Cash
of
PV
Benefits
Economic
or
Inflows
Cash
of
PV
R
32. Basic rule:
If benefit-cost ratio (R) >1, then the project should
be undertaken.
Problems?
Sometimes it is not possible to rank projects with Pi:
• Mutually exclusive projects of different sizes
Not necessarily true that RA>RB that project “A” is better.
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Cont…
33. -The Benefit-Cost Ratio Does Not Adjust for Mutually Exclusive Projects of
Different Sizes.
For example:
Project A: PV0of Costs = $5.0 M, PV0 of Benefits = $7.0 M
NPV0
A = $2.0 M RA = 7/5 = 1.4
Project B: PV0 of Costs = $20.0 M, PV0 of Benefits = $24.0 M
NPV0
B = $4.0 M RB = 24/20 = 1.2
According to the Benefit-Cost Ratio criterion, project A should be chosen over
project B because RA>RB, but the NPV of project B is greater than the NPV of
project A. So, project B should be chosen.
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Cont…
34. Risk Analysis in Investment Appraisal
Risk is inherent in capital budgeting decisions as they
involve cost and benefits extending over a long
period of time during which many things can change
in unanticipated ways.
• Risk in capital budgeting means Uncertainty about a
project’s future profitability.
• Risk in capital budgeting is indicated by
Sensitivity analysis
Scenario analysis
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35. Sensitivity Analysis:
Shows how changes in a variable such as unit
sales affect NPV or IRR.
Each variable is fixed except one. Change this one
variable to see the effect on NPV or IRR.
Answers “what if” questions, e.g. “What if sales
decline by 30%?”
Identifies dangerous variables.
Ignores relationships among variables.
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Cont…
36. Scenario Analysis:
Examines several possible situations, usually
worst case, most likely case, and best case.
Provides a range of possible outcomes.
Assumes that inputs are perfectly correlated--all
“bad” values occur together and all “good” values
occur together.
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Cont…
37. ‘’
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Chapter end questions
1. What is capital budgeting? Why is it significant for a firm?
2. Why are long-term investment decisions so critical for a firm?
3. ‘‘If a firm has excess capital, it could invest in all acceptable projects.’’ Do
you agree with this statement? Justify your position.
4. How could risk be incorporated in evaluating projects?
38. Selam Ltd wants to buy a new item of equipment, which will be used to
provide service to customers of the company. Two models of equipments are
available in the market, one with slightly higher capacity and greater reliability
than the other. The expected cost and profits of each item are as follows:
Equipment item Equipment item
X Y
Capital Cost Br.80,000 Br.150,000
Life 5 years 5 years
Profits before depreciation
Year 1 50,000 50,000
Year 2 50,000 50,000
Year 3 30,000 60,000
Year 4 20,000 60,000
Year 5 10,000 60,000
Disposal value 0 0
ARR is measured as the average annual profit after depreciation, divided by
the average net book value of the assets. Which item of the equipment
should be selected, if any , if the company’s target ARR is 30 % ?
Exercise 4.1
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39. Exercise 4.2
• Bethel Company is choosing between two equal-risk,
mutually exclusive capital expenditure projects- M
and N. The relevant cash flows for each project are
given below. The firm’s cost of capital is 14%.
Project M Project N
Initial Investment Br.28,500 Br.27,000
Year 1 Br. 10,000 Br. 11,000
Year 2 10,000 10,000
Year 3 10,000 9,000
Year 4 10,000 8,000
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40. • Instructions:
• A. Calculate each project’s payback period.
• B. Calculate the NPV for each project.
• C. Compute the IRR for each project.
• D. Summarize the preferences dictated by each
measure, and indicate which project you would
recommend. Explain why.
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Cont…
