Capital Budgeting is about how one should evaluate the financing options based on the superior financial performance through mathematical techniques. These techniques have been discussed in the presentation in detail.

1. Second Edition
Planning, Incurring, Monitoring & Controlling Capital Expenditures
Ahmad Tariq Bhatti
FCMA, MA (Economics), BSc
Dubai, United Arab Emirates

2. CAPITAL BUDGETING
2

3. OBJECTIVES
3

4. 4
Capital Budgeting (CB) refers to the complete process of
generating/initiating investment proposals, evaluating,
ranking and selecting the best alternative(s), monitoring
and making follow up on investment(s) made.
 Provides assessment for the financial feasibility of
investment options.
 Evaluates, how an investment opportunity is worthwhile
and how it fits to the company’s strategy, goals and
objectives?
 CB techniques are invariably used for all types of
investment opportunities from the purchase of a new piece
of machinery to a whole factory.
DEFINITION

5. 5
NATURE
CB Decisions have long-term impact on the business stability,
growth & success
CB Decisions involve huge investment of funds
CB Decisions are more complicated from concerns of future cash
flow estimates and their evaluation at the time of making
investment
CB Decisions are not easily reversible mainly because of loss of
investment
IMPORTANCE
Huge amount of resources are involved that has impact on
business strategy, growth, and survival.
Difficult to “bail out”, once an investment is made.
The capital investments are challenging and critical to the
success of the company. An incorrect decision may end with the
company’s closing-out from the market.

6. CONCEPT
6
 Investment refers to an outlay of funds on which
management expects a return. An investment creates
value for shareowners when expected returns from
investment exceed its cost.
 Capital Expenditure refers to long term
commitment of resources that provide future benefits
to business.
 Why investment is made?
 Expansion Plans, Growth Strategies, Capacity Increase
 Increase of efficiency of the manufacturing facilities
 Deploying or replacing latest technology
 Acquisition of Fixed Assets, Copy Rights, Franchises, Licenses,
Patents
 Establishing new brands, new lines of business, new products
 Opening new offices, new factories, overseas branches

7.  Independent Projects are projects where selection or
rejection of one project does not have any impact on the
selection or rejection of the other project. Management can
select any number of projects from the given options.
 Mutually Exclusive Projects are projects that
compete each other, acceptance of one project becomes
automatic rejection of the other or vice versa. The projects
compete with each other based on the superior financial
performance. There can be any number of projects for a
subject and competing with each other. Management has to
decide about one project from all alternatives or options.
 Decision Rules: The decision rules for independent and
mutually exclusive projects slightly differ. The way of
looking at investment opportunities under both types varies.
RELEVANT CONCEPTS
7

8. PROCESS
8
CB is a five steps process that is followed by the investment
managers in the order given as below:
 Initiating, generating and gathering investments ideas.
 Analyzing the costs and benefits for proposed investments by:
– Forecasting costs and benefits for each investment.
– Evaluating the costs and benefits based on CB techniques.
 Ranking the relative superiority of each investment alternative
based on financial performance worked out and choosing the best
investment opportunity from the given set of opportunities.
 Implementing the investment alternative chosen.
 Monitoring & making follow-up on the investment made on
regular basis to see how far this investment opportunity has been
effective in the given framework of the company to achieve its
desired objectives.

9. DECISION MATRIX
9
High Medium Low
High
Build
aggressively
– invest & grow
Build
aggressively
– invest & grow
Build gradually
– improve &
defend
Medium
Build
aggressively
– invest & grow
Build gradually
– improve &
defend
Divest
Low
Build gradually
– improve &
defend
Divest Divest
Business Strength
MarketAttractiveness

10. EVALUATION TECHNIQUES
10
A: Traditional Techniques
1. Payback period (PB)
2. Discounted Payback Period (DPB)
3. Accounting Rate of Return (ARR)
B: Discounted Cash Flow (DCF)/
Time Adjusted (TA) Techniques
1. Net Present Value (NPV)
2. Internal Rate of Return (IRR)
3. Modified Internal Rate of Return (MIRR)
4. Terminal Value (TV)
5. Profitability Index (PI) or Benefit/Cost Ratio
Important Note
These techniques provide reliable evaluation under conditions of
perfect certainty. They are, nevertheless, widely used in practice in the
face of uncertainty.

11. EVALUATION TECHNIQUES
11
Traditional Techniques
Discounted Cash Flow or
Time Adjusted Techniques
PB
Discounted PB
NPV
MIRR
IRR
TV
PI or B/C Ratio
ARR

12. DECISION RULES
FOR ALL CAPITAL BUDGETING TECHNIQUES
12
# Tech.
Accept or Reject Criteria for …
Single or Independent Project(s) Mutually Exclusive Projects
1. PB Less than the Target Period Shortest Payback Period
2. DPB Less than the Target Period Shortest Payback Period
3. ARR Above the Target Rate With the highest ARR
4. NPV A positive NPV With the highest positive NPV
5. IRR Higher than the Target Rate (Cost of
Capital)
With the highest IRR
6. MIRR
Higher than Target Cost of Capital
(i.e. WACC)
With higher MIRR
7. TV
If PVTS>PVO Accept,
And if PVTS<PVO Reject
With the highest PVTS>PVO
8. PI (B/C Ratio) PI exceeding 1 Higher PI

13. MERITS & DEMERITS
TRADITIONAL TECHNIQUES
13
# Tech. Merits Demerits
1. PB
 Simple and easy to understand and use.
 Objective – using cash flows.
 Liquidity – commercially realistic.
 Cautious & risk averse – ignores later cash
flows.
 First level estimator – gives rough idea
about the recouping of the investment.
 Ignores the time value of money.
 Ignores cash flows after the
payback period.
 Don’t recommend the acceptable
pay back period for the projects.
2. DPB
 Provides more accurate estimate of cash
inflows.
 Provides more accurate estimate of the time
frame for the recovery of initial investment.
 Ignores cash flows after the
recovery of initial investment.
 More difficult to calculate than
PB.
3. ARR
 Simple and easy to calculate and use.
 Aids internal and external comparisons.
 Looks at the whole life of the project.
 A useful tool to measure divisional
managerial performance.
 Subjective – profit, not cash flows.
 Ignores the time value of money.
 Difficulty in use when with same
ARR and various project sizes.

14. MERITS & DEMERITS
DCF TECHNIQUES
14
# Tech. Merits Demerits
1. NPV
 Takes account of the time value of
money.
 Instrumental in understanding exact
addition to shareholder’s wealth.
 Takes account of risk.
 Looks at total benefits over the
entire life of the project.
 Particularly useful for mutually
exclusive projects.
 Adverse effects on accounting profits in
the short run.
 How to choose discount rate? As NPV
is dependent on discount rate. Bank
rate, or WACC or another?
 May not give satisfactory results where
projects have different lives.
 In case the projects have different cash
outlays, it may not give dependable
results.
2. IRR
 Takes account of the time value of
money.
 Easy to be understood by managers.
 Takes into account total cash
inflows and total outflows.
 Involves tedious calculations.
 Difficult to use in choosing projects of
varying sizes.
 Difficult to choose when projects have
the same IRR.
 Not dependent on the discount rate.

15. MERITS & DEMERITS
DCF TECHNIQUES
15
# Tech. Merits Demerits
3. MIRR
 Quicker to calculate than IRR.
 MIRR is invariably lower than IRR
that may be due to more realistic
assumption about re-investment rate.
 There is much confusion about the re-
investment rate used in this formula.
 One implication of MIRR is that the
project may not generate cash flows as
predicted and that NPV of the project is
overstated.
4. TV
 Explicitly uses re-investment of cash
inflows.
 Mathematically easier.
 Easier to understand than NPV or
IRR.
 It suits better to cash budgeting.
 The major weakness of this
technique that it utilizes interest
rates that are uncertain for future
cash inflows.
5. PI
(B/C Ratio)
 Better technique than NPV in
situations where capital rationing
issues are involved.
 In mutually exclusive projects NPV
appears to be superior technique than PI.
 Difficult to understand.

16. 16
ISSUES
 When investment amount in given projects is different then the results from
NPV and IRR techniques shall lead to different conclusions.
 When length of the given projects in terms of time is different then the
results obtained from NPV and IRR techniques shall lead to different
conclusions.
 When the interest rates of given projects are different then the results
obtained from NPV and IRR shall lead to different conclusions.
 When timing of cash flows is different i.e. timing of cash flows from the two
projects differs such that most of the cash flows from one project come in the
early years while most of the cash flows from other project come in the later
years, the results from NPV and IRR techniques shall lead to different
conclusions.
NPV compared w. IRR
RESOLUTION OF ISSUES
 The value of early cash flows depends on the return that is earned on those cash
flows, i.e. the rate at which these funds are re-invested.
 The NPV method implicitly assumes that the rate at which cash flows can be re-
invested is the cost of capital,
 The IRR method assumes that the company re-invest the funds at the IRR.
 The best assumption is that projects cash flows is re-invested at the cost of
capital, that goes for the recommendation of NPV method.

17. NPV, IRR & MIRR
17
 NPV and IRR always lead to the same accept/reject decision for independent
projects.
 NPV and IRR may lead to different accept/reject decisions for mutually
exclusive projects.
 Where NPV and IRR give different accept/reject decision then NPV results
should be accepted.
 NPV assumes re-investment of cash inflows at r (opportunity cost of capital).
 IRR assumes reinvestment of cash inflows at IRR.
 IRR indicates the minimum rate expected by the investors to get their
investment back from the project. They definitely get idea from IRR that how
much extra earnings are required to cover their cost of capital and net return on
their investment.
 Re-investment of cash inflows at opportunity cost, r, is more realistic, so NPV
method is best. NPV should be used to choose between mutually exclusive
projects.
 MIRR assumes cash inflows are reinvested at WACC.
 MIRR also avoids the problem of multiple IRRs. MIRR is better than IRR.
When there are non-normal cash flows and there are more than one IRRs, use
MIRR.
 IRR is an estimate of a project’s rate of return, so it is comparable to the Yield
To Maturity (YTM) on a bond.

18. CRUX OF ALL CAPITAL
BUDGETING TECHNIQUES
18
The purpose of evaluation under all capital budgeting
techniques is to estimate the monetary benefit arising out
of investment made in a given project.
If a project is estimated to maximize
shareholder’s wealth at the end of a given period
of time by returning surplus monetary benefit
than the investment made, then decision is made
to take up the project for investment.

19. NON-FINANCIAL FACTORS
19
Company Goodwill, Image & Reputation
Management may reject an investment opportunity, as it will reflect badly on the
company goodwill, image and reputation.
Company Policies, Objectives & Culture
Management is bound to check, if the investment opportunity conforms to the
policies, objectives and culture of the company?
Environmental, Social, Legal & Ethical Issues
Management is required to make sure that the investment opportunity under
consideration is, legally, environmentally, socially and ethically acceptable and
viable.
Impact on Stakeholder Relationships
Management appraises the impact of the investment on competitors, shareholders,
employees, buyers, bankers, suppliers and government institutions, etc.
Management can reject a project based on non-financial factors though
the financial performance of a project is found satisfactory.

20. ACCOUNTING PROFIT
COMPARED TO CASH FLOWS
20
Most investment decision models use predicted cash flows instead of accounting profits.
Why investment managers pay more attention to cash flows rather than accounting
profit in their all calculations for investment decision-making?
In the simplest words, accounting profits reflect the profitability of a company over a
given period of time under the principles of accrual accounting, whereas, cash flows
tell about the cash position in a given period of time under cash basis of accounting.
Cash position is important for liquidity point of view whereas profitability indicates
viability of the company. A company with excellent profit figures may be very bad in
generating cash flows that are necessary to survive even in the short term.
Cash flows reflect on the management of cash cycle of the company so that
company would be able to pay-off its short term obligations whenever they fall due.
A company making huge loss may still be having very good cash flows that keep the
liquidity of the company excellent and thus vehicle of the company is moving forward.
Investors emphasize at the cash flows because the project performance is based on
reliable cash flow streams more than profitability viz exposed to number of
estimated amounts. Cash flows reflect the exact happening without using estimated
figures for number of allocations and provisions like depreciation, bad debts, and many
others.

21. 21
NORMAL VS NON NORMAL CASH FLOWS
Normal cash flow is the cash flow stream that comprises of initial investment
outlay and then positive net cash flow throughout the project life. It is also
called conventional cash flow stream.
Whereas non-normal cash flows have investment injections during the project
life as well, this is also known as un-conventional cash flow stream
The nature of the cash flow pattern is important in capital budgeting. Because
when the cash flows stream is non-normal, multiple-IRR problem arises.
Case # Yr. 0 Yr. 1 Yr. 2 Yr. 3 Yr. 4 Yr. 5 Pattern
1 - + + + + + N
2 - + + + + - NN
3 - - - + + + N
4 + + + - - - N
5 - + + - + - NN
• Cash out-flow (-)
• Cash In-flow (+)
• Normal Cash Flow Stream (N)
• Non Normal Cash Flow Stream (NN)

22. TIME VALUE OF MONEY
22
What is the difference between AED. 1 received now and
AED.1 received in a year’s time?
AED.1 received now has more value than that is received after a year.
The factors that change the value of money over a given
period of time are mentioned as below:
– Interest rate
– Inflation
– Currency devaluation
– Other risks to materialise the money
For example
The annual interest rate is 10%, I lend AED. 1 now and will get back after
1 year, how much worth of that AED.1 in a year’s time?
? x (1+10%) = AED. 1
? = AED. 0.909
10% is called “cost of capital”; “?” is called the “discount factor”

23. PRESENT VALUE
23
Finding present values is called discounting, and it is simply the reverse of
compounding. In general, the present value of a cash flow due n years in the
future is the amount which, if it were on hand today, would grow to equal the
future amount. By solving for PV in the future value equation, the present
value, or discounting, equation can be developed and written in several forms:
).PVIF(FV=
i+1
1
FV=
)i+(1
FV=PV ni,n
n
nn
n






Where:
PVIFi, n = Present Value Interest Factor at given rate and number of periods
PV = Present Value, or investment amount at the start of the project
i = interest rate per annum
n = number of periods
FVn = future value after n periods

24. CAPITAL RATIONING
24
The management has not only to determine the profitable investment
opportunities, but it has also to decide about that combination of
projects which delivers highest NPV within the available funds.
There are two types of capital rationing.
External Capital Rationing
-- Factors that are outside the company due to financial market
conditions.
Internal Capital Rationing
-- Factors that are within the company due to policy, procedure or
other constraints.
Capital Rationing is about selecting projects in a way that helps a
company completing them within the given financial resources.
Financial resources are limited, therefore, should be used in way that is
the best combination from company’s wealth maximization point of
view.

25. ILLUSTRATIVE MODEL
25
There are two mutually exclusive projects A and B for the
consideration of XYZ company. The data for the initial investments
and subsequent cash inflows is given on next slide.
Calculate:
– PB, DPB, ARR
– NPV, IRR, MIRR, TV & PI
Provide recommendations based on the results of budgeting
techniques to make the accept or reject decision in relation to
Project A or B?
Important note
Project A and Project B are competing each other and only one of them can be
selected (i.e. mutually exclusive projects). The project that has superior
financial performance shall be selected. The performance of these two mutually
exclusive projects shall be evaluated under 8 capital budgeting techniques.

26. CASH FLOWS FOR PROJECTS A & B
Year
Project A:
Net Cash flows in/(out)
Project B:
Net Cash flows in/(out)
For the year Accumulated For the year Accumulated
AED. AED. AED. AED.
0 (100,000) (100,000) (100,000) (100,000)
1 45,000 (55,000) 30,000 (70,000)
2 40,000 (15,000) 30,000 (40,000)
3 35,000 20,000 44,000 4,000
4 50,000 70,000 66,000 70,000
26
 The depreciation charge is AED. 20,000 per annum.
 The residual value for both projects is the same, AED. 20,000
 Interest rate is 10% per annum
 There is no tax imposed on the incomes of these projects.

27. ASSUMPTIONS & FEATURES
OF THE MODEL
27
 The amounts of initial cash outlays (investments) are same,
 The project lives are equal i.e. 4 years
 Total amount of cash inflows over the entire lives of projects are equal,
 Residual values at the end of the projects are same,
 Interest rates are same,
 The total amount of depreciation expense on these projects over the lives of
is same,
 There is no tax imposed on the incomes earned on both projects,
 There is no further investment after the initial one for the two projects,
 The Projects A and B have continuous stream of cash inflows during the
entire period related to them i.e. normal cash flows,
 The cash inflows though normal but are unequal for both Projects A & B.
 It is assumed that non-financial factors relating to these two projects are
satisfactory. And there is as such no qualification re the non-financial factors.
 Projects A and B are mutually exclusive projects.
Note
Interest rate is used alternatively as discount rate, hurdle rate, cut-off rate,
required rate, etc., etc.

28. 1. PAY BACK PERIOD
28
Calculation for Project A
= (change in cash flow required to reach zero/total cash flow in the year) + complete years
= (15,000/35,000) + 2
= 0.43 + 2 years = 2.43 years
Calculation for Project B
= (40,000/44,000) + 2
= 0.91 + 2 years = 2.91 years
Decision Rules
Project A has recovered the initial investment in 2.43 year whereas Project B has
recovered initial investment in 2.91 years. Project A has recovered initial
investment faster than Project B, therefore Project A is SELECTED.
Important note
A variation of this technique that involves Present Values of cash inflows is
known as Discounted Payback Period. It gives exact idea about re-couping of
original investment to the business.

29. 2. DISCOUNTED PAY BACK PERIOD
29
CALCULATION FOR PROJECT A
Year
Net Cash flows
in AED.
Discount Factor
for AED.1 @ 10%
p.a.
Present Value in
AED.
1 2 3=1x2
0 (100,000) 1.000 (100,000)
1 45,000 0.909 40,905
2 40,000 0.826 33,040
3 35,000 0.751 26,285
4 50,000 0.683 34,150
Discounted Payback Period for Project A
= 3 yrs. + (230/34,150)yr. = 3.007 yrs.
N.B.: The period indicates the recovery of initial investment plus cost of
capital in 3.007 years.

30. 30
CALCULATION FOR PROJECT B
Year
Cash flow in
AED.
Discount Factor for
AED. 1 @ 10% p.a.
Present Value in
AED.
1 2 3=1x2
0 (100,000) 1.000 (100,000)
1 30,000 0.909 27,270
2 30,000 0.826 24,780
3 44,000 0.751 33,044
4 66,000 0.683 45,078
Discounted Payback period for Project B
= 3 yrs. + (14,906/45,078)yr. = 3.331 yrs.
Decision Rule
The project that has longer discounted payback period shall be rejected. The Project B has longer
period to recoup the investment than Project A, therefore, Project B is rejected and Project A is
selected. This technique is the refinement of the Pay Back Method. It is also interesting to note that
results for acceptance or rejection are same under these two techniques. However, we have got the
exact idea about the recovery of the initial investment to the business.

31. 3. ACCOUNTING RATE OF RETURN
31
: Calculate annual profit
Annual Profit = Income - Depreciation
: Calculate average profit
Average Accounting Profit = Total Profits / # of Yrs.
: Calculate average capital invested
Average Capital = (Initial Investment + Residual Value)/2
: Calculate Accounting Rate of Return
ARR = (Average Profit/Average Capital) x 100
Annual Profit in the context of this model refers to the earnings from the project less all
other expenses including depreciation. The model used here gave us only depreciation
expense, therefore, it is deducted from the income given in each year. This is for the
reason of simplicity of the model. Further, cash inflows are the income in the absence of
any other expense for example, only depreciation is the expense to be charged against
these earnings In practice, we take net profit after tax for this working.

32. ARR CALCULATION
32
Project A
Average Accounting Profit = (Income – Depreciation)/4
Average Accounting Profit = (170,000 - 80,000)/4
= 22,500
Average investment = (Initial Investment + Residual Value)/2
= (100,000 + 20,000)/2 = 60,000
ARR = 22,500/60,000 x 100 = 37.50%
Project B
Average Accounting Profit = (170,000-80,000)/4 = 22,500
Average Investment = (100,000 + 20,000)/2 = 60,000
ARR = (22,500/60,000) x 100 = 37.50%

33. ACCOUNTING RATE OF RETURN
33
Decision Rules
For Independent Projects
Ranking shall be made of all independent projects based on their estimated ARR. The
projects that have higher estimated ARR than the minimum required ARR shall be
selected and all other projects shall be rejected.
For Mutually Exclusive Projects
The project with higher ARR is to be selected for mutually exclusive projects.
There are two check points for mutually exclusive projects.
 All the competing projects should have higher ARR than the minimum required.
 The project with higher ARR shall be selected and the other shall be rejected.
 In this model, both projects have same ARR i.e 37.50%, So first, management shall
see if the estimated ARR for both Projects A and B is higher than the minimum
required ARR. For example, minimum ARR is 25%. Then management shall be
indifferent, as to select which of these two projects. Management shall extend their
studies further into the results of other capital budgeting techniques.
 It is hereby advised to prepare a schedule that summarizes results from all CB
techniques to give a complete picture to the evaluator on one page. Please refer to
slide # 55 for the summarized results noted from each CB technique.

34. 4. NET PRESENT VALUE
34
 The XYZ company’s interest rate is 10% p.a.
 Discount Factors @ 10% p.a. for AED. 1 are as given below:
Year 1 = 0.909
Year 2 = 0.826
Year 3 = 0.751
Year 4 = 0.683
 Formula to calculate Discount Factor @ 10% p.a. for AED. 1 is given as follows:
Discount Factor = 1/(1+10%)^n
 
.
1
0
1
CF
r
CF
NPV t
t
n
t


 
NPV = Net Present Value
CFt = Cash in-flows for given periods
CFo = Initial Investment
r = Discount Rate

35. NPV CALCULATION FOR PROJECT A
35
Year
Net Cash
flows in AED.
Discount
Factor for
AED.1 @ 10%
p.a.
Present Value
in AED.
1 2 3 = 1 x 2
0 (100,000) 1.000 (100,000)
1 45,000 0.909 40,905
2 40,000 0.826 33,040
3 35,000 0.751 26,285
4 50,000 0.683 34,150
NPV 34,380

36. NPV CALCULATION FOR PROJECT B
36
Year
Cash flow in
AED.
Discount Factor for
AED. 1 @ 10% p.a.
Present Value in
AED.
1 2 3=1x2
0 (100,000) 1.000 (100,000)
1 30,000 0.909 27,270
2 30,000 0.826 24,780
3 44,000 0.751 33,044
4 66,000 0.683 45,078
NPV 30,172

37. 37
NPV = NPV(RATE%, VALUES)
Project A = NPV(10%, values) = AED. 31,285
Project B = NPV(10%, values) = AED. 27,457
Important Note
In our manual workings, all individual discounting factors have been rounded off to
four digits. In Excel workings, the system has taken full discounting factors without
rounding them off. There is definitely a difference in both workings. But results are
consistent and do not allow the decision be changed. For all practical purposes
except under exam conditions, we should use Excel formula to reach the exact
decision.
Difference
Difference in Project A NPV = 34,380 – 31,285 = 3,095
Difference in Project B NPV = 30,172 – 27,457 = 2,715
Calculation of NPVs by using EXCEL
Formula

38. 38
Discount Rate NPV Project A NPV Project B
AED. AED.
10% 31,285 31,285
13% 23,072 18,599
16% 15,998 11,032
19% 9,886 4,552
22% 4,594 (1,009)
25% - (5,791)
28% (3,995) (9,910)
IMPORTANT NOTE
The point where the NPV profile crosses the horizontal axis indicates a
project's IRR. This is the point where IRR is equal to the discount rate and
therefore makes NPV of projects equal to zero.
Profiling of the Project A & B on
the basis of their NPVs

39. 39
(15,000)
(10,000)
(5,000)
-
5,000
10,000
15,000
20,000
25,000
30,000
35,000
10 13 16 19 22 25 28
NPVofProjectsA&BinAED.
Discount Rate (%)
Profiling of Projects A & B on NPV Basis
NPV Project A
NPV Project B
Discount Rate
We can clearly see in the graph the results from using of different discount
rates for projects A and B. The NPV of both projects come to zero at 22%
and 25% discount rates. This is the graphical determination of IRR as well.

40. NPV DECISION RULES
40
NOTE
In the case of both Projects A and B, NPV is reducing when discount rates are increasing.
To generalize, when discount rate increases, NPV decreases and vice versa.

41. 5. INTERNAL RATE OF RETURN
41
IRR is the discount rate which delivers a zero NPV for a given project. That means a rate
at which PV of all cash inflows equals to total investment at a given point in time.
IRR Calculation for Project A
NPV = AED. 34,380 when the discount rate is 10%
NPV = ??? When the discount rate is 25%
Year
Cash flow in
AED.
Discount Factor for AED.
1 @ 25% p.a.
Present Value in
AED.
1 2 3=1x2
0 (100,000) 1.000 (100,000)
1 45,000 0.800 36,000
2 40,000 0.640 25,600
3 35,000 0.512 17,920
4 50,000 0.410 20,500
NPV (20)
N.B. : If we reduce the IRR to get the NPV exactly equal to zero. Then after
rounding off it shall be again equal to 25%. Therefore, IRR for Project A is 25%.

42. 42
IRR Calculation for Project B
NPV = AED. 30,172 when the discount rate is 10%
NPV = ??? When the discount rate is 25%
Year
Cash flow
in AED.
Discount Factor for
AED. 1 @ 25% p.a.
Present Value in
AED.
1 2 3 = 1x2
0 (100,000) 1.000 (100,000)
1 30,000 0.800 24,000
2 30,000 0.640 19,200
3 44,000 0.512 22,528
4 66,000 0.410 27,060
NPV (7,212)
NOTE
NPV of Project B is negative @ 25% discount rate. The higher the discount rate, the lesser is the
NPV . In order to have zero NPV, we have to reduce the discount rate from 25% to 22%. Please refer
to working on slide # 42.

43. CALCULATING IRR WITH EXCEL
FOR PROJECT A
43
Year Cash flow in AED.
0 (100,000)
1 45,000
2 40,000
3 35,000
4 50,000
IRR for Project A = IRR(values, [guess])
This formula produces an IRR for Project A of 25%.
Tip
Select any cell where you want to see the result. Write =IRR(values, [guess]).
In the place of values give range of cells as given in the above table including
investment at Y0.

44. 44
CALCULATING IRR WITH EXCEL
FOR PROJECT B
Year Cash flow AED.
0 (100,000)
1 30,000
2 30,000
3 44,000
4 66,000
IRR for Project A =IRR(values, [guess])
This formula produces an IRR for Project A of 21.42%.
TIP
Calculating IRR with EXCEL is easier than from the interpolation formula,
as given here-in-above. So it is advised to calculate IRR with EXCEL.

45. 45
Project B: IRR Calculation by using Interpolation Formula
Total change in NPV = 30,172 – (– 7,212) = 37,384
Total change in discount rate = 25% – 10% = 15%
IRR = 10% + 30,172/37,384 x 15% = 22%
The discount rate is chosen by hit and trial method. In this example, we have
reduced discount rate from 25% to 10% to find out the exact rate that shall make
the project NPV equal to Zero. And we found the exact rate of 22% that gives
NPV equal to zero by using Interpolation Formula.
Decision Rules
 If Project A’s IRR>Project B’s IRR then select Project A , &
 If Project B’s IRR>Project A’s IRR then select Project B
 In this case Project A’s IRR>Project B’s IRR, therefore, Project A is selected.
Because its IRR 25% which is higher than that of Project B’s 22%.
 It is also worth noting here that IRR>Discount Rate of 10%. If these two projects
were not competing each other (i.e. independent projects), then both would have
been selected. If IRR<Discount rate of 10%, then both project would have been
rejected.
Calculating IRR by using Interpolation Formula

46. 6. MODIFIED INTERNAL RATE OF RETURN
46
MIRR is used to gauge an investment’s attractiveness. It is
employed to rank alternative investments of equal size. There are
mainly two problems of IRR that are resolved by MIRR.
I. IRR assumes that interim positive cash flows are re-invested at the same rate
of return as that of the project that generated them. This is usually an un-
realistic scenario and more likely situation is that the funds will be re-
invested at a rate closer to the company’s cost of capital. IRR, therefore,
often gives an unduly optimistic picture of the projects being examined.
Generally, for comparing projects more fairly, Weighted Average Cost of
Capital (WACC) should be used for re-investing the interim cash flows.
MIRR correctly assumes reinvestment at opportunity cost = WACC.
II. More than one IRR can be found for projects with alternative positive and
negative cash flows, which leads to confusion and ambiguity. MIRR finds
only one value.

47. MIRR FORMULA
47
MIRR =
𝑛 𝑭𝑽 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝐶𝑎𝑠ℎ𝑓𝑙𝑜𝑤𝑠, 𝑟𝑒𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 𝑟𝑎𝑡𝑒
−−−−−−−−−−−−−−−−−−−−−−−−− −
𝑷𝑽(𝐶𝑎𝑠ℎ 𝑜𝑢𝑡𝑙𝑎𝑦, 𝑓𝑖𝑛𝑎𝑛𝑐𝑖𝑛𝑔 𝑐𝑜𝑠𝑡)
-1
Where n is the number of equal periods at the end of cash flows occur.
MIRR can be calculated by using Excel Formula that is given as below:
MIRR = MIRR(range, finance_rate, reivestment_rate)
Where:
 Range: is the range of cells that represent a project’s cash flows
 Finance_rate: is the interest rate that company pay’s to its banks
 Reinvestment_rate: is the rate that company expects to receive on reinvestment of cash
inflows

48. MIRR DECISION RULES
48
Calculation
According to the data given at slide 26, Cost of Capital for the Project A and B is same at 10%
p.a. According to the assumption used in the formula for MIRR, the minimum return on re-
invested cash inflows is equal to Cost of Capital or Weighted Average Cost of Capital
(WACC) instead of IRR of the given projects.
MIRR for Project A = MIRR(range, 10%, 10%) = 18.44%
MIRR for Project B = MIRR(range, 10%, 10%) = 17.50%
Decision Rules
In case of independent projects, the project having MIRR greater than Cost of Capital is
acceptable. For mutually exclusive projects, the project having higher MIRR shall be selected.
Conclusion
Project A has higher MIRR than that of Project B. Therefore, A should be selected according
to the criteria established for acceptance and rejection of projects under MIRR.

49. 7. TERMINAL VALUE
49
This technique assumes that each cash inflow is re-invested in an other
opportunity at a certain rate of return from the moment it is received till the
moment the project is finished.
So each cash inflow shall be compounded separately based on its expected rate
of return. The total compounded cash balance shall be discounted at the rate of
interest XYZ agreed with its banks. This technique shall give us better
estimation of cash inflows at the end of the project. In addition to data given at
slide 26, following data shall be used in the calculation for Terminal Value of
Projects A & B:
At the end of year Expected rate of return (%)
1 7
2 9
3 6
4 8

50. TV CALCULATION
50
Yr. RoI YuI CF
Net cash
inflows
Project A
Total
compounde
d sum for
Project A
Net cash
inflows for
Project B
Total
compounded
sum for
Project B
1 2 3 4 5 6 = 4 x 5 7 8 = 4 x 7
% AED. AED. AED. AED.
1 7 3 1.225 45,000 55,125 30,000 36,750
2 9 2 1.188 40,000 47,520 30,000 35,640
3 6 1 1.060 35,000 37,100 44,000 46,640
4 8 0 - 50,000 50,000 66,000 66,000
Total 170,000 189,745 170,000 185,030
Abbreviations used in the table:
RoI: Rate of Interest expected from the market (minimum expected rate can be used)
YuI: Years under investment
CF: Compounding factor based on given rates
Yr.: Year

51. TV RESULT
51
Now, we can calculate the Present Value of the compounded sums for
Project A and Project B in the following manner:
Project A compounded sum x PV factor @ 10% = AED. 189,745 x 0.683
Present Value for Project A compounded sum = AED. 129, 596
Project B compounded sum x PV factor @ 10% = AED. 185,030 x 0.683
Present Value for Project B compounded sum = AED. 126,375
Important Note
 A variation of Terminal Value (TV) is based on the pattern of NPV
technique and is known as Net Terminal Value (NTV) technique.
 Symbolically, NTV = PVTS – PVO.
 It has the same Decision Rules that are used for NPV technique. If NTV is
positive accept the project and if it is negative then reject it.

52. DECISION RULES FOR TV
52
For single project, If the Present Value of the Total of compounded re-invested cash
inflows (PVTS) is greater than the Present Value of the Outflows (PVO),
the proposed project is accepted, otherwise not.
For multiple projects (mutually exclusive projects), the project having PVTS
greater than all competing projects when compared with PVOs relating to them,
shall be selected. Symbolically,
PVTS>PVO Accept
PVTS<PVO Reject
Conclusion
In both projects PVTS is greater than PVO. Since we have to select any one of
them, that is Project A because its PVTS is greater than Project B when both
compared with their PVO which is same in this case.

53. 8. PROFITABILITY INDEX (PI)
53
Profitability Index (PI) or Benefit/Cost Ratio (B/C Ratio)
measures Present Value per Dirham invested.
It is a ratio of PV of future cash inflows by PV of cash outlays (ie net
investment).
PI = PV of expected cash inflows /PV of cash outflows
We calculate here PI for Projects A & B.
PI for Project A = 134,380/100,000 = 1.344
PI for Project B = 130,172/100,000 = 1.302

54. DECISION RULES FOR PI
54
If PI for any single project exceeds 1, the project can be accepted. For
the mutually exclusive projects, the project that has higher PI should
be considered for investment.
Conclusion
In the given illustration of two Projects A and B, Project A has higher
PI than that of Project B. Management should select Project A out of
the proposed investment opportunities.

55. SUMMARY OF RESULTS
55
# Technique
Results for Mutually Exclusive Projects…
Accept
Project
A B A or B?
1. PB 2.43 years 2.91 years A
2. DPB 3.007 years 3.331 years A
3. ARR 37.50% 37.50% N/A
4. NPV AED. 34,380 AED. 30,172 A
5. IRR 25% 22% A
6. MIRR 18.44% 17.50% A
7. TV AED. 129,596 AED. 126, 375 A
8. PI (B/C Ratio) 1.344 1.302 A
Final Conclusion
Based on the results of all CB techniques used in this illustration, we recommend the
management of XYZ company to go for Project A.

56. ABBREVIATIONS
56
# Abbreviation Description
1 AED. UAE Dirham
2 ARR Accounting Rate of Return
3 CB Capital Budgeting
4 DPB Discounted Payback Period
5 DCF Discounted Cash Flow
6 IRR Internal Rate of Return
7 MIRR Modified Internal Rate of Return
8 NPV Net Present Value
9 NTV Net Terminal Value
10 PB Payback Period
11 PI Profitability Index (also known as B/C Ratio)
12 PVO Present Value of Cash Outflows
13 PVTS PV of Total Compounded Reinvested Cash inflows
14 WACC Weighted Average Cost of Capital

57. 57

58. Thank You!
Ahmad Tariq Bhatti
Works & lives in
Dubai, UAE
For Feedback & Queries:
at.bhatty@gmail.com