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CAPITAL BUDGETING
Second Edition
Planning, Incurring, Monitoring & Controlling Capital Expenditures
Ahmad Tariq BhattiFCMA, MA (Economics), BScDubai, United Arab Emirates
CAPITAL BUDGETING
2
OBJECTIVES
3
To understand the nature and importance of investment decision-making in organisations
To understand the concept of time value of money
To understand eight investment appraisal techniques and to evaluate investment opportunities through these techniques
To provide ranking based on financial performance of all competing projects
To make recommendation for the best investment opportunity
Summarize merits & demerits of each evaluation technique
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
NATURECB Decisions have long-term impact on the business stability, growth & successCB 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 investmentCB 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.
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
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
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.
DECISION MATRIX
9
High Medium Low
HighBuild
aggressively – invest & grow
Build aggressively
– invest & grow
Build gradually – improve &
defend
MediumBuild
aggressively – invest & grow
Build gradually – improve &
defendDivest
LowBuild gradually – improve &
defendDivest Divest
Business Strength
Mar
ket
Att
ract
iven
ess
EVALUATION TECHNIQUES
10
A: Traditional Techniques1. Payback period (PB)2. Discounted Payback Period (DPB)3. Accounting Rate of Return (ARR)
B: Discounted Cash Flow (DCF)/Time Adjusted (TA) Techniques4. Net Present Value (NPV)5. Internal Rate of Return (IRR)6. Modified Internal Rate of Return (MIRR)7. Terminal Value (TV)8. Profitability Index (PI) or Benefit/Cost Ratio
Important NoteThese techniques provide reliable evaluation under conditions of
perfect certainty. They are, nevertheless, widely used in practice in the face of uncertainty.
EVALUATION TECHNIQUES
11
Traditional TechniquesDiscounted Cash Flow or Time Adjusted Techniques
PB
Discounted PB
NPV
MIRR
IRR
TV
PI or B/C RatioARR
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
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.
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.
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
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.
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.
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.
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.
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
NORMAL VS NON NORMAL CASH FLOWSNormal 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)
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. 0.90910% is called “cost of capital”; “?” is called the “discount factor”
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
1FV =
)i + (1FV =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 projecti = interest rate per annum n = number of periods FVn = future value after n periods
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.
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 noteProject 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.
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.
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.
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.
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
CALCULATION FOR PROJECT B
YearCash 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 RuleThe 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.
3. ACCOUNTING RATE OF RETURN
31
Step 1: Calculate annual profit
Annual Profit = Income - Depreciation
Step 2: Calculate average profit Average Accounting Profit = Total Profits / # of Yrs.
Step 3: Calculate average capital invested Average Capital = (Initial Investment + Residual Value)/2
Step 4: 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.
ARR CALCULATION
32
Project AAverage 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 BAverage 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%
ACCOUNTING RATE OF RETURN
33
Decision RulesFor 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 ProjectsThe 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.
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 = 0.909Year 2 = 0.826Year 3 = 0.751Year 4 = 0.683
Formula to calculate Discount Factor @ 10% p.a. for AED. 1 is given as follows: Discount Factor = 1/(1+10%)^n
.
10
1
CFr
CFNPV t
tn
t
NPV = Net Present Value
CFt = Cash in-flows for given periods
CFo = Initial Investment
r = Discount Rate
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
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
NPV = NPV(RATE%, VALUES)Project A = NPV(10%, values) = AED. 31,285Project B = NPV(10%, values) = AED. 27,457
Important NoteIn 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.
DifferenceDifference in Project A NPV = 34,380 – 31,285 = 3,095Difference in Project B NPV = 30,172 – 27,457 = 2,715
Calculation of NPVs by using EXCEL Formula
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 NOTEThe 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
10 13 16 19 22 25 28
(15,000)
(10,000)
(5,000)
-
5,000
10,000
15,000
20,000
25,000
30,000
35,000
Profiling of Projects A & B on NPV Basis
NPV Project A
NPV Project B
Discount Rate
Discount Rate (%)
NP
V o
f P
roje
cts
A &
B in
AE
D.
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.
NPV DECISION RULES
40
Results of the workingsProject A has NPV of AED. 34, 380Project B has NPV of AED. 30, 172
Decision RulesThe project that has higher NPV is superior in terms of its financial performance
and is therefore should be selected.
ConclusionProject A has higher NPV than that of Project B. Therefore, Project A should be
selected.
NOTEIn 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.
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 ANPV = AED. 34,380 when the discount rate is 10%NPV = ??? When the discount rate is 25%
YearCash 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
IRR Calculation for Project BNPV = AED. 30,172 when the discount rate is 10%
NPV = ??? When the discount rate is 25%
YearCash 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.
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%.
TipSelect 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
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%.
TIPCalculating 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
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
6. MODIFIED INTERNAL RATE OF RETURN
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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.
MIRR FORMULA
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MIRR = -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
MIRR DECISION RULES
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CalculationAccording 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 RulesIn 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.
ConclusionProject 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.
7. TERMINAL VALUE
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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
TV CALCULATION
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Yr. RoI YuI CFNet cash inflows
Project A
Total compounded 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 investmentCF: Compounding factor based on given ratesYr.: Year
TV RESULTS
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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. 126,375Important 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.
DECISION RULES FOR TV
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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 AcceptPVTS<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.
8. PROFITABILITY INDEX (PI)
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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 = 1.344PI for Project B = 130,172/100,000 = 1.302
DECISION RULES FOR PI
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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.
ConclusionIn 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.
SUMMARY OF RESULTS
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# TechniqueResults 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.
ABBREVIATIONS
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# 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
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Thank you.
THANK YOU!
Thank You!
Ahmad Tariq Bhatti
Works & lives in
Dubai, UAEFor Feedback
& Queries:at.bhatty@gma
il.com
