Capital Budgeting Techniques
by Binam Ghimire
1
Objectives
 Understand and apply various investment appraisal
techniques (PBP, Discounted PBP, ARR, NPV, PI and
IRR), Comparing NPV and IRR, IRR pitfalls, MIRR and
Capital Rationing
2
Capital Budgeting: Meaning
 Answer to the questions: Should an investment be
made? Whether or not an investment is worth
undertaking? If there are alternatives which investment
option provides better cash flows and rate of return?
 Tool to analyse and appraise investments. Sometimes
known as investment appraisal
 The process of analysing, comparing and selecting the
right investment project
3
Capital Budgeting: Significance
 Purpose: Expansion, Improvement, Replacement and
Research and Development. These involve large capital
investments
 Making the right decision
 Firms future
 Sensitive to shareholders wealth
4
Capital Budgeting:
Steps
 Estimation of Cash Inflows and Outflows
 Collection of relevant information
 Selection of appropriate capital budgeting tool(s)
 Calculation and analysis of benefit (loss)
 Appraisal and Decision Making
5
Types of Project and decision making:
Independent Projects
 Independent projects: Cash Flows of one project is
not affected by the Cash Flows of another.
 Example, installation of brick factory and installation of
sugar mill are independent projects.
 Cash flows of former project do not affect the cash flows
of latter one.
 If budget permits, both projects can be launched
provided they meet the set evaluation criteria.
 Decision regarding such projects can be taken
independently.
6
Types of Project and decision making:
Dependent Projects
 Dependent projects: Cash Flows of one project is
affected by the Cash Flows of another.
 Example: Construction of dam and canal in irrigation
project.
7
Types of Project and decision making:
Mutually Exclusive Projects
 Mutually Exclusive projects: Cash Flows of one
project is affected by the Cash Flows of another and
selection of one rejects the other
 Simple Example: Buying a car for your family (Deciding
for a Toyota means not buying Honda or Ford)
 Other Examples: Labour intensive production process
versus capital intensive production process, frock lift
versus conveyor belt, deep well versus canal irrigation
8
Types of Project and decision making:
Replacement Projects
 Replacement projects: due to the wear and tear, and
advent of new technology, existing machine need to be
replaced with new one.
 Thus, the projects falling in this class are classified into
two—maintenance of business and cost reduction.
 Should the existing operation be continued?
 Replace with new one due to the obsolescence.
 Lower the input costs such as labor, materials, and
electricity.
9
Types of Project and decision making:
Expansion Projects
 Expansion projects: Available capacity not sufficient
to meet the demand.
 Add production capacity.
 Expand business: in different geographical regions e.g.
opening new retail outlets.
10
Types of Project and decision making:
Diversification Projects
 Diversification projects. Entering either into the new
products or new markets
 Acquisition of new equipment and plant and latter one
requires substantial amount of money.
11
Techniques:
1. Payback Period
 PBP is the number of years required to cover the cost
of the project
 It is calculated by adding project’s cash inflows to its
cost until the cumulative Cash Flows for the project
turns positive
12
Payback Period:
Formula
 When Cash Inflows are even every year
Investement
PBP 
Annual Cash Inflows
 When Cash Inflows are uneven, we cumulate the Cash
Inflows for all such duration that it is equal to the
investment amount. The total duration that equates
Cash Inflows with Investment (Cash Outflow) is the PBP
 PBP is generally measured in years although we may
convert it into months or weeks or even days
13
Payback Period:
Example
Project A
CFt
Cumulative
PaybackA
Project B
CFt
Cumulative
PaybackB
0
-100
-100
== 2
2
2.33
3
20
-80
50
-30
100
0
90
30 / 90
+
0
1.6
1
-100
-100
== 1
1
70
-30
+
= 2.33 years
2
100 50
0 20
30 / 50
60
3
20
40
= 1.6 years
14
Payback Period:
Decision Making
 Independent Project: Compare with the target of the
company (maximum acceptable period) or industry
average
 Mutually Exclusive Projects: Select the one with shortest
PBP
 Question: In the example for project A and B which
project will you accept 1) they are independent 2) they
are mutually exclusive
15
Payback Period:
Advantages and Disadvantages
 Advantages
Simple: Easy to calculate and understand
Provides an indication of a project’s risk and liquidity
Useful for short-term decision making
 Disadvantages
Ignores the time value of money (TVM)
Ignores CFs occurring after the payback period. This
also implies that the method overlooks the risk of CFs
after the PBP
16
Capital Budgeting Techniques:
2. Discounted Payback Period
 Bring CF to PV and Find the Payback. Considers the
TVM. For Project A:
0
Project A
10% 1
CFt
-100
20
PV of CFt
-100
18.18
Cumulative
-100
-81.82
Disc PaybackA ==
2
+
2
2.6 3
50
90
41.32
-40.50
40.50 / 67.62
67.62
27.12
= 2.6 years
17
Capital Budgeting Techniques:
Payback Period
 Choose the correct for PBP:
A) Does not account properly for time value of
money
B) Does not account properly for risk
C) Cutoff period is arbitrary
D) Does not lead to value-maximizing decisions
E) A, B and C
F) All of the above
18
Capital Budgeting Techniques:
3. Accounting Rate of Return
 ARR is:
 the average annual profit/ initial cost of investment
 Sometimes instead of initial cost of investment, average
cost of investment is also used. To find the average
cost, we need to sum the initial cost + the residual
value and divide by 2
19
Accounting Rate of Return:
Formula
 ARR (%) =
Average Annual Profit
ARR 
Χ 100
Initial Investment
 When Cash Flows are given, profit is the difference
between the total of Cash Inflows and Cash Outflows. If
depreciation is available it should be deducted from
Cash Inflows to find the profit
20
Accounting Rate of Return:
Example
Project A
CFt
ARRA
ARRB
1
2
3
-100
20
50
90
= 20/100 x 100 = 20%
Project B
CFt
0
0
1
2
3
-100
70
50
20
= 13.33/100 x 100 = 13.33%
21
Accounting Rate of Return:
Decision Making
 Independent Project: Compare with the target/
expected rate of return of the company. Compare with
industry average
 Mutually Exclusive Projects: Select the one with highest
ARR
 Question: In the example for project A and B which
project will you accept 1) they are independent 2) they
are mutually exclusive
22
Accounting Rate of Return:
Advantages and Disadvantages
 Advantages
Easy to calculate and understand
Easy to compare with target and or other investment
projects
 Disadvantages
Is based on profit and not Cash Inflows. So affected
by noncash items such as depreciation
Ignores timing of profit
23
Capital Budgeting Techniques:
4. Net Present Value (NPV)
 NPV is the sum of PV of Cash Inflows and PV of Cash
Outflows of a company.
 If the investment is made today NPV is the difference
between the PV of all Cash Inflow streams of the future
less the investment amount
24
Net Present Value :
Formula
n
CFt
NPV  
t
t 0 1  r 
 The investment or cash outflow is often CFo. Hence the
formula may be written as
n
CFt
NPV  
 CF0
t
t 1 1  r 
25
Net Present Value :
Example
Project A
Year
0
1
2
3
CFt
PV of CFt
-100
-£100
20
18.18
50
41.32
90
67.62
NPVA = £27.12
NPVB = ?
26
Net Present Value :
In Microsoft Excel
 In Microsoft Excel, NPV function wizard can be used to
calculate NPV.
 NPV(Rate, Value1) + Investment Amount. Here the Rate
is Discount Rate in %. Value means Cash Flow Stream
which can be selected for all rows. Close the bracket
and add the investment as: + Investment Amount which
is a negative value. In the example above for Project A
it is: NPV(10%, 20+50+90)+(-100)
27
Net Present Value :
An Example in Microsoft Excel
 Consider three alternative projects, A, B and C.
 They all cost $1,000,000 to set up but project’s A and C
returns $800,000 per year for two years starting one
year from set up. Projects B also returns $800,000 per
year for two years, but the cash flows begin two years
after set up.
 Whilst project C costs $1,000,000 to set up it requires
$500,000 initially and $500,000 at termination (a clean
up cost for example).
 If the firm uses a discount rate of 20% which is the
better project?
28
NPV Example in Microsoft Excel
 Project A:
interest rate
Year
Cash Flow
discount factor
PV
NPV=
20%
0
1
2
-$1,000,000
$800,000
$800,000
1.000
0.833
0.694
-$1,000,000.00 $666,666.67 $555,555.56
3
$0
0.579
$0.00
4
$0
0.482
$0.00
$222,222.22
 Project B:
interest rate
Year
Cash Flow
discount factor
PV
NPV=
20%
0
-$1,000,000
1.000
-$1,000,000.00
-$151,234.57
1
$0
0.833
$0.00
2
$0
0.694
$0.00
3
4
$800,000
$800,000
0.579
0.482
$462,962.96 $385,802.47
29
NPV Example in Microsoft Excel
 Project C:
interest rate
Year
Cash Flow
discount factor
PV
20%
0
1
2
-$500,000
$800,000
$300,000
1.000
0.833
0.694
-$500,000.00 $666,666.67 $208,333.33
NPV=
$375,000.00
3
$0
0.579
$0.00
4
$0
0.482
$0.00
30
NPV Example Decision Making
 Project C has the highest NPV and therefore if only one
project can be undertaken it should be C.
 However if more than one project can be undertaken
then both A and C should be selected since they both
have positive NPV’s.
 Project B should be rejected since it has a negative NPV
and would therefore destroy wealth.
 It makes sense that project C should have the highest
NPV, since its cash outflows are deferred relative to the
other projects, and its cash flows are early.
 In contrast project B has all the costs up front but the
cash inflows are deferred.
31
Net Present Value:
Decision Making
 Independent Project: Accept when NPV > 0
 Mutually Exclusive Projects: Select the one with highest
NPV
 Suppose a project has a positive NPV, but the NPV is
small, say, only a few hundred dollars then the firm
should still undertake that project if there are no
alternative projects with higher NPV as a firms wealth is
increased every time it undertakes a positive NPV
project.
32
Net Present Value:
Decision Making
 A small NPV, as long as it is positive, is net of all input
costs and financing costs so even if the NPV is low it still
provides additional returns.
 A firm that rejects a positive NPV project is rejecting
wealth!
 Question: In the example for project A and B which
project will you accept 1) they are independent 2) they
are mutually exclusive
33
Net Present Value:
True or False?
 Discuss:
A) A key input in NPV analysis is the discount rate.
B) In the formula - r represents the minimum return that
the project must earn to satisfy investors.
C) r varies with the risk of the firm and /or the risk of the
project.
Above – Advantages or Disadvantages??
34
Net Present Value:
Advantages and Disadvantages
 Advantages
Considers TVM
Considers all the CFs
Tells if the investment will increase the firm’s value
Useful for comparing similar projects with same costs
 Disadvantages
Requires an estimate of the cost of capital
Expressed in value and not in percentage term
35
Capital Budgeting Techniques:
5. Profitability Index (PI)
 PI is the measurement of relative profitability of the
project. It shows the present value per £ of initial
investment of the project. It is given by the following
equation
PV of Future Cash Flows
PI 
Initial Outlay
 Or PI =
n
CFt

t
(1

r)
t 1
CF0
36
Profitability Index :
Decision Making
 The IRR decision rule is then:
If PI > 1, accept the project
If PI < 1, reject the project
 The PI equal to 1 indicates the zero NPV. Similarly the
PI greater than 1 implies positive NPV of the project.
Conversely, the PI less than 1, implies negative NPV
 Applying the same rationale of NPV, we make a decision
under PI method
 Find out the PI for project A and B
 In the example for project A and B which project will
you accept 1) they are independent 2) they are mutually
exclusive
37
Capital Budgeting Techniques:
6. Internal Rate of Return (IRR)
 IRR is the rate that equates the PV of Cash Inflows with
PV of Cash Outflows.
 The IRR of a project can be defined as the rate of
discount which, when applied to the projects Cash
Flows, produces a zero NPV i.e. it is the rate that will
force NPV to be zero
38
Internal Rate of Return:
Formula
 IRR =
n
CFt
0

t
t 0 1  IRR 
 IRR will give you a rate of return and therefore is
measured in percentage
39
Internal Rate of Return:
Example
Project A
 At 10% NPVA as we saw before is > 0 so try higher
percentage, say 20%
Year
CFt
PV of CFt
0
-100
- £100
1
20
£16.67
2
50
£34.72
3
90
£52.08
NPVA =
£3.47
 At 20% NPVA > 0 so try another higher percentage
say 25%
40
Internal Rate of Return:
Example
Project A
 Calculation of NPVA at 25%
Year
CFt
PV of
0
-100
1
20
2
50
3
90
NPVA =
CFt
-£100
£16
£32
£46.08
-£5.92
 At 25% NPVA is < 0 so IRR is between 20 % and 25
%
41
Internal Rate of Return:
Example
Project A
 By Interpolation, we get
At 20% NPV = £3.47
AT 25% NPV = - £5.92
So, by linear interpolation, IRRA =
20+[3.47/(3.47-(-5.92)]x(25-20)
= 21.84%
 IRRB=?
42
Internal Rate of Return:
In Microsoft Excel
 In Microsoft Excel, IRR function wizard can be used to
calculate the IRR
 Using the wizard in Microsoft Excel, it is simply selecting
all Cash Inflows and Investment Amount (in negative)
inside the parenthesis
43
Internal Rate of Return:
For Uniform Cash Inflows
 The calculation is easier than for uneven Cash Inflows
 IRR can be calculated locating the Factor in Annuity
Table for present value.
 Factor is calculated as Initial Investment / Cash Inflow
per year.
 If the exact rate can not be found then you need to do
the Interpolation
 Example: suppose an investment of £100 will provide a
benefit of £60 each year for next two years. What is the
IRR?
44
Internal Rate of Return:
For Uniform Cash Inflows
 Factor = Initial Investment/ Annual Cash Flow
= 100/ 60 = 1.6667. Locating the Factor in Annuity Table
for present value for 2 years, we get closest value at
12% and 13 %
 By interpolation,
Present Value
12%
1.6901
1.6901
TR
1.6667
13%
1.6681
Difference 0.0234
0.022
IRR = 12 + 0.0234/ 0.022 x (13-12) = 13.06%
45
Internal Rate of Return:
Decision Making
 The IRR decision rule is then:
Accept if IRR greater than or equal to some
predetermined cost of capital. (The cost of capital is
the discount rate we would have used in a NPV
analysis).
 In the example for project A and B which project will
you accept 1) they are independent 2) they are mutually
exclusive
46
Internal Rate of Return:
Advantages and Disadvantages
 Advantages
Considers TVM. Considers all the CFs
Tells if the investment will increase the firm’s value
 Disadvantages
Requires an estimate of the cost of capital
47
NPV and IRR: the methods
 NPV positive: when cost of capital is < IRR
 NPV negative: when cost of capital > IRR
 Explaining above using NPV profile
CF for Year 0, 1 and 2 are -1,500, £500 and £1,500
respectively.
Calculate NPVs at Discount Factor: 0 %, 6%, 12%,
18%, 24%, 30% and 36% respectively and present
the NPV profile
48
NPV Profile
600
500
400
300
NPV
(£)
200
100
0
0
-100
6
12
18
24
30
36
Discount Rates (%)
-200
-300
49
NPV and IRR: mutually exclusive
projects
 NPV and IRR: Check the NPV and IRR calculations for 2
projects given below. Assume Discount Factor of 7% for
NPV calculation. Amount in £.
Year
0
1
2
3
4
5
IRR
NPV
Labour
-10,000
1,000
3,000
4,000
5,000
6,000
Machine
-10,000
5,000
4,000
3,000
3,000
2,500
20%
26%
£4,912.48 £4,686.70
 The NPV of Labour project > Machine. But IRR of
Machine > Labour.
50
NPV and IRR: mutually exclusive
projects
 Here we need to understand Cross Over Rate: Crossover rate is the discount rate where NPVs of two
projects are equal i.e. NPV of Project A equals NPV of
Project B
NPV
 NPV
ProjectA
ProjectB
CF
CF
CF

 ... 
 CF 
1  k  1  k 
1  k 
CF
CF
CF

 ... 
 CF
1  k  1  k 
1  k 
A1
A2
1
A2
An
2
A2
1
n
A0
An
2
n
B0
We can now therefore solve for K
CFA1 - CFB1 CFA2 - CFB2
CFAn - CFBn
+
+
...
+
– (CFA0 - CFb0) = 0
(1 + k)
(1 + k)2
(1 + k)n
51
NPV and IRR: mutually exclusive
projects
In this case it is 9% (Note that here Cost of capital is
only 7%)
10000
8000
6000
9
4000
2000
0
0
5
10
15
20
25
30
-2000
-4000
52
NPV and IRR: mutually exclusive
projects
 If projects are independent, the two methods always
lead to the same accept/reject decisions.
 If projects are mutually exclusive then it depend on k
(cost of capital/ discount rate) and cross over rate
If k > crossover point, the two methods lead to the
same decision and there is no conflict.
If k < crossover point, the two methods lead to
different accept/reject decisions. In such a case, we
need to select the project with higher NPV.
53
IRR pitfall: Multiple IRRs
 When project cash flows have multiple sign changes,
there can be multiple IRRs.
 Example:
Year
0
1
2
3
4
5
6
Cash Flows
-2000
1600
300
300
300
300
-300
 Here we have more than one IRR.
54
Multiple IRRs
 IRRs: -50% and 15%.
2500
2000
1500
NPV
(£)
1000
500
0
-50
-25
-15
0
15
25
50
-500
-1000
Discount Rate (%)
55
No IRRs
 Find the IRR for the following cash flows:
 Year 1, 2 and 3 : £1,000, £-3000 and £2,500
respectively
56
NPV and IRR: compared
 Relative and absolute measurement
 IRR might not be usable for projects with unconventional
cash flows
 In the case of mutually exclusive projects, IRR may give the
conflicting decision.
 IRR does not hold the value additivity principle. (According to
the value additivity principle, if we know the value of the
separate projects accepted by the management, we can
calculate the value of the firm by adding up those
projects).We can not add up IRRs of the projects and find out
the IRR for the projects in combination. So, for project X and
Y, IRR(X) + IRR(Y) is not equal to IRR (X+Y).
57
NPV and IRR: compared
 IRR does not consider the scale of investment. In the
case of mutually exclusive projects, it considers only the
rate of return but does not consider the scale of
investment.
 Example: Project X and Y are two mutually exclusive
projects. Suppose these are one year projects. Project X
requires £ 5,000 investment and Project Y does £ 1,000.
Further let us suppose that the required rate of return
on the investment is 10 percent. At the end of the year,
Project X and Y generate cash inflows of £ 6,250 and £
1,500.
58
NPV and IRR: compared
 IRR of Project X is 25 percent and of Project Y is 50
percent.
 Here, Project Y has the higher IRR than that of Project
X.
 But NPV of Project X Rs 681.82 and of Project Y is Rs
363.64.
 Thus, IRR does not consider the investment scale and it
is not consistent to the shareholder wealth maximization
criterion.
59
NPV and IRR: compared
 Theoretically, NPV shows how much the market value of
the firm will rise if project is accepted and IRR shows
what rate of return will the project yield if it is accepted.
 NPV and IRR are different with respect to the
assumption of reinvestment rate. NPV assumes that
cash inflows are reinvested at required rate of return
and IRR assumes that they will be reinvested at project
rate of return.
60
7. Modified Internal Rate of Return
(MIRR)
 MIRR overcomes the IRR problems (Conflicting
Decisions and Multiple IRRs).
 MIRR assumes a single outflow at time 0 and a single
inflow at the end of the final year of the project.
61
MIRR
 Steps:
Convert all investment phase outlays as a single
equivalent payment at time 0 using cost of capital.
All net cash inflows of project are converted to a
single net equivalent terminal receipt at the end of
the project’s life (assuming a reinvestment rate equal
to the company’s cost of capital).
MIRR is the nth root of TV inflows / PV outflows and
subtracting 1 (where n is the length of the project in
years)
62
MIRR
 Example: A Project has the following cash flows. Find
the IRR
0
CFt
-800
1
5,000
2
-5,000
63
MIRR
 We can solve the followings to find IRR
0   800 
5000
 5000

1  IRR 1  IRR 
2
 The above can be solved at both 25% and 400%
 i.e. the project has two IRRs
 There will be as many IRRs as many change in signs
64
MIRR
 MIRR to resolve the problem
 Steps
Find out the PV of outflows at cost of capital (say
10%)
Find out the FV of inflows at cost of capital
65
MIRR
 PV of outflows
 -800 + (-5000/(1.10)2) = 4,932.23
 FV of inflows at 10% = 5,000 x 1.10 = 5,500
 £4,932.23 = £5,500/ (1+MIRR)2
 MIRR = (5,500/ 4932.23)1/2 – 1
5.6%
 Can we now devise a formula for MIRR?
66
MIRR
 Formula MIRR:
MIRR: (Terminal Value Inflows/ PV Outflows)1/n – 1
Where Terminal Value Inflows is
TV   CIF 1  k 
n
n t
t
t 0
PV of Cash Outflow is
COF
PV  
1  k 
n
t
t 0
t
67
MIRR
 Advantages:
MIRR solves the problem of multiple returns. MIRR
converts the unconventional cash flow into
conventional cash flows.
MIRR is based on the assumption that cash inflows
are reinvested at cost of capital. This assumption is
more realistic than the assumption of regular IRR.
So, MIRR is better indicator of profitability of the
project.
68
MIRR
 Disadvantages:
NPV and MIRR of mutually exclusive projects give the
same decision provided the size and life of the
projects are equal. But NPV and MIRR give the
conflicting decision when projects differ in size
measured in term of investment.
First, cash outflows and inflows are converted into
the present value and terminal value respectively and
then based on the present value of the outflows and
terminal value of cash inflows, MIRR is calculated.
Hence the calculation process is difficult.
NPV solves all the problem so not needed in reality
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Capital Rationing
 Choosing the capital Expenditure when resources are
limited.
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Capital Rationing
 Shareholders’ wealth will be maximised if a company
undertakes all possible positive NPV projects
 Capital Rationing implies there are insufficient funds
hence it is not possible to select all projects (although
with positive NPV)
 Thus, capital rationing refers to the situation where
the firm is constrained to raise necessary funds to invest
in all projects with positive NPV.
 Capital rationing: a firm limits its capital expenditure to
less than the amount required to finance the optimal
capital budget. (optimal capital budget – budget for all
with +’ve NPVs).
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Capital Rationing
 Why capital rationing?
Capital ceiling for capital investment.
Target capital structure therefore reluctant to raise
debt capital in excess of optimal debt ratio.
Reluctant to issue new common share due to the fear
of dilution of controlling power in management.
 All these factors put constraints to select all projects
with positive NPV and the management is bound to
make sub-optimal capital budget
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Capital Rationing
 Two Types: Hard and Soft.
 Hard rationing is external e.g. imposed by lenders
 Soft rationing is internal e.g. by senior managers
 The shortage of fund may be for
Single Period
Multi Period (This requires linear programming
techniques)
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Capital Rationing
 Single Period: The shortage of fund is only for present
period and will not arise in the future. There can be
three different scenarios:
The projects are divisible
The projects are indivisible
The projects are mutually exclusive
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Capital Rationing
 Solve the followings:
 Peel Co has identified 4 positive NPVs as follows
Project
NPV (£ m)
Investment (£ m)
A
60
9
B
40
12
C
35
6
D
20
4
 Capital is limited to £12 million
 Which projects should be taken if a) projects are
independent and divisible b) independent and indivisible
c) mutually exclusive
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Capital Rationing
 Solution to a) independent and divisible
Project
NPV (£ m)
Investment PI
A
60
9
6.67
B
40
12
3.33
C
35
6
5.83
D
20
4
5
 Select A and C
 Solution to b) independent and indivisible – Trial and
Error Hence Either A or B or C +D
 Solution to c) project with highest NPV - A
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Thank you
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