Capital budgeting
Learning objectives
• Understand the concept of capital budgeting i.e.
long term investments
• The nature and scope of investment decisions
• The methods of appraising the investment decisions
1
Define
The decision as to which projects should be
undertaken by a corporation is known as the
‘investment decision’, and the process is known
as ‘capital budgeting’
Capital budgeting is essentially the process used to
decide on the optimum use of scarce resources
2
Steps in CBP
• Identify the Invst. Opportunities
• Select the feasible ones
• Evaluate the project as to whether or not the
proposal provides an adequate return to investors
• Accept & implement the project
• Online monitoring
3
Investment evaluation techniques
Categorized into two groups
1. Non-discounting techniques:
– Payback
– (Average) accounting rate of return (ARR)
2. Discounting techniques
–
–
–
–
Net present value
Internal rate of return (IRR)
PI (profitability method)
TV (terminal value method)
4
The payback technique
• This method involves determining the time taken for the initial
outlay to be repaid by the project’s expected cash flows
• PB =
Initial Investment (Co)
Annual Cash Inflow (CI)
Unequal cash flows
Cumulative cash inflow
5
Example:
Year
Project B
Cum NCF
0
1
-2000 1500
2
3
200
0
4
5
300 200
6
Payback
300
1500 1700 1700
6
Example:
Year
Project A
Cum CF
0
-2000
Payback
1
600
600
A
2
3
4
5
400 900 200 200
1000 1900
6
200
100
 3
 3.5 years
200
7
Project
Co
C1
C2
C3
X
-4000
0
4000
2000
Y
-4000
2000
2000
0
PB
8
Project
Co
C1
C2
C3
A
-10000
+10000
B
-10000
7500
7500
C
-10000
2000
4000
12000
D
-10000
10000
3000
3000
9
Selecting project according PB
• When selecting among a number of projects, the
one with the shortest payback period should be
chosen
• However, there is little guidance on what an
appropriate payback period should be, making it
difficult to decide whether a project should be
accepted or not.
10
Limitations of PB
• Calculation of payback period ignores the time value of money
• Cash flows that occur after the end of the payback time are
ignored in the calculation of payback period. Yet, these latter
cash flows may be significant in making the decision.
• Cutoff period is subjective
• Cannot rank projects that have the same PB
• Does not indicate the project wealth creation
11
DPB
• Where cash flows are discounted
• PB is calculated
12
CALCULATE THE PB & DPB @10%
Co
C1
C2
C3
C4
X
-4000
3000
1000
1000
1000
Y
-4000
0
4000
1000
2000
13
Average /Accounting rate
of return (ARR)
The ARR is given by:
averageincome
ARR 
averageinvestedcapital


EBIT
t (1  T )
/
n



t 1


ARR 
I 0  / 2
n
14
Example:
Calculate the ARR for a
2-year project that
involves a machine
costing Rs100 lacs and
is expected to generate
EBDIT of Rs 60 L & 70 L
in years 1 & 2.
The machine is to be
depreciated on a
straight-line basis, and
the corporate tax rate is
30%.
Step 1
Calculate average net income
Year
1
2
EBDIT
60
70
Less depreciation
50
50
Taxable income
10
20
Less tax (30%)
3
6
Net income
7
14
Average = (7 + 14) / 2 = 10.5
15
Example:
.
Step 2
Calculate average investment
Year
0
1
2
Machine cost
100
100
100
Less accum.
depreciation
0
50
100
100
50
0
Investment
Average investment = (100 + 50 + 0)
/ 3 = 50
16
Example:
Step 3
Calculate the ARR
Avg incom e
Avg invest edcapit al
10.5

 21%
50
Step 4
Compare the ARR to a target or “cutoff” rate to accept or reject
17
Acceptance rule
• Acceptance rule:
• The ARR is compared with a predetermined
ARR target, or ‘cut-off’ rate, to determine
whether to proceed with a project
• When n projects then select the one with
greatest ARR
18
Limitations of ARR
Is based on accounting figures which are not necessarily
related to cash flows and are based on accounting
techniques that may vary from company to company
Ignores the time value of money
Requires an arbitrary target or “cut-off” rate, but there is
little theoretical or other guidance in setting an
appropriate target ARR
19
Net present value (NPV)
• Calculate the PV of all future cash inflows and
cash outflows that will result from undertaking a
project
• These positive and negative present values are
then netted off against one another to determine
the net present value of the project
20
Acceptance rule
• The firm should accept all positive-NPV projects and reject
negative-NPV projects, because NPV is a measure of the
increase in firm value (and therefore the wealth of the firm’s
owners) from undertaking the project
• If the NPV of a project is zero, it is a matter of indifference as
to whether the firm should undertake the project or pay the
available cash back to shareholders
• This is because zero NPV indicates that the project yields the
same future cash that the investors could obtain by investing
themselves
21
• The net present value is calculated as
follows:
n
NPV  
t 1
where:
CIFt
k =
C0 =
any)
n =
CIFt
1  k 
t
 C0
=cash flow generated by the project in year t
the opportunity cost of capital
the cost of the project (initial cash flow, if
the life of the project in years
22
• NPV is the sum of the present values of a
project’s cash flows at the cost of capital
NPV

C0
PV outflows

C1
1+k 
1

C2
1+k 
2


Cn
1+k 
n
PV inflows
 If PVinflows > PVoutflows, NPV > 0
23
• Decision Rules
– Stand-alone Projects
• NPV > 0  accept
• NPV < 0  reject
– Mutually Exclusive Projects
• NPVA > NPVB  choose Project A over B
24
Example:
Apply the NPV rule to a project that costs Rs 210 L
and yields Rs 216 L in one year when the opportunity
cost of capital is 7%.
n
NPV  
t 1
CIFt
1  K 
t
 C0
216L

 210L   Rs8L
1.07
Since the NPV is negative, it should be
rejected.
25
Example:
A company is considering whether to purchase a
machine worth Rs 500,000 that will generate Rs
150,000 p.a. over the next 5 years. What is the NPV
of this project, given an opportunity cost of capital of
10%?
n
NPV  
t 1
CIFt
1  k t
1  1  k  n 
 C 0  CIF 
  C0
k


1  1.15 
 150,000
  500,000  Rs68,618
 0.1 
26
27
• The advantages of NPV technique are:
• It always ensures the selection of projects
that maximise the wealth of shareholders
• It takes into account the time value of money
• It considers all cash flows expected to be
generated by a project
• Value additivity : NPV (A+B) = NPV(A)+NPV(B)
28
• Limitations are:
• It requires extensive forecasts of the costs
and benefits of a project, which can be
problematic
• Ranking of projects changes with change
in CFs / K
29
30
Internal rate of return (IRR)
• The IRR technique is also based on a DCF model, but
focuses on the rate of return in the DCF equation rather than
the NPV
• The IRR is defined as the discount rate that equates the
present value of a project’s cash inflows with the present
value of the its cash outflows
• This is the equivalent of saying that the IRR is the discount
rate at which the NPV of the project is equal to 0
31
• A project’s IRR is the return it generates on the
investment of its cash outflows
– For example, if a project has the following cash flows
0
1
2
3
-10,000
2,000
4,000
6,000
The “price” of receiving
the inflows
• The IRR is the interest rate at which the present value of
the three inflows just equals the NR 10,000 outflow
32
• Defining IRR Through the NPV Equation
– The IRR is the interest rate that makes a
project’s NPV zero
IRR :
C0
PV outflows

C1
1IRR 
1

C2
1IRR 
2


Cn
1IRR 
PV inflows
33
n
34
• Stated formally:
n
0
t 1
where:
CIFt
C0 =
any)
n =
irr =
CIFt
1  irr 
t
 C0
=the cash flow generated by the project in year t
the initial cost of the project (initial cash flow, if
the life of the project in years
the internal rate of return of the project
35
• The unknown variable can be solved by trialand-error
• NPV and IRR use the same framework and
inputs, so they should result in the same
accept/reject decision
36
Acceptance of project
• The decision rule is to accept a project if its
IRR is greater than the cost of capital and
reject it if its IRR is less than the cost of capital
• When IRR > k : accept
• When IRR < k : reject
37
Example:
Apply the IRR rule to a project that costs Rs100 L
and yields Rs106 L in one year when the
opportunity cost of capital is 7%.
n
0
t 1
CIFt
1  r 
t
 C0
106L
0 
 100L
1  irr
 irr  6%
38
Example:
The IRR solved by trial and error.
YEAR
Net cash
flows
0  2000 
0
1
2
3
4
5
-2000
-1000
2000
2000
-1000
4000
 1000
2000
2000
 1000
4000




1  irr 1  irr2 1  irr3 1  irr4 1  irr5
To solve this problem using trial-and-error, you select a
discount rate and substitute it into the equation. If the NPV is
negative (positive) the discount rate is too high (low). By
narrowing down the difference between the two rates, we can
approach the IRR. In this case the IRR is approximately 31%.
39
40
Short cut method for IRR
• Calculate the PB
• Look in PV annuity table for the PB in the year
row
• Find two rates close to the PB
• Actual IRR by INTERPOLATION
 PB  DFr 
IRR  r  

 DFrl  DFrh 
41
• The project cost is Rs 36000 and is expected to generate
CF of Rs 11200 p.a. for 5 years. Calculate the IRR
•
•
•
•
Solution
PB = 36000/11200= 3.214 (PVAF)
Table PVAF look for PB in 5th row
16% & 17%
 3.274  3.214
16  
  16.8%
 3.274  3.199
 3.214  3.199
17  
  16.8%
 3.274  3.199
42
Limitations
It is difficult to calculate – in most circumstances it
can only be found by trial-and-error
For projects involving both positive and negative
future cash flows, multiple internal rates of return
can exist
It can give an incorrect ranking when evaluating
projects of different size
43
PI- Profitability Method
• PI =
PV of cash inflows
PV of cash outflows
Acceptance rule
When PV > 1
44
Example
Initial investment of a project is 100000 and it generates CF of
Rs 40,000, Rs30,000, Rs 50,000 and Rs 20,000 in year 1
through 4. calculate the NPV & PI of the project at 10%.
45
Terminal value method
• Here the assumption is that each cash flow is
reinvested at a certain rate of return from the moment it
is received until the termination of the project.
• Example
• Original outlay is 10,000, years 5, CF 4000 p.a. for
5yrs, k 10%.
• In year 1&2 the CF reinvested at 6%
• In year 3 to 5 the CFs reinvested at 8%
46
Yr
int
1
4000
6
Reinvst
yrs
4
FVF
TFV
1.262
5048
2
4000
6
3
1.191
4764
3
4000
8
2
1.166
4664
4
4000
8
1
1.080
4320
5
4000
8
0
1.0
4000
22796
Find the PV of 22796 at 10% . 22796 X .621 = Rs 14156.3
47
NPV Vs IRR
• SIZE DISPARITY
PROBLEM
A
B
Co
-5000
-7500
C1
6250
9150
IRR
25
22
K 10%
NPV
681.25 817.35
48
Time disparity problem
Yr
A
B
0
105000
105000
1
2
3
60000
45000
30000
15000
30000
45000
4
15000
75000
IRR
20
16
NPV
@8%
23970
25455
49
Unequal lives project
• Two projects A with service
life of 1 yr, B with 5 yrs.
Initial investment in both
projects 20,000 each.
IRR
NPV
A
20
1816
B
15
4900
• Project A CF 24000, B 5th yr
40200. at 10%
50
Lending & Borrowing type
Co
C1
IRR
NPV@10%
X
-100
120
20%
9
Y
+100
-120
20%
-9
51