Faculty of Law and Management FUNDAMENTALS OF FINANCE .docx

Faculty of Law and Management
FUNDAMENTALS OF FINANCE
Lecture 5: Investment Evaluation Techniques
Presented by:
Dr Balasingham Balachandran
Professor of Finance
Department of Finance, La Trobe Business School
Investment Evaluation Techniques
2 These slides have been drafted by the La Trobe University
School of Economics & Finance based on Berk (2011).
Topic Overview
evaluation
)

limited
These slides have been drafted by the Department of Finance,
La Trobe Business School based on Berk (2014).
Learning Objectives
drawbacks
limited so that it cannot take all positive- NPV
projects
3
4
investments

should be undertaken
determine
the value of the projects available to them
undertake is
known as ‘capital budgeting’
valuation of
individual projects
Investment evaluation and capital budgeting
5
-term investment
projects, the outlay is made in the expectation of generating
future cash flows
nvest in a project, the key
consideration is whether or not the proposal provides an
adequate return to investors

– capital
budgeting
– is essentially a process to decide on the optimum use of scarce
resources
Investment evaluation and capital budgeting
6
There are three fundamental stages in making capital budgeting
decisions:
with a project – the most
important being the financial ones
technique to decide
whether a project is acceptable, or optimal amongst alternative
projects
reject a project
The capital budgeting process

7
-known
investment evaluation techniques
(DCF) model:
t present value (NPV)
-based techniques:
Investment evaluation techniques
8
g projects, it is important to keep in mind the
type of projects being considered

as long as there are sufficient funds are available, a
company should invest in all acceptable independent
projects
Types of projects
9
can
only choose one of them – the one that is ranked highest by
the evaluation technique being used
in the sense that accepting one project affects the cash flows
of another

the scope of this subject
Types of projects
10
future cash
inflows and cash outflows that will result from undertaking a
project
and negative present values are then netted off
against one another to determine the net present value of the
project
-NPV projects and reject
negative-
NPV projects, because NPV measures the increase in value from
the
project
Net Present Value (NPV)

11
between
undertaking the project or paying the available cash back to
shareholders
e zero NPV indicates that the project yields the
same
future cash that the investors could obtain by investing
themselves
end of the
project exceeds the cash flow that investors could have
generated
12
–that
is, in
terms of cash today.

The NPV decision rule
NPV = PV (Benefits) – PV (Costs)
(Eq. 8.1)
13
where:
CFt = cash flow generated by the project in year t
r = the opportunity cost of capital
CF0 = the cost of the project (initial cash flow, if any)
n = the life of the project in years
The net present value of a project is calculated as
follows:
0

1
NPV
1
n
t
t
t
CF
CF
Using the NPV Rule
fertiliser
plant at a cost of $81.6 million.
after the first
year, and lasting four years as shown by the timeline below:

14
Month: 0 1 2 3
4
Cash Flow: ($81.60) $28 $28 $28 $28
Cost of capital is10%
get an NPV of
$7.2 million, which is positive.
million and will
increase the value of the firm.
15
Using the NPV Rule
NPV = -81.6 +
28

+
28
+
28
+
28
1+r (1+r)2 (1+r)3 (1+r)4
capital.
project’s NPV over
a range of discount rates.
16
NPV Profile
is positive only when the
discount rates are less than 14%.

17
Example:
A company is considering whether to outlay $500,000 for a
machine
that will generate $150,000 p.a. over the next 5 years. What is
the
NPV of this project, given an opportunity cost of capital of
10%?
18
wealth of
shareholders
project

project,
which can be problematic
-finance-trained managers to
understand
Payback Period
• Payback period is the amount of time required for an
investment
to generate cash flows to recover its initial cost.
• Steps in estimating the payback period are:
investment.
• An investment is acceptable if its calculated payback is less
than
some prescribed number of years.

20
The payback technique
year before full recovery
cost to be recovered at start of year
cash flow during year
21
Example:
Calculate the payback period for the following project.
Year 0 1 2 3 4 5 6
Project A -1000 100 200 800 100 100 100

22
Example:
Year 0 1 2 3 4 5 6
Project A -1000 100 200 800 100 100 100
Cum NCF
23
Example:
Year 0 1 2 3 4 5 6
Project A -1000 100 200 800 100 100 100
Cum NCF -900

24
Example:
Year 0 1 2 3 4 5 6
Project A -1000 100 200 800 100 100 100
Cum NCF -900 -700
25
Example:
Year 0 1 2 3 4 5 6
Project A -1000 100 200 800 100 100 100
Cum NCF -900 -700 100

26
Example:
Year 0 1 2 3 4 5 6 Payback
Project A -1000 100 200 800 100 100 100
Cum NCF -900 -700 100 200 300 400 2.88 yrs
At the end of the third year, the sign of the cumulative net cash
flow
has changed from negative to positive. Therefore the payback
occurred during the third year. If we assume the year 3 cash
flow
is earned evenly
during year 3, the
payback period is:
years88.2
800
700

A
Payb ack
27
Example
Cash flows for projects A to F are given
below:
Year A B C D E F
0 -900 -900 -900 -900 -900 -900
1 300 300 100 600 600 300
2 300 300 200 200 200 300
3 300 300 600 100 100 300
4 - 300 - - 100
Calculate the payback period for these projects A-F.
Which one is the best investment?

28
Example
Cash flows for projects I and D are given
below:
Year Project I Project D
0 (100) (100)
1 10 70
2 60 50
3 80 20
29
Example continued
The significant cash flows occur in later years!
10 80 60
0 1 2 3
– 100

=
Cumulative – 100 – 90 – 30 50
PBPI 2 + 30/80 = 2.375
years
0
2.375
Project I
30
30
Example Continued
The significant cash flows come early!
70 20 50
0 1 2 3
– 100
Cumulative – 100 – 30 20 40
PBPD 1 + 30/50 = 1.6 years

0
1.6
=
Project D
30
Decision Criteria Test - Payback
• Does the payback rule account for the time value of money?
• Does the payback rule account for the risk of the cash flows?
• Does the payback rule provide an indication about the
increase in value?
• Should we consider the payback rule for our primary
decision rule?
Evaluation of Payback Period

ey and risk ignored.
-off date.
-term projects or Lacks a decision
criterion grounded in
economics.
33
payback
period, except that the cash flows are discounted to present
value

the
outlay from discounted cash flows
takes account of the time value of money (for cash flows
within the payback period) but does not allow for risk, ignores
cash flows after the payback period and is subject to an
arbitrary cut-off
The discounted payback technique
34
Example:
Calculate the discounted payback period for the following
project
(discounting cash flows at a required rate of return of 10%).
Year 0 1 2 3 4 5 6
Project A -1000 100 200 800 100 100 100
Disc CF
Cum NCF

35
Example:
project
Year 0 1 2 3 4 5 6
Project A -1000 100 200 800 100 100 100
Disc CF -1000
Cum NCF
36
Example:
project

Year 0 1 2 3 4 5 6
Project A -1000 100 200 800 100 100 100
Disc CF
-1000
Cum NCF
1.1
100
37
Example:
project
Year 0 1 2 3 4 5 6
Project A -1000 100 200 800 100 100 100
Disc CF
-1000

= 91
Cum NCF
1.1
100
38
Example:
project
Year 0 1 2 3 4 5 6
Project A -1000 100 200 800 100 100 100
Disc CF
-1000
= 91
Cum NCF

1.1
100
2
1.1
200
39
Example:
project
Year 0 1 2 3 4 5 6
Project A -1000 100 200 800 100 100 100
Disc CF
-1000
= 91

= 165
Cum NCF
1.1
100
2
1.1
200
40
Example:
project
Year 0 1 2 3 4 5 6
Project A -1000 100 200 800 100 100 100
Disc CF
-1000

= 91
= 165
= 601
= 68
= 62
=56
Cum NCF
1.1
100
2
1.1
200
3
1.1
800
4
1.1

100
5
1.1
100
6
1.1
100
41
Example:
project
Year 0 1 2 3 4 5 6
Project A -1000 100 200 800 100 100 100
Disc CF
-1000
= 91

= 165
= 601
= 68
= 62
=56
Cum NCF -909
1.1
100
2
1.1
200
3
1.1
800
4
1.1
100

5
1.1
100
6
1.1
100
42
Example:
project
Year 0 1 2 3 4 5 6 DPB
Project A -1000 100 200 800 100 100 100
Disc CF
-1000
= 91

= 165
= 601
= 68
= 62
=56
Cum NCF -909 -744 -143 -74 -12 44 5.22 yrs
years22.5
56
12
A
Payb ackDisc
1.1
100
2
1.1
200

3
1.1
800
4
1.1
100
5
1.1
100
6
1.1
100
Decision Criteria Test – Discounted Payback
• Does the discounted payback rule account for the time value
of money?
• Does the discounted payback rule account for the risk of the
cash flows?
• Does the discounted payback rule provide an indication

about the increase in value?
• Should we consider the discounted payback rule for our
primary decision rule?
Evaluation of Discounted Payback
Advantages
- Includes time value of money
- Easy to understand
- Does not accept negative NPV
investments
Disadvantages
- May reject positive NPV investments
- Arbitrary determination of acceptable
payback period
- Ignores cash flows beyond the cut-off

date
- Biased against long-term investments.
45
capital,
and is based on accounting income and historical cost asset
figures
:
Average Accounting Rate of Return (ARR)
“cut-
off” rate, to determine whether to proceed with the project
capital invested average
income average
46
There are four stages in calculating the ARR:

estimated (Note that
“income” takes into account not only cash but non-cash items
such as depreciation
(after depreciation) is
estimated
should be accepted
47
Example: Step 1
Calculate the ARR for a 2-
year project involving a
machine that costs $100m
and will yield cash flows of
$53m & $65m in years 1 &

2.
The machine is to be
depreciated on a straight-
line basis, and the
corporate tax rate is 30%.
Calculate average net income
Year 1 2
Cash flow
Less depreciation
Taxable income
Less tax (30%)
Net income
48
Example: Step 1

and will yield cash flows
of $53m & $65m in years
1 & 2.
line basis, and the
Year 1 2
Cash flow 53 65
Less depreciation
Taxable income
Less tax (30%)
Net income

68
Example: Step 1
1 & 2.
line basis, and the
Year 1 2
Cash flow 53 65

Less depreciation 50 50
Taxable income
Less tax (30%)
Net income
50
Example: Step 1
1 & 2.
line basis, and the

Year 1 2
Cash flow 53 65
Taxable income 3 15
Less tax (30%)
Net income
51
Example: Step 1

1 & 2.
line basis, and the
Year 1 2
Cash flow 53 65
Taxable income 3 15
Less tax (30%) 1 5
Net income
52
Example: Step 1

1 & 2.
line basis, and the
Year 1 2
Cash flow 53 65
Taxable income 3 15
Less tax (30%) 1 5
Net income 2 10

53
Example: Step 1
1 & 2.
line basis, and the
Year 1 2
Cash flow 53 65

Taxable income 3 15
Less tax (30%) 1 5
Net income 2 10
Average = (2 + 10) / 2 = 6
54
Example: Step 2
1 & 2.

line basis, and the
Calculate average investment
Year 0 1 2
Machine cost
Less accum.
depreciation
Investment
55
Example: Step 2

1 & 2.
line basis, and the
Year 0 1 2
Machine cost 100 100 100
Less accum.
depreciation
Investment
56
Example: Step 2

1 & 2.
line basis, and the
Year 0 1 2
Less accum.
depreciation
0
Investment

57
Example: Step 2
1 & 2.
line basis, and the
Year 0 1 2
Less accum.

depreciation
0 50
Investment
58
Example: Step 2
1 & 2.
line basis, and the

Year 0 1 2
Less accum.
depreciation
0 50 100
Investment
59
Example: Step 2
1 & 2.

line basis, and the
Year 0 1 2
Less accum.
depreciation
0 50 100
Investment 100 50 0
60
Example: Step 2

1 & 2.
line basis, and the
Year 0 1 2
Less accum.
depreciation
0 50 100
Investment 100 50 0
Average investment =
(100 + 50 + 0) / 3 = 50

61
Example: Step 3
1 & 2.
line basis, and the
Calculate the ARR
Step 4

Compare the ARR to a target or
“cut-off” rate to accept or reject
62
Example: Step 3
1 & 2.
line basis, and the

Calculate the ARR
Step 4
%12
50
6
capital invested Avg
income Avg
63
Example: Step 3

1 & 2.
line basis, and the
Calculate the ARR
Step 4
%12
50
6
income Avg

64
Example: Step 3
1 & 2.
line basis, and the
Calculate the ARR
Step 4

%12
50
6
income Avg
65
The ARR technique has a number of disadvantages,
including the fact that it:
related to
cash flows and are based on accounting techniques that may
vary
from company to company

-off” rate, but there is
little
theoretical or other guidance in setting an appropriate target
ARR
66
on the
rate of return in the DCF equation rather than the NPV
present value
of a project’s cash inflows with the present value of its cash
outflows
rate at
which the NPV of the project is equal to 0
Internal Rate of Return (IRR)

67
Stated formally:
0
1
0
1
n
t
t
t
F
CF
where:
Ft = cash flow generated by the project in year t

C0 = the cost of the project (initial cash flow, if any)
n = the life of the project in years
r = the internal rate of return on the project
68
calculator or
by trial-and-error
than the
cost of capital and reject it if its IRR is less than the cost of
capital
that these
methods use the same framework and inputs, so they should
result in
the same accept/reject decision

69
Example:
Apply the IRR rule to a project that costs $100 million and
yields
$106 million in one year when the opportunity cost of capital is
7%.
70
Example:
yields
7%.

0
1
0
1
106
0 100
1
6%
n
t
t
t
CF
CF
irr
m
m
r
r

71
Example:
yields
7%.
0
1
0
1
106
0 100

1
6%
n
t
t
t
CF
CF
irr
m
m
r
r

72
Example:
yields $106
million in one year when the opportunity cost of capital is 7%.
If the hurdle rate is set at
the cost of capital (7%),
the project is not
acceptable since the IRR
is below the hurdle rate.
0
1
0
1
106
0 100

73
NPV
technique, it shares most of the latter’s advantages
s a percentage rate of return that is intuitive to most,
and can
easily be compared with rates of return on alternative
investment
Example —IRR
Initial investment = –$200
Year Cash flow
1 $ 50
2 100
3 150
n Find the IRR such that NPV = 0

50 100 150
0 = –200 + + +
(1+IRR) 1 (1+IRR) 2 (1+IRR) 3
50 100 150
200 = + +
(1+IRR) 1 (1+IRR) 2 (1+IRR) 3
a is a discount rate which gives a positive NPV
b is a discount rate which gives a negative NPV
c is the positive NPV at the discount rate a
d is the negative NPV at the discount rate b
)(
)(
dc
c
abaIRR

IRR - Trial and Error Method
Example —IRR (continued)
Trial and Error
Discount rates NPV
0% $100
5% 68
10% 41
15% 18
20% –2
IRR is just under 20%
77
Example
What is the project’s IRR?
10 80 60

0 1 2 3 IRR = ?
– 100
PV3
PV2
PV1
0 = NPV
IRR = 18.13% (by calculator)
78
Example - Calculator
Solution
100 – ve CFi (C0)
10 CFi (C1)
60 CFi (C2)

80 CFi (C3)
COMP IRR 18.13%
RCL CFi 2nd F C-CE = (clears CF registers)
79
Conventional Projects
the beginning of the project
a series of cash inflows
–ve to
+ve); if so it is classed as conventional

80
Non-conventional Projects
mmon is a cash outflow to set up the project,
followed
by a series of cash inflows, then a terminal cost to complete the
project (e.g., repair a damaged site)
urn, can occur in these
cases
(i.e., where a project has more than one sign change in the

series
of CFs)
81
Inflow (+) or Outflow (–) in Year
0 1 2 3 4 5 C or NC?
– + + + + + C
– + + + + – NC
– – – + + + C
+ + + – – – C
– + + – + – NC
Examples of Cash Flows

82
Multiple Internal Rate of Returns (Multiple IRRs)
2
230 132
0 100
1 1r r
Multiple rates of return.
YEAR 0 1 2

Net cash flows -100 230 -132
Solving for the IRR, we find that IRR = 10% or 20%.
If the cost of capital were, say, 15%, it is unclear whether the
project should be undertaken using IRR.
An application of the NPV technique would resolve this
problem. (NPV = +$64.69).
83
Example
and will generate the following cash flows:

– $150,000
eturn is 15%
84
Example continued
Since the cash flows are non-conventional and indicate two sign
changes, there could be (at most) two IRRs – which is correct?
NPV = $1,769.54, so this suggests the project should be
accepted
Need to check to see if there are two IRRs

Can do this by drawing an NPV profile, i.e., calculate NPV for
different
values of the company cost of capital, r
85
Example continued
r (%) NPV ($)
0 – 8,000.00
5 – 3,158.41
10 – 52.59
15 1769.54
20 2,638.89
25 2,800.00

30 2,435.14
35 1,681.15
40 641.40
45 – 605.60
NPV @ 15%
86
Example continued
($10,000.00)
($8,000.00)
($6,000.00)

($4,000.00)
($2,000.00)
$0.00
$2,000.00
$4,000.00
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55
Discount Rate
N
P
V
IRR
NPV

Graph of NPV Profile
87
Example continued
would accept the project
e get 10.11%, we would reject
it
should accept

88
Example - No IRR
Year Cash Flows
0 – 9,000
1 8,000
2 2,000
3 4,000
4 12,000
5 – 20,000
(Try various values of r and see what happens to NPV!)

89
Independent Projects
same
accept/reject decision, except for those non-
conventional projects where the CF patterns
result in either multiple, or no, internal rate of
return
90

decision for independent projects
IRR < r
0
Reject
NPV
($)
r (%)
IRR
IRR > r
and NPV > 0
Accept

Independent Projects continued
91
Mutually Exclusive Projects
be accepted, we need to rank them in
order of
acceptability
in the
scale or timing of the CFs), ranking should be based on NPV
and is

preferred
92
Example - Mutually Exclusive Projects With Different Scale of
CFs
Cash flows for Projects I and D:
Year Project I Project D Project I-D
0 (100) (100) 0
1 10 70 (60)
2 60 50 10
3 80 20 60

problem case, and so we need to check it!
93
Example - Construct NPV Profiles
IRRI and IRRD, and the crossover point (i.e., IRRI-D), and
graph them:
r
0
5
10
15

20
NPVI
50
33
19
7
– 4
NPVD
40
29
20
12

5
94
Example - Crossover Point
1. Find the difference between the CFs of the
projects (see data for Project I – D on slide 60)
2. Calculate the IRR for these CF differences
3. Can subtract cash flow of project D from project I
or vice versa
4. If the profiles don’t cross, then one project
dominates the other

95
Example - Graph of NPV Profiles
-10
0
10
20
30
40
50
60
0 5 10 15 20 23.6
NPV ($)

Discount Rate, r (%) IRRI = 18.1%
IRRD =
23.6%
Crossover Point =
8.7%
D
I
96
Example - Mutually Exclusive Projects
r1 8.7 r2

NPV $
r %
IRRD =
23.6%
IRRI = 18.1%
I
D
r1 < 8.7: NPVI > NPVD , IRRD > IRRI
r2 > 8.7: NPVD > NPVI , IRRD > IRRI
Crossover
point = 8.7%

97
ferences
investments
funds, so a high r favours smaller projects
period provide more CFs in the
early years for reinvestment

they are discounted over shorter periods), and so NPVD >
NPVI
Why Do NPV Profiles Cross?
98
The higher the opportunity cost, the more valuable are these
funds, so
a high r favours smaller projects
The IRR does not take into account the size of projects.
YEAR 0 1 IRR Which project is
better if the
opportunity cost of
capital is 5%?

Small project -10 15 50%
Large project -100 122 22%
project, and
returns $90m to shareholders, which is then reinvested at the
opportunity cost of capital (5%), their total wealth at the end of
the year
99

The IRR does not take into account the size of projects.
YEAR 0 1 IRR Which project is
better if the
opportunity cost of
capital is 20%?
Small project -10 15 50%
Large project -100 122 22%
The small project is favoured by the IRR technique. However:
project, and returns $90m to
shareholders, which is then reinvested at the opportunity cost of
capital (20%), their
15).

100
Example - Mutually Exclusive Projects
Period Project A ($) Project B ($)
0 – 500 – 400
1 325 325
2 325 200
IRR 19.43% 22.17%

NPV $64.05 $60.74
101
Example continued
($40.00)
($20.00)
$0.00
$20.00
$40.00
$60.00

$80.00
$100.00
$120.00
$140.00
$160.00
0 0.05 0.1 0.15 0.2 0.25 0.3
Discount Rate
N
P
V A
B
Crossover Point =
11.8%

IRRA = 19.43%
IRRB =
22.17%
102
Summary re NPV vs. IRR
-conventional cash flows – where cash flow signs
change more than once

flows is substantially different
103
Drawbacks or Problems with IRR

IRR rule to make investment decisions, the IRR itself
remains a very useful tool.
error in the cost of capital and the average return of the
investment.
make investment decisions can be hazardous.
104
IRR Versus the IRR Rule

ine on IRR
timing of cash flows can lead to ranking projects incorrectly
using the IRR.
opportunity with the largest IRR can lead to a mistake.
are choosing between projects, or anytime when your
decision to accept or reject one project would affect your
decision on another project. In such a situation, always rely
on NPV.
105
Choosing Between Projects

Choosing Between Projects when Resources are Limited
different amounts of a particular resource.
e is a fixed supply of the resource so that you cannot
undertake all possible opportunities, simply picking the highest-
NPV
opportunity might not lead to the best decision.
106
107
Choosing Between Projects when Resources are Limited

- the NPV per unit
of resources consumed.
FORMULA
– 8.4
PI =
Value created
=
NPV
Resources consumed Resource consumed
Table 8.4: Possible projects for $200 million budget

Choose B and C instead of A to maximize NPV
108
Problem:
together a project proposal to develop a new home networking
router.
project
will require 50 software engineers.
hire
additional qualified engineers in the short run.
other
projects for these engineers:

109
Example 7.5 Profitability Index with a Human Resource
Constraint
Problem: How should NetIt prioritise these projects?
110
Example 7.5 Profitability Index with a Human Resource
Constraint
Project NPV ($ millions) Engineering Headcount
Router 17.7 50
Project A 22.7 47
Project B 8.1 44

Project C 14.0 40
Project D 11.5 61
Project E 20.6 58
Project F 12.9 32
Total 107.5 332

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