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UNIT 3
NET PRESENT
VALUE AND OTHER INVESTMENT
CRITERIA
There are
several investment appraisal method to determine
whether an
investment is profitable to
undertake.
3.1
Introduction
An investment
is worth undertaking if it creates value for its
owners. In the
most
general
sense,
we
create
value
by
identifying
an
investment
that
is
worth more in the
marketplace than it cost us to acquire.
Suppose a run-down house
was bought for $$250,000 and we spent $$50,000
on
renovation.
The
total
investment
is
$$300,000.
When
the
work
is
completed, you place the house back on
the market and find that it is worth
$$400,000. The market value exceeds the
cost by $$100,000. In other words,
this
$$100,000 is the Value added to the house by the
management.
The
real
challenge,
of
course,
was
to
somehow
identify
ahead
of
time
whether
or
not
to
invest
the
$$250,000
in
the
run-down
house
in
the
first
place.
This
is
what
we
called
Capital
budgeting,
and
that
is
to
determine
whether a proposed
investment or project will be worth more than
its cost
once it is in
place.
3.2 Net Present Value ( NPV
)
Net
present
value
of
an
investment
is
the
difference
between
an
investment’
market
value
and
its
cost
.
It
is
the
amount
of
value
the
investment create.
In the
above example, the NPV is $$100,000.
In other words,
NPV is a
measure of how much value is created or added
today by undertaking an
investment
. Given our goal of creating
value for
the stockholders, the capital
budgeting process can be viewed as a search
for investments with positive net
present values
1
Discounted
Cash
Flow
(
DCF
)
valuation,
is
the
process
of
valuing
an
investment by discounting its future
cash flows.
Rule for NPV.
An investment should be accepted if the NPV is
positive
and rejected if it is
negative.
Advantages and Disadvantages of the NPV
method
Advantages:
a.
It
will give the correct decision advice assuming a
perfect capital market.
It will also
give correct ranking for mutually exclusive
projects .
b.
NPV
gives an absolute value.
c.
NPV allows for the time value of the
cash flows.
Disadvantages
:
a.
It is very
difficult to identify the correct discount rate.
b.
NPV as method
of investment appraisal requires the decision
criteria to
be specified before the
appraisal can be undertaken.
E.g.
Suppose an investment has the following
projected cash flows: $$2000 in the
first 2 years, $$4000
in the
next 2 years and $$5000 in the
last
year. It will
cost
$$10,000
to
begin
the
investment.
The desired
(interest)
rate
of
return
for
the investment
is 10% per annum. What
is the NPV of the investment
and should
be investment be given the go-ahead?
Solution:
2
0
1 2
3 4
5
|_____________|_____________|________
_____|______________|_____________|
-10,000 2000 (A)
2000(B) 4000(C)
4000(D) 5000(E)
Amount
n
Discount Factor = 1/ ( 1 +
0.1)
n
PV
-10,000
0
1
- 10,000
2000(A)
1
0.909
1818
2000(B)
2
0.826
1652
4000(C)
3
0.751
3004
4000(D)
4
0.683
2732
5000(E)
5
0.621
3105
NPV
$$2311
The
NPV
=
$$2311
and
it
is
positive.
This
mean
that
the
investment
is
returning more than the desired
interest rate of return of 10% per year.
Therefore, the investment should be
given the go-ahead.
3.3 The Payback Method
It is very common in practice to talk
of the payback on a proposed
investment.
Payback is the
length of time it takes for an investment to
recover its initial cost.
Rule : Based on the Payback
rule, an investment is acceptable if its
calculated payback period is less than
some pre-specified number of
years
.
E.g.
An initial investment cost $$60,000 and
the cash flows are $$20,000 in the first
year, $$30,000 in the second year,
$$50,000 in the third year and $$35,000 in
the fourth year. What is the payback
period?
3
Year
1
2
3
4.
Cash Flow
$$20,000
30,000
50,000
35,000
Cumulative
Cash Flow
$$20,000
50,000
100,000
135,000
Amount remaining after the
first 2 cash flow = 60,000
–
50,000
= 10,000
Remaining amount
= 10,000 / 50,000
= 0.2 years
Therefore, the
payback period = 2.2 years
= 2 years 0.2x 12 months
= 2 years and 2.4 months
= 2 years 3 months
Advantages and Disadvantages of Payback
Method.
Advantages
Disadvantages
1. Easy to
understand
1. Ignores the time value of
money
2. Requires an
arbitrary cut off point
3. Its emphases
on liquidity ( getting
3. Ignores cash
flows beyond the cut
back the money )
off date
4. Used mainly in
relative minor
4. Biased against long
term projects
decisions where a quick
idea of the
like research and
development
payback period is desired.
( Avoid
( including investing in your
lengthy and detailed analysis )
children ) and new project where the
return could be slow.
4
3.4 The Discounted
Payback Rule
The discounted
payback period is the length of time until the sum
of the
discounted cash flows is equal
to the initial investment.
Rule
:
Based
on
the
discounted
payback
rule,
an
investment
is
acceptable if its discounted payback
time is less than some pre-specified
number of years.
E.g.
An initial investment cost $$60,000 and
the cash flows are $$20,000 in the first
year, $$30,000 in the second year,
$$50,000 in the third year and $$35,000 in
the fourth year. The desired interest
rate of return on this investment is 8%.
What is the discounted payback time?
Solution
Year n
Cash
Flow
1
2
3
4.
$$20,000
30,000
50,000
35,000
Discount
Factor = 1/( 1
+ 0.08
)
n
0.926
0.857
0.794
0.735
PV
$$18,520
25,710
39,700
25,725
Cumulative PV
$$18,520
44,230
83,930
109.655
Amount remaining
after 2 years = 60,000
–
44,
230
= $$15,770
Remaining year =
(15, 770 /39,700) x 12
= 4.7 months
Therefore, the discounted payback time
= 2 years and 5 months.
5
Advantages
:
1.
This method
take into account the time value of money.
2.
Easy to
understand.
3.
Does not accept negative estimated NPV
investments.
Disadvantages
;
1.
May reject
positive NPV investment.
2.
Requires an arbitrary cutoff point.
3.
Ignores cash
flows beyond the cutoff date.
4.
Biased against
long term projects, such as research and
development and
new projects.
3.5 Average Accounting
Return ( AAR )
Another
approach
to
making
capital
budgeting
decisions
is
the
average
accounting return ( AAR ). AAR is
always defined as :
Some measure of average accounting
profit
Some measure of average
accounting value
.
The specific definition will be :
Average net
income
Average book value.
6
Rule : Based on the average accounting
return, a project is acceptable if its
average accounting return exceeds a
target average accounting return.
E.g.
To
open
a
new
store
in
a
shopping
mall,
the
required
investment
for
renovation is $$400,000.
The store has a four-year lease and everything
will
be
reverted
to
the
mall
owner
after
that
time.
The
required
investment
would be 100 percent depreciated (
straight line ) over the 4 years. The profit
is taxed ( corporate tax ) at
25
%. There is no tax and no tax relief
for
losses.
The table below
gives the revenue and expenses for the 4 years. We
intend
to
have
an
average
accounting
return
of
20%
per
annum.
Should
project be accepted?
Year 1
Year 2
Revenue
350,000
390,000
Expenses
150,000
160,000
Solution:
Annual
depreciation = $$400,000
4
=
$$100,000
Year 1
Revenue
350,000
Expenses
-150,000
Earning
before
200,000
depreciation
Year 3
360,000
150,000
Year 4
220,000
150,000
Year 2
390,000
-160,000
230,000
Year 3
360,000
-150,000
210,000
Year 4
220,000
-150.000
70,000
7
Depreciation
-100,000
- 100,000
- 100,000
- 100,000
Earning before
tax
100,000
130,000
110,000
- 30,000
Tax @ 25%
- 25,000
-32,500
- 27,500
0
Net income
75,000
97,500
82,500
- 30,000
Average net
income = 75,000 + 97,500 + 82,500
–
30,000
4
= $$56,250
Average book value of investment
= Initial book value+ Final book value
2
= $$400,000 + 0
2
= $$200,000
AAR
= Average net income x 100
Average book value
=
56,250 x 100
200,000
= 28.125 %
Since
our
intended
average
accounting
return
is
20%
per
annum,
the
project is considered acceptable.
Advantages of
AAR
1.
Easy to compute and understand.
2.
Accounting
information
is
always
available
and
therefore,
it
is
always
possible to calculate
AAR.
Disadvantages of AAR
8
1.
AAR is not a
true
rate of return of
investment because it failed to take
into account the time value of money (
discounting ).
2.
Uses an
arbitrary cutoff point and a benchmark to
consider whether the
investment is
acceptable.
3.
Based on the book value and not the
cash flows and the market value of
investment.
3.6 The
Internal Rate of Return ( IRR)
The
most
important
alternative
to
NPV
is
the
Internal
Rate
of
Return,
universally known as the IRR.
With IRR, we try to find a single rate
of
return
for
the
investment
that
summarizes
the
merits
of
a
project
.
Furthermore,
we want this
rate to be an “internal” rate in the sense that
it only depends on the cash flows of a
particular investment
and not on
the rate of interest offered by banks
and elsewhere.
Rule : Based
on the IRR rule, an investment is acceptable if
the IRR exceeds
the required ( desired
) return. If should be rejected
otherwise.
The IRR on an investment
is
the required return that results in a zero NPV
when it is used as the discount rate.
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Formula: IRR by Linear interpolation.
IRR
= Interest 1 + . NPV1 . x
( Interest 2
–
Interest 1 )
NPV1 + | NPV2 |
NPV1 is the net present value corresponds to the
interest rate 1
NPV2 is
the net present value corresponds to the interest
rate 2
E.g.
A project has a total up-front cost of
$$4500. The cash flows are $$2000 in the
first year, $$3000 in the second year
and $$2500 in the third year.
a.
Calculate the NPV at 10% and 20% and
hence, calculate the IRR.
b.
If
we
require
a
15%
return
for
our
investment,
should
we
take
this
investment?
Solution:
Calculate the NPV at say, 10%
Amount
Year n
Discount
factor
PV
= 1/ ( 1 +
0.1)
n
-4500
0
1
- $$4500
2000
1
0.909
1818
3000
2
0.826
2478
1000
3
0.751
751
NPV = 547
Calculate the NPV at say, 20%
10
Amount
Year n
-4500
0
- $$4500
2000
1
1666
3000
2
2082
1000
3
579
NPV = -173
To
estimate the IRR, draw a graph of NPV ( on the
y-axis ) against interest
rate.
The estimated IRR is
17.60%.
By calculation
( Linear Interpolation ):
Interest 1 = 10 %
Interest 2
= 20
NPV1 = $$547
NPV
2 = | -173 | = 173
IRR by
formula = 10 + ( 547 ) x ( 20
–
10 )
547 + 173
= 17.60 %
Since we require
a 15% return in investment, the above project is
acceptable.
Advantages of
IRR
Discount
factor
= 1/ ( 1 + 0.2)
n
1
0.833
0.694
0.579
PV
11
1.
It gives the
results in terms of percentage and the management
is
familiar with percentage.
2.
It looks into
cash flows and take into account the time value of
money.
Disadvantages of IRR
1.
Since it
reports in terms of percentage, it ignores the
difference in
project magnitude and so
is unreliable when evaluating project of
great different in sizes.
2.
Decision rule
break down for multiple IRR
3.
Method cannot
be viewed upon to give correct advice for mutually
exclusive investment decisions.
3.7 Multiple
Rates of Return
The
problems
with
the
IRR
come
about
when
the
cash
flows
are
not
conventional, that is along the way, we
have to further
invest cash into the
investment. If we were to find the
IRR, there may be more than one IRR
and
the we do not know which is the correct or true
IRR to take.
E.g.
Suppose we intend to invest
in a project with an initial amount of $$6000.
The cash flow in the first year will be
$$15,500. In the second year, we
anticipate that we have invest a
further $$10,000 to maintain the place. Show
that the above investment has several
IRR.
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