Capital investment appraisal
1
Introduction
As investments involve large resources, wrong
investment decisions are very expensive to correct
Managers are responsible for comparing and
evaluating alternative projects so as to allocate
limited resources and maximize the firm’s wealth
Basic techniques of making capital investment
appraisal for evaluating proposed capital
investment projects
2
Investment appraisal methods
Considering the time value of
money concept
•Net present value
•Internal rate of return
Ignoring the time value of
money concept
•Payback period
•Accounting rate of return
3
Net present value method
4
Time value of money
When facing different investment proposals, the
management should choose the project that can
generate the greatest addition of value to the
company. For example,
Project A Project B
Initial investment
$100
$100
Cash inflow at end of year
Year 1
$110
Year 2
$121
5
At first sight, some may think that project B
is better because it has a higher cash inflow.
However, the time value of money concept
states that a dollar today is always worth
more than a dollar in the future
The two projects are of equal value to the
company because their present values are
the same
6
After taking timing of cash flow into consideration,
Project A Project B
Present value of cash flow
(interest rate is 10% per annum) 110
121
(1+10%)
(1+10%)2
= $100
$100
The two projects are of equal value to the company
because their present values are the same
7
Factors leading to the changes in
value of money
Opportunity cost of money
Erosion of purchasing power due to
inflation
Uncertainty and risk
8
Opportunity cost of money
Opportunity cost of money refers to the cost
incurred or income forgone by not using the
money for other purpose
For surplus cash, the opportunity cost is the
interest income forgone by investing the
cash in other investments or depositing it in
the bank
9
Erosion of purchasing power due
to inflation
Inflation refers to the continual increase in
the general price level of goods or services
During a period of inflation, prices of goods
increase while the purchasing power of
money decrease. The purchasing power of a
dollar today is greater than that of the future
10
Uncertainty and risk
Investors tend to avoid risk. The uncertainty
involved in future cash inflows is much higher
than that in present cash inflows
If the level of risk rises, investors will expect a
higher return as compensation.
For example, suppose an investor expects $100 for
return now. After adding a 10% risk premium, he
will expect $110 one year later
11
Discounting
12
Discounting
According to the time value of money concept, a
dollar in one year is not worth the same as a dollar
in anther year.
In evaluating a multi-year investment, cash
inflows and outflows are generated in different
years
It is necessary to convert the cash flows for
different years into a common value at a common
point of time, either at present or in the future
13
Discounting is the process of reducing
future cash flows to present values with the
use of an interest rate
Present value = FVn
(1+r)n
Where FV = Future value of an investment
n= Number of years
r= Appropriate interest rate
14
Example
15
John has won a lucky draw. He is deciding whether to receive the
Prize money of $3000 today or the following set of cash flows
over the next three years:
Year
Cash flow
1
$1100
2
$1210
3
$1331
Future values
Discount processes Present value
Year 1 $1100
$1100/1.1
$1000
Year 2 $1210
$1210/1.12
$1000
Year 3 $1331
$1331/1.13
$1000
16
Net present value method
17
Net present value method
Net present value (NPV) method is a process that
uses the discounted cash flow of a project to
determine whether the rate of return on that
project is equal to, higher than, or lower than the
desired rate of return
With the NPV method, we can compare the return
on investment in capital projects with the return on
an alternative equal risk investment in securities
traded in financial market
18
Calculation procedures
Determining the discount rate
2. Calculating the NPV:
1.
FV1
FV2
NPV = (1+r)1 + (1+r)2
FV3
+
+
3
(1+r)
FVn
(1+r)n - I0
where FV = future value of an investment
n = no. of years
r = Rate of return available on an equivalent risk
security in the financial market
I 0= initial investment
19
3.
Interpreting the NPV derived as follows:
NPVs
<0
Comments
Reject the project
Reasons
=0
Indifferent to accept
or reject the project
The rate of return from the project is
equal to the rate of return from an
equivalent risk investment
>0
Accept the project
The rate of return from the project is
greater than the rate of return from an
equivalent risk investment
Highest Accept the project
The rate of return from the project is
small than the rate of return from an
equivalent risk investment
If various project are considered, the
project with highest positive NPV
should be chosen
20
Example
21
A company is considering making several investments in the
Production facilities for the new products with an estimated useful
Life of four years. The cash inflows and outflows are listed as follows:
Project
A
B
C
D
$
$
$
$
Initial investment
900000
1000000
303730 1500000
Cash inflow
Year 1
120000
400000
100000
10000
Year 2
250000
400000
100000
10000
Year 3
400000
400000
100000 1000000
Year 4
1300000
400000
100000 1000000
The appropriate discount rate of these investment is 12%
22
Required:
(a) Calculate the NPV of each investment and determine whether
to accept it or not (assuming the company has unlimited
resources)
(b) If the company has limited resources, determine which
investment should be accepted by referring to the highest NPV
23
(a)
Project A
120000
250000
400000
1300000
+
+
+
NPV = 1.12
2
3
1.12
1.12
1.124 - 900000
= $517327 (accepting)
Project B
40000
400000
+
NPV = 1.12
1.122
+
400000
400000
+
1.123
1.124 - 1000000
= $214920(accepting)
24
(a)
Project C
100000
100000
100000
100000
+
+
+
NPV = 1.12
2
3
1.12
1.12
1.124 - 303730
= $0 (indifferent to accept or reject)
Project D
10000
10000
+
NPV = 1.12
1.122
+
1000000 1000000
+
3
1.12
1.124 - 1500000
= -$135801(rejecting)
(b) With limited resources, the company should only accept project A
because it generates the highest NPV
25
Advantages of NPV
Consistency with the time value of money
concept
Consideration of all cash flows
Adoption of cash flows instead of
accounting profit
26
Internal rate of return
27
Internal rate of return
The internal rate of return is the annual percentage
return achieved by a project, of which the sum of
discounted cash inflow over the life of the project
is equal to the sum of discounted cash outflows
If the IRR is used to determine the NPV of a
project, the NPV will be zero.
The company will accept this project only if the
IRR is equal to or higher than the minimum rate of
return or the cost of capital
28
Calculation procedures
1.
By trial and error, find out the discount rate that
will give a zero NPV
FV1
FV2
NPV = (1+r)1 + (1+r)2
FV3
+
+
3
(1+r)
FVn
(1+r)n - I0 = 0
where FV = future value of an investment
n = no. of years
r = internal rate of return
I 0= initial investment
2.
If the NPV is positive, try a higher discount rate
in order to give a negative NPV and vice versa
29
3.
After getting one positive NPV and one
negative NPV, use interpolation to find out
the rate giving zero NPV
P
IRR = L +
(H – L)
P–N
Where L = Discount rate of the low trial
H = Discount rate of the high trial
P = NPV of cash flows of the low trial
N = NPV of cash flows of the high trial
30
4.
In evaluating an investment project, the
IRR is compared with the management’s
predetermined rate
IRRs
Comments Reasons
< lowest acceptable level of return Reject
NPV<0
= lowest acceptable level of return Accept
NPV=0
> Lowest accepted level of return
Accept
NPV>0
Highest
Accept
If several project are
considered, the
highest IRR should
be chosen
31
Example
32
A project costs $400 and produces a regular cash inflow of $200 at
the end of each of the next three years. Calculate the IRR. If the
minimum rate of return is 15 %, suggest with reason whether you
Should accept the project or not.
$200
$200
NPV = (1+r)1 + (1+r)2
$200
+
(1+r)3
Assuming the discount rate is 22%
$200
$200
$200
+
+
NPV = 1.22
1.222
1.223
Assuming the discount rate is 24%
$200
$200
$200
NPV = 1.24 + 1.242 + 1.243
- $400 = 0
- $400 = 8.4
- $400 = -3.8
33
P
IRR = L +
(H – L)
P–N
Where L = Discount rate of the low trial
H = Discount rate of the high trial
P = NPV of cash flows of the low trial
N = NPV of cash flows of the high trial
IRR = 22% +
8.4
(24 – 22)%
8.4 – (-3.8)
= 23.38%
Since the IRR (23.38%) is higher than the minimum rate of return (15%),
The project should be accepted
34
Payback period
35
Payback period
Payback period is the period of time it takes
for a company to recover its initial
investment in a project
The method measures the time required for
a project’s cash flow to equalize the initial
investment
36
Acceptance criterion
< predetermined cutoff period Accept the project
> Predetermined cutoff period Reject the project
37
Example
38
A company is considering making the following mutually exclusive
Investments in the production facilities for the new products with an
Estimated useful life of four years. The cash inflow and outflows are
Listed as follows:
Project A
Project B
$
$
Initial investment
900000
1000000
Cash inflow at the end of year
Year 1
700000
600000
Year 2
100000
400000
Year 3
100000
400000
Year 4
1300000
400000
Project A : 3 years
Project B: 2 years
Project B takes only two years to recover its initial investment. With
The shortest payback period, the company will accept project B
39
Advantages of payback period
Easy to adopt
Facilities further evaluation

After obtaining an acceptable payback period,
the project will be evaluated by other financial
capital budgeting techniques
40
Disadvantages of Payback period
Ignore the cash flows after payback period
Adopt an arbitrary standard for the payback
period
Ignores the timing of cash flow
41
Discounted payback period
The payback period method is criticized for
ignoring the timing of cash flows, therefore
discounted cash flows are used to calculate
the discounted payback period
42
Example
43
A company is considering making the following mutually exclusive
investments in the production facilities for the new products with an
estimated useful life of four years. The cash inflow and outflows are
listed as follows:
Project A
Project B
900000
1000000
Year 1
700000
600000
Year 2
100000
400000
Year 3
100000
400000
Year 4
1300000
400000
Initial investment
Cash inflow at the end of year
Discount cash inflow (20%)
44
Project A
$
900000
Project B
$
1000000
Initial investment
Discounted cash flow
Year 1
700000 = 583333
400000 = 500000
1.21
1.21
Year 2
100000 = 69444
400000 = 277778
1.22
1.22
Year 3
100000 = 57870
400000
= 231481
1.23
1.23
Year 4
100000 = 626929 400000 = 192901
1.24
1.24
Discount payback period
Project A
3+ 900000-710647 = 3.3 years
626929
Project B
2+ 100000-777778 = 2.96 years
231481
45
Accounting rate of return
46
Accounting rate of return
The accounting rate of return compares the
average accounting profit with the average
investment cost of project
The accounting profit can be expressed
either before tax or after tax
47
Calculation procedures
Average net profit per year (over the life of the project)
ARR =
Average investment cost
Total profit
Average net profit per year = No. of life of the project
Initial investment
Average investment cost =
2
48
Acceptance criterion
In evaluating an investment project, the ARR of the project is
compared with a predetermined minimum acceptable accounting
Rate of return:
ARRs
< minimum acceptable rate
= minimum acceptable rate
> minimum acceptable rate
Highest
Comments
Reject project
Accept project
Accept project
Choose highest ARR
49
Example
50
A company is considering whether to buy specialized machines
For a new production line. The purchase price of machinery is
$400000 and its estimated useful life is four years. There is no scrap
Value after four years
The project income statements:
Year1
Year 2
Year 3
Year 4
$
$
$
$
Revenue
310000
280000
280000
310000
Depreciation 10000
100000
100000
100000
Other expenses150000
100000
110000120000
Profit before tax 60000
80000
70000
90000
Taxation (15%) 9000
12000
10500
13500
51000
68000
59500
76500
Should the company buy the new machinery if the minimum acceptable
Rate of return is 20%?
51
51000+68000+59500+76500 = $63750
Average net income =
4
400000+0
= $200000
Average investment =
2
The cost of machinery is $400000 at the beginning
The cost of machinery is $0 at the end as depreciation is provided
On straight line method and there is no scrap value
$63750
ARR = $200000 = 31.875%
Since the ARR is 31.875%, which is higher than the minimum
Acceptable rate of 20%, the company should invest in the new
machinery.
52
Advantages of ARR
It is easy to understand and compute
It avoids using gross figures. Therefore, it
enables comparisons to be made between
projects with different useful lives
53
Disadvantages of ARR
It ignores the time value of money
ARR method seems to be less reliable than
the NPV method. It adopts the accounting
profit instead of cash flows calculation. The
change of depreciation method may also
alter the accounting profit
54