Investment Appraisal
Methods of Investment Appraisal
1: The Payback Period
Payback is ‘The time required for the cash inflows from the capital
investment project to equal the cash outflows’. This method attempts
to forecast how long it will take for the expected net cash inflows to
pay back the net investment outlays (what money was initially put
into the venture).
When deciding between two or more competing projects, the
usual decision is to accept the one with the shortest payback.
Payback should be a first screening process, and if a project gets
through the payback test, it ought then to be evaluated with a more
sophisticated project appraisal technique.
When payback is calculated, we take profits before depreciation
because profit before depreciation is likely to be a rough
approximation of cash flows.
Illustration
KLJ are considering purchasing a new machine. The machine will cost
$550000. The management accountant of KLJ has estimated the
following additional cash flows will be received over the next 6 years
if the new machine is purchased:
Year 1: $40000
Year 2: $65000
Year 3: $140000
Year 4: $175000
Year 5: $140000
Year 6: $70000
KLJ has a target payback of 4 years. Calculate the payback period for
the new machine and advise KLJ whether or not to proceed with the
investment.
1
Year
0
1
2
3
4
5
6
Cash Flow
(550000)
40000
65000
140000
175000
160000
70000
Cumulative Cash Flow
(550000)
(510000)
(445000)
(305000)
(130000)
30000
100000
Payback is achieved sometime between years 4 & 5
The cumulative cash flow becomes positive in year 5, so payback is 4
years plus (130000/160000 x 12) months = 4 years 10 months.
KLJ have a target payback period of 4 years. The payback is after this
target, so the advice to KLJ would be to not undertake the
investment.
Advantages of Payback
 Long payback means capital is tied up
 Focus on early payback can enhance liquidity
 Investment risk is increased if payback is longer
 Shorter-term forecasts are likely to be more reliable
 The calculation is quick and simple
 Payback is an easily understood concept
Disadvantages of Payback
 It ignores the timing of cash flows within the payback period,
the cash flows after the end of the payback period and
therefore the total project return
 It ignores the time value of money. This means that it does
not take account of the fact that $1 today is worth more in one
year’s time.
 The method is unable to distinguish between projects with the
same payback period
 The choice of any cut-off payback period by an organization is
arbitrary
 It may lead to excessive investment in short-term projects
 It takes account of the risk of the timing of cash flows but does
not take account of the variability of those cash flows.
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Example of why payback alone is an inadequate project
appraisal method
Capital cost of asset
Profits before depreciation
Year 1
Year 2
Year 3
Year 4
Year 5
Project P
$60000
Project Q
$60000
$20000
$30000
$40000
$50000
$60000
$50000
$20000
$5000
$5000
$5000
Project P paybacks back in 3 years and 3 months while Project Q
paybacks in 2 years 6 months. Using payback alone to judge projects,
project Q would be preferred. But the returns to Project P over its life
are much higher than the returns from Project Q. Project P will earn
total profits before depreciation of $200000 on an investment of
$60000, whereas Project Q will earn total profits before depreciation
of only $85000 on an investment of $60000.
Questions on Payback
1: An investment of $15 million is expected to generate net cash
flows of $3.5 million each year for the next 6 years. Calculate the
payback for the period
2: A haulage company has three potential projects planned. Each will
require investment in two refrigerated vehicles at a total cost of $120,000.
Each year has a three-year lifespan. The three projects are:
 Lease the vehicles to a meat-processing factory which will take
the risks of finding loads to transport and will bear all driver
costs for a three-year period. Expected net cash inflows, after
deducting all expected cash outflows are $60,000 per annum.
 Enter into a fixed price contract for three years to carry frozen
foods from processing plants in the UK to markets in
Continental Europe, returning with empty vehicles. This will
require employing drivers on permanent contracts. Expected
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cash inflows after deducting all expected cash inflows are
$45,000 per annum.
 Employ a contracts manager to find loads for outward and
return journeys but avoid any contract for longer than a sixmonth period so as to have the freedom to take up
opportunities as they arise. Drivers will be hired on short-term
contracts of three months. Expected cash inflows, after
deducting all expected cash outflows are $40,000 in Year 1 ;
$70,000 in Year 2 and $80,000 in Year 3.
(a) Use the above information to calculate the payback period.
3: Abbly Machines (AM) is considering making an investment of
$1.2m on launching a new product. They have undertaken some
market research and have estimated that the new product could
generate the following cash flows:
Year
Cash flow ($)
1
140000
2
265000
3
340000
4
560000
5
290000
AM requires payback within 4 years. Advise if they should go ahead
with the investment
4: Snocold Ltd (SL) is considering two projects. Both cost $450000
and only one may be undertaken. SL uses the payback method for
appraising investments and requires payback within three years. The
details of the cash flows for the two projects are given:
Year
1
2
3
4
5
Project A
200000
150000
100000
50000
20000
Project B
50000
120000
190000
310000
260000
Advise SL which project they should undertake.
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2: AVERAGE RATE OF RETURN (ARR)
The average rate of return, like the payback period method, looks at the
expected net cash flows (income - expenses) of the investment project. It
then measures the average net return each year as a percentage of the
initial cost of the investment. Let's look at an example. A firm is looking
at buying a new automatic painting machine. The cost of the machine is
200,000 and the expected net cash flows are:
Year
1
2
3
4
5
Net cash flow 50,000 55,000 65,000 75,000 75,000
The total return from the project over the five years is 320,000 (the sum
of the five years). If we subtract the original cost of 200,000 from this, we
get the net return from the investment to be 120,000. This took 5 years to
earn and so the annual return is 120,000 divided by 5 which is 24,000 per
annum. To get the average rate of return, we use the following formula:
Average rate of return = Net return per annum x 100
Capital cost
From the figures above this gives us:
Average rate of return = 24,000 x 100
200,000
= 12%
This suggests that every £1 worth of investment yields an average 12p
return each year.
Take the following information:
Project 1
Project 2
Cost
$60,000
$50,000
Project 3
$100,000
Return Y1
Y2
Y3
Y4
Y5
$20,000
$20,000
$30,000
$30,000
$30,000
$10,000
$10,000
$15,000
$15,000
$20,000
$10,000
$10,000
$10,000
$15,000
$15,000
5
Total
$70,000
Project 1:
Average net profit
ARR =
$60,000
=
$130,000
(70000 - 60000)/5 = $2000
Net return per annum
Capital outlay (cost)
$2000
x
$60,000
x
100
1
100
1
= 3.33%
Calculate the ARR for the other two projects
The drawbacks to the ARR method of project appraisal
 The ARR method does not take account of the timing of the
profits from the project. Whenever capital is invested in a
project, money is tied up until the project begins to earn profits
which pay back the investment. Money tied up in a project
cannot be invested anywhere else until the profits come in.
 It is based on accounting profits which are subject to a number
of different accounting treatments
 It is a relative measure rather than an absolute measure and
hence takes no account of the size of the investment
 It takes no account of the length of the project
 Like the payback method, it ignores the time value of money
Advantages
 It is quick and simple to calculate
 It involves a familiar concept of a percentage return
 Accounting profits can be easily calculated from financial
statements
 It looks at the entire project life
 Managers and investors are accustomed to thinking in terms of
profit, and so an appraisal method which employs profit may
therefore be more easily understood.
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3: Net Present Value
Discounted Cash Flow
The DCF method has gained widespread acceptance for it recognizes
that the value of money is subject to a time preference, that is, that $1
today is preferred to $1 in the future unless the delay in receiving $1
in the future is compensated by an interest factor (receiving interest
back on the loan).
The DCF method attempts to evaluate an investment proposal by
comparing the net cash flows accruing over the life of the investment
at their present value with the value of funds about to be invested
EXAMPLE
Given that the rate of interest is 10%, $1 invested now will be
equal to $1.10 at the end of the year. Conversely, the value of
$1.10 in a year’s time is worth $1 today if the rate of interest is
10%.
The value of $1 at the end of the year at 10% is $1 + 0.10 = $1.1
The value of $1 at the end of 2 years at 10% is ($1.1)² = $1.21
The value of $1 at the end of 3 years at 10% is ($1.1)³ = $1.331
The value of $1 at the end of 4 years at 10% = 1.4641
The value of $1 at the end of 5 years at 10% = 1.61051
You can also use the Discount Tables for this section
The present value of $1 receivable at a future date is as follows:
$1 receivable in one year is
$1/(1.1) =$0.9091
$1 receivable in 2 years is
$1/(1.21) = $0.8264
$1 receivable in 3 years is
$1/(1.331) = $0.7513
$1 receivable in 4 years is 0.6830
$1 receivable in 5 years is 0.6209
The value of money is, therefore, directly affected by time, and the
rate of interest is the method is used to express the time value of
money. Compound interest tables and discount tables are available
which show the value of money at different interest rates over a
number of years.
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Discounted cash flows
1: $5000 is invested in an account earning 2.75% interest p.a.
Calculate the fund value after 12 years.
2: $5000 is invested for 10 years in an account earning 5% interest
p.a. Calculate how much this will be worth at the end of the 10 years.
3: Find the preset value of $2000 receivable in 6 years’ time, if the
interest rate is 10% p.a.
4: How much would $40000 receivable in 4 years time be worth in
today’s value, if the interest rate is 7%?
5: HJK Ltd can either receive $12000 in 2 years time or $14000 in 4
years time. The interest rate is 6%. Advise HJK which they should
select.
6: Find the present value of $15500 receivable in 5 years’ time, if the
interest rate is 7% p.a.
Determining the discount factor
It is usual for the project manager to have discount rates set as part
of the organizational policy. There are three factors which determine
the discount rate:
a. The rate charged for the use of the capital
b. The rate due to inflation (so that the purchasing power is not
reduced)
c. A premium factor due to the fact that the investor is taking a
risk that the capital amount may never be repaid.
Overall rate = (1 + a)(1+b)(1+c)
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NET PRESENT VALUE
The NPV method compares the present value of all the cash inflows
from a project with the present value of all the cash outflows from a
project. The NPV is calculated as the PV of cash inflows minus the PV
of cash outflows.
 If the NPV is positive, it means that the present value of the
cash inflows from a project is greater than the present value of
the cash outflows. The project should be undertaken.
 If the NPV is negative, it means that the present value of cash
outflows is greater than the present value of inflows. The
project should not be undertaken.
 If the NPV is exactly zero, the present value of cash inflows
and cash outflows are equal and the project will be only just
worth undertaking.
The net investment outlays are subtracted from the present value of
the net cash outlays leaving a residual figure, which is the net
present value. A decision is made in favour of a project is the NPV is
a positive amount.
A1
(1 +I) ¹
Where
+
a2
(1 + I) ²
an
>
A
(1 + I) ⁿ
A = the initial project cost
a = the net annual cash inflows
I = the cost of capital (rate of interest)
n = the expected life of the project
Example
Corween Ltd is considering a project which has a life of five years and
which will produce an annual inflow of $1000. The investment outlay
is $3000 and the required rate of return is 10%
9
Year
Inflow
Discount Factor
(at 10%)
Present Value
of inflow
1
$1000
0.9091
$909.1
2
$1000
0.8291
$826.4
3
$1000
0.7513
$751.3
4
$1000
0.6831
$683.1
5
$1000
0.6208
$620.8
Present value of net inflows
$3790.7
Cost of investment outlay
$3000.0
Net Present value of Project
$790.7
Thus the project is accepted, as NPV is positive.
The Net Present Value (NPV) method
Example: NPV
Slogger has a cost of capital of 15% and is considering a capital
investment project where the estimated cash flows are as follows:
Year
0
1
2
3
4
Cash Flow
(100000)
60000
80000
40000
30000
DF (15%)
1.0
0.87
0.756
0.658
0.572
NPV
PV
(100000)
52200
60480
26320
17160
56160
The PV of cash inflows exceeds the PV of cash outflows by $56160
which means that the project will earn a DCF yield in excess of 15%.
It should therefore be undertaken.
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Advantages and disadvantages of NPV
Advantages of NPV
 Considers the time value of money – discounting cash flows
back to present value takes account of the impact of interest.
 Is an absolute measure of return – the NPV of an investment
represents the actual surplus raised by the project. This allows
a business to plan more effectively
 Is based on cash flows not profits – the subjectivity of profits
makes them less reliable than cash flows and therefore less
appropriate for decision-making
 Considers the whole life of the project – methods such as
payback only considers the earlier cash flows associated with
the project. NPV takes account of all relevant flows.
Discounting the flows takes account of the fact that later flows
are less reliable.
 Should lead to the maximisation of shareholder wealth. If the
cost of capital reflects the shareholders’ required return then
the NPV reflects the theoretical increase in their wealth. For a
commercial company, this is considered to be the primary
objective of business.
Disadvantages of NPV
 It is difficult to explain to managers. To understand the
meaning of the NPV calculation requires an understanding of
discounting. The method is not as intuitive as methods such as
payback
 It requires knowledge of the cost of capital. The calculation of
the cost of capital is, in practice, a complex calculation
 It is relatively complex – for the reasons explained above NPV
may be rejected in favour of simpler techniques.
 A disadvantage of the NPV calculation is that it requires you to
make projections. You must estimate the dollar amount of the
project's cost as well as its future income. In most cases, the NPV
calculation will not be 100 percent accurate. A project may incur
unforeseen costs that decrease its profitability. Income projections
are difficult to determine with exact precision. In addition, a
project may incur a negative cash flow instead of the projected
positive one.
 The present value of a project is expressed in a dollar amount.
Some business managers would rather see a percentage or rate of
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return. Although the NPV calculation discounts future cash flows
using a required rate of return, it does not reveal the project's actual
return. The calculation only reveals whether the project will return
the required rate. A project may have a positive net present value,
but the return may turn out to be less than desired. Higher dollar
amounts do not necessarily translate into higher returns.
Questions on Net Present Value
1: Project B needs an investment of £30000 at a discounting rate of
12%. Is this a viable venture?
Project B
Year 0
Discounting 30000
rate 12%
Discounting
factor
Discounted
cash flow
Year 1
7000
Year 2
8500
Year 3
9900
Year 4
15500
Year 5
17000
2: The management of C Co plc is considering investing $25000 in a
project with a potential life of six years. The company’s cost of capital
is 18% per year. The net cash flows are projected as follows:
Year
0
1
2
3
4
5
6
Net Cash Flows
(25000)
4000
6000
10000
10000
10000
10000
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3: A project requires an initial investment of $2.4 million. The
following cash flows have been estimated for the life of the project:
Year
1
2
3
4
5
Cash flow ($)
500000
700000
900000
450000
200000
Using a discount factor of 10%, calculate the NPV of the project.
4: Slogger has a cost of capital of 15% and is considering a capital
investment project, where the estimated cash flows are as follows:
Year
0
1
2
3
4
Cash Flow
(100000)
60000
80000
40000
30000
Calculate the NPV of the project, and assess whether it should be
undertaken.
5: Norwell Industries Ltd is studying two projects, each of which
requires a net investment outlay of $3000. Both have a useful life of
five years, and the estimated profile of the net cash inflows is:
Year
Project A
Project B
1
2
3
4
5
$500
$1000
$1500
$2000
$2000
$2000
$1500
$1500
$1000
$500
The desired minimum rate of return is 10%
(a) Calculate the Net Present value for both Project A and Project
B using the discount factor of 10%
(b) Which project should the firm choose, according to NPV
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6: MKP Ltd is considering two mutually exclusive projects with the
following details:
Project A
Initial investment $45000
Scrap value in year 5 $2000
Year
1
Annual
20000
cash flows
2
15000
3
10000
4
10000
5
10000
3
3000
4
2000
5
2000
Project B
Initial investment $10000
Scrap value in year 5 $1000
Year
1
Annual
5000
cash flows
2
4000
Assume that the initial investment is made at the start of the project
and the annual cash flows are at the end of each year. The scrap
values should be treated as cash inflows in year 5.
Calculate the NPV for Projects A and B if the cost of capital is 10%
7: A project requires an initial investment of $500000. The following
cash flows have been estimated for the life of the project:
Year
1
2
3
4
Cash flow ($)
120000
150000
180000
160000
The company uses NPV to appraise projects. Using a discount factor
of 7%, calculate the NPV of the project and recommend whether the
project should be undertaken.
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Combined investment appraisal methods
1: Smiley Sweets is contemplating introducing a new machine into
the production process. This will cost $59000. The budgeted after-tax
profits and total cash income flow were as follows:
Year
1
After tax 0
profits
Cash
13000
income
2
3000
3
8000
4
9000
34000
21000
27000
It will cost the firm $14000 to scrap the machine at the end of year 4
Assume that financial standards set for accepting investment
proposals by the business are that they must:
a) Give an average rate of return of at least 16%
b) Give payback in 3 years
c) Have a positive NPV (cost of capital is 15%)
2: A company is considering which of two mutually exclusive projects
it should undertake. The company anticipates a cost of capital of 10%
and the net after tax cash flows of the projects are as follows:
Year
0
1
2
3
4
5
Project X
(200000)
35000
80000
90000
75000
20000
Project Y
(200000)
218000
10000
10000
4000
3000
(a) Calculate the payback period of each project
(b) Calculate the Average Rate of Return (ARR) of each project
(c) Calculate the NPV of each project
(d) Determine the best project to pursue
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3: David Jones, the marketing director at Branigans, is keen to see the
company diversify into neckties and he has to set up a small team to
look at possible alternatives. They have identified two options.
Project 1 involves marketing ties in Europe and will cost $300,000,
while Project 2 costing $200,000 involves concentrating on the UK
market. David Jones has produced budgeted figures for the two
projects.
Project 1
$’000
70
100
175
250
300
Year
1
2
3
4
5
Project 2
$’000
50
75
100
225
500
Calculate
(a) The Payback Period
(b)The average rate of return (ARR)
(c) Calculate the Net Present Value of each project assuming a
discount factor of 14%
4: Zerfy sees an opportunity for a new product, gryavia, which is
likely to have a five-year commercial life. The capital expenditure
required for equipment is $750,000 and it is expected to have no
scrap value at the end of the five years. The estimated cost of capital
is 20%.
The estimated profits/losses for the five years are as follows:
Year 1
Year 2
Year 3
Year 4
Year 5
$250000
$200000
$150000
$100000
($100000)
Calculate
(a) The Payback period
(b)The average rate of return
(c) The net present value
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