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LO 2: Investment Appraisal
Methods
Dr Fidelis Akanga
Learning outcomes
By the end of this unit
Explain capital investment decision and
Investment appraisal methods
Apply the main investment appraisal
methods
Understand and discuss the strengths and
weaknesses of these methods
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Principal Assumptions
Cash inflows and outflows are known with certainty
Sufficient funds available to enable acceptance of all
projects with positive NPV
Firms operate in environments with no taxes and no
inflation
Cost of capital is risk free
Capital Investment Appraisal
Definition of Capital Investment appraisal
Capital Investment appraisal is an application of a set
of quantitative methods used by managers to make
decisions on how to best invest funds in the long term
(Weetman, 2010:261)
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Types of capital investment
Replacement of obsolete assets
Cost reduction e.g. IT system
Expansion e.g. new building & equipment
Strategic proposal: improve delivery service, staff
training.
Diversification for risk reduction
Research and Development
Need for Investment Appraisal
Large amount of resources are involved and wrong
decisions could be costly
Difficult and expensive to reverse
Investment decisions can have a direct impact on the
ability of the organisation to meet its objectives
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Investment Appraisal Process
Stages:
Identify objectives. What is it? Within the corporate
objectives?
Identify alternatives.
Collect and analyse data. Examine the technical and
economic feasibility of the project, cash flows etc.
Decide which one to undertake
Authorisation and implementation
Review and monitor: learn from its experience and
try to improve future decision – making.
Investment Appraisal Methods
Proposed
Capital
Project
2.
Accounting
Rate of
Return
1. Payback
4. Internal
Rate of
Return
3. Net Present
Value
5.
Profitability
Index
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Investment Appraisal Methods
1. Payback period
This is the length of time it takes to repay the cost
of initial investment
In case where there are competing projects, the
one with the shorter payback period should be
accepted
Payback period
We can approach payback in two ways;
Equation method (for uniform cash flows)
Cumulative method (uniform & non uniform
cash flows)
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Payback period
In the case of uniform cash flows, payback
period can be calculated as:
Net initial investment
Uniform increase in annual cash flows
Then multiply the remainder (decimal) by 12
to get number of months
Payback period
Example 1
LBS Ltd uses the payback period as its sole
investment appraisal method. LBS invests
£30,000 to replace its computers and this
investment returns £9,000 annually for the
five years. From the information above
evaluate the investment using the payback.
Assume that £9,000 accrues evenly
throughout the year.
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Payback period
Solution:
= 30,000
9,000
= 3.3333
0.333x x12 = 3.996 approx 4
= 3 years, 4 months
Payback period
Example 2: Cumulative method
ABC invests in an investment of £6.2m. Cash
flows is as follows:
Year  Cash flow (£) 
1  1,200,000 
2  2,200,000 
3  2,500,000 
4  1,700,000 
AssignmentTutorOnline
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Example 2 Solution
After year 3, we still
have a balance of
£300,000 to
complete payment.
So we divide this
balance by year 4
cash flow and
multiply by 12.
= 300,000
1,700,000
= 0.176 x 12 = 2
Year  Cash flow (£)  Cumulative cash flow (£) 
0  (6,200,000)  
1  1,200,000  1,200,000 
2  2,200,000  3,400,000 
3  2,500,000  5,900,000 
4  1,700,000  7,600,000 
Payback period = 3 years, 2 months
Advantages of payback
• Simple to calculate and understand
• Focuses on project’s cash flows rather than accounting
profits. Hence more objectively based
• Favours projects with short/quick payback periods. This
tends to minimise risk and may also produce faster
growth for the company
Once the relevant cash flows are calculated, payback is
easy to apply and to explain to management
Capital rationing: it ensures the recycling of cash into
new projects with the least delay.
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Disadvantages of payback period
method
Method ignores time value of money
Ignores cash flows after the payback period
Investment Appraisal Methods
2. Accounting Rate of Return (ARR)
This method takes the average accounting profit which
the investment will generate and expresses it as a
percentage of the original investment or the average of
initial investment in the project as a measure of a
project’s profitability (or viability).
ARR = Average Annual Profit * 100%
Original Investment in Project
Where there is a scrap value at the end of the useful life
of the project,
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Accounting Rate of Return (ARR)
Accounting Rate of Return (ARR)
In assessing individual project, it is normal for
companies to have a minimum ARR below which
investment will not be undertaken.
The minimum could be a rate which previous
investments have achieved, or it could be an
industry average.
Where there are competing projects, the one with
the higher or highest ARR would be accepted.
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Accounting Rate of Return (ARR)
Accounting Rate of Return (ARR)
Solution to Example 3.
Average Accounting Profit =
( 250 +1000 + 1000 + 20,750) / 4 = 5625
Original investment = 45,000
ARR = (5625/45000) * 100 = 12.5%
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Accounting Rate of Return (ARR)
Advantages of ARR

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 Disadvantages of ARR Based accounting profits rather than cash flows, which are subject to a number of different accounting policies. It does not take into account of the length of the project 

 
 
 It ignores the time value of money 
Investment Appraisal Methods
Discounted Cash flow (DCF) methods
Net Present Value (NPV)
Internal Rate of Return
Both use cash flow (rather than accounting
profits)
Cashflows covering the whole life of the project
are taken into account;
Both take into account time value of money
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Discounted Cash flow (DCF)
methods
 DCF methods operate on the principle that money received or paid at different times cannot be compared directly. Rather they need to discounted (or reduced) to equivalent present values before any comparison can be made. Note: time value of money concept still applies even if 
 

there is no inflation (i.e. inflation rate 0%).
The presence of inflation simply increases the
discrepancy in values of monies received or paid at
different times.
Discounted Cash flow (DCF)
methods
 DCF methods operate on the principle that money received or paid at different times cannot be compared directly. Rather they need to discounted (or reduced) to equivalent present values before any comparison can be made. Note: time value of money concept still applies even if 
 

there is no inflation (i.e. inflation rate 0%).
The presence of inflation simply increases the
discrepancy in values of monies received or paid at
different times.
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Discounted Cash flow (DCF)
methods
1. Net Present Value (NPV)
Present value: the amount of money you must invest or
lend at the present time so as to end up with a
particular amount of money in the future.
Discounting: finding the present value of a future cash
flow
Net Present Value (NPV) – the difference between the
present values of cash inflows and outflows of an
investment
Opportunity cost of undertaking the investment is the
alternative of earning interest rate in the financial
market.
Net Present Value (NPV)
Net Present Value of an Investment is the present
value of all its present and future cash flows,
discounted at the opportunity cost of those cash
flows.
In case of competing projects, the project with
Highest NPV is accepted
NPV calculations can be approached in two ways;
Summation method
Columnar method
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Net Present Value (NPV)
Net Present Value (NPV)
Example 4
A company can purchase a machine at the price of
£2200. The machine has a productive life of three
years and the net additions to cash inflows at the
end of each of the three years are £770, £968 and
£1331. The company can buy the machine without
having to borrow and the best alternative is
investment elsewhere at an interest rate of 10%.
Evaluate the project using the NPV method
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Net Present Value (NPV)
Discounted Cash flow (DCF)
methods
2. Internal rate of Return (IRR)
Internal Rate of Return – is the discount rate
that equates the present values of an
investment’s cash inflows and outflows.
Internal Rate of Return (IRR) – is the discount
rate that causes/brings an investment’s NPV
to be zero
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Internal Rate of Return (IRR)
Internal Rate of Return (IRR)
Example 5
A company can purchase a machine at the price of
£2200. The machine has a productive life of three
years and the net additions to cash inflows at the
end of each of the three years are £770, £968 and
£1331. The company can buy the machine without
having to borrow and the best alternative is
investment elsewhere at an interest rate of 10%.
Evaluate the project using the IRR method
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Internal Rate of Return (IRR)
Solution to Example 5
IRR Try 15%
Year  Cash flow  Discount  Discounted 
PV  Factor (15%)  Cash flow 
0 (2200) 1.000 (2200)
1 770 0.8696 669.59
2 968 0.7561 731.90
3 1331 0.6575 875.13
NPV 76.62
Internal Rate of Return (IRR)
• Year Cash flow DC (16%) PV
• 0 (2200) 1.000 (2200)
• 1 770 0.8621 663.83
• 2 968 0.7432 719.42
• 3 1331 0.6407 852.77
• NPV 36.01
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Internal Rate of Return (IRR)
• Year Cash flow DCF (17%) PV
• 0 (2200) 1.000 (2200)
• 1 770 0.8475 652.58
• 2 968 0.7305 711.48
• 3 1331 0.6244 831.08
• NPV (4.86)
Internal Rate of Return (IRR)
Using the formula above the IRR can
be computed as follows.
15+(76.62/76.62 – 4.86)x(1715)
15+(76.62/81.48)x(2)
15+(0.940353461)x2
= 16.88%
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Investment Appraisal Method
3. Profitability Index
The Profitability Index (PI) is based on the
comparison of the net present value of the cash
flow with the amount of the original investment.
It is, therefore, a measure of the increase in the
capital sum that the net present value
represents.
Projects are thus ranked in order of profitability.
Profitability Index
The profitability index is calculated in the following
manner:
Present value of cash flows = profitability index
Original amount invested (PI)
The index shows the return (in Present Value terms)
per each of £1 of original investment.
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Profitability Index
Thus, the higher the profitability index, the
higher the return earned on the project.
The lower the profitability index, the less
profitable the project;
And if the index falls below 1, this means that
the project has failed to meet the required
rate of return.
Profitability Index
Example 6.
We have 3 Projects :
A  B  C  
Cost PV of Cashflows @ 10% 
100,000  50,000  200,000 
110,993  63,444  214,450  
NPV Profitability Index (110,993/100,000) 
10,993 1.110 
13,444 1.269 
14,450 1.072 
Thus, although all 3 projects have positive NPVs, project B provides a
better return for each £ invested.
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Reading List
Drury, C. (2018), Management & Cost
Accounting, 10th Edition. Chapter 13.
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