Investment Appraisal
Discounting Methods
NPV & IRR
Investment appraisal
• This refers to a series of analytical
techniques designed to answer the
question - should we go ahead with
a proposed investment?
• There are four techniques and all
involve a comparison of the cost of
the investment project with the
expected return in the future
The four techniques
Payback
Accounting
rate of return
The time taken to recover the
cost of the investment
Profits earned on investment
expressed as a % of the cost of
the investment
Net present
The present value of net cash
value
flows received in the future less
the initial cost of the
investment
Internal rate of The discount rate that causes
return
the net present value of an
investment to be zero
The non-discounting
methods
• The first two methods are nondiscounting methods
• The financial return from an investment
comes in a stream over a number of
years
• The non-discounting methods make no
distinction between the return which
comes in in ten years time from the
return that will come during the current
year
• In other words these methods ignore the
time of money
The discounting
methods
• The significant feature of these methods
is that they take into account the time
value of money
• What this means is that we recognise
money received in the future does not
have the same value as money received
today
• The test of this proposition is simple:
which do you prefer £1000 in your hand
today of the promise of £1000 in five
years time?
Don’t confuse discounting
with inflation
• It is an error to believe that we
discount in order to make
adjustments for future inflation
• Even if inflation was zero we would
still subject the future stream of
earnings to discounting
• Discounting is all about making an
adjustment for having to wait for a
return
Discounting
• We discount the value of the return
received in the future because of the
inconvenience of having to wait
• Money promised in the future is worth
less than the same money received today
• Discounted cash flow involves
discounting (reducing) the future
expected cash inflows and outflows of a
potential project back to their present
value today
Present value
• Present value places a value for today on
earnings to be received at some future
date
• It is the cash equivalent now of a sum
receivable or payable at a future date
• The basic principle of discounting is that
if we wish to have £x in a years time we
need to invest a certain sum less than £x
now at the interest rate of r% in order the
required sum of money in the future
• In effect, it is compound interest in
reverse
The superiority of the
discounting methods
• NPV and IRR take into account:
– profits over the whole life of the project
– the timing of the return
• But
– may be difficult to apply
– lacks consideration of short term
liquidity
Net present value (NPR)
NPV is a technique which discounts future
expected cash flows to today’s monetary values
using an appropriate cost of capital
Net present value
• This compares the initial cost of the
project with the future discounted cash
flows it generates
• NPV = the discounted cash inflow minus
the initial cost of the investment
• If NPV is positive, the project will be
considered profitable and worthwhile
• If it is negative, it will be considered
unprofitable and will be rejected
Example of NPV
DATA:
• Initial outlay: £3m
• Chosen rate of discount:10%
• Cash inflow:£0.5m, £1.0m, £1.5m, £2.0m,
£2.0m in successive years
• The capital cost is known and incurred
today
• The return is what is expected and will
be enjoyed in the future
• As it comes in the future it will be subject
to discounting
Example of NPV
Year
Cash flow
(£m)
0
-3.0
Discount
factors @
10%
One
Present
value (£m)
1
0.5
0.91
0.455
2
1.0
0.83
0.83
3
1.5
0.75
1.125
4
2.0
0.68
1.36
5
2.0
0.62
1.24
NPV =
2.01
-3.0
Notes to the example
• Year zero refers to now - the year zero
figure refers to cost of equipment it is
shown as negative cash flow
• The present value is the value of money
received in the future. It is calculated by
multiplying the cash inflow for the year
by the appropriate discount factor
• Add up the present values in the final
column not forgetting to deduct the
negative figure for year zero
Example of NPV
• The sum of the (positive) cash inflows is
£5.1m
• But we need to subtract the initial cost of
£3m
• This gives a net present value of £2.1m
• The fact that NPV is positive is
significant
• The project has passed the test. The sum
of the discounted cash flows exceeds the
initial cost of the investment
But where did the discount
factor come from?
• The simple answer to the question is that it
comes from a table of discount factors
reproduced in many accounting books (and are
always supplied by exam boards)
• But this begs the question where did the
numbers come from in the first place?
• Think of compound interest- if we now reverse
the formula for compound interest we get
• Present value
– = Future value of the inflow (in n years)
– (1+r) to the power of n
– Where r is the rate of discount and n the
number of years
Extract from a table of
discount factors
Year
8%
10%
12%
14%
1
.93
.91
.89
.88
2
.86
.83
.80
.77
3
.79
.75
.71
.67
4
.74
.68
.64
.59
5
.68
.62
.57
.52
General rules
Positive NPV
Zero NPV
Negative
NPV
The project is accepted the return exceeds the
required rate of return
The project is acceptable the return equals the
required rate of return
The project is rejected - the
return is less than the
required rate of return
Choice of projects
• Suppose the firm is faced with a
choice of projects
• Eliminate all projects with a
negative NPV
• Then choose the project with the
highest positive NPV
Which discount rate?
• A different discount rate would
produce a different result
• At one rate a project might be
profitable-at a higher rate of
discount it might be unprofitable
• The higher the chosen discount rate
the more is discounted from size of
the return
• The choice of rate is key to the
validity of the technique
Choice of discount rate
• Factors taken into account in the choice of rate
• The opportunity cost of investment - the return
on other types of investment
• Cost of capital - what the firm will have to pay
to raise capital
• Management objectives - the rate of return
required
• Degree of risk involved - the higher the risk the
higher the chosen rate
• Return on similar project in the past
• Inflation rate - in periods of inflation the falling
value of money is an additional complication. A
higher rate will be chosen to compensate for
this additional factor
Advantages of NPV
• It recognises the whole life of a project
• It takes into account net cash flow and
outflows for the duration of the project
• It takes into account the time value of
money i.e. money in the future is worth
less than the same amount of money
received today
• It makes allowance for the opportunity
cost involved in investing
Disadvantages of NPV
• Involves complex calculations
• Easily misunderstood
• Not useful for preliminary screening
of investment projects
• Difficult to choose a discount rateespecially for a long term project
• Often based on an arbitrary rate of
discount
• Results are highly sensitive to
assumptions such as discount rate
and planning horizon
Internal Rate of Return
The true interest rate earned by the
investment over the course of its
economic life
Internal rate of return
• This is defined as the annual % return
achieved by a project at which the sum of
the discounted cash inflows over the life
of the project is equal to the of the
discounted cash outflows
• The rate of discount at which discounted
cash inflow equals the cost of the
equipment
• The rate of discount where NPV = Zero
• Whereas NPV is expressed as a sum of
money, IRR is the expected yield in %
terms
Internal rate of return
• Identify the rate of discount at
which the discounted cash inflow
equals the cost of the project
• At this point the NPV will be zero
• The ascertaining of the IRR enables
decision makers to compare IRR
with the required rate of return on
investment laid down by top
managers
Example
•
•
•
•
•
•
•
Capital cost: £40,000
Cash inflow: £10,000 per year for 5 years
Subject £10k p.a. to various discount factors
NPV @ 12% =£36,050 minus £40,000= (£3950)
NPV @8% =£39,993 minus £40,000 =(£7)
NPV @ 6% =£42,I20 minus £40,000 =£2120
The IRR is somewhere between 6% and 8% but
closer to 8% say 7.%
• Go ahead if the cost of capital is less than 7.9%
How to identify the IRR
• Trial and error – apply different
rates of discount until you find an
approximation
• Construct graph plot NPV for
various discount rates
• Linear interpolation-find the point
where the curve cuts the x axis
(where NPV = zero)
IRR at graphical
analysis
Internal Rate of
Return
+
2%
-
4%
6%
8%
Rate of Discount
Decision rule
• Go ahead with the proposed
investment if the IRR exceeds the
rate of interest on borrowed money
• Where there is a choice of projects,
choose the one with the highest IRR
Compare IRR with NPV
IRR
• Considers time value
of money
• Involves discounting
• Provides information
in the form of a %
understood by
managers, especially
non-financial
managers
• A discount rate does
not have to be
specified in advance
NPV
• Considers the time
value of money
• Involves discounting
• Unlike IRR it takes
into account the
relative size of
investment
• Variations in discount
rate over the life of
project can be built
into NPV – but not IRR
Limitations of
investment appraisal
• Investment appraisal techniques
only considers quantitative factorsthey ignore important qualitative
factors
• They are only as reliable as the data
• The return used in the calculation is
the expected return This is based
on forecasts which may or may not
turn out to be correct
Quantitative factors to consider in
investment appraisal
• Aims of the
organization
• Reliability of the
data
• Level of risk
• Compatibility with
existing systems
and production
requirements
• Personnel and
human relations
• The economy
• Image and
marketing
• Consistency with
other company
policies
• Stakeholders
• Subjective criteria
of decision makers