1. Investment Appraisal Discounting Methods
NPV & IRR

2. 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

3. The four techniques Payback
The time taken to recover the cost of the investment
Accounting rate of return
Profits earned on investment expressed as a % of the cost of the investment
Net present value
The present value of net cash flows received in the future less the initial cost of the investment
Internal rate of return
The discount rate that causes the net present value of an investment to be zero

4. The non-discounting methods
The first two methods are non-discounting 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

5. 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?

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. Example of NPV Year Cash flow (£m) Discount factors @ 10%
Present value (£m)
-3.0
One 1
0.5
0.91
0.455 2
1.0
0.83 3
1.5
0.75
1.125 4
2.0
0.68
1.36 5
0.62
1.24
NPV =
2.01

14. 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

15. 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

16. 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

17. 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
.62
.57
.52

18. General rules Positive NPV
The project is accepted - the return exceeds the required rate of return
Zero NPV
The project is acceptable - the return equals the required rate of return
Negative NPV
The project is rejected - the return is less than the required rate of return

19. 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

20. 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

21. 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

22. 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

23. Disadvantages of NPV Involves complex calculations
Easily misunderstood
Not useful for preliminary screening of investment projects
Difficult to choose a discount rate-especially 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

24. Internal Rate of Return
The true interest rate earned by the investment over the course of its economic life

25. 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

26. 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

27. Example Capital cost: £40,000
Cash inflow: £10,000 per year for 5 years
Subject £10k p.a. to various discount factors
12% =£36,050 minus £40,000= (£3950)
=£39,993 minus £40,000 =(£7)
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%

28. 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)

29. IRR at graphical analysis
Internal Rate of Return + 2% 4% 6% 8%
Rate of Discount -

30. 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

31. 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

32. Limitations of investment appraisal
Investment appraisal techniques only considers quantitative factors-they 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

33. 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