Investment Appraisal Investment Appraisal Discounting MethodsDiscounting Methods

NPV & IRR

Investment appraisalInvestment 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 techniquesThe 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

The non-discounting The non-discounting methodsmethods

• 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

The discounting methods 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 Don’t confuse discounting with inflationwith 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 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 valuePresent 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 The superiority of the discounting methodsdiscounting 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)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 valueNet 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 NPVExample 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 NPVExample of NPV

Year Cash flow (£m)

Discount factors @

10%

Present value (£m)

0 -3.0 One -3.0

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

Notes to the exampleNotes 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 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 But where did the discount factor come from?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 Extract from a table of discount factorsdiscount 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 rulesGeneral 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

Choice of projectsChoice 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?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 rateChoice 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 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 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

Internal Rate of ReturnInternal Rate of Return

The true interest rate earned by the investment over the course of its

economic life

Internal rate of returnInternal 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 returnInternal 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

ExampleExample

• 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 IRRHow 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 analysisIRR at graphical analysis

+

-Rate of Discount4% 6%2% 8%

Internal Rate of Return

Decision ruleDecision 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 NPVCompare 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 Limitations of investment appraisalappraisal

• 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

Quantitative factors to consider in Quantitative factors to consider in investment appraisalinvestment 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