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attractiveness of a project. These are summarised in the table below. We will

then illustrate how they can be applied in the practical examples section that

follows.

Summary of additional economic analysis required for projects:

17 Building block 1: Economic value

Indicator Brief description

Internal rate of return (also This is the time value of money which, if applied, would

called IRR or DCF return) cause the project to have a zero NPV. It can give some

idea of how big the â€˜safety marginâ€™ is between the project

and economic break even where it has a zero NPV.

It also aids comparison between projects of different

size. Generally speaking, the higher the IRR the better

although this approach can introduce significant biases

which will be discussed later.

Discounted payback This is how long it will be before the initial investment

is recovered and the positive cash flows have been

sufficient to build back to a zero NPV. It is where the line

in the value profile chart crosses the x axis. This gives

another indication of risk in how long one has to wait

before the project has paid back its initial investment.

The idea is that the longer the wait then, all other things

being equal, the greater is the risk. Again, this is a useful

concept but it has the drawback that it ignores cash

flows after payback.

Investment efficiency This is a â€˜bangs per buckâ€™ measure which states how

much value is created per unit of constraint. So if money

is the limiting factor, the efficiency might be NPV per

dollar of initial capital cost or it could be NPV divided

by the maximum negative NPV shown on the chart. If

engineering capability was the constraint, the efficiency

could be NPV per engineering man year utilised. This

concept is most useful when there is a clear and obvious

constraint and investments must be prioritised.

Sensitivities These are calculations of the project outcome under

different assumptions. Sensitivities give the answer to

questions of the type: â€˜what if?â€™ They are an essential

part of any project appraisal. The problem with them

concerns deciding when to stop, as there are always so

many things to consider. Each sensitivity will have its

own NPV, IRR, discounted payback and investment

efficiency.

The first three items are what I term â€˜economic indicatorsâ€™ for the main

case. These complement the primary economic indicator which is NPV. The

final item makes the point that many cases need to be investigated in order

to understand the effect of different assumptions. Each new case will have its

own set of economic indicators.

18 The five financial building blocks

Part 3: Practical examples

I will now take the economic value model and show how it can be applied

in three different situations. I will use these examples to show how the

economic indicators can add further insights on top of what is achieved by

simply considering value.

Example 1: Uncle Normanâ€™s birthday treat

Uncle Norman talks to you on your 15th birthday. This is the generous offer

that he makes:

â€˜Everybody can have just one special birthday. You know that on that day you will

get a super present from me. Do you want this to be on your 16th, your 18th or

your 21st birthday? The longer you wait, the more you will get and on your other

birthdays I will still give you your usual $500. At 16 you can have $10,000 but wait

until you are 18 and this will be $12,500. If you wait until you are 21, Iâ€™ll give you

$16,000.â€™

Which should you choose if your time value of money was 10%?

The first step is to calculate the cash flows for the various options. These

will be as follows:

16th 17th 18th 19th 20th 21st

Special day birthday birthday birthday birthday birthday birthday

16th birthday $10,000 $500 $500 $500 $500 $500

18th birthday $500 $500 $12,500 $500 $500 $500

21st birthday $500 $500 $500 $500 $500 $16,000

The next step is to calculate the appropriate discount factor. The cash flows

are all exactly one year apart and the first is in one yearâ€™s time. This means

we can simply take the factors from our discount factors table above. We

then multiply the various cash flows by the discount factors to calculate their

present values:

16th 17th 18th 19th 20th 21st

birthday birthday birthday birthday birthday birthday

Discount factor 0.909 0.826 0.751 0.683 0.621 0.564

19 Building block 1: Economic value

Present value of cash flows (= cash flow Ã— discount factor)

16th birthday $9,090 $413 $376 $342 $310 $282

18th birthday $455 $413 $9,388 $342 $310 $282

21st birthday $455 $413 $376 $342 $310 $9,024

All that remains to be done is to work out the present value of each of the

three options. This is simply the sum across each row. The results are:

16th birthday option: NPV $10,813

18th birthday option: NPV $11,190

21st birthday option: NPV $10,920

This analysis shows a priority order of 18th birthday, 21st birthday and finally

16th birthday. There is not a lot of difference in the numbers so one might

well want to test the model a little further and in particular, to test what is

driving the decision.

The above table has been computed line by line using discount factor

tables. This approach was adopted in order to make the various steps abso-

lutely clear. It is, however, generally preferable to build a spreadsheet model

to carry out any analysis. This allows one to avoid small rounding errors8

and, more importantly, allows one to carry out â€˜what if?â€™ tests.

Two key assumptions to investigate concern the discount rate and the

present on non-special birthdays. For example, a higher time value of money

would favour the 16th birthday option. This is because the 16th birthday

option gives you the large sum of money earlier and increasing the time value

of money is giving the signal that money in the future is relatively less attract-

ive. We can use a trial and error approach9 to find what time value of money

makes the 16th birthday option exactly equivalent in present value to the

18th birthday option. It turns out that at a discount rate of 12.39% the 16th

and 18th birthday options are each worth $10,486. At any rate above this, the

A spreadsheet model of the Uncle Normanâ€™s birthday treat scenario shows that the correct NPVs (to

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the nearest dollar) are:

16th birthday option: NPV $10,814

18th birthday option: NPV $11,193

21st birthday option: NPV $10,927

The go l seek function can also be used if one wants to find the answer as soon as possible. I r com-

e goal ek n ion n o e df ns nd he wer s on s o sibl . recom-

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mend, however, that when you are investigating such a situation you should adopt a trial and error

approach. This gives a much fuller picture of how the decision you are investigating is influenced by

changes in the assumptions.

20 The five financial building blocks

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