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The numbers in this table are called annuity factors. They can be particu-

larly useful for doing quick calculations such as investigating how much we

could afford to spend in order to generate a given saving that will last for a

number of years. So, for example, from the bottom row, eight years column

we can see that if you spend anything less than $5.335 in order to generate

eight annual savings of $1 then you can justify making the investment if your

discount rate is 10%.

Finally, in relation to annuity factors, note that as one looks further and

further into the future the extra value from an additional year decreases. In

fact, the factor converges on a figure of one divided by the discount rate. We

will learn why later in this book. For now we can simply note that this pro-

vides a very useful way of calculating the present value of a sum that will be

maintained for ever with the first payment happening in one yearâ€™s time. You

simply divide it by the discount rate.

14 The five financial building blocks

Introducing the concept of net present value

We are now ready for the most important section in this chapter. This con-

cerns the concept of net present value or NPV for short. We have shown how

any sum of money can be adjusted to its equivalent in present value terms. So

if we think of a project as a series of cash flows, we can adjust all of these to

their present value equivalent. The total of all of these present values, some

of which will be positive and some of which will be negative, is called the net

present value of the project. The word â€˜netâ€™ is added in order to make it clear

that the value being quoted is the net of inflows and outflows not just the

value of inflows ignoring the investment cost.

NPV is the primary focus of this book and readers will learn more about

why this number is so important as they progress through the chapters. For

the time being it should be evident that the NPV of a project represents simply

another way of stating the value test of whether it is worthwhile going ahead

with it. A positive NPV means that overall you are getting more present value

back than you have invested. So if you are considering just a single project

you know that in principle it is worthwhile as long as the NPV is zero or

greater. It should also be clear that if you have to choose between projects you

should always choose the highest NPV alternative.

NPV and project evaluation

Many financial evaluation decisions concern projects. These decisions are

typically of the type â€˜is it worth spending this much money in order to

generate what will hopefully be a stream of positive cash flows into the

future?â€™

Projects can be thought of as having a value profile, as illustrated in the

following chart. This plots the cumulative present value of the cash flows

associated with a project. The perspective of the chart is that it shows the

present value of the money invested in, and taken from, a project. On the

x axis we show the point in time being considered. In a typical project the

initial cash flows are negative. This means the line immediately goes below

zero. Once the investment phase of the project is over (i.e. after two years in

the example shown in the chart) it should start to generate positive cash flow.

This means the cumulative present value line starts to rise. If the project is

worthwhile it will finish up with a positive NPV. That is to say the line will

finish above the present value equals zero axis.

15 Building block 1: Economic value

A close inspection of this chart will reveal that the curve goes downwards

in the final year. What might the cause of this be? Well, the line goes down

because a cash outflow is anticipated in the final year. There may, for example,

be some clean-up costs associated with the project or some costs for laying

staff off.

We can observe from the chart that it takes about eight years before the

initial investment is recovered and the cumulative present value returns to

zero. The point when the cumulative present value returns to zero is referred

to as discounted payback.

The exact shape of the curve will be a function of both the anticipated

cash flows and the discount rate. The particular project that was chosen had

assumed a 10% discount rate. If we lower the discount rate the NPV will rise

and discounted payback will occur earlier. Increasing the discount rate will

NPV

Present Value $m

0 1 2 3 4 5 6 7 8 9 10 11 12 13

Time (years)

Fig. 1.2 Typical value profile for a project

Discount

Rate

5%

Present Value

10%

15%

20%

0 1 2 3 4 56 7 8 9 10 11 12 13

Fig. 1.3 Effect of discount rate on present value

16 The five financial building blocks

lower NPV and delay discounted payback. The following chart shows how,

for this hypothetical project, the profile of cumulative present value changes

as the discount rate is changed.

The first point to note with this chart concerns how the lines get further

apart as we move into the future. This illustrates how the effect of discount-

ing becomes amplified as the time period increases.

We can also see that as the discount rate is increased so the discounted

payback point increases. We can also see how there must be a discount rate

for this project which results in it having a zero NPV. Extrapolation sug-

gests this rate must be about midway between 15% and 20%. The discount

rate which results in a zero NPV is referred to as the internal rate of return

or IRR for short. The concept of the discount rate which causes a project

to have a zero NPV is an important one and will be returned to later in

this book.

Real life project evaluation

So far we have defined our decision rule as â€˜always select the option which

maximises NPVâ€™. Now with a project, where the choice is to invest or not to

invest, one could imagine the decision rule becoming â€˜invest in all positive

NPV projectsâ€™. Indeed, this is what the theory of value would tell us to do.

There are, however, practical reasons why most companies do not adopt this

approach.

The first concern is that resources are often limited. The resource that is

limited may be people to implement projects or money to invest in them.

Either way, a company may not be able to invest in all positive NPV projects.

It may need to choose between two worthwhile options. There are also issues

concerning risk. It is very rare for a project to be concerned only with certain-

ties. Some projects may be so big that the risks associated with them could

have severe impacts on the company.

How can these considerations be reflected in decision making rules? This

is a very big question. At this stage we will consider the simplest answers.

More will emerge as we progress.

What is necessary is to look beyond just NPV. There are a number of other

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