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expect to be asked to give up all their possessions. One says to the other, â€˜Can I pay you back that $100

that I owe you?â€™ The logical reply here might be to ask for the money later! I only say â€˜might beâ€™ because

if you were insured you might think that taking the money now was the smart thing to do.

This is the first and last time in this book that I will invent an extreme example that apparently

disproves a simple and generally true assertion. Business, in my view, is not a pure science and rules

have exceptions. Part of the skill of business is to know when to trust to a rule and when to realise that

the old adage that â€˜the exception proves the ruleâ€™ must be applied.

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4 The five financial building blocks

concerned the choice between $100 now but an anticipated $200 in a yearâ€™s

time, many, but not all, would be prepared to wait. In principle, for a situ-

ation such as this there is a sum of money that you anticipate in the future

which will just compensate you for giving up the certainty of receiving

money now.

This simple question of money now versus money later is at the heart of

most financial decisions. Take for example the decision to invest in a new

piece of machinery. How should an organisation decide whether or not to

invest money in the hope of getting more back later? What about the deci-

sion to sell a business? This concerns receiving money now but then giving

up the uncertain flow of cash that the business would have generated in the

future. In this section I will set out an approach which can be adopted to give

answers to such questions. It is called the economic value model. Through

it we are able to make rational choices between sums of money at different

times in the future.

This economic value model has its most obvious uses in companies that

are quoted on stock markets because it allows decision making to be clearly

aligned with the best interests of shareholders. It is, however, of more general

use. It makes sense for individuals to consider important financial decisions

from this perspective. It is also used in the public sector. A good example

comes from the UK. Here, HM Treasuryâ€™s so called Green Book sets out the

recommended approach for appraisal and evaluation in central government.

This too, applies the economic value model albeit that it uses an alternative

name for it, namely â€˜discountingâ€™.

The time value of money

Let us return to the question of an individual deciding between $100 now and

$200 a year later. How do you think the decision would be made? If you were

faced with this question, what factors would you want to consider? Please

think also about whether you would consider yourself typical of others. Can

you see how different categories of people and different situations could lead

to different decisions? Now think also about a similar transaction only this

time where an individual was borrowing $100 today but had to repay $200

the following year. How do you think he or she would decide about this?

My guess is that the longer readers think about these questions, the more

possible answers they will come up with. There are, however, likely to be

some generic categories of answers. One category will concern the financial

situation of the individual to whom the offer is made. Is he/she desperately

5 Building block 1: Economic value

short of money or will the cash simply make a marginal improvement in

an already healthy bank balance? The second category of answer will con-

cern the risks associated with the offered $200 in the future. Just how sure

are you about this sum of $200 in a yearâ€™s time? Is this a transaction with

your trusted rich Uncle Norman or your fellow student Jake who you know

is about to go off backpacking around the world and is seeking a loan to fund

the purchase of the ticket for the first leg of the journey? Uncle Norman will

pay whereas Jake will do so only if he can afford it! Then, when it comes to

borrowing money, categories of answer are likely to concern things like the

use to which the money will be put, the alternative sources of cash and, cru-

cially, the consequences of failure to repay.

So we can see there are many reasons why the exact trade off between

money now and money later may change. In any situation, however, there

should be a sum of money in the future that balances a sum of money now. I

will call the relationship between money now and a balancing sum of money

in the future, the time value of money.

Quantifying the time value of money

The time value of money can be quantified as an annual interest rate. If the

initial sum of money (traditionally called the principal) were termed P and the

interest rate were r% then the balancing sum in one yearâ€™s time would be:

Balancing future sum = P Ã— (1 + r )

In the $100 now or $200 in a yearâ€™s time example above, the implied annual

interest rate is 100%. Had we felt that a 15% time value of money was appro-

priate we would have been indifferent between $100 now and $115 in one

yearâ€™s time.

Quoting the time value of money as an annual interest rate creates a com-

mon language through which investments can be compared. If we did not

express things in a common way we would face the practical difficulty that

we could only compare investments that were over the same period of time.

In this section we will consider the formula which governs how the time

value of money works. We can then use this formula as one means of quanti-

fying what our time value of money is.

Readers will hopefully be familiar with the difference between compound

interest and simple interest. With compound interest, when interest is added

it then counts towards the balance that earns interest in the future. With sim-

ple interest the interest is only paid on the original sum. So with compound

6 The five financial building blocks

interest at 10% an initial investment of $100 grows to $110 after one year and

$121 after two years. By contrast, with simple interest it only grows to $120

after two years. The extra $1 in the compound interest case comes as a result

of earning interest on interest.

The time value of money works exactly like compound interest. This is

because with each year of delay the sum of money we anticipate in the future

has to grow at the time value of money. The formula for it is:

FV = PV Ã— (1 + r )n

Where:

PV is the sum of money now (termed the present value);

FV is the balancing sum of money in the future (termed the future value);

r is the time value of money expressed as an annual percentage;

n is the number of years in the future that the balancing sum will be

received.

This means that if we can decide on the future value that balances a present

value a given number of years in the future, we can calculate the implied time

value of money. So, for example, if we know that in a particular situation we

are indifferent between $100 now and $112.5 in three yearsâ€™ time we could

calculate our time value of money as 4.0%.3

This book will devote a lot more attention to the topic of setting the time

value of money in later chapters. It is sometimes called different things such

as the cost of capital or the discount rate. At this early stage in our journey

towards financial expertise, however, all that is needed is an acceptance of

the principle of the time value of money and that this works exactly like com-

pound interest. This principle holds that for any situation there is a balancing

point where future expectations are just sufficient to justify investing today.

The balancing point is characterised by the position where a decision maker

is indifferent between a sum of money now and a sum of money later. Once

we have identified a balance, we can back-calculate from it the implied time

value of money.

Armed with this time value of money we could then assess similar trade

offs that involved different amounts of money and different time periods. We

could, for example, use this single time value of money to apply to any offers

Donâ€™t worry if the maths behind this looks a little complex at this stage. We will have plenty of opportun-

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ities to learn how to do the sums as this chapter progresses. For the time being, if you are not sure you

could have calculated the 4% figure, simply check it is right by doing the sum 100 Ã— 1.04 Ã— 1.04 Ã— 1.04.

7 Building block 1: Economic value

from our rich Uncle Norman while we would probably have a different, and

almost certainly higher, rate for any offers involving backpacking student

friends like Jake.

The concept of value

The value concept allows us to translate any sum of money at one point in

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