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when it comes to dealing with risk in the context of big publicly owned com-

panies. This building block will introduce this new way of looking at risk. It

is called portfolio theory and it provides one of the cornerstones of modern

corporate finance.

It is portfolio theory that will allow us to return to the question of how it is

that risk must influence the way we choose the appropriate CoC for our valu-

ations. This theory will also help us decide what makes a good assumption

to plug into our economic models. The building block, therefore, serves as a

crucial integrator of the preceding four.

I must start off by defining what I mean by risk. My dictionary defines risk

with words to the effect that it is a nasty event or outcome. This, I believe, is

the view of risk that we have grown up with. Unfortunately, in the context

of corporate finance, risk means something different. It means what I think

would more properly be called uncertainty. I wish corporate finance had not

used the word risk as it theorised about what it terms â€˜risk and rewardâ€™ and

about the â€˜equity risk premiumâ€™. I am, however, stuck with what has gone

In particular I will assume that readers are familiar with concepts such as the odds of something

1

happening and of the probability of something happening. Readers will know that if you list all of the

possible outcomes the sum of their individual probabilities will be 100%. Readers should also be able

to calculate probabilities of two or more things happening together.

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143 Building block 5: Risk

before me. Since this is a book about corporate finance I too have to use the

term risk when I really mean uncertainty.2 The building block is called risk

but it is about how we deal with uncertainty.

The building block has five parts. In the first part I will introduce some

key techniques and terminologies. The particular focus at this stage will be

on what makes a good assumption and the concept of expected values. In the

second part I will introduce the portfolio effect. This has some implications

which can be hard to grasp but is actually simply an embodiment of the old

adage of not putting all your eggs in one basket. In the third section I will

introduce the idea of risk monetisation which gives us a means of taking

rational decisions in relation to risk. I will then be ready to discuss various

ways of categorising risk in the fourth section. Between them these will help

to provide checklists which we can use when trying to identify risks before

they hit our projects. The final section will contain plenty of questions so that

readers can practise what they have learned.

Part 1: Techniques and terminology

What sets market price?

Up to now this book has focused on how to carry out financial calculations

given a particular set of assumptions. We have described the idea of present-

ing particular sensitivities to decision-makers so that they will have a better

feel for the range of outcomes that might come about. We have also seen how

to turn the approach round and find what particular assumptions will, for

example, give a zero NPV.

We have learned that in principle the value of something is given by its

NPV, but which NPV? If NPVs are simply a function of what assumptions

are made, what assumptions should we make when deciding what something

is worth? Take, for example the question of the value of a producing oil well.

The most important assumption here is likely to be the oil price, but what

To illustrate the difference between risk and uncertainty you can consider a popular game show that

2

gives money to its lucky contestants. Whatever happens, a contestant will win some money. What

makes the show so gripping is the way the exact amount varies between the smallest coin in the realm

and a life-changing sum. To the man in the street this show has no risk because a contestant can only

win. From the perspective of corporate finance there is uncertainty because the range of winnings is

so large. Corporate finance refers to this uncertainty as risk.

144 The five financial building blocks

price should we use? There is a wide range. Here are ten possible assumptions

just for starters!

â€¢ the lowest possible number (e.g. lowest price in the previous 20 years);

â€¢ a realistic worst case (e.g. lowest annual average in the previous 20 years);

â€¢ a slightly pessimistic case;

â€¢ the average price over the last 20 years;

â€¢ the average price adjusting for inflation;

â€¢ a respected consultantâ€™s forecast;

â€¢ a different but equally respected consultantâ€™s forecast;

â€¢ the forward market price;

â€¢ todayâ€™s price; and

â€¢ your estimate of the most likely price.

If we were to carry out ten valuations using the above assumptions we would

gain ten insights but we would still not know what to expect the market value

of the oil well to be.

Would it be sensible to assume that market value was set by a pessimistic

oil price assumption? Surely the answer must be â€˜noâ€™. Although one could

imagine a buyer wanting to buy an oil field for a price that allowed their com-

pany a high chance of profit, why should a seller sell in such a situation? The

concept of a market price is such that it requires willing buyers and willing

sellers. A fair market price does not allow a buyer an unfair profit because at

that price another buyer would offer to buy for a slightly higher price.

We will now investigate what the fair market price should be for a sim-

ple situation where possible outcomes and their associated probabilities are

known. We will then gradually make the situation more complex until it

becomes clear that there is one particular basis for setting assumptions which

should allow the fair market price to be established.

Our situation concerns the roll of a dice. If the result is a 1 then the payout

is zero. If it is a 2, a 3, a 4 or a 5 then the result is a payout of $2. If the result is

a 6 then the payout is a magnificent $4. If all payments are immediate, what

would be the fair market price of the right to play this game? The answer, I

suggest, is clearly $2. If you pay $2 to play then you have one chance in six

of losing $2 but four chances in six of breaking even and one chance in six

of winning $2. Is it â€˜fairâ€™ that somebody playing the game on these terms

should have a chance of losing money? The answer is â€˜yesâ€™ because they have

an exactly equal chance of winning.3

It is quite common to hear the argument made that the market price for playing a game such as this

3

just once should be lower than the price for playing the game several times (obviously in the several

145 Building block 5: Risk

But did we choose $2 because it was the most likely payout or because it

was the middle of the range between the best and the worst outcomes or

because it was the average of all possible outcomes? A price of $2 meets all

three of these criteria.

We can change the game and quickly see that the most likely outcome is

not what is setting the market price. Suppose the payouts were nil if a 1, a 2

or a 3 were rolled and $4 if the result was 4, 5 or 6. Once again, $2 would be

the fair market price but this time it is not the most likely outcome, it is an

impossible outcome to achieve on a single roll. It is, however, the middle of

the range and also the average outcome.

A further twist will allow us to see whether it is the middle of a range or

the average which we should be prepared to pay. Suppose the payout was nil

if the outcome was not a 6 and $12 if the outcome was a 6. Again our intui-

tion tells us the answer is a fair value of $2. We simply know to take a sixth

of $12. It is the average outcome which sets value, not the most likely or the

middle of the range.

Now with the roll of a dice the individual outcomes are equally likely. We

can add one final twist to our hypothetical game to see that it is the weighted

average outcome that we are using to set value and not simply the average.

The weighted average is the sum of the individual outcomes times their prob-

abilities. With a simple roll of a dice the probabilities are all the same and we

can just add up the answers and divide by six. To calculate a weighted aver-

age, each possible outcome is multiplied by its probability and the weighted

average is then the sum of these numbers.

We will now illustrate this effect by changing our dice game to the draw-

ing of lots. Suppose a box contains 600 tokens. The tokens are marked 1, 2,

3, 4, 5 or 6. The payouts are as in our dice-rolling game but instead of having

100 of each number in the box, we now have 80 each of the 1 to 5 numbers

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