7.5 Decision making 283
have a value of $2 million. They call this a
‘Level C’ result. This, of course, would mean a
net loss for the company when the
exploration costs are subtracted, but the
analysts also calculate that the probability of a
Level C result is very low. They set it at 0.1 (or
10%). They also claim that there is a similar
(10%) probability of a large gas deposit – a
‘Level A’ result – with a value as high as
$12 million. The most likely prediction,
however, is somewhere between: a ‘Level B’,
worth around $7 million.
If the company abandons the project and
looks for a safer venture, there is a second
option of putting the extraction rights up for
auction, in the hope that a richer company,
able to take bigger risks, will want to buy
them. Zenergies’ accountants have estimated
that there is a 40% chance of selling the rights
for as much as $5 million, and a 50% chance
of a sale for around $3 million. (That leaves a
slim, 10%, chance that there will be no sale,
or an offer so small that selling is not a viable
option.)Activity
Discuss what the company should do,
and why.Commentary and continuation
Statistically there are big gains to be made, but
also significant risks involved. The question is
which is most likely, and by how much. It is
unlikely, though not impossible, that the yield
will be as low as $2 million, with a consequent
loss of $1 million. That is the worst-case
scenario. It is likely to be about $7 million,
with a profit of $4 million; and it may be as
much as $12 million, with a profit of
$9 million. Compared with this there is the
less risky option of selling the rights to extract
the gas.Decision trees
Mathematically, consequences can be
measured by multiplying the value
(importance) of a particular outcome by its
probability. (This is basically what we did in
the simple case of buying a car.) If all the
possible outcomes of a given decision are
added up, that gives us an idea of its overall
desirability, which can be compared with
that of the other available choices,
calculated in the same way. A formal,
graphical representation of this can be made
by means of a decision tree diagram, like
those used in problem solving
(see Chapter 6.3).
Tree diagrams are used in a range of
real-life situations where decisions are
influenced by factual data or evidence. We
find examples in business, politics,
economics, medicine, sport, and many other
widely different disciplines. (Watch a baseball
coach studying pages of percentages before
deciding when or whether to bring on a new
pitcher.) Real-life decisions can be highly
complex. They can also have very important
and far-reaching consequences. If you look
up ‘decision trees’ on the internet, you will
find some bewilderingly complicated
examples. But the underlying principle is
simple, as we have seen.
Here is a fictional, but broadly realistic,
scenario. A small energy company, Zenergies,
has discovered a deep deposit of shale gas,
with unknown commercial potential. The
board have to decide whether to proceed with
extraction of the gas, at a cost of $3 million,
or abandon the project because it may be
unprofitable.
The key factors are the known costs and the
possible returns. The returns, and therefore
the possible profits, depend on the size of the
gas deposit. Although this is unknown,
geologists and market analysts have estimated
that on the lowest estimate the gas would