242 Unit 6 Problem solving: further techniques
This decision tree, like most real ones, has two
types of branch. The first branch shown here
is a choice: whether to take the fixed or
variable rate investment. In the upper branch
we have three different probabilities. These are
things that cannot be controlled. It is
conventional to show choices as squares,
probabilities (or chances) as circles, and end
points as triangles.
In this case, the lower branch results in
interest of $250 (5% of $5000) in the first year,
and $262.50 (5% of $5250) in the second year,
making a grand total of $5512.50.
The method of calculation of the figures in
the upper branch is as follows:
Mary earns $300 in the first year (6%
interest), giving her $5300 at the start of the
second year.
In the second year:
• there is a 60% chance of rates being 3%
and her earning $159 interest
• there is a 20% chance of rates being 6%
and her earning $318 interest
• there is a 20% chance of rates being 8%
and her earning $424 interest.Decision trees
The decision tree is an extension of the
probability tree diagram which is used in
commerce and industry to help make strategic
and financial decisions. In this case such
things as costs or times are recorded on the
different branches of the tree and used to
estimate the average cost or time for each
strategy. This will become clearer with an
example; this is a very simple situation chosen
to illustrate the method.Mary has $5000 to invest and can leave it for
two years. She has a choice between a fixed
rate investment at 5% interest per year, or a
variable rate scheme which may rise and fall.
The variable rate scheme pays 6% in the first
year, but may be different in the second year.
She has looked at the financial press, and the
opinion of the experts is that interest rates have
a 20% chance of rising to 8%, a 20% chance of
rising to 6% and a 60% chance of falling to 3%.
Which investment should she choose?
A decision tree diagram for this situation is
shown below.