Performance Management exam technique: decision trees

Hello my name is Jo and I'm a subject
specialist at BPP. Welcome to this presentation for ACCA F5
performance management, where we're going to be looking at decision
trees. An overview of the session then we're going to start off by having a look
at some of the definitions which are relevant for preparing our
decisions trees, we're also going to be having a look at
the approach, so the order to tackle the question and also
the methodology for tackling a question, and we're going to be looking at
that with respect to June 2013's question 1. So, first of all then how does decision trees fit into the F5 syllabus? Well the F5 syllabus area B is on decision-making and that's further
split down into different areas, one of which is
dealing with risk and uncertainty in decision-making. The areas then of
this particular aspect that we will be looking at are part E where you're asked, or could
be asked to draw a decision tree and use it to solve a
multi-stage problem and also to calculate the value of
perfect and imperfect information, and this is
what was tested in June 2013.

It was the first time that this area
was tested and as you can see it's quite a small area of
a very large syllabus which should remind us of the point then
that it's not a good idea to try and question spot in F5. Everything can and will be tested. Okay so let's start off by thinking what a decision tree is. Frequently in exam
questions we assume that variables are known with certainty, for example our revenue. However in reality it could
be subject to uncertainty and in different
circumstances we might want to make different decisions.

A decision tree helps us to do this with
a diagrammatic representation of all of the different decisions and
different possible outcomes which could occur. So what are the steps
that are involved? Well first of all then we need to construct
our decision tree and that will be done using relevant
costs. Secondly we need to evaluate our
decision tree and we would do that using expected
values and both of these steps would be needed in order for us to answer the question
about what decision should be made given a particular set of circumstances.

The
decision then could get very complicated, however in the exam due to limited time
and marks available they're likely to be fairly straightforward.
So what is a relevant cost then if we're going to
use those costs when constructing our tree. A relevant cost then is a future incremental cash flow, so when we talk
about the future cash flow we're talking about one that and is going to be impacted on
the decision that we make, something that we've already decided to
do or already committed to for example a survey or some research
that has already been undertaken is in the past and cannot be changed. Its
incremental because it rises as a result of the decision that is
being made so for example additional costs or additional revenues
over and above those that the company would already be receiving. It also needs to be a cash flow so we're
not going to be including things like depreciation which are notional costs, so we're revising here another of the syllabus B areas which could come into play.

We also need
to think about how we calculate expected values for when
we're evaluating our decision tree. So
the expected value then is equal to the sum of the probability
times by the outcome and in an exam question you can
expect that the probabilities and the outcomes will be given to you, and they'll probably be given to you as discounted cash flows that the
time value of money is taken into consideration. Let's have a look then at what was required
in the exam in June 2013, in question 1 Gym Bunnies. Always a good idea then to
start off looking at the requirements before you read through the scenario in
detail so that when you're reading the scenario you
know what it is that is being expected of you. The mark allocation also provides a good
indication of the amount of time that you need
to spend on a requirement, so part A of this question then was worth
twelve marks so we'd looking to spend about 20 minutes
on it and it's here then with that we're being
asked to use expected values to prepare and fully label a decision tree which
shows the options available.

We're also being
asked to make a recommendation on the decision that they should make so
we're going to have to draw and construct our tree but we're also going to need to evaluate it
and as we see in F5 questions, the requirement
here is very clear about what is expected of you. So there's even a reminder about the need
to make sure that all of the branches of your tree are labelled. Let's have a look then at the content of the scenario and you can see that I've highlighted
the key decision here so the key decision is whether or not we
should be expanding. A lot of other information then in
the blurb is good for scene setting but isn't going to be of that much use to us, it's the detail below about the different
options that we're going to need to use when we start constructing our tree.

This is the first time that this was
tested in F5 so it may have come as a little bit of a
shock to candidates who opened the paper in June 2013, but there had been an
article written about it and also all areas of the syllabus can
and will be tested. Perhaps because it was new and an area
that students were unfamiliar with it was one of the weaker questions which
is why it's the focus of this presentation. So we're going to think about how best to
approach our decision tree and how to construct it, you can see here than that I've got the
conventions for a decision and outcome as a square for a decision and
a circle for an outcome.

It's stated in the examiner's report then for June 13 that if these conventions were used then there was no need to use the key therefore I can see no reason
why you would opt to use anything other than those standard
conventions in the construction of your tree. A few other helpful points
to remember then make sure that you label your branches so here if we talking about 6,000 members
make sure your branch reflects that this is what's going to happen if we have 6,000 members. Make
sure that you use a whole page as well, use a whole page of your
exam booklet and start in the centre leaving plenty of space, that way if
you've missed out a small branch then you can fit it in
much easier than if you've got a tiny little
tree, it's also much clearer and easier for the person who is going
to be marking this.

Make sure that you use a ruler as well
we don't want it to look like a spider has crawled across your page, it should be clear and professional
presentation of your answers. And make sure that you work from left to right when you're constructing
your tree. Don't do a rough version, you haven't got
time in the exam, you've got twenty minutes to draw your tree and to evaluate it so by all means plan it first of all and think about the different options but you haven't got time to do a rough tree first. This is a skill that you need to
practice, one of my students said to me the other day this was the tree that was going to be neat, it wasn't the first one that he'd ever done and it wasn't neat, you need to make sure that you're practicing these because as you do things you get much better at them
and they'll start to look and flow much easier. So as you can see
then what I've done here is I've started to
draw up my decision tree and I've started with a square in the
middle because I'm making a decision about whether or not Gym Bunnies should
be expanding the club.

Option 1 then is deciding that they are
not going to have an expansion so it's going to be no expansion, here it
was quite explicit that no expansion was an option, but you
should remember even if it's not clear that the company always has an option
to do nothing, but there probably will be
repercussions as there were here which is that membership numbers are
going to fall. So I've labeled my branch then that its no
expansion and option 1 and then at the end I
have worked out how much that's going to
lead to as total contribution for the year. So we've got our price then which is
going to be 640 and we've got 5,250 members and you can see there that's
going to lead to us to 3.36 million for the year, and by leaving plenty of space it's very
clear for the marker to see that that's what I wanted to achieve here.

So start with the easy branch first of all and
then go onto the more complicated one which is option 2 here which is to expand. The revenue is constant then at 720 per member but the uncertainty is based around both
the membership numbers and also the costs. What you can see is that I've labelled from my option 2, I've labelled the
branches with the number of members and then I've got another circle for
another outcome something else which the company can't control so they're not making
a decision here which is going to be the cost of either
120 dollars per member or 180 dollars per member. And I work all the way through my
branches calculating the revenues that are going to be obtained each year
for those members. A methodical approach then is
necessary making sure that you tick off the information in the question once you've used it. Next we're starting to add the probabilities and this is a
very good test about whether or not you've included all of the possible outcomes. So when you label then the probabilities, I use a decimal
because that's what I'm going to multiply my outcomes by to give me the expected
values.

From every outcome then the
probabilities must add up to 1, so there's a 50%
chance then that costs will be 120 and a 50%
chance that costs will be 180 so I therefore know that I've included all of the possible outcomes. If my
probabilities didn't come to 100% I would know that either I had made a
mistake or more likely I had missed out a possible outcome. Sometimes you might not be given the
probabilities of all of the outcomes and you might need to deduce one so if there's a
20% chance of something happening you know that there's an 80% chance of
the other option occurring. Label then all of your
squares and circles next so that you can begin the evaluation,
when we were constructing the tree we worked from left to right and when we're evaluating
it we're going to work from right to left.

So start in the top right corner of your tree
and start to use letters as a way of referring to the different points, and you
can see here then that I've started with A as when I've got
six thousand members and then the outcome about what the
costs are going to be, because I'm now going to evaluate those. Your evaluation should take place on a
separate sheet and you can use those letters to reference clearly to the
points. If you have space and time you can pop
your expected values onto the tree afterwards.

So here you can see then my evaluation of
the tree and I'm working from right to left, so I'm
starting with that point A and working down to my ultimate
decision at the point D. So the expected value then at point A, there's a 50% chance that we're
going to get 3.6 million and a 50% chance of 3.24 million, so there's
different outcomes depending on the level of costs per member, and we can work out then how much that's
going to equate to per annum.

The expected values then at C are going to
take the chances of those membership numbers being 6,000 and membership numbers being 6,500 so we're working backwards to our startpoint multiplying our different outcomes by
the probabilities. Whenever we reach a square then we will
be making a decision, and the decision here to be made at D remember
is whether or not to expand the gym, so there is only one decision
to be made in this question.

The decision then needs to reflect the costs of the
refurbishment as well so what we've got to do now then is to
translate the figures that we've calculated into those for the three years because the
costs of the refurbishment for the expansion
are going to be shared across the three years of result. So you
can see then that option 1 which was to have no expansion over three years is going to lead us to
a result of just over 10 million dollars, whereas option 2 even once we've taken
into consideration the costs and the probabilities of the different
membership numbers and the different outcomes for costs
per member you can see that we've got a
higher expected value of 10.4 million. The final
stage then of answering part A is to very clearly state our decision,
we're not just going to leave our figures dangling there and expect the marker to
interpret them for us, so we can see then that we need to choose
option 2.

So the final mark then available for
stating the decision based on your results. This requirement remember was worth 12
marks and in the examiner's report we saw that many students were able to
achieve this and hopefully they're able to achieve it
within the twenty minutes so they didn't run out of time elsewhere on the paper. They scored well then if they'd used a logical and methodical approach to the question. With part B then it
was a very different story so 6 marks here, not as many marks but we
needed to calculate the maximum price that they should pay to obtain exact information about the impact that this expansion
would have on membership numbers. So this is where we're looking at the
second syllabus of requirement of the value of perfect information. Very few candidates answered this correctly;
it was a very tricky requirement and it needed a logical
approach with good technique and clear layout. In a question like 1b a good technique is to actually leave
it, if you see this question so early on in the exam it's very likely that many students
wouldn't have known what to do with it.

So let's go through the rest of the paper, score lots of marks and come back to this at the end. Having a look then at the
value of perfect information is requiring us to layout and understand what we mean by
perfect information. So what we going to assume when we're doing these calculations in B is that we always make the right
decision, so that's what we mean by perfect information. So what we have to decide is what decision
would we make in certain circumstances. Well what decision
would we make if the membership numbers were going to
be (a) 6,000 or (b) 6500 If they were going to be 6,000 option 1 over the three years gave us 10.08 million whereas option 2, by the time we
taken into consideration the cost of the refurbishment would have only given us an expected
value of 9.9 million. So if the gym owners knew that membership
numbers would only rise by 750 as a result of the expansion then they would have decided not to go
ahead with the expansion and actually to pursue option 1.

If however in option B the
membership numbers were going to be 6.500 so that was the second possibility then we
can see that option 2 is higher because it gives us an
expected value of 10.755 million. So our expected value if we always make
the right decision is that if membership numbers are
going to be 6000 we'd actually choose no expansion and so
there's a 40% chance of that happening so we need to multiply the 0.4 by the 10.08 million that we would have
received from no expansion, and we need to add that to the 60% chance of membership numbers being 6,500 and us have chosen the expansion. And what you can see here then is that we end up
with an expected value 10.485 million. So what is the value of our perfect
information, how much should we pay for it? Well it's the difference between the
expected value with the perfect information and the expected value without it
which is what we calculated in part A, and what you can see here is the
maximum that they'd be prepared to pay is $72,000. Good layout then is important when you're doing
something like this, so we're going to have the value of perfect information as the difference between the expected
value with it and the expected value without it.

In reality perfect information is not
likely to be 100% correct, or any information that
we can get is not likely to be 100% correct
it's more likely to be a best indication, so for example if
you're going to have a barbecue or you wanted to have a barbecue at the weekend you might consult the weather
forecast before deciding whether or not it's a good idea. Now it will give you a good indication of
whether or not it's going to rain but it doesn't claim to be 100% correct.

Calculating the values then when we've got
imperfect information is more time consuming and its unlikely to be tested at F5 because of the amount of
marks that would need to be awarded for it. If it is though it's just more complex
way of the same calculations that we've already been doing. The final part of this requirement then in
Part C was discussing the problems of using expected values for decisions of this nature, although it
was part C I think that a good exam technique
would be to answer this before you started to draw your decision tree and definitely before you did part B.
These are easy straightforward knowledge marks
that you should be looking to try and pick up at the beginning of the paper because you can
highlight them during the reading time. The biggest danger here would have been
spending too much time on this and failing to notice that it was only
worth 2 marks because if you wrote reams and reams
here you are going to be capped at 2 marks and you're going to waste valuable time that you could of needed elsewhere. So we're looking at knowledge marks here, so expected values then are most suitable for repeated decisions.

Well clearly GB are only going to be making the decision about whether or not to do this expansion once. Secondly the probabilities are
hard to estimate, we haven't got a crystal ball and there is some uncertainty here about
what's going to happen to the membership numbers beyond which
we've reflected in our tree. Also expected value is suitable for investors then who have a risk mutual
attitude to risk we don't know what the
attitude to risk of the managers of GB is. So definitely would recommend doing part
C first, nice and straight forward but making sure that you highlight 2 marks and
make sure that you cap yourself at 2 points.

I hope that you found this presentation
useful, if you want more information you can consult the Student Accountant
archives and there's an article in there from
January 2013 called decision trees which has been
written by a member of the F5 examining team. You'll also find articles on questions
and explanations for you to practice in your approved study text or question
bank. Good luck with your F5 exam, thank you
for listening..

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