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..