3.3 Decision Making Techniques

hello welcome to 3.3 decision making techniques this is one of the areas of theme three that students find the most difficult mainly because of the the latter three topics in this unit investment appraisal decision trees and critical path analysis they both well all of them require extensive amounts of calculations and can be quite tricky if you don&#39;t come back to them on a regular basis quantitative sales forecasting is the first Topic in this unit and actually if you watch the theme 2 video about sales forecasting I typically teach them very similarly so with Quantum of sales forecasting we&#39;re mainly looking at the the numeracy side of things in terms of sales forecasting so rather than thinking about the the factors that might affect predicting sales we&#39;re looking at the numeric side of things so there&#39;s the correlation between two variables and you would look at that on a scatter diagram and you would be looking at first of all whether there was a positive and negative or no correlation but you&#39;d also be looking at how close to the line of best fit if you do a line of best fit through there how close the line of best fit the data points are because the closer to the line of best fit the stronger the correlation is you would be looking at extrapolation and this is about looking at data that we have and trends that we already have and trying to extrapolate where we think those Trends might continue you can take a lot of that with a Pinter so I mean you look at the example I&#39;ve got on the screen you can see there that sales are increasing you can&#39;t just expect that because they have in the past they&#39;re going to continue to increase forever but there is some relevance to doing this because it can show you the trend that you&#39;re on and certainly if you don&#39;t have any action where things might end up especially useful for when you start to see the sort of downward trend we also have moving averages and smoothing out fluctuations fluctuations and data and the key thing with moving averages in theme three is you could see this as a calculation so you might be asked to calculate a three period or four period moving average my best bit of advice for this it they can be quite tricky and can quite easily catch people out my big bit of advice for moving averages would be to go into the description of this video have a look at the exam question finder and go to 3.3.1 and you&#39;ll see some examples of past paper questions that have asked questions on moving averages that&#39;s the best way to practice this basically the next topic is investment appraisal first of all what is investment appraisal investment appraisal is a way of assessing whether an investment that a business is going to make is a good financial decision so you think about this this is mostly used when there&#39;s when there&#39;s significant Investments at risk and large amounts of money and you want to try and identify the likelihood that it&#39;s going to be successful but also you know how is it going to make its money how quickly is it going to pay back Etc so this would be used if a business was for example maybe buying new Machinery or buying or expansion launching a new Factory or launching a new range of stores or something like that and there&#39;s three methods in investment appraisal we&#39;ve got payback period average rate of return and Net Present Value so payback period is how long it takes for the investment project to recoup the initial cost of the investment in the first place average rate of return that I mean pay-per-view is probably the most easy one to get your head around concept wise average rate of return is how much of the investment cost so how much of the investment that we&#39;ve spent on this project do we get back as profit every year and so hopefully when you see the examples that one will make a little bit more sense but effectively it&#39;s a measure of profitability from a project and then Net Present Value conceptually is probably the trickiest it takes into consideration the fact that money in the future is not worth the same as that same sum of money now so for example if someone came up to you and said you can have a hundred pounds now or you can have 100 pounds in a year&#39;s time you&#39;re better off taking it now because if you have that money now you&#39;ve got the opportunity to do something with it whereas if you don&#39;t receive that money for a year you can&#39;t do anything with it for a year even if you took it and just put it in a bank for a year because of Interest you&#39;d have more money than the 100 pounds in a year&#39;s time and so with that in mind future cash flows so money you&#39;re not going to receive for five years is not worth the same as that money value now you&#39;ll when we get to that part we&#39;ll we&#39;ll talk through that in a bit more detail now we need this table for investment appraisal and we&#39;re going to add a little bit to this table in a short while when we do Net Present Value but for payback period and average rate return this is all we really need and this could be sell out in a few different ways you might not get cash flow you might get cash inflows and outflows and therefore have to work out cash for yourself you might get cash flow given but the general concept here is we&#39;ve got years zero to four year zero means right now like today so the beginning of year one year one means at the end of year one year two means the end year two Etc and then our cash flow is effectively how much money this project has cost us and generated over the course of that year so if we look at year zero in this situation let&#39;s imagine that our project cost us one million pounds these figures are on Thousand so one thousand is one million we put this in Brackets because that shows that&#39;s it that&#39;s an outflow We have basically spent one million pounds on this investment but over the course of the first year we&#39;ve received a cash flow of 100 180 and so that would mean that would be our cash inflows subtract our cash outflows it&#39;s effectively our net cash flow for the project in year two hopefully as time goes on we&#39;ll make a little bit more money from this project as it becomes more established in year two we make 330 000 pounds in year three we make 320 000 pounds in year four we make 460 000 pounds so this cumulative cash flow cumulative just basically means like a running tool so we&#39;re going to start with uh minus one thousand and this is what&#39;s going to allow us to calculate our payback period for our payback period we need to figure out when our cumulative cash flow becomes positive because that&#39;s going to allow us to determine when we&#39;ve received our 1 million pounds back so at the end on year zero we&#39;ve obviously spent 1 000 or 1 million pounds at the end of year one we&#39;re now still in in debt to this project we&#39;re still on minus eight hundred and twenty thousand but we have made 180 000 pounds worth of progress into this I&#39;ve put it in red because at that point it&#39;s quite clear we still haven&#39;t paid back yet we still haven&#39;t recouped the whole one million pounds by the end of year two we&#39;ve generated another 330 000 pounds in cash flow so we would be sitting at negative 490 so we&#39;re just kind of adding these two are tall as we go through so we&#39;re still we still haven&#39;t paid back we&#39;re still in the negatives but we&#39;re closer at the end of year three minus 170 000 so we&#39;re still not there yet but you can see that we&#39;re making progress and then I by time we get to the end of year four we&#39;re into positives so by this point we&#39;ve made our we&#39;ve made our one million pounds back we&#39;ve got a effectively we&#39;ve got a profit on this project of 290 000 pounds and so we&#39;ve reached that payback period not at the end of year three but by the end of year four so we&#39;ve reached it in three years and something and what we need to do is we need to work out what the something is so how do we do that well this is where we&#39;d use that little formula I&#39;ve got on there it&#39;s not the most scientific formula it&#39;s not the easiest one to remember but the the concept of it effectively is is at the end of year three how much money do we still have to make in order to reach that point where we where we hit zero and the answer is 170 so that&#39;s our last negative cumulative cash flow how much do we make the following year so if we need to make 170 during the fourth year to reach payback and we make 460. effectively we&#39;re working out how far into that 460 000 pounds did we reach 170 so if we do the last negative Community cash flow so my so 170 divided by 460 and we times it by 12 reason we Times by 12 is to figure it out in months we should get 170 over 460 times 12 is 4.43 so that means it&#39;s 4.343 months through the third day through the fourth year so the payback period is in three years 4.43 months now that&#39;s again that&#39;s not really a perfect model to be honest because that&#39;s assuming you&#39;re going to make the exact same amount of cash flow at every single month throughout the year which you know isn&#39;t necessarily realistic you&#39;re probably going to get different levels of sales in different months depending on your product and just generally that&#39;s not how business kind of works in reality but it still gives you a bit of a model model so you would look at this and you would you know I guess the key thing here is it depends on how quickly you need the money back if the business is has a cash flow um focus then they may wish to prioritize a quicker payback period that might be the most important thing ultimately I guess the main thing is that it does actually pay back so you could for example have a situation where it doesn&#39;t actually pay back and in which case over the length of the project it&#39;s not actually recouping the investment and obviously from from a start still from a start that&#39;s going to be just a no-brainer you&#39;re not going to bother going with that project the second of these is the average rate of return and this one does have a more kind of clear easy to understand formula but the concept&#39;s a little bit more tricky for this formula we&#39;re looking at the average net profit so we&#39;re going to do net profit divided by the number of years so in this situation that&#39;s going to be 290 000 pounds in net profit the project lasts four years so 280 divided by four and then we&#39;re going to divide that by the investment cost and times about 100 to get a percentage so we should have 290 divided by four divided by a thousand times by 100 gives us a figure of seven point two five percent now what that means is every year of the four years this business makes 7.25 of the initial cost as profit now that&#39;s obviously a good thing because if this figure is positive it means that your project is profitable and you&#39;re getting effectively 7.25 of your initial investment cost each year as profit so over the course of the four years that&#39;s going to add up to 290 000 pounds um but you would if you&#39;re you know you might have a target for this and you would want that that Target&#39;s going to be you want to be pretty high to that Target basically because the higher this is the more profitable your business has become your project has become the final step in Net Present Value which is the one I mentioned earlier about the the consideration of future values of money is net present value and so in order to work out our Net Present Value we basically need to Discount our cash flows what I mean by that is we have to quantify the fact that the money that we receive in four years time is not worth the same as it would be if we had that money now so if we took it if we look at year four year Four&#39;s cash flow is 460 000 pounds what we&#39;re effectively saying here is that 460 000 pounds that we&#39;re gonna receive in four years is not worth as much as if we had four hundred and sixty thousand pounds now because if we had 460 000 pounds now we could invest it we could use it to hopefully turn it into more money so we&#39;re going to apply all of these cash flows by a discount factor and the key thing here is the further away we get from now the less valuable that money is so these discount factors are going to decrease the value of this money more significantly the further away we go from present day so this is our table we&#39;re going to look at a discount factored column and we&#39;re going to add a Net Present Value column we&#39;ll talk about that person value in a minute but for now let&#39;s focus on the discount factors year zero we&#39;re going to go with a one discount Factor that&#39;s today so that money is worth exactly the same so times it by one is effectively times net by 100 percent after a year we&#39;re going to see it&#39;s effectively 90.9 percent of its value so we&#39;re going to times it by 0.909 after two years we&#39;re going to say it&#39;s even less valuable that 330 000 is worth much less than 330 000 it&#39;s worth well effectively 82.6 of that so we&#39;re timesing it by 0.826 after three years 0.751 and after four years 0.683 so you can see there that we are discounting these cash flows by more the further away they are from now because money in a year&#39;s time is more valuable than money in four years time the discount factors are given to you you don&#39;t need to know them you don&#39;t need to memorize them they will be given to you in the exam to be honest if you see them in the exam you know you&#39;re going to have to calculate net present value so there&#39;s the big clue basically if you see that you&#39;re going to have to calculate this and the formula is pretty straightforward you just take your cash flow and you times it by the discount Factor one thing that&#39;s worth really being careful about don&#39;t times your cumulative Cash Flow by this figure times your cash flow by this figure so minus 1000 times by one is going to be minus one thousand 180 times 0.909 is going to be 163.62 so what we&#39;re seeing is that because of that cash flow that 108 000 pounds is in a year&#39;s time it&#39;s not worth 180 000 pounds to US it&#39;s worth the equivalent of 163 620 pounds to US the 330 000 in year two is worth 272 000 and 500 a the year three figure is worth 240.32 and then the year four figure is worth 314.18 now the final answer we need is just by adding these all together so if we add together all these neprising values including the negative we should get a total in this situation of negative 9 300. what that basically means is that this project when you take into consideration that feature cash flows are not worth as much as they are now has an actual has a negative Net Present Value so that might be a reason why a business may not go with this effectively you&#39;re more likely to have a negative Community crash flow if if you don&#39;t make very much of a profit on the project as overall so when it&#39;s discounted that Profit just disappears or potentially if you receive the vast majority of your cash flow really later on in the project so you get most of your money back in the future like quite significantly in the future that&#39;s the case in this one so the the biggest cash flow we get is in year four well year four is also the least valuable cash flow in terms of current value because so far away in the future so in this situation minus 9 300 you know it&#39;s not a huge amount negative but it is still negative and so a business would use those mod those measures to try and identify whether their project is worth doing and so you could see that in a essay question usually going to be on paper three if you see it as an essay question you could see it as a format calculation but make sure you know how to calculate these the best thing about this is if you just change the cash flows like if you change that column of cash flow figures and you start with a negative and then you do some some positive cash flows below that as long as you positive cash flows add up like so years one two three and four as long as they add up to more than the cash flow in year zero then you should be able to work through all of these calculations and so you can practice that as many times as you want but it&#39;s well worth having a look at past exam questions on investment appraisal to get an idea it&#39;s just one of those things where once you&#39;ve gone through the process a few times it&#39;s actually pretty straightforward as a process you just need to know what you&#39;re doing and hopefully this has helped a little bit decision trees and critical path these are the ones that have kind of diagrams to follow so this is the decision tree one&#39;s pretty straightforward actually but you know when you haven&#39;t looked at it for a while it can be quite daunting a decision tree effectively looks like this so we&#39;ve got a series of decisions that a business needs to make and we&#39;ve got the chances of potential outcomes so if we take the the square for example this is the decision and we&#39;ve got three options here we&#39;ve got the new product to launch a new product and that little number underneath that costs that that&#39;s the cost so to launch a new product cost six million pounds we&#39;ve got up entering a new market and that could be like taking an existing product into a new country that&#39;s going to cost eight million pounds you&#39;d expect going into a new country maybe a little bit more expensive and then we&#39;ve always got the option of doing nothing we&#39;ll talk about when that might be useful in a little bit once we&#39;ve done some of these calculations so those are our decisions and when we make these decisions there is a chance that these decisions provide an outcome so with a new product it&#39;s either going to be a success or it&#39;s going to be a failure sometimes you might see three so for example you might see success High success medium success low success but in these ones to just keep it simple on this example and for the benefit of fitting everything onto this this slide and we&#39;ll just do the two so let&#39;s do success and failure so in this situation we have 0.8 success 0.2 failure that represents percentages so that&#39;s effectively an 80 chance of success and a 20 chance of failure the new market is a little bit more risky so we can see that reflected in the fact that there&#39;s a lower chance of success 60 chance of success 40 chance of failure the other thing we need to know though is what this success and failure will actually look like in terms of financial reward so for the new product if we say that success is going to generate 30 million failure is going to generate 4 million for the new market success is going to generate 80 million failure is going to generate 8 million so that&#39;s not too bad the failure it still recoups your your cost but it&#39;s not considered a success whereas with a new product if we fail we actually generate less money than we&#39;ve spent which potentially could be a problem we&#39;ll figure it out there&#39;s two calculations we do here the process is really straightforward we&#39;re going to do them for new product and for the new market so the first is called our expected value and this is effectively when we look at the outcome for a new product for example if we look at the two potential outcomes we want to calculate a weighted average to to identify if we did this in a simulation we did this 100 times what would the average outcome be the expected value of this decision so to do this we just take our outcomes and multiply them by the by the by the probability so 13 times 0.8 is 10.4 4 times 0.2 is 0.8 and if we add them together we get our expected outcome so 11.2 million and what that means basically is that if we did this if we did this 100 times on average we should receive about 11.2 million thing is you&#39;re never actually gonna receive 11.2 million because it&#39;s either going to be a successor it&#39;s going to fail and to be honest you know this is all based on projection anyway so you&#39;re not necessarily going to get 13 million if you are successful you&#39;re not necessarily going to get four million if you fail but it&#39;s it&#39;s you know it&#39;s a it&#39;s a tool for use for decision making it wouldn&#39;t be the only thing you&#39;d use and so we get an expected value of 11.2 million if we make that decision what we haven&#39;t considered though at this point is we haven&#39;t considered the cost so when we calculate our net gain we need to take into consideration the cost so on that gain is just going to be our expected value minus the cost so 11.2 million minus 6 million is 5.2 million so 5.2 million net gain the expectation there is if we choose the new product we should get a net gain on average of 5.2 million pounds after we&#39;ve taken into consideration the cost of this new product so what we want to know basically is whether that net gain is higher than the net gain for the other option the new market option so let&#39;s do the expected value first so that&#39;s going to be 18 times 0.6 is 10.8 8 times 0.4 is 3.2 add them together get us 14 million so that is higher but remember this was more expensive so our net gain is going to be 16 million minus 8 million is 6 million so in this situation our net gain for the new market is higher therefore based on this data alone that would be the better option now that doesn&#39;t necessarily mean it definitely will be the right option doesn&#39;t necessarily mean that&#39;s going to work but that&#39;s what the kind of weighted averages of this data shows and that&#39;s how you do a decision tree and again as I mentioned with investment appraisal if you want to practice this there&#39;s two there&#39;s two options really you could just change the numbers on the one that&#39;s on the screen and give it another give it another go do the calculations or have a look in that exam question finder look at 3.3.3 and see if you can find any practice questions there are some in there obviously on decision trees and give them a go the final Topic in this unit is critical path analysis critical path analysis is effectively looking at a project over a period of time and trying to identify how long each activity in that project takes and how long the entire project is going to take so that we can identify any areas where we maybe couldn&#39;t have delays maybe any areas where we can&#39;t have delays without delaying the entire project so a critical path diagram will look something like this there&#39;s a series of circles a series of lines the key thing to be aware of here is that the activities are the lines not the circles and that&#39;s that&#39;s one of the most common mistakes you see in the critical path is when when people are starting to be introduced to it they think that the circle is the activity the circle is the point between the activities or before in the after an activity so we&#39;re going to number these and these numbers don&#39;t really mean anything other than just allowing us to point to one and say node one node two node three four five six so node one for example that first Circle that is not an activity that&#39;s the point before the next two activities begin so let&#39;s put some some letters to these activities so we&#39;ve got activities A B C D E and F and then the numbers on the other side of the line that&#39;s the duration and let&#39;s say for example this could be in weeks so activity a whatever it is takes three weeks activity B takes one week activity C takes one week D takes two weeks e takes one week F takes one week I&#39;ve kept the numbers really simple for the sake of this example but you could change those numbers to any other numbers and you&#39;d be able to do the same thing so node one is the point before A and B begin node two is the point after B is finished but before c has begun if we go along to the right right to the end node six node six is the point at which f is finished there&#39;s obviously nothing coming after ffs obviously the last activity in this in this project but hopefully you can get a bit of an idea how this all looks so there&#39;s a process we&#39;re going to go through in order to calculate this I&#39;ll explain the theory behind these as well but if you nothing else if you know the process then doing this is actually pretty straightforward so the first step is to calculate the earliest start times and they&#39;re going to go in if you look at our nodes our nodes have got the section on the left which basically says the node number one two three four five six the the other half is split into two kind of corners or two quarters the top quarter that&#39;s where earlier start time is going to go and that basically references the earliest point at which the next activity can start so the earliest start time for the next activity and we&#39;re going to calculate this going left to right we&#39;re going to add as we go and if we&#39;ve got more than one option we&#39;ll see this use the largest tool I&#39;ll explain why women get to one so we&#39;re going to start with zero so I&#39;m going to do these in green just so you can kind of see them easier um if we get to node three you&#39;ll notice that there are two paths to get to node three there&#39;s a and then there&#39;s B and C so we&#39;re going to come back to that because we can&#39;t do that one until we&#39;ve had a look at activity B first so node two the early is the earliest start time for activity c c can&#39;t begin until B is being completed if B takes one week we can&#39;t start see until after one week so we&#39;re going to do left to right we&#39;re gonna add so that is going to be one and then here&#39;s where we&#39;ve got the two options so we&#39;ve got two Pathways to get into node three we&#39;ve got a which takes three weeks and we&#39;ve got B and C which combined take two weeks so one plus one is two we&#39;re going to use the largest tool so we&#39;re gonna put three in there let me explain why that&#39;s the case that number there that number three represents the earliest point at which the next activity can start so it&#39;s the earliest start time for d D can&#39;t begin until both A and C have been completed because A and C feed into that third node well if a takes three weeks and B and C takes two weeks you can&#39;t start D until A&#39;s been finished so you go with the longest one because you can&#39;t start day until both I don&#39;t know what it is it&#39;s a made of example maybe it is really important to doing d so we&#39;re going to use the largest number and then the rest of this is going to be pretty straightforward because there&#39;s no multiples but uh three plus two is five five plus one is six six plus one is seven so what we&#39;ve identified there is that this entire project takes seven weeks so you might have a deadline for this it might be the deadline was eight weeks in which case were great if the deadline was five weeks we&#39;re in a bit of trouble here so the next step is to identify the critical path and the critical path is the longest path to get to the end of the project and what this is is this shows which activities can&#39;t be delayed without delaying the entire thing that&#39;s why these activities are critical it&#39;s critical that they get done on time so the longest path to get us to the end of the project was a d e f B and C went on that because they didn&#39;t contribute to that number seven it was a 3 D2 E1 F1 three plus two plus one plus one we can show this on the graph by just putting these little hash marks on those lines so I mean that&#39;s kind of how you identify that that&#39;s on the critical path what that means is none of those activities can be delayed a d e and f if they&#39;re delayed the entire project delayed so if e for example took three weeks instead of one well that means you&#39;re not gonna be able to start F until eight weeks which means you&#39;re going to finish on nine weeks instead of seven weeks so these can&#39;t be delayed the third the third step to this is to calculate the latest finish times this is probably I think this is the one that students struggle with the most and I understand it because you&#39;ve just been thinking about the start time for the next project you&#39;re not going to think about the finish time for the previous project I guess the key trick is to just do what you&#39;ve did for the earlier start times but in Reverse so we&#39;re going to go from right to left we&#39;re going to subtract and we&#39;re going to use the smallest total so drop the seven you see this in red to make it clear make it easy seven minus one is six six minus one is five five minus two is three and then here we&#39;ve got obviously to get to zero we&#39;ve got two paths going backwards so we&#39;re going to do three minus one is two and then we&#39;ve got two options into getting into node one we&#39;ve got uh three minus three is zero two minus one is one remember we&#39;re going with the smallest note total so we&#39;re gonna go with zero now the trick here or the the hint I guess is that all of the nodes on the critical path which is nodes in this situation one three four five and six they will have the same earlier start time as late and latest finish time because there&#39;s no delaying any of these they&#39;ve got to be right on time whereas node two isn&#39;t on the critical path so there is going to be a difference between the earlier start time the latest finish time in that node what that allows us to do is it allows us to identify whether there is any float time so students can quite often get their head around clinical path analysis but in doing so we&#39;ll forget about the flow time it&#39;s in the same way that students can get their head around break even and then forget about margin of safety and so they think they&#39;ll break even and do but then margin safety comes up and suddenly it&#39;s like hold on I&#39;ve forgotten all about that flow time is that for critical path the flow time is basically the slack time there is for an activity that can be delayed all of the activities on the critical path we&#39;ve already established they can&#39;t be delayed so there&#39;s no flow time and you can do this calculation and you the answer would just be zero so the calculation is just on the bottom right corner there the latest finish time for that activity minus the duration of that activity minus the earliest start time for that Activity The key thing here is you need to take the finish time from the finish of the activity so the end of the activity and then the start time from the start of the activity so if we took for example d the finish time for D is five that red five in in node four the duration is two the start time for node three is three so you do five minus two is three minus three equals zero there&#39;s only two activities on this act on this whole project that can have float time they&#39;re the ones that are critical so we&#39;ve got B and C so let&#39;s calculate the flow time for B and C so B the latest finish time is two that&#39;s at the end of that&#39;s at the finish of B so that node 2 red number so two minus one minus zero two is the latest finish time one is the duration zero is the start time at the start of of B two minus one equals zero is one float so that means there&#39;s one week of flow time so B could be delivered by a week but today is by a week sorry and that would be absolutely fine that wouldn&#39;t affect the long term like deadline of the project C also has a flow time of one three minus one minus one equals one flow time one thing that&#39;s worth bearing in mind here is it&#39;s quite clear about that little section there b and c B and C takes two weeks a takes three weeks so of course they have one float week There&#39;s a they could they could be one delayed if B is delayed by a week C no longer has flow time because if B is divided by a week two plus one is three so if that&#39;s delayed that becomes critical if those activities that have flow time are delayed by more than their flow time or by their flow time they will become critical activities where they can&#39;t be delayed again with that the best thing you can do is do some practice have a look at the questions on past exam papers to be honest with the critical path activities the examples that they give you are pretty linear they&#39;re pretty easy to follow so it&#39;s well worth having a look at those um if you&#39;ve got any questions check them in the comments and uh it goes without saying obviously this is a not a comprehensive recap this is just a bit of a review to just check that you kind of know what you&#39;re talking about and um hopefully you do if you&#39;ve got any questions check them in the comments and check out the other videos um by time you see this one all of theme three will be available and so all theme one two three and four are all linked in the comments so make sure you check them all out as part of your revision um and if you&#39;re preparing for a paper too then have a look at the preparing um four paper two video as well which is also on the channel okay see you next time

hello welcome to 3.3 decision making techniques this is one of the areas of theme three that students find the most difficult mainly because of the the latter three topics in this unit investment appraisal decision trees and critical path analysis they both well all of them require extensive amounts of calculations and can be quite tricky if you don&amp;#39;t come back to them on a regular basis quantitative sales forecasting is the first Topic in this unit and actually if you watch the theme 2 video about sales forecasting I typically teach them very similarly so with Quantum of sales forecasting we&amp;#39;re mainly looking at the the numeracy side of things in terms of sales forecasting so rather than thinking about the the factors that might affect predicting sales we&amp;#39;re looking at the numeric side of things so there&amp;#39;s the correlation between two variables and you would look at that on a scatter diagram and you would be looking at first of all whether there was a positive and negative or no correlation but you&amp;#39;d also be looking at how close to the line of best fit if you do a line of best fit through there how close the line of best fit the data points are because the closer to the line of best fit the stronger the correlation is you would be looking at extrapolation and this is about looking at data that we have and trends that we already have and trying to extrapolate where we think those Trends might continue you can take a lot of that with a Pinter so I mean you look at the example I&amp;#39;ve got on the screen you can see there that sales are increasing you can&amp;#39;t just expect that because they have in the past they&amp;#39;re going to continue to increase forever but there is some relevance to doing this because it can show you the trend that you&amp;#39;re on and certainly if you don&amp;#39;t have any action where things might end up especially useful for when you start to see the sort of downward trend we also have moving averages and smoothing out fluctuations fluctuations and data and the key thing with moving averages in theme three is you could see this as a calculation so you might be asked to calculate a three period or four period moving average my best bit of advice for this it they can be quite tricky and can quite easily catch people out my big bit of advice for moving averages would be to go into the description of this video have a look at the exam question finder and go to 3.3.1 and you&amp;#39;ll see some examples of past paper questions that have asked questions on moving averages that&amp;#39;s the best way to practice this basically the next topic is investment appraisal first of all what is investment appraisal investment appraisal is a way of assessing whether an investment that a business is going to make is a good financial decision so you think about this this is mostly used when there&amp;#39;s when there&amp;#39;s significant Investments at risk and large amounts of money and you want to try and identify the likelihood that it&amp;#39;s going to be successful but also you know how is it going to make its money how quickly is it going to pay back Etc so this would be used if a business was for example maybe buying new Machinery or buying or expansion launching a new Factory or launching a new range of stores or something like that and there&amp;#39;s three methods in investment appraisal we&amp;#39;ve got payback period average rate of return and Net Present Value so payback period is how long it takes for the investment project to recoup the initial cost of the investment in the first place average rate of return that I mean pay-per-view is probably the most easy one to get your head around concept wise average rate of return is how much of the investment cost so how much of the investment that we&amp;#39;ve spent on this project do we get back as profit every year and so hopefully when you see the examples that one will make a little bit more sense but effectively it&amp;#39;s a measure of profitability from a project and then Net Present Value conceptually is probably the trickiest it takes into consideration the fact that money in the future is not worth the same as that same sum of money now so for example if someone came up to you and said you can have a hundred pounds now or you can have 100 pounds in a year&amp;#39;s time you&amp;#39;re better off taking it now because if you have that money now you&amp;#39;ve got the opportunity to do something with it whereas if you don&amp;#39;t receive that money for a year you can&amp;#39;t do anything with it for a year even if you took it and just put it in a bank for a year because of Interest you&amp;#39;d have more money than the 100 pounds in a year&amp;#39;s time and so with that in mind future cash flows so money you&amp;#39;re not going to receive for five years is not worth the same as that money value now you&amp;#39;ll when we get to that part we&amp;#39;ll we&amp;#39;ll talk through that in a bit more detail now we need this table for investment appraisal and we&amp;#39;re going to add a little bit to this table in a short while when we do Net Present Value but for payback period and average rate return this is all we really need and this could be sell out in a few different ways you might not get cash flow you might get cash inflows and outflows and therefore have to work out cash for yourself you might get cash flow given but the general concept here is we&amp;#39;ve got years zero to four year zero means right now like today so the beginning of year one year one means at the end of year one year two means the end year two Etc and then our cash flow is effectively how much money this project has cost us and generated over the course of that year so if we look at year zero in this situation let&amp;#39;s imagine that our project cost us one million pounds these figures are on Thousand so one thousand is one million we put this in Brackets because that shows that&amp;#39;s it that&amp;#39;s an outflow We have basically spent one million pounds on this investment but over the course of the first year we&amp;#39;ve received a cash flow of 100 180 and so that would mean that would be our cash inflows subtract our cash outflows it&amp;#39;s effectively our net cash flow for the project in year two hopefully as time goes on we&amp;#39;ll make a little bit more money from this project as it becomes more established in year two we make 330 000 pounds in year three we make 320 000 pounds in year four we make 460 000 pounds so this cumulative cash flow cumulative just basically means like a running tool so we&amp;#39;re going to start with uh minus one thousand and this is what&amp;#39;s going to allow us to calculate our payback period for our payback period we need to figure out when our cumulative cash flow becomes positive because that&amp;#39;s going to allow us to determine when we&amp;#39;ve received our 1 million pounds back so at the end on year zero we&amp;#39;ve obviously spent 1 000 or 1 million pounds at the end of year one we&amp;#39;re now still in in debt to this project we&amp;#39;re still on minus eight hundred and twenty thousand but we have made 180 000 pounds worth of progress into this I&amp;#39;ve put it in red because at that point it&amp;#39;s quite clear we still haven&amp;#39;t paid back yet we still haven&amp;#39;t recouped the whole one million pounds by the end of year two we&amp;#39;ve generated another 330 000 pounds in cash flow so we would be sitting at negative 490 so we&amp;#39;re just kind of adding these two are tall as we go through so we&amp;#39;re still we still haven&amp;#39;t paid back we&amp;#39;re still in the negatives but we&amp;#39;re closer at the end of year three minus 170 000 so we&amp;#39;re still not there yet but you can see that we&amp;#39;re making progress and then I by time we get to the end of year four we&amp;#39;re into positives so by this point we&amp;#39;ve made our we&amp;#39;ve made our one million pounds back we&amp;#39;ve got a effectively we&amp;#39;ve got a profit on this project of 290 000 pounds and so we&amp;#39;ve reached that payback period not at the end of year three but by the end of year four so we&amp;#39;ve reached it in three years and something and what we need to do is we need to work out what the something is so how do we do that well this is where we&amp;#39;d use that little formula I&amp;#39;ve got on there it&amp;#39;s not the most scientific formula it&amp;#39;s not the easiest one to remember but the the concept of it effectively is is at the end of year three how much money do we still have to make in order to reach that point where we where we hit zero and the answer is 170 so that&amp;#39;s our last negative cumulative cash flow how much do we make the following year so if we need to make 170 during the fourth year to reach payback and we make 460. effectively we&amp;#39;re working out how far into that 460 000 pounds did we reach 170 so if we do the last negative Community cash flow so my so 170 divided by 460 and we times it by 12 reason we Times by 12 is to figure it out in months we should get 170 over 460 times 12 is 4.43 so that means it&amp;#39;s 4.343 months through the third day through the fourth year so the payback period is in three years 4.43 months now that&amp;#39;s again that&amp;#39;s not really a perfect model to be honest because that&amp;#39;s assuming you&amp;#39;re going to make the exact same amount of cash flow at every single month throughout the year which you know isn&amp;#39;t necessarily realistic you&amp;#39;re probably going to get different levels of sales in different months depending on your product and just generally that&amp;#39;s not how business kind of works in reality but it still gives you a bit of a model model so you would look at this and you would you know I guess the key thing here is it depends on how quickly you need the money back if the business is has a cash flow um focus then they may wish to prioritize a quicker payback period that might be the most important thing ultimately I guess the main thing is that it does actually pay back so you could for example have a situation where it doesn&amp;#39;t actually pay back and in which case over the length of the project it&amp;#39;s not actually recouping the investment and obviously from from a start still from a start that&amp;#39;s going to be just a no-brainer you&amp;#39;re not going to bother going with that project the second of these is the average rate of return and this one does have a more kind of clear easy to understand formula but the concept&amp;#39;s a little bit more tricky for this formula we&amp;#39;re looking at the average net profit so we&amp;#39;re going to do net profit divided by the number of years so in this situation that&amp;#39;s going to be 290 000 pounds in net profit the project lasts four years so 280 divided by four and then we&amp;#39;re going to divide that by the investment cost and times about 100 to get a percentage so we should have 290 divided by four divided by a thousand times by 100 gives us a figure of seven point two five percent now what that means is every year of the four years this business makes 7.25 of the initial cost as profit now that&amp;#39;s obviously a good thing because if this figure is positive it means that your project is profitable and you&amp;#39;re getting effectively 7.25 of your initial investment cost each year as profit so over the course of the four years that&amp;#39;s going to add up to 290 000 pounds um but you would if you&amp;#39;re you know you might have a target for this and you would want that that Target&amp;#39;s going to be you want to be pretty high to that Target basically because the higher this is the more profitable your business has become your project has become the final step in Net Present Value which is the one I mentioned earlier about the the consideration of future values of money is net present value and so in order to work out our Net Present Value we basically need to Discount our cash flows what I mean by that is we have to quantify the fact that the money that we receive in four years time is not worth the same as it would be if we had that money now so if we took it if we look at year four year Four&amp;#39;s cash flow is 460 000 pounds what we&amp;#39;re effectively saying here is that 460 000 pounds that we&amp;#39;re gonna receive in four years is not worth as much as if we had four hundred and sixty thousand pounds now because if we had 460 000 pounds now we could invest it we could use it to hopefully turn it into more money so we&amp;#39;re going to apply all of these cash flows by a discount factor and the key thing here is the further away we get from now the less valuable that money is so these discount factors are going to decrease the value of this money more significantly the further away we go from present day so this is our table we&amp;#39;re going to look at a discount factored column and we&amp;#39;re going to add a Net Present Value column we&amp;#39;ll talk about that person value in a minute but for now let&amp;#39;s focus on the discount factors year zero we&amp;#39;re going to go with a one discount Factor that&amp;#39;s today so that money is worth exactly the same so times it by one is effectively times net by 100 percent after a year we&amp;#39;re going to see it&amp;#39;s effectively 90.9 percent of its value so we&amp;#39;re going to times it by 0.909 after two years we&amp;#39;re going to say it&amp;#39;s even less valuable that 330 000 is worth much less than 330 000 it&amp;#39;s worth well effectively 82.6 of that so we&amp;#39;re timesing it by 0.826 after three years 0.751 and after four years 0.683 so you can see there that we are discounting these cash flows by more the further away they are from now because money in a year&amp;#39;s time is more valuable than money in four years time the discount factors are given to you you don&amp;#39;t need to know them you don&amp;#39;t need to memorize them they will be given to you in the exam to be honest if you see them in the exam you know you&amp;#39;re going to have to calculate net present value so there&amp;#39;s the big clue basically if you see that you&amp;#39;re going to have to calculate this and the formula is pretty straightforward you just take your cash flow and you times it by the discount Factor one thing that&amp;#39;s worth really being careful about don&amp;#39;t times your cumulative Cash Flow by this figure times your cash flow by this figure so minus 1000 times by one is going to be minus one thousand 180 times 0.909 is going to be 163.62 so what we&amp;#39;re seeing is that because of that cash flow that 108 000 pounds is in a year&amp;#39;s time it&amp;#39;s not worth 180 000 pounds to US it&amp;#39;s worth the equivalent of 163 620 pounds to US the 330 000 in year two is worth 272 000 and 500 a the year three figure is worth 240.32 and then the year four figure is worth 314.18 now the final answer we need is just by adding these all together so if we add together all these neprising values including the negative we should get a total in this situation of negative 9 300. what that basically means is that this project when you take into consideration that feature cash flows are not worth as much as they are now has an actual has a negative Net Present Value so that might be a reason why a business may not go with this effectively you&amp;#39;re more likely to have a negative Community crash flow if if you don&amp;#39;t make very much of a profit on the project as overall so when it&amp;#39;s discounted that Profit just disappears or potentially if you receive the vast majority of your cash flow really later on in the project so you get most of your money back in the future like quite significantly in the future that&amp;#39;s the case in this one so the the biggest cash flow we get is in year four well year four is also the least valuable cash flow in terms of current value because so far away in the future so in this situation minus 9 300 you know it&amp;#39;s not a huge amount negative but it is still negative and so a business would use those mod those measures to try and identify whether their project is worth doing and so you could see that in a essay question usually going to be on paper three if you see it as an essay question you could see it as a format calculation but make sure you know how to calculate these the best thing about this is if you just change the cash flows like if you change that column of cash flow figures and you start with a negative and then you do some some positive cash flows below that as long as you positive cash flows add up like so years one two three and four as long as they add up to more than the cash flow in year zero then you should be able to work through all of these calculations and so you can practice that as many times as you want but it&amp;#39;s well worth having a look at past exam questions on investment appraisal to get an idea it&amp;#39;s just one of those things where once you&amp;#39;ve gone through the process a few times it&amp;#39;s actually pretty straightforward as a process you just need to know what you&amp;#39;re doing and hopefully this has helped a little bit decision trees and critical path these are the ones that have kind of diagrams to follow so this is the decision tree one&amp;#39;s pretty straightforward actually but you know when you haven&amp;#39;t looked at it for a while it can be quite daunting a decision tree effectively looks like this so we&amp;#39;ve got a series of decisions that a business needs to make and we&amp;#39;ve got the chances of potential outcomes so if we take the the square for example this is the decision and we&amp;#39;ve got three options here we&amp;#39;ve got the new product to launch a new product and that little number underneath that costs that that&amp;#39;s the cost so to launch a new product cost six million pounds we&amp;#39;ve got up entering a new market and that could be like taking an existing product into a new country that&amp;#39;s going to cost eight million pounds you&amp;#39;d expect going into a new country maybe a little bit more expensive and then we&amp;#39;ve always got the option of doing nothing we&amp;#39;ll talk about when that might be useful in a little bit once we&amp;#39;ve done some of these calculations so those are our decisions and when we make these decisions there is a chance that these decisions provide an outcome so with a new product it&amp;#39;s either going to be a success or it&amp;#39;s going to be a failure sometimes you might see three so for example you might see success High success medium success low success but in these ones to just keep it simple on this example and for the benefit of fitting everything onto this this slide and we&amp;#39;ll just do the two so let&amp;#39;s do success and failure so in this situation we have 0.8 success 0.2 failure that represents percentages so that&amp;#39;s effectively an 80 chance of success and a 20 chance of failure the new market is a little bit more risky so we can see that reflected in the fact that there&amp;#39;s a lower chance of success 60 chance of success 40 chance of failure the other thing we need to know though is what this success and failure will actually look like in terms of financial reward so for the new product if we say that success is going to generate 30 million failure is going to generate 4 million for the new market success is going to generate 80 million failure is going to generate 8 million so that&amp;#39;s not too bad the failure it still recoups your your cost but it&amp;#39;s not considered a success whereas with a new product if we fail we actually generate less money than we&amp;#39;ve spent which potentially could be a problem we&amp;#39;ll figure it out there&amp;#39;s two calculations we do here the process is really straightforward we&amp;#39;re going to do them for new product and for the new market so the first is called our expected value and this is effectively when we look at the outcome for a new product for example if we look at the two potential outcomes we want to calculate a weighted average to to identify if we did this in a simulation we did this 100 times what would the average outcome be the expected value of this decision so to do this we just take our outcomes and multiply them by the by the by the probability so 13 times 0.8 is 10.4 4 times 0.2 is 0.8 and if we add them together we get our expected outcome so 11.2 million and what that means basically is that if we did this if we did this 100 times on average we should receive about 11.2 million thing is you&amp;#39;re never actually gonna receive 11.2 million because it&amp;#39;s either going to be a successor it&amp;#39;s going to fail and to be honest you know this is all based on projection anyway so you&amp;#39;re not necessarily going to get 13 million if you are successful you&amp;#39;re not necessarily going to get four million if you fail but it&amp;#39;s it&amp;#39;s you know it&amp;#39;s a it&amp;#39;s a tool for use for decision making it wouldn&amp;#39;t be the only thing you&amp;#39;d use and so we get an expected value of 11.2 million if we make that decision what we haven&amp;#39;t considered though at this point is we haven&amp;#39;t considered the cost so when we calculate our net gain we need to take into consideration the cost so on that gain is just going to be our expected value minus the cost so 11.2 million minus 6 million is 5.2 million so 5.2 million net gain the expectation there is if we choose the new product we should get a net gain on average of 5.2 million pounds after we&amp;#39;ve taken into consideration the cost of this new product so what we want to know basically is whether that net gain is higher than the net gain for the other option the new market option so let&amp;#39;s do the expected value first so that&amp;#39;s going to be 18 times 0.6 is 10.8 8 times 0.4 is 3.2 add them together get us 14 million so that is higher but remember this was more expensive so our net gain is going to be 16 million minus 8 million is 6 million so in this situation our net gain for the new market is higher therefore based on this data alone that would be the better option now that doesn&amp;#39;t necessarily mean it definitely will be the right option doesn&amp;#39;t necessarily mean that&amp;#39;s going to work but that&amp;#39;s what the kind of weighted averages of this data shows and that&amp;#39;s how you do a decision tree and again as I mentioned with investment appraisal if you want to practice this there&amp;#39;s two there&amp;#39;s two options really you could just change the numbers on the one that&amp;#39;s on the screen and give it another give it another go do the calculations or have a look in that exam question finder look at 3.3.3 and see if you can find any practice questions there are some in there obviously on decision trees and give them a go the final Topic in this unit is critical path analysis critical path analysis is effectively looking at a project over a period of time and trying to identify how long each activity in that project takes and how long the entire project is going to take so that we can identify any areas where we maybe couldn&amp;#39;t have delays maybe any areas where we can&amp;#39;t have delays without delaying the entire project so a critical path diagram will look something like this there&amp;#39;s a series of circles a series of lines the key thing to be aware of here is that the activities are the lines not the circles and that&amp;#39;s that&amp;#39;s one of the most common mistakes you see in the critical path is when when people are starting to be introduced to it they think that the circle is the activity the circle is the point between the activities or before in the after an activity so we&amp;#39;re going to number these and these numbers don&amp;#39;t really mean anything other than just allowing us to point to one and say node one node two node three four five six so node one for example that first Circle that is not an activity that&amp;#39;s the point before the next two activities begin so let&amp;#39;s put some some letters to these activities so we&amp;#39;ve got activities A B C D E and F and then the numbers on the other side of the line that&amp;#39;s the duration and let&amp;#39;s say for example this could be in weeks so activity a whatever it is takes three weeks activity B takes one week activity C takes one week D takes two weeks e takes one week F takes one week I&amp;#39;ve kept the numbers really simple for the sake of this example but you could change those numbers to any other numbers and you&amp;#39;d be able to do the same thing so node one is the point before A and B begin node two is the point after B is finished but before c has begun if we go along to the right right to the end node six node six is the point at which f is finished there&amp;#39;s obviously nothing coming after ffs obviously the last activity in this in this project but hopefully you can get a bit of an idea how this all looks so there&amp;#39;s a process we&amp;#39;re going to go through in order to calculate this I&amp;#39;ll explain the theory behind these as well but if you nothing else if you know the process then doing this is actually pretty straightforward so the first step is to calculate the earliest start times and they&amp;#39;re going to go in if you look at our nodes our nodes have got the section on the left which basically says the node number one two three four five six the the other half is split into two kind of corners or two quarters the top quarter that&amp;#39;s where earlier start time is going to go and that basically references the earliest point at which the next activity can start so the earliest start time for the next activity and we&amp;#39;re going to calculate this going left to right we&amp;#39;re going to add as we go and if we&amp;#39;ve got more than one option we&amp;#39;ll see this use the largest tool I&amp;#39;ll explain why women get to one so we&amp;#39;re going to start with zero so I&amp;#39;m going to do these in green just so you can kind of see them easier um if we get to node three you&amp;#39;ll notice that there are two paths to get to node three there&amp;#39;s a and then there&amp;#39;s B and C so we&amp;#39;re going to come back to that because we can&amp;#39;t do that one until we&amp;#39;ve had a look at activity B first so node two the early is the earliest start time for activity c c can&amp;#39;t begin until B is being completed if B takes one week we can&amp;#39;t start see until after one week so we&amp;#39;re going to do left to right we&amp;#39;re gonna add so that is going to be one and then here&amp;#39;s where we&amp;#39;ve got the two options so we&amp;#39;ve got two Pathways to get into node three we&amp;#39;ve got a which takes three weeks and we&amp;#39;ve got B and C which combined take two weeks so one plus one is two we&amp;#39;re going to use the largest tool so we&amp;#39;re gonna put three in there let me explain why that&amp;#39;s the case that number there that number three represents the earliest point at which the next activity can start so it&amp;#39;s the earliest start time for d D can&amp;#39;t begin until both A and C have been completed because A and C feed into that third node well if a takes three weeks and B and C takes two weeks you can&amp;#39;t start D until A&amp;#39;s been finished so you go with the longest one because you can&amp;#39;t start day until both I don&amp;#39;t know what it is it&amp;#39;s a made of example maybe it is really important to doing d so we&amp;#39;re going to use the largest number and then the rest of this is going to be pretty straightforward because there&amp;#39;s no multiples but uh three plus two is five five plus one is six six plus one is seven so what we&amp;#39;ve identified there is that this entire project takes seven weeks so you might have a deadline for this it might be the deadline was eight weeks in which case were great if the deadline was five weeks we&amp;#39;re in a bit of trouble here so the next step is to identify the critical path and the critical path is the longest path to get to the end of the project and what this is is this shows which activities can&amp;#39;t be delayed without delaying the entire thing that&amp;#39;s why these activities are critical it&amp;#39;s critical that they get done on time so the longest path to get us to the end of the project was a d e f B and C went on that because they didn&amp;#39;t contribute to that number seven it was a 3 D2 E1 F1 three plus two plus one plus one we can show this on the graph by just putting these little hash marks on those lines so I mean that&amp;#39;s kind of how you identify that that&amp;#39;s on the critical path what that means is none of those activities can be delayed a d e and f if they&amp;#39;re delayed the entire project delayed so if e for example took three weeks instead of one well that means you&amp;#39;re not gonna be able to start F until eight weeks which means you&amp;#39;re going to finish on nine weeks instead of seven weeks so these can&amp;#39;t be delayed the third the third step to this is to calculate the latest finish times this is probably I think this is the one that students struggle with the most and I understand it because you&amp;#39;ve just been thinking about the start time for the next project you&amp;#39;re not going to think about the finish time for the previous project I guess the key trick is to just do what you&amp;#39;ve did for the earlier start times but in Reverse so we&amp;#39;re going to go from right to left we&amp;#39;re going to subtract and we&amp;#39;re going to use the smallest total so drop the seven you see this in red to make it clear make it easy seven minus one is six six minus one is five five minus two is three and then here we&amp;#39;ve got obviously to get to zero we&amp;#39;ve got two paths going backwards so we&amp;#39;re going to do three minus one is two and then we&amp;#39;ve got two options into getting into node one we&amp;#39;ve got uh three minus three is zero two minus one is one remember we&amp;#39;re going with the smallest note total so we&amp;#39;re gonna go with zero now the trick here or the the hint I guess is that all of the nodes on the critical path which is nodes in this situation one three four five and six they will have the same earlier start time as late and latest finish time because there&amp;#39;s no delaying any of these they&amp;#39;ve got to be right on time whereas node two isn&amp;#39;t on the critical path so there is going to be a difference between the earlier start time the latest finish time in that node what that allows us to do is it allows us to identify whether there is any float time so students can quite often get their head around clinical path analysis but in doing so we&amp;#39;ll forget about the flow time it&amp;#39;s in the same way that students can get their head around break even and then forget about margin of safety and so they think they&amp;#39;ll break even and do but then margin safety comes up and suddenly it&amp;#39;s like hold on I&amp;#39;ve forgotten all about that flow time is that for critical path the flow time is basically the slack time there is for an activity that can be delayed all of the activities on the critical path we&amp;#39;ve already established they can&amp;#39;t be delayed so there&amp;#39;s no flow time and you can do this calculation and you the answer would just be zero so the calculation is just on the bottom right corner there the latest finish time for that activity minus the duration of that activity minus the earliest start time for that Activity The key thing here is you need to take the finish time from the finish of the activity so the end of the activity and then the start time from the start of the activity so if we took for example d the finish time for D is five that red five in in node four the duration is two the start time for node three is three so you do five minus two is three minus three equals zero there&amp;#39;s only two activities on this act on this whole project that can have float time they&amp;#39;re the ones that are critical so we&amp;#39;ve got B and C so let&amp;#39;s calculate the flow time for B and C so B the latest finish time is two that&amp;#39;s at the end of that&amp;#39;s at the finish of B so that node 2 red number so two minus one minus zero two is the latest finish time one is the duration zero is the start time at the start of of B two minus one equals zero is one float so that means there&amp;#39;s one week of flow time so B could be delivered by a week but today is by a week sorry and that would be absolutely fine that wouldn&amp;#39;t affect the long term like deadline of the project C also has a flow time of one three minus one minus one equals one flow time one thing that&amp;#39;s worth bearing in mind here is it&amp;#39;s quite clear about that little section there b and c B and C takes two weeks a takes three weeks so of course they have one float week There&amp;#39;s a they could they could be one delayed if B is delayed by a week C no longer has flow time because if B is divided by a week two plus one is three so if that&amp;#39;s delayed that becomes critical if those activities that have flow time are delayed by more than their flow time or by their flow time they will become critical activities where they can&amp;#39;t be delayed again with that the best thing you can do is do some practice have a look at the questions on past exam papers to be honest with the critical path activities the examples that they give you are pretty linear they&amp;#39;re pretty easy to follow so it&amp;#39;s well worth having a look at those um if you&amp;#39;ve got any questions check them in the comments and uh it goes without saying obviously this is a not a comprehensive recap this is just a bit of a review to just check that you kind of know what you&amp;#39;re talking about and um hopefully you do if you&amp;#39;ve got any questions check them in the comments and check out the other videos um by time you see this one all of theme three will be available and so all theme one two three and four are all linked in the comments so make sure you check them all out as part of your revision um and if you&amp;#39;re preparing for a paper too then have a look at the preparing um four paper two video as well which is also on the channel okay see you next time

Transcript for:3.3 Decision Making Techniques

Transcript for:
3.3 Decision Making Techniques