this is a lecture from open tuition to benefit from the lecture you should download the free lecture notes from open tuition comm this is the final lecture on cash management chapter 6 of the free lecture notes and in this lecture I want to explain the Miller or which there can be some calculations which I come to but more important is understanding what the idea is and I think you agree the idea is I think very sensible what is is this that obviously and from day to day my cash balance will be changing you know some days I receive a lot of money from receivables the cash balance gets very high other days I'm paying odds of expense isn't the cash balance gets very low now we already know we don't want to hire cash balance if we got same I have to have surplus cash this week it would make sense to put it on short term deposit to be earning some interest but then other weeks I'm getting lower cash I'll take the cash back and the son of way works is this if I did a graph over time I'll do cash budgets and I think maybe maybe on average not to be safe I need 10,000 in the bank so I might start with 10,000 and maybe over the next few days or weeks and receiving lots of cash and a balance is going up well my body said we don't want too much cash in the current account is wasting money but he don't deposit so I'll set myself an upper limit I might say oh if ever it is it gets as 18,000 are making up figures here but if every gets as high as 18,000 then I'll put money on deposit safe got to 18,000 what I'll do is output 8,000 on deposit and the balance so that the balance goes back to 10,000 that's our mailing some interest and maybe over the following few weeks our carry on receiving more money and it carries on going up again but again as soon as it hits this limit up put on it of 18,000 again we'll put 8,000 on deposit it goes back down to 10 and have now 16,000 octopus's however maybe the next few weeks I've got a lot of expenses and the cash balance starts falling off I'm got money falling a bit but I'll set a bottom limit talk about how am i set my limits later but suppose I've set a bottom limit of Oh 7000 because you know i dint let it drop below 7 I've done my cash budgets and I reckon we got at least seven overtime and so as soon as it drops to seven then I'll take money back from deposit I'll take 3000 from deposit so that it goes back to 10,000 and we carry on like that they don't have a set these limits if ever it takes 18,000 and put on deposit to go back to 10 if every gets as low as 7th I take back from deposit again he goes back to ten some forever putting on the positive taking away which of course these days with internet banking is it's easy enough you know almost every day you could put money on deposit or take money off deposit and in that way you're making the best use of them and you are earning interest those limits for very obvious reasons the eighteen thousand in my example would call the upper limit the seven thousand we call the lower limit and finally the ten thousand in my example we call the return point so that's what men are all are suggesting I say again I think that is very sensible indeed however they went further suggesting how we went about calculating these other loan limits and the return point first of all the lower limit the lower limit so there's no formula for it for it it depends on the business having done the cash budgets the lower limit is the absolute minimum they dare operate with so that is decided by the business there's no ruler so every company's different I'm a very small company ups my lower limit is just one or two thousand a huge company then I said a lower limit at fifty thousand and some Peaks whatever from their budgets they think they need the minimum they don't have to keep operating and that would be given you in the economic there any numbers you would be told what the lower limit is as far as the upper limit is concerned the other limit is the lower limit which again and you would be told plus what we call the spread and a spread there is a formula for and I've typed it just of an example three the spread is this formula three times 3/4 times transaction cost times variance of cash flows and divided by the interest rate ^ third now I'll explain what each of those terms means in a moment you can see quite a messy formula that former though is given in the exam I'll show you how it calculates what those figures mean in a minute with the example but lower limit you'll be told in practices up to the company to decide upper limit you calculate the spread using the formula you add it to the lower limit and finally the return point again I've typed it out there but it's the lower limit switch again you'll be given plus one-third of the spread and again you are given that for me I think the exam so these two you're given you just need them to use them the lower limit it'll be given in the question the only extra thing you need to remember is the upper limit lower limit plus the spread so let's have a look look at example 3 a company has decided it needs a minimum balance of 10,000 so straightaway that is the lower limit the transaction cost of making transfers to and from deposit is five dollars so that's not be talking about in the formula every time you move to and from deposit the sign to be a cost involved well the firm the form is the transaction cost each time which in our example is five dollars the standard deviation of cash flows is 2,000 per day now this is very annoying because although some of you at school or at university may have heard of the standard deviation in May they have no nothing fact in paper before the follow on paper you cannot be expected to calculate a standard deviation and to know me to explain now really would be wasting your time basically what it's measuring is obviously your cash flows we've already said will change from day to day yeah think back to my graphs sometimes they get hung here sometimes to get lower the standard deviation measures the extent of how much higher and lower they get so you see if my cash who was always about 10,000 and only went up and down a little bit the standard deviation would be very low if on the other hand my cash on average is 10,000 but sometimes it's a lot higher than sometimes a lot lower the standard deviation is a lot higher but again calculating it is not in the syllabus if he does ask this you would be given it however and this is even more annoying the formula has variance in it well the ver and this if you want to be safe you'd better learn the variance is the standard deviation squared now that isn't given it's very annoying than the examiner you know very standard deviations aren't in the syllabus they're not mentioned anywhere else in bed therefore Nyonya and you're not required to calculate them it's just very annoying therefore it expects you to know that the variance is struggle devotion squared if you only ask the numbers in this way once so whether he does it again like this it may have to be seen in other questions he's actually amended to be easier for you even what actually needed to learn before to use the quarter however to be safe learn that and certainly them that has been tested on and to be safe learn that even have that something irrelevant once finally the interest rate is 5% per annum by zero if you divided by 365 its point zero one four percent per day this is the exact question did some in at asked if he does it like this again if he gives you standard deviation per day he will give you the interest rate per day this is exactly how he set it in the exelon you wouldn't be expected to calculate yourself the daily interest rate having said that now let's stick in all those figures in the formula for the spread the spread is three times 3/4 times the transaction cost as I said a few minutes ago in example 3 it's $5 per transaction times the variance of the cash flows and again as I said a minute ago the variance is the standard deviation squared so x mm squared divided by the interest rate of per day now he'll be very careful you should already be aware from earlier lectures 1% it's the same as point zero one point zero one he said one at percent point one percent is zero point zero zero one point zero one percent is 1/10 of that it's point zero zero zero one now the reason I'm saying that if here the interest rate I've got 1 percent a year the daily rate is point zero one four percent so just as point zero one percent is the same as point zero zero zero one point zero one four percent is the same as point zero zero zero one four finally is to the power one-third and how you do this is up to you and with scientific calculator taking something to the power of third should be easy enough but you should I think be clear from school that something to the power of third is the same as the cubed root of the number so when you're doing this on your calculator in a minute obviously we've got to work out all of this bit when you come to do it to the power of third either use an X to the power Y button on your calculator a third or the scientific calculator you should have a button for like that to get the fume through directly it doesn't matter they're both the same anyway let's do it the middle in the brackets first of all 3/4 times 5 times 2,000 times mm mm squared equals divided by point zero zero zero one four equals a huge number to the power a third so it's the power Y point a third is 3 3 3 3 P P P equals x 3 and I get and it does take some practice with your calculator so make sure I get the spread equal to 14 - 4 9 14 - routing in fact I'm calling 40 to 50 I'm not gonna mess around with one now again you have to do that once in one exam a long time ago in more recent example it's been asked he's told you what the spread is B and you've not actually needed to use the formula but you arguing the formula he could require you to use it and so you'd better make sure you can sort it out on the calculator I mean got the spread it's now easy because remember we set the lower limit I'll always be given the question and it's 10,000 the upper limit 10,000 plus the spread and finally the return point the lower limit ten thousand remember this formula is given the return point the lower limit 10,000 plus 1/3 times the spread which gives us what 14 - 15 divided by 3 is 4 750 plus 10,000 I get 14 and 750 and there we are so I'm not going to walk back to my picture the beginning but we took my 14 750 we're never the Mart is the upper limit of 20 for 250 we've got the difference on deposit so it goes back to 14 750 if ever the bounce drops as low as 10,000 we take the difference from deposit to go back to 14 750 so there we are I think I've said enough about the formula being messy and again practice to be safe but it is these days of mine you'll need to use it more importantly is to learn that and you give them that one this those two formula that you likely to need if he gives you the spread you can get the upper limit of the return point and also appreciate if he gives you the lower limit and the upper limit you can calculate the spread because it's the difference between the two and once you've got the spread the return point season okay so that's it for cash and that's it for the working capital part of the syllabus