this is a lecture from open tuition to benefit from the lecture you should download the free lecture notes from open tuition com all right we're still looking at cash management which is the chapter six of the free lecture notes in the previous lectures first of all I had a chat about the reasons for holding short-term cash in the last lecture I went through the first of the three techniques you're supposed to be aware of which were cash budgets which is certainly very important this ledger is also something called the Bao whole model mr. Bao mole if then did it which I'm not sure I think is terribly practical you'll see what I mean as we go through it I don't really like it but it's in the syllabus although the examiner I think I'm right in saying he saw me ever mentioned it twice in the whole history thing except last ten or fifteen years so it said the least important of the three but for safety we better go through it and as you'll see that there is a formula an old idea it is actually very very similar to the logic we used in inventory control so here if you haven't been through the lectures on mentoring control do because I don't have to explain all the logic all over again but to explain what it is and how we applied next year look at the example - sorry example - next year a company forecasts of cash requirements of 1.5 million that's how much of cash we think we need next year the use being constant throughout the year so you know whatever that divided by 12 is this how much we expect to need each month we've got plenty of investments in investments in excess of this amount which you're earning is known and a half percent a year and so what we're gonna have to do since we need one and a half million we are going to have to sell some of our investment now we are interested 5% of our current account bank balance and the cost of selling investments is 150 dollars per transaction so we know we're gonna have to sell investments to get the cash we need and there's a charge each time every time we sell any investments there's a charge of a hundred fifty and so I'm going to get the cash I need we could sell investments at the beginning of the year of one and a half million we've got enough for the year then if it only cost us 150 in transactions but we'd be losing interest on the whole one and a half million for the whole year and so what might be better is to say well let's sell seven hundred and fifty thousand half the one and a half million every six months because if we sell 750 thousand every six months but okay we're having to sell twice which means paying hundred and fifty dollars twice during the year but we'll only be losing interest on the seven hundred and fifty thousand for the first six months and then of course certain number seven fifty I will have sort of told the one a half million for the second six months but we'll be losing less interest and so on with any number of possibilities how often we sell our investments the more sales we make then the more 150 s we're gonna have to pay tree in the year but the more sales would make the less will be selling each time and so the less interest at 9% will be learn accent we're losing and to show you how it works look at part a suppose we decide to sell 150,000 of investments each time calculate the total cost figure to the company well there are three things we need to consider first of all every time you make a sale now we've got the cost of selling so the selling costs or ago how much will it cost us well it'll be the number of sales we make well we need one and a half million in total if we selling a hundred and fifty thousand each time we'll make ten sales during the year and the cost well times the cost each time which is hundred and fifty so over a year it will cost us one thousand five hundred what else sort of the cost well this done lost interest and what we do is this we say well the first sale we're selling that what is it and forced it oh that's me rub that hapless confuses remember we're selling hundred and fifty thousand each time so we made the first sale and we losing interest on one hundred and fifty thousand but then we sell another hundred and fifty so then with losing interest on a total of three hundred thousand then later we sell another 150 we been losing interest on hundred four hundred fifty thousand and so on and by the end of the year we've ended up selling all one and a half million and we losing interest on the full one and a half million so the beginning we're just losing interest on hundred and fifty by the end when we've got all the money out we're losing interest on one and a half million well we say on average how much are we losing money on so the average withdrawal at the beginning of the year for sale one hundred and fifty thousand to start let's go we're only losing interest on that much by the end of the year we've had ten sales and we're losing interest on the full one and a half million and so the average we're losing interest on average over the year one hundred and fifty plus one and a half million is eight hundred and twenty five thousand and how much interest are we losing nine and a half percent but our investments are currently earning a twenty five nine and a half percent seventy eight thousand three seventy five finally there's one thing which we might call helps us makes things not quite as bad in that every time we sell any investments we the money goes into our current account so what happens you see a little picture over time we sell investments 150 thousand so we've got a hundred and fifty thousand that we can put on our current account and earn interest and we'd use it so as we use it it'll fall to zero then we sell another 150 and we can put not enough current account but it gradually goes down over time and so on well any money in the current account will be earning as interest at 5% and although we've got those two big costs we are going to be earning interest on our current account and the amount will earn you running in 250 but then to zero and to be on average it's as though we're earning interest on 75,000 throughout the year and so to get the net cost of it all the interest earned we're selling hundred and fifty each time so as I just tried to explain our current account balance 750 down to zero backed up to 50 and so on the average in the current account is 150 over to 75 thousand and when earning interest on it in the current account at what was it five percent which reduces the overall cost where of us involved seventy five thousand five percent will earn interest of three 750 so the overall cost of this policy 15 hundred plus 78 375 minus three 750 seventy six thousand 125 per year now that's if we sell hundred and fifty thousand each time but as I said earlier there's any number of possibilities we could sell two hundred thousand each time we sold two hundred thousand each time we need fewer sales so that selling cost of the year a bit lower but on the other hand livings two hundred thousand each time we'd be losing more interest that Custer Buick the thinker's will change and what we want of course is to decide how much should we sell each time to minimize the total cost well just like with inventory control there is a formula and it's actually the same formula at the same basic logic they're the economic quantity to sell each time should he be under the 50 each time should it be 200 each time and so on to give the minimum cost it's the same formula effectively as I say as in better control it's two times well I'm not going to copy the whole formula doctor you've got it two times in the notes two times the annual cash requirement times the cost of ordering the cash the selling costs over the net interest cost of holding cash now rather than write all that down because is typed for our question that may explain what each means two times the annual cash required well for example to the total we require over the year is 1.5 million times the cost of ordering cash well that's the cost of selling our investments each time the cost of selling investments 150 per transaction divided by the net interest cost of holding cash well that means we could be earning on our investments or we are any nine and a half percent so sell the investments and you losing that nine and a half but we can earn 5% in the current account so we say the net interest cost is nine and a half percent or point zero neither half percent is point zero I'm five minus five percent five percent this point zero five so the net interest cost is the difference of four a percent or point zero four five and so what does that give us and again I mentioned in earlier chapter you must have a scientific calculator for the sex and otherwise you could have to mess around because one and half a million won't fit but what does he come to two times 1.5 million times 150 divided by point zero four five equals there 1 to the power 10 or something the square root of that it's 100,000 so about the economic quantity we did it in part a selling over 250 thousand each time the cheapest cost would be to sell a hundred thousand each time Part C says at the eoq you and the economic quantity what is the total cost per year let's check and let's check it is a lot of cost than what we had before again the three costs the selling costs that make sense what we need to make it's one and a half million in total we're selling a hundred thousand each time and so will be fifteen at sales and each time costs a hundred and fifty me and so over a year to two fifty there's the lost interest on our investments and just like before the beginning of the year were only losing interest on a hundred thousand because we've only made that one sale but by the end of the year we're losing interest on the full one and a half million so on average we're losing interest our government had eight hundred thousand we're losing interest at nine and a half percent so the loan lost interest seventy-six thousand finally though although it's that's the interest we losing we are saving a bit the interest on our current account and this time because we're selling over a thousand each time the balance of our current account keeps going between a hundred zero so on average this 50 thousand in the current account and that's earning us yes five percent fifty thousand five percent will receive interest of two thousand five hundred and so what's the net cost if we sell out a thousand each time to two fifty plus seventy six thousand minus to five hundred seventeen fun leave 750 and is that cheaper than what we had before yes it is hundred fifty time was costing seventy six one two five this is only costing 75 750 that doesn't prove this is the best but try any quantity you want 200,000 each time 50,000 each time and so on any other quantity the total cost over the year will be higher the optimum the best quantities so each time is from the formula 100,000 so there we are that's powerful I repeat what I said in the beginning now I'm not sure how practical were these you know quite frankly yes I think so tiny bit certainly for most companies but to be safe you better make sure you're happy with it is an dramatic it's not hard especially if you want to be with inventor of control okay well that's about a while there's one last technique which I'll deal with in the next lecture which is actually I think much more realistic but you'll see something called Miller or