this is a lecture from open tuition to benefit from the lecture you should download the free lecture notes from open tuition calm ok this lecture is on chapter nine of the free lecture notes which is headed up discounted cash flow further aspects and in this chapter there are three special situations you could have to deal with in the exam which all have their own each of them has its own special technique but they aren't completely separate there's something called capital rationing something called replacement to something called lease ursus by but because they are completely separate there are three separate lectures which would seem logical and this first one is on capital rationing and to explain what we mean by that and how we approach it in the terminology related to it can you turn straight to example 1 on the second page well look at it with me it says the company has the following 4 projects available ABCD for each of them you've got the cash flows a project a and outflow of 500 and then an inflow of 221 a year for three years and here I've calculated the MPD's for you at a cost of capital of 10% now there we are a gives an MPB of 50 B 57 C 30 60 50 now can they exam the examiner could if you wanted to make the question a bit longer by half you calculate the mtv's but we don't to do that you know that's not a copy the rustling problem all it would do would take a bit longer my MPVs are correct so don't go wasting time checking me however suppose I gave you that my companies got the following four projects available as the cash flows only mpps and suppose there was nothing else forget all the bit below for the minute suppose I gave you that and said what shall we do what should the company do now most people say oh we should do project B why because he gives the highest and PB well no you're making an assumption which isn't there if I told you your can only choose one of those four projects then fine you choose the one with the high step PV which would be B but I didn't say that there are simply four projects are favourable they all give a positive NPV and so if there was no other information you would accept all four projects he'll accept any projects as a positive NPV again I didn't say you had to choose four available if the positive will do four that's fine except for the fact that to do all four how much cash should we need a would need five hundred be we'd need another six hundred see 300 D 400 so to do all four we need to have capital available a five 11 14 1800 he have enough capital available to all four but the problem is look at Part B capital is restricted for some reason we've only talked about why it might happen later but for some reason we've only got 1600 available we can't do all four because there isn't enough cash that would need 1800 so chemical rationing is when there's a limit on the cash available Part A if there is no capital rationing you will do all four projects if we get as much cash as we want if I can get 1800 we'll do all four but our problem is when we come to Part B there's only 1600 available clearly I hope we can't do all four so the question is how am I going to invest the 1,600 to get the best total NPV I also though look at Part B he says to come because restricted to 1600 also says the projects are what we call infinitely divisible but what infinity visible meaningless as I go through a thing you degrees normally a bit impractical PD comes in the exam invent divisible means we can do any fraction of a project for example we could do 50% of a we could do half of a 10% of a 80% of a we allowed to do any fraction of a project it also means that if we do do for example 50% of a we assume it means exactly 50% of the outflow is needed we assume we'll get exactly 50% of the inflows and therefore we'd get 50% of the NPV so again mean is for example if we do 10% of a project remember we can do any fraction if we do do for example 10% it will be 10% of all the cash flows and therefore 10% of the NPV attempts that was an example obviously you know if you do 60% we'll get 60% of the cash flows and 60% of the NPV which again I don't think is most case is terribly practical you know even if you can do a half a project I think it would be unusual to expect to get exactly half the returns a fine you believe them divisible although we can do any fraction of a project we cannot do more than a hundred percent of each project so I can do half of a if I want but we can't do two A's the maximum we can do away is 100% so there's a situation in B the question is again how are we going to invest the 1,600 available so as to get the highest possible MP Li and it's no good just saying oh these look at B it gives us 57 that must be the best the trouble is B needs the biggest outlay of 600 you know it might be better to use our money choosing C C only means half the outlay and it gives more than half the return that's all the approach we have to take is something that if you've done f5 is actually similar to key factor analysis but still we do is this for each project we know how much is needed at time zero the capital at time zero Ami's 500 be neat 600 300 and 400 we know the MPB that will be generated from each 50 57 36 and 50 and because they're divisible we then calculate what MPV would be generated for every dollar invested the net present value per dollar invested a gives us 50 mp3 from that way of 500 well the NPV for every dollar invested is fifty divided by five hundred ten cents point one so for every dollar we protonate and get ten cents what about B we get 57 for an outlay of 600 but dollar is point zero nine five nine and a half cents for C 36 from our way of 300 is 12 cents and finally D 50 from an outlay of 400 the net present value per dollar invested twelve and a half cents we want to invest our money in whichever way gives the biggest NPV and so the best one to go for would be dig and we'll get twelve and a half cents per dollar second best would be seen at 12 cents per dollar third best a at ten cents per dollar and fourth best would be mean now we can go through and decide how we're going to invest the best one is project D so we'll invest as much as we can indeed but remember that most we can invest is a hundred percent of the project so the most we can invest in D is 400 now remember we did sixty hundred available Wheeling West 400 Indy was 1200 remaining what MPP would be generated well since we're investing in a hundred percent of D Oh give him to presenter the NPV the NPV will be 50 I've still got 1200 left we can't invest more in D maximum a hundred percent so we'll go to the one that's next best which is see how much does he need three hundred so I can do all of C will invest three hundred and because we're in all of C the NPV will be 36 how much left we've still 900 left count investing more of C so go to the next best which is a a needs 500 so we can't afford to do all of a 100% as he's reading all the money we'll get 10% the MVD which is 50 we've still 400 left and so of course the counting that's more Rene it'll have to go into the last one B and here of course we can't do all of thee will invest four hundred to do all of the would require six hundred so what we're doing four sixths or two-thirds of B and how much everything will regenerate well B gives us nine and a half cents per dollar and so the envy we will get from B is thirty eight or if you prefer since we're investing in four sixth or two thirds of B we'll get four sixths or two thirds of the NPV which again is 38 so there's how we'll invest and as a result what is the maximum NPV 50:36 1538 174 there is the maximum and PV so I don't know I think that's a straight forward exercise as I've already said the question could be that bit longer by having you do the MPD's first but otherwise and be mean per dollar invested and off we go and one tiny bit of terminology I don't actually like this word but the NPV per dollar invested is also referred to as the profitability index so if there is any mention of profitability index in the exam that's all it means I don't like it because of course with MPD's we'll get cash flows enough profits sounds I think it's a dreadful name to give it anyway there we are except of course that was where we had capital rationing and the projects were infinitely divisible and 174 is the maximum every new energy let me try any of a combination of investing 1600 and the MV will be lower however look at C Part C again we've got capital rationing 1600 available we can't do all four in full but the difference here the projects are not infinitely divisible so this time we can't do fractions of a project each project you either do all of eight hundred percent or you do none of it so what are we going to do here well here there is no what you might call quick way all you can do are the only way we came to it is to list out the various possibilities what I mean is we got kind of food to do a B and C not to take 1100 to 1400 but we obviously can't afford to do D as well because we haven't got enough money alternatively we could choose to do a C and D that would need 500 800 1200 but again we can't do B as well we can afford it we only afford to do three of the projects we can't do all four so another possibility solver we could do a B and D but not seeing we can do B C and D but not a so there we are there are four different what you might call combinations that we can afford to do we can only do three of the projects not all four and whatever's the best of those even whichever gives the biggest total NPV so what are the totals if we do a B and C we have 50 from a 57 from B 36 from C so the total NPV 50 plus 57 plus 36 is 143 if we do a C and D they gives 50 C gives 36d gives 50 so total of one of three sinks a B and D a 50 B 57 C 36 oh sorry a B and D I beg your pardon egg 50:57 D 50 so total of 1 5 7 and the final possibility BCD 57 36 and 50 a total of 1 for free now those are the only four ways we could choose to invest the money whichever's the heist is the best so in fact the best would be one at 5 7 and that's how we should invest ami empty now two things here firstly some people say well I could have spotted them just by looking at it only if you can fine but the danger is in the middle of an exam I think sometimes to look obviously not obvious but the time it takes if you are us this I would list the possibilities you know we're not perfect when you're rushing it may be very easy to miss something and with their uncle certainly wouldn't mean we clear what you were doing you know even if I've missed something here it's obvious what I'm trying to do I don't get most of marks secondly now this worries some people avoid me and is the best how much a capital investment would be required to do a nice five hundred to do B need 600 to do D needs 400 right five six four yes a total of 1500 we have 1600 available other people say well we can see with the other hundred we can't invest the other hundred in projects see because they're not infinite divisible but what's gonna happen to the other hundred now some people say oh budget on deposits and then we can earn interest well fine yes but if that was possible we'd have been told it would effectively have been a fifth investments but there's no mention of being able to do anything else with our money so what about the other hundred well the answer is quite simple one way or another the 1600 available is being borrowed where I were actually going to able to go out and borrow 1600 but even if we've got 1600 already in the bank effectively it's being borrowed from shell as its shell goes money and if we're not going to use it even know where to invest the money they should give it back to the shareholders so you haven't got the money are we going to borrow it well there's not quite in borrowing 1600 when you only need 15 how could you only borrow 1500 I say again even if the money's in the bank it's effectively being borrowed from shelves it's their money and so if you don't need it give it back to share let's give them a dividend so the answer is here don't borrow the other 100 some people ask me is that practical of course it is if I'm if it's just that I'm able to borrow sixteen hundred I think you'd agree is stupid to borrow 1,600 and pay interest if you only need 1500 this misses about gimmick dividends to share list that is true you know companies they don't give all the money to shareholders as dividend normally why because they use the money to expand the company but if they can't find any projects to invest in it shouldn't just sit there with shareholders money when there's nothing to do with it if there's no where to invest them they need the extra hundred stop borrowing from the Sharon was getting back to Cheryl there's to visit alright finally because that's all the arithmetic involved capital rational now why are we copied Russian in the first place you know why is there on the cash available well there are two reasons it could occur the most obvious is what we call hard capital rationing and hard capital rationing is the situation where lenders will not lend us anymore you know daily there's a limit to how much any company is going to be able to borrow and if the most we can borrow is 1600 fun that's hard capital rationing boo-boo the other reason though is actually more common it's called soft cover the rationing and well this is just think about this if you're working and earning a salary and if you wanted to buy a car then I'm sure if you're owning a reasonable salary the bank would lend you money depending on how much you're earning and so both the bank would be prepared to lend you a $20,000 does that mean you're automatically going to borrow $20,000 and buy the biggest car you can or you might well say well the bank will lend me 20 thousand but you know I'm having to pay interest on that I don't want to borrow that much I'll only borrow 15,000 and buy a smaller car that's what normally happens you know I can't believe all of you watching this all go out and borrow as much as you possibly can you would limit yourself and the same comes with companies the company might be able to borrow two thousand four something but they chose to limit the amount to sixteen hundred and if that's the reason it's soft rationing it's where then we can borrow but we have limited the amount we prepared to borrow without that's clear it doesn't affect the arithmetic at all you know the arithmetics are saying whatever the reason for the limits for the capital rationing but the examiner more than one occasion has us to why capital might be Russian Inc rationed rather and he expects you to differentiate explain the hard the soft the two reasons all right we'll ask the first of the three further aspects capital rationing in the next lecture we'll look at the next one which is replacement