this is a lecture from open tuition to benefit from the lecture you should download the free lecture notes from open tuition com this is the second lecture on chapter 9 what you looking at further aspects of discounted cash flow in the last lecture we dealt with capital rationing in this lecture we're looking at something called replacement if I'm just offer a few minutes to explain what it is we're talking about a good example is this it is cars many companies get cars to their employees and of course cars don't last forever and so every soften they have to buy new cars then we place the car so sumer an employee needs a car for a long time effectively forever we're going to replace it periodically and how long should we wait before we give them a new one you know we're not going to wait till it just stops working completely we may decide to give them a new one every four years let's say but why not every three years - every five years and what we need to take into account is if you think about it with cars the older a car gets the more you want me to have to pay running costs repairs and so on and the older a car gets the less you'll be able to sell it for when we come to change it I sort of say money we might say well let's replace this car very often if we replace forgetting new car every you know we're keeping them running costs low the repair bills son would be expensive in the earlier years and of course if we give a new car every year we'll get a high promise when we come to sell it the only downside of course is if you give them a new car every year you are having to pay for the custom a new one every year you know make them wait five years you have to pay out the cost every five years but that's the problem trying to decide you see we need the car effectively forever how often shall we replace it shall we bless every year every two years every three years or whatever look at my example this is a machine a machine cost 72,000 and has a maximum life of three years the running costs eacher as follows first year 72 second year 96 third year 12 the older it is the more expensive it's costing to actually run it the scrub values depends when we come to sell it if we decide to sell after a year we'll get 24,000 but if we wait two years will only get 16 6 and if we're in 3 years we'll only get 9 6 and our question our problem is how often should we replace it because again the longer we wait to wait 3 years the running costs get very high and we get a much lower scrap value I'll show you every place every 1 year the running costs will be a lot lower the scrap value will be a lot higher but we'll be having to spend me 72 thousand a lot more often well there's not really a quick way we've no choice but to cost each of them annulled and we're only concern with the costs we are going to assume that the revenue from the machine will be the same whatever happens you know and I get revenue of 20,000 a year however often I replace all I'm concerned about is which would be the cheapest way of replacing which will be the minimum cost but we no choice but to cost out each of the alternatives I'm going to cost out replace every 2 years when I've done that although I will do every one here every three year this would be a good idea when you see now we do it for every two years it would be a good idea for you to have a go yourself reinvesting every one year and every three years and then check with the lecture however what are the cash flows it will replace every two years the two steps to it step one we calculate the present value of the first machine so easy enough what are the cash flows it is the replays over two years the first machine the last two years we've got the running costs it's 7200 in the first year 9600 in the third a second year sorry we've got the original purchase price 72,000 at times 0 and if we keeping it 2 years will scrap it the sale proceeds after 2 years and if we've kept it 2 years we'll get sixteen thousand six hundred and so the net cash flow each year seventy two thousand seven two hundred an inflow of seven things set to work on the present volume discount in the normal way and it says the cost of capital is fifteen percent and so the discount factors for one year at fifteen percent point eight seven for two years point seven five six and therefore the present values seventy two thousand seven two hundred six two six four five two nine two and watch the signs you know in flow remember we're only looking at effectively the costs of this machine because I want the cheapest cost and so what's the total present value at that first machine seventy two thousand seventy two nine seven two so no problem there that's the first machine but of course the minute we sell that machine in two years time we'll be mined a new machine and we assume the same cash flows keep getting repeated every time I buy a machine it's effectively got a present value 32 slight 972 972 now but it'll be like me 72 972 again in two years time in four years time every two years forever well I want to compare that with perhaps replacing every three years but every three years whatever the present value was it'll be paying that out every three years they're not comparable how can you compare 72 thousand over two years with I don't know maybe eighty thousand every three years we can't so to make them comparable step two we calculate what we pull [Music] the equivalent annual cost now here there is a formula which isn't given on the formula sheet you're gonna have to learn it I hate writing formula out explaining but this is one time when I'll write the formula excuse me we'll do the arithmetic but then afterwards I will it could be then easier then to explain that why we have this formula but the equivalent annual cost is the present value of the first machine divided by the annuity discount factor for the replacement period now obviously I explained what I mean and put the numbers in for this one but although this certainly isn't asked in every exam it always could and so to be safe you'd have better learn this and what it is is this remember we're doing two year replacement here so the present value of the first machine is 72 nine at seven - I'm not vote about rocky's rounded because we're saying isn't it the brackets meant it was a cost what we're going to company equipment annual costs or maybe brackets so 72 denies him - divided by the annuity discount factor for the replacement period well here we're doing two year replacement so it's the two year annuity discount factor at the cost of capital which for this question is 15% so two years at 15% the factor the annuity is one point six two six and so the equivalent annual cost seventy to ninety seven to do 90 by one point six two six he's 44 eight seven eight and we're saying I'll explain to you in one second we're saying that this machine with those cash flows in the question replacing it every two years a fifteen percent would be exactly the same as impressive a attempts as paying out forty four thousand eight seventy eight per year for Evan now as I say I will explain why and I don't you doubt to explain why and they accept but it's awful to learn a formula just because it's there I'm saying that the machine is like paying out 44 878 per year in one year in two years three years four years and so on forever well if I said to you what's the present value of those two it's an annuity just look to 40 for a year for two years the present value you'd multiply by the to be renew atif actor which is one point six two six and it'll give you a present value of seventy to ninety seven to those two years are effectively the same as seventy two thousand at time zero what about the next two years well surely it's a two year annuity it just starts two years later and if I multiply by the annuity factor whether we said to do 972 again but because these are two years later at time three instead of one time for said of two it's seventy two thousand two years later at time 2 and similarly the next two years would be like 72 972 at time four which is what we already said that this machine I said was like hanging out seventy to ninety seven to every two years all I've done is work backwards room ooh and said well effectively it's like paying out forty four eighty seven eight every year and if we can do the same for a one year and three year replacement when you'll be able to compare this is forty-four thousand a year a three year replacement is fifty thousand a year this is cheaper and so on okay well there is no quick way apart from costing them all out and in fact in recent years in the eggs where this has been asked in the exam I think he's on have you had to cost out two cycles here we're going to do three I do really suggest you undergo yourself before you watch the rest of this lecture see what you get and check with me I mean that's your choice our carry-on and I'll do three-year replacement and then one year so the two steps first of all the present value of the first machine well this time we're keeping it for three years so the running costs seven two in the first year 96 in the second twelve thousand in the third the purchase price seventy two thousand at time zero and the scrub proceeds if we're keeping it three years we only scrap at time three and receive 9600 so the net flows seventy two thousand seven 209 at six hundred a net what is it two thousand four hundred the present values multiplied by the discount factors of fifteen percent for one year point eight seven two years point seven five six point six five eight oh dear of dear and so the present values and 200 times 0.8 power email writing seven zero six two six four nine thousand six hundred times point seven five six seven two five eight a two thousand four hundred point six five eight one five seven nine the total present value oh dear sorry press the wrong button seventy two thousand six two six four seven two five eight one five seven million eighty-seven 101 however that's step one and remember it's equivalent therefore to 87,000 every three years than ever the step two to make it comparable the equivalent annual cost the present value of the first cycle the first machine its three-year replacement so divided by the three year annuity factor of 15 percent two point two eight three it's therefore equivalent to 38 one five two per annum forever well before I compare here I wanted to do three it's every two years every three to death and every one year so let's now finally do one year replacement will take many cents step one the present value of the first machine if you only give it one year we've got the running costs for the first year seven two hundred we've got the original cost type-0 seventy two thousand and we've got the scrap the sale proceeds we're selling after one year we get twenty four thousand so now 472 an inflow of the checking year 16 800 the discount factors of 15 percent for one year 0.87 the present values therefore the total present value 57 3 8 4 so it's like night about 57 384 now in one year in two year and so on however we still need step two the equivalent annual cost to get an equivalent amount every year from time one honors the present value of the first machine divided by the one year annuity factor at fifteen percent gives us finally sixty five nine five nine every year while not to infinity all right well I hope my arithmetic is right but now we can make the decision the choice is to replace every year which is like paying out 66,000 every year forever alternatively every two years like paying out forty four thousand every tuning every year rather forever Oh replacing every three years which is like paying thirty eight thousand every year forever any one of those could be the best you know in this particular case the cheapest is thirty eight one five two and therefore we will replace every three years but don't you agree there was no way of knowing in advance we had to check all three and any one of the three could have been the best laughter there we are me again as always his time consuming but once you've got it it's not hard it is very repetitive in the exam as I've said in no recent questions it's not asked that often but it may be for your exams assess if only how do you do it for two I think last time it was do it for two years and three years so it was that bit shorter but which was the cheaper of the two if you are asked to write about it you know what reservations would you have well though you've all the normal reservations that we discussed in an earlier chapter you know the cash flows their estimates and all that sort of thing have you had a couple of big extra reservations here one is that we are assuming that we'll carry on replacing this machine forever you know what if I said we're all the gods need to achieve six years well you either replace every three years and just by twice are you replace every two years and by three times or you replace every neither about six times now but the answer could well be completely different if it's just over a six year period here we're assuming it would be carry on replacing forever a second problem perhaps a silly one but still what about replacing every two and a half years that might eat them we can't do it and you never be asked to do it but you know in real life it might be a better option a final problem but major problem and a huge one is of course we are assuming that as we replace the cash flows keep repeating that's very enlightening when we think about a car similar panchal machine but if you think about a car over the years cars have improved cars these days the running costs tend to be a lot lower than they were 10 or 20 years ago and the same thing happens in the future do you really think that you know in another 10 years cars will still cost the same and have the same running costs in the same scrap values and it's very unlikely tell us more cars and machines become obsolete you know new models appear will we even be able to buy the same machine in ten years time or certainly in ten years time a new machine will have replaced it which could have completely different cash flows so though it's perhaps a neat an idea got huge reservations for a country point of view anyway that was the second of the special techniques there's one more so the last lecture of this chapter will be on the third one lease versus Buy