this is a lecture from open tuition to benefit from the lecture you should download the free lecture notes from open tuition com ok we're now moving on to the second section of the syllabus which is investment appraisal which will always account for a substantial number of the questions in the exam and by measured appraise are we talking about investments in new machines or new projects you know maybe we're thinking of buying a new machine actual coasters half a million we've done estimates as to what returns we expect to get from the machine and its motion of deciding is the Machine worth buying should we accept the new machine or not should we reject it well possibly that may be a choice between two machines which of the two would be the better now everything in this first chapter which I've said methods the basic calculations is revision that from paying that f2 and so I shouldn't need to spend too long I will quickly refine I shouldn't need to spend too long on it there are three methods to be aware of which I'll go through but by far the most important one is discounted cash flow and in this chapter again I just want to go through the basic arithmetic for arriving a discounted cash flow which is exactly the same as in paper f2 I'll explain as we go through where the extra difficulty comes in f9 which isn't the basic mechanics at all now because if you wish not to go through fairly quickly if you didn't do paper 2 or if you've forgotten paper F 2 if anything they're doing here because I'm doing this chapter reasonably quickly if there's anything that you're at all unsure about then go to the paper f2 lectures and watch there where I talk a lot more about why we're doing it but I'm going to here anyway let's make a start as I say by far the most important technic is discounted cash flow or net present values and to hopefully remind you to revise what's involved can you look at example one with me it shouldn't take too long a machine will cost eighty thousand it has an expected life of four years with an anticipated and expected scrap value of ten thousand so the end of four years we expect to sell it for ten thousand the net operating cash inflows each year are as follows 20,000 30,000 40,000 10,000 in each of one year two year three year four year and what we mean by net operating cash inflows is the profits each year in cash terms because discounted cash flow looks at the expected cash flows and I'll explain why afterwards I just want to go through mechanics as to wall but the net cash we expect to generate from our operations into the four years is a size there's a cost of capital of ten percent I'll say a lot more about cost of capital later that in itself is all section of the extent of the syllabus but amazing it means that that's the cost of money that's effectively the interest we're paying but ten percent and we are asked to calculate the net present value in general whether or not it should be accepted well the whole idea behind necklace of values discounted cash flows couldn't be more simple we basically are looking to see over the entire life of the project this do we expect there to be a net cash surplus or a net cash deficit here let me write down the cash flows it's gonna cost 80,000 well the first flow we always say well is now time zero so we'll have a cost of eighty thousand a payment a cash outflow so negative times 0 and then we've got inflows the net cash receipts each year of 20,000 30,000 40,000 10,000 and then an extra cash receipt in the fourth year because at the end of the four years we're going to scrub it and the scrap value that's not the question 10,000 well those are the expected cash flows and were it not for one pretty obvious problem in a minute the decision would be obvious because over the entire life is there a net cash surplus or a net cash deficit we pay our dainty we get back a total of fifteen ninety over than ten so if you pay updating a package of ten there's a net cash surplus of 30,000 and if there's a cache service we will accept the project and it mean an overall cash deficit if we paid out more than we received then we would reject the one basically is always involved in net present value calculations except of course though although there is a cache service of 30,000 it is taking a total of four years to generate and over that period there is an interest cost that that 80,000 either we're having to borrow money are we paying interest or even if we've got 80,000 spare cash back cash could have been earning this interest by putting it in the project whichever way we look at it it's costing us the interest and so have the mean if there was no interest involved there is a surplus of 30,000 because of interest the service will be lower we need a way of taking the interest into account and the way we do it is by discounting by working out the equivalent amount now and what I mean by that is 80,000 now is obviously 80,000 no we're going to get an inflow of our 20,000 in one year but we simply say with interest at the cost of capital e here is 10% in the question how much no would be equivalent to getting 20,000 in a year's time well if it were X now then with interest of 10% in a year's time X would have grown at 2x plus 10% or x times one point one that's taking X and adding on point one or 10% of X we want it to be equivalent to 20,000 in a year's time and so we say the equivalent now we divided by 1.1 X is 20,000 divided by 1.1 or standardly we say we multiply by 1 over 1.1 and so the equivalent amount no 20,000 divided by 1.1 is 18 and 1 8 2 don't work in that sense in the exam always for the moment at the nearest dollar and we're simply saying that 18001 82 now in a year's time if you add on interest a 10% would've grown is equivalent to 20,000 a year we call that the present value and we say we multiply the figure we multiply by is the discount factor similarly though was 30,000 in two years time well again what's the equivalent amount now if it was X now with ten percent a year to after one year it will add on interest to one year it would be x times one point one x plus point one ten percent of X but then there's another 10 percent for a second year so multiply by 1 point 1 again 1 point 1 naught squared well we wanted that to have grown to 30,000 and so the equivalent amount now X 30,000 divided by 1.1 squared or we always write it as x 1 over 1 point 1 squared which is 30,000 divided by 1 point 1 squared is twenty four seven nine three and so on and in general terms the discount factor the figure we x is 1 over 1 plus R where R is the rate of interest 10% is point 1 15% is point 1 5 and so on 2 the power n where n is the number of years so for one year 10% 1 over 1.1 to power 1 the two years 101.1 to the power 2 3 years what I want but what to power 3 and so on however although you must be able to discount that way to save you messing around with wonderful 1.1 1 over 1.1 squared and so on you are given a tables in the exam and if you turning the course notes the lecture notes it's one of the early pages you'll find two sets of tables one is headed a present value table I explained what the other table is after but the present value table it gives you the form here at the top one plus R to the power minus n well I think you should know from school anything to the minus power is 1 over the figure to the positive power it's another way of writing it however although you aren't given the formula rather than as I say messing around what's go ahead it isn't hard it takes time you are given a discount factor for any rate of interest helped as you can see to 20% at the top of the columns for any number of years down the rows up to 15 and so in the exam however quick it may be on a calculator to do one over one point world 1 over 1 point 1 squared in the exam and use the tables so instead of multiplying by 1 over 1 point 1 if you look at the tables the interest rate is 10 percents of the 10% column for one year the first road area is 0.99 which is 1 over 1.1 they've can't get it for you and so the present value 20,000 times point 909 18 of 118 now a slightly different is because the tables are rounded to 3 decimal places but they examine expects you to use tables 18 180 and similarly for 2 years instead of having to mess around 1 over 1.1 squared it's the 10% column the two year old we multiplied by 0.8 to 6 and the present value again slightly different 24 780 but that's simply the rounding and the tables and as you'll see later not only would he expect you to use the tables but also even in real life we're not worried about a few dollars that will be ridiculous and carrying on that way with 40,000 in 3 years so a 10% column 3 year rail 0.751 gives the present value of 30 thousand and forty a foggy four years the discount factor ten percent column for euro is point six eight three I hope by all means do the to ten thousand separately if you want orient Dewey twenty thousand intelligent in four years time twenty thousand point six eight three the present value is 13 at six sixty two together so they are the present values the equivalent amount now effectively by discounting we've removed the interest and therefore the net surplus or deficit after accounting for interest and on even flows eighty one eighty plus twenty four seven eighteen plus thirty thousand and fourteen thirteen the six sixteen a total of eighty six sixty less the outflow of eighty thousand there's a net cash surplus in this case of six six sixty I said in the beginning of maybe no interest to be as soon as the thirty thousand all we've done here is effectively remove the interest the surface as you expect is lower we call that for fairly obvious reasons the net present value or the NPV and our decision well as I said in the beginning if there is a surplus if it's positive as it is here it is positive there is a certain such accounting for interest therefore we will accept the project had it been negative and have been a deficit after accounting for interest we would reject the project it's as simple as that make sure you can use the tables I'll give you some practice in a second do note the tables only go from one to 20 percent in whole percents and almost always in the exam you're dealing with a whole interest rate if you ever did get a situation where you needed to discount a do five and a half percent well found a percent isn't in the tables then you would have to News 1 over 1 plus up Arceus 5 + r % 1 over 1 plus 0.05 5 to the power n the number of years it's unlikely but he could check you on it so check you could do it from those principles but assuming you are given a whole interest rate 1% 2% or whatever then again you're expected really to use the tangles now that's funny don't ya they as I said this really is revision from F 2 so if you are at all and she'll go back and watch they have two lunches but people get so excited and say ridiculous things about NPV and all money's money in two years is worth less than it is now because of inflation well that's nothing at all to do with it all we doing we're looking to see is there a net cash surplus or deficit the discounting is simply to account for the cost of money the cost of capital effectively the interest and that's not hard as you'll see where the problem comes in F million it's not doing the actual discounting this has to become automatic and isn't one of their many marks you not going to get many marks just for multiplying by four figures from the tables where the problem comes at have Melanie is getting these cash flows in the first place you won't simply be told is twenty thirty fourteen ten but that the authorization for they'll deal with all that in the later chapters alright let's know the basics remembering that only 50% of the exam will involve calculations look at example two it says in the previous example what reservations might you about our decision we decided to accept because the net cash flow after accounting for interest is positive for surplus but what reservations would we have well all sorts of reservations first of all the accuracy of the estimated cash flows you know the question told us it's gonna cost a generic resume I'm certain of that who gave me AB or the Machine and we said they expected net cash inflows each year are twenty thirty forty Turner well those are our only estimates it's impossible to estimate precisely you know the actual cash inflows may be how they may be lower and if they turn out if we turned out to have overestimated and the cash flows are lower then of course the MPP will be lower they may even be negative we'd have made the wrong decision now the scrap value we estimate will get ten thousand in four years how on earth do we know how much we'll get in four years you know it's only an estimate we might end up getting nothing in four years well again if any of those cash flows turn out to be different the NPV will be different if it's still negative they're positive rather they're no problem but if it ever ended up being negative we'd have made the wrong decision come if you go on and on there you know all of those cash flows potentially are estimates the life of the project we think it's a machine we think it will last for years how do we know in the last four years they last longer it may last shorter it was an estimate again different life different mbv maybe a different decision what else the accuracy of the cost of capital now the question told us it was 10% to use 10% for the two problems first of all we've assumed it stays at 10% all four years and of course in real life it might not interest rates change it may go up may go down it would affect the net present value in f9 we always assume it stays at 10% and in fact in theory it will I'll explain that later I can explain everything once but although we always assume it stays at 10% or whatever we're told because even realize that might not be the case the other problem is even if we assume it stays constant is how do we know it's 10% you know if you simply a question about borrowing from the bank you know what the interest rate is but as you'll see in the next section of the syllabus companies borrowed from different sources they borrow money from shell as they borrowed money from wellness and you will see in the next section the syllabus that it's impossible in real life to calculate the cost of capital and precisely the best we could ever do is say it's about 10% we maybe 11 ascetic maybe 12% if he's different than 10% then that present value would be different again provided he was still positive we're happy to go ahead but if ever turned out to be negative we'd have made the wrong decision what else something a lot of people don't realize but it's a factor we are assuming and we always do assume unless you told different that operating cash flows occur at the ends of years well now what I mean by hands we were getting 20,000 in the first year and when I discounted we effectively removed one year's interest we divided by 1.1 to remove one year's interest that was assuming that we pay out a two thousand now it'll perhaps 1st of January and that the 20,000 is received one year later perhaps the dinners December not whenever one days interest never but we're getting it in one year's time in two years time and so on no cuz he realize my machine today for 80,000 we may earn 20,000 the first year but it'll be spread throughout the year you know if it was spread evenly maybe you're receiving bits under two thousand a month or something and so we should be discounting a bit of it for one committee for two months but we can do that but you'll never be required to improve now we effectively assume that we get the cash at the end of the year end of two years end of three years and therefore remove one year's interest two years interest three interest we've assumed that the cash flows there are the ends of years and the last as you'll see in some later chapters on occasion you may be tones different but otherwise we always make that assumption what else this may seem to some of your selling point but something the examiners always mentioned in his written answers to this sort of question we've only considered financial factors what about things like the effect on the environment you know I can remember one question so a long time ago now a very long time but one exact question where it was a company buying a machine and one of the costs involved was the fact we'd have to pay farming's because it would be polluting the river and so we you know put in the costs and all we expect to earn this and we expected to pay this fine and was the net present value positive or negative but completely ignore the fact that it's polluting the river maybe we shouldn't be doing it at all even if it ended up giving this a cash service and finally I think I've said enough we're looking at cash flows not profits you know I said though the beginning the net operating cash it flows it's like the profits but in cash terms and you know full well from earlier exams a profit of ten thousand this year doesn't mean that you've necessarily a cash surplus of ten thousand each year you can take the profit you bring in all your sales but comes only half the customers have paid us this year but cash profitable ever in profits with charting of charge depreciation but depreciation doesn't involve paying out cash then that cash flow will be different and so we've not looked at the profits wound to the net cash flows in theory that's better because his cash that's needed to pay dividends they'll cover the losses if young got the cash she can't pay a dividend and its cash has needed to grow the company to buy more machines again I don't care how much profit are made it's a cash that I need to be able to pay dividends to be able to expand the company and so in theory its cash flows that we should look at net present value in theory is the best way of making decisions but don't forget shareholders you see the majority of shareholders the first thing they look at when they get these financial statements is the profit if profits higher the happy if profits lower they're not and so as far as shareholders are concerned they are likely to be more concerned with the profits makes shadows we need to keep happy and yet we're not looking at the profit figures at all it's the cash flows now that's something again I can sell a lot more about mate no we can't withhold service lecture but it is a reservation in theory is cash flows that matter but it shows a horriston in profits perhaps we should be looking at profits instead okay well as I said I don't to get too boring because this should all be a revision but the basic mechanics of discounting that has to become automatic as I've said before it's the cash flows with the problem how we arrive at twenty thirty forty ten that's coming item but once we've got the cash flows discounting should take long a few cents and he's never going to count for very many box alright there's still a lot more in this chapter and still revision of paper to just to introduce what I'm going to do in the next chapter I said that one reservation about my decision here is that we've assumed the cost of covenants ten percent and yet you'll never be silly you know what if the cost of capital turns out to be 11% 12% 13% I think you'd agree I hope you'd agree that the more expensive money is the less worthwhile the project is going to be if a cost of money turned out to be 12 cents surely when we strip out the interest the net present value is going to be lower and so what's terribly important or could materially important is to know how much I could afford it to change by you know maybe is I think it's 10% maybe this is 11% oh the net present value a bit lower but if it's still going to be positive I'm still happy to go ahead maybe if it's 12% it'll be lower still if it's still positive I'm still happy to go ahead but if ever the cost of capital changed so as for the mvv to be negative then of course we should repeal jetting after that reason you can be asked to calculate something known as the internal rate of return which actually I don't like the word because it's not really a rate of return at all the definition the only definition of the internal rate of return of the IRR the only definition is it's the rate of interest for which the net present value equals zero now I discuss the importance of it and how we would use it later you can be nice to calculate the internal rate of return and is asking what rate of interest would end up giving an NPV of zero and this project we've had here we think the cost of money is ten percent and the NPV is positive I said a minute ago and I hope you do agree that the higher the cost of money is the less the surplus the lower the net present value will be and we want to know for the same project the same cash flows what rate of interest will make the NPV zero well he 11% will it be 12 witnesses even and so on well as you'll see the way we do it in the exam and in real life is effectively by guessing and if you look at example 3 Part A says for the same project calculate the NPV let's guess calculate what their people will be if the cost of capital is 15% now I'm going to stop this luncheon here because I really think you should have a go at it yourself shouldn't tell you many seconds if you understood how discounted at 10 percent then there should be no problem discounting at 15 in the next lecture I will do Part A they will discount a fifteen percent again the NPV and then I'll explain how we go about getting the internal rate of return