hi everybody this is lecture five that corresponds to chapter five from your textbook and today we will talk about the application of the present values and time value of money in general to a very important analysis in finance that is so called investment rules so if you remember from our introductory discussion one of the most important questions that the financial manager needs to address is how to make smart investments so for example you may have five different projects and each of those projects has its merits in terms of technology innovation good product demand and so on and so forth so they're all viable alternatives your job is a manager is to make sure that that project is good from financial perspective so the question is what does it mean for an investment project to be viable financially so that's exactly what we are going to learn today that's why it's called net present value and other investment rules so we will focus on the ways to identify good investment opportunities it turns out that the best possible rule that you can utilize what to address that question is net present value rule so if you remember from our discussion from the previous lecture the net present value is equal to initial cash flow with minus sign because that's your cash outflow plus present value of all of the future cash flows okay so basically again you can write NPV as excuse me something like this minus C of 0 plus C if 1 over 1 plus R plus CF 2 over 1 plus R squared and so on all the way to CF let's call it M divided by 1 plus R to the power of n so what you're doing again you are subtracting your initial cash flow because that happens today so you don't need to worry about discounting but any subsequent future cash flows cash flow is discounted using R so just to remind you again R is your best available market alternative so R is where you can put your money alternatively so if you don't go with this project you could put it in some market alternative that has very similar riskiness and yield rate of return equal to R so R is the benchmark so I'm going to call it benchmark rate of return on a market alternative ok so for example if you are trying to invest in development of new product you estimate approximately what is the risk of those future cash flow and again that's that's a very important task so you will learn about that later but while you estimate the risk you figure out what is going to be an appropriate benchmark so the higher the risk the higher rate of return you will use to discount those future cash flows because if you look at investment alternative of similar risk those investment alternatives will usually provide higher rate of return so again for instance if it's relatively risky project you are might be rate of return on a stock market portfolio if it's a very low risk project your appropriate R might be something like rate of return on the corporate bond if it's absolutely lowest risk project almost like risk-free project then you might want to look at something like government Security's okay but the idea is are is correlated with risk so R is driven by the risk of project cash flows okay so for now just assume that that risk is already given to you and R is given to you but in the future you'll see how to estimate that are in the proper way so once you discount those future cash flows what you are doing you are implicitly comparing the profitability of that project with your market alternative so if NPV is greater than zero and we discussed that already you could think about it as as if you have beaten the market alternative so you know in unofficial terms it means that you beat market alternative or market benchmark benchmark art so somehow the rate of return on your investment exceeds the market alternative okay so again positive NPV means that you make an economic profit or abnormal profit so you're making money above the amount that you would have gotten if you simply put it in the market at rate of return art okay now obviously NPV less than zero means that you losing money in that present value terms okay so you do not beat the market alternative so you do not beat market benchmark okay so again it does not mean that you're not making money from accounting perspective but from financial perspective that project is not good because you simply could do better so again think about it this way if I'm running my own business and I make let's say I don't know hundred thousand dollars a year looks like I'm making money but from financial perspective I might be much better off you know not running that business and instead invest that money in the stock market and do nothing so if I simply put mine in stock market I might be getting more money than running my own business so what happens here the net present value of your business is negative because it means that you're not even providing rate of return high enough compared to best available market benchmark okay so some businesses exist that are actually negative and PDS but usually those are small businesses that are not publicly traded so you don't have pressure from the shareholders so the businesses that have negative NPV these are normally done for other purposes not only just to make money but for personal satisfaction so you might claim that well the reason I'm running my own business is because I just like what I do okay so you could write you know you could run a bicycle shop yeah if you just invest that money in stock market you may do better but you just want to run bicycle shop because you want to provide that service to public you really enjoy biking that's your hobby you really like service those bikes you just derive some personal satisfaction so I want to make sure that you understand that we do not take into account those types of considerations so for us if you're running publicly traded company there is no personal attachment here you want to make sure that you create net present value positive projects so that you've beaten that benchmark alternative okay so the net present value would be our golden standard for figuring out investment opportunities so what are the steps in estimating NPV so obviously number one you need to understand what is your initial investment so how much money you need that cf0 to start the project number two you need to estimate your future cash flows to the best of your ability the size and the timing and number three you need to figure out what is the appropriate discount rate or the benchmark are okay so we will talk about each of those things later on so for now all of it will be given to you so we are trying to simply get familiar with the calculation itself and the properties of net or net present value the actual estimation process is a lot more complicated so your minimum acceptance criteria is that NPV has to be greater than zero okay now sometimes satisfying the minimum acceptance criteria ms not enough so think about it this way the minimum acceptance criteria is used when you have multiple projects that are not mutually exclusive so you could take all of them as long as they beat the market alternative so in this case you would use minimum acceptance so you want to make sure that it's positive NPV if it's negative NPV you don't want to take that project even if you have unlimited resources it would just not be a smart decision okay so the minimum acceptance applies when there is no conflict between the project you could take all of them as long as they satisfy positive NPV threshold however sometimes you have multiple projects that compete with each other for example they compete for resources or they compete for space for instance you could have a piece of land and you have two options one project is to build a plant okay and produce a certain product to do manufacturing another project could be to build apartment complex and rent it out so you cannot have both because you have limited space okay you have limited resource land so the question now is let's say both of them have positive NPV so they both are better than putting money in stock market for example so they both beat the market benchmark how do you choose between them and the answer is very simple you just take the project that has the highest net present value so that's why we call it a ranking criteria okay so another example which is somewhat similar when we admit students to the University so let's say you know you're applying to college of business for some master degree in finance okay or MBA well we have our minimum criteria your GPA for example has to be no less than three for example so if we have enough seats compared to applicants we will accept pretty much anybody who has GPA more than three so that would be our minimum acceptance if you have less than three you'll be rejected no matter what however if we have a lot of applicants and we have limited capacity right now we start discriminating if we start differentiating between different applicants and we start looking at ranking so now satisfying the minimum criterion is not enough having GPA greater than three is not enough you have to have GPA high enough to eliminate your competition so what's going to happen we will rank students on the basis of GPA now I'm not saying that's exactly how we're doing it I'm just giving an example okay all right so so why that present value is is so good well there are certain features there are several features of net present value that make it an ideal rule for identification of of good investment projects so the first feature is that it turns out that every time you accept a positive NPV project you automatically benefit your shareholders and the reason for it is very very simple think about it this way again positive NPV okay so let me go back here positive NPV means that you beat market alternative but what is market alternative market alternative is what your shareholders could do by themselves if instead of investing in your project give money back to shareholders in the form of dividends they can always reinvest that money at that market rate so if you pay me dividends I could always buy stocks of some companies some kind of diversified portfolio and that would be my rate of return if instead you invest in your project and you provide rate of return that exceeds the market alternative you automatically doing something better then I can do as a shareholder on my own so you benefit me automatically because you add value so positive NPV automatically implies that you benefit your shareholder because you do something that shareholder cannot achieve on his or her own okay so that's one of the most important features of NTD except in positive NPV automatically benefits shareholders so NPV uses cash flows that's very important it doesn't use accounting incomes it uses all the cash flows not just the first three or first five it uses all of the cash flows unlike other methods like payback period and finally it discounts them properly so when it discounts those cash flows it makes sure that the correct discount rate is utilized so that the time value of money is used and the discount rate truly reflect the riskiness of the project now because accept in positive NPV is benefits shareholders what follows is that the value of the firm automatically rises by net present value of the project so let's say you take a project that has NPV equal to 1 million dollars that is the amount of money you will add to the value of the company automatically ok also what follows is that the total value of the firm would be simply the sum of values of the different projects so if you simply sum up NPVs of all of your projects you will come up with the total value of the company and that's exactly what financial analysts do when they devaluations they look at the projects they try to estimate the net present values and that's how they come up with overall valuation the overall number for what the firm is worth okay and finally let me just emphasize that net present value rule rule assumes that all of the cash flows can be reinvested at the discount rate okay so what does it mean it means that you are getting your cash flows over time okay the moment you got the money you're the benchmark alternative is to immediately reinvest at the market rate okay okay so now you can always calculate net present value using using the formula that I gave you but alternatively you can do it using spreadsheet so it turns out that there is NPV function okay so all you have to do is just to pull something like equal to + PV and then you specify your required rate of return your benchmark rate and then you highlight the range the range of your cash flows and that's it the only catch is that for some reason the way Excel is programmed the assumption is that your first cash flow happens in period one not in theory at zero so let me show you what's happening here so normally we have something like this here is your period zero one two three and so on so here's your minus C if 0 you initial investment and then you have CF 1 CF 2 and let me do one more CF 3 ok so now if you calculate npv it would be equal to minus C of 0 plus CF 1 divided by 1 plus R plus CF 2 divided by 1 plus R squared plus CF 3 divided by 1 plus R to the power of 3 and so on ok but now here's what Excel does and again that's just just a strange quark just a strange feature of Excel which nobody knows why it's that way instead of starting in period 0 the assumption in Excel is that your first cash flow happens in period 1 so not now but 1 period from now so you have minus CF 0 CF 1 CF 2 and then CF 3 so now what's going to happen if you want to calculate npv that's actually what Excel does and I'm gonna call it NPV ii ii mean in excel it would be equal to minus CF 0 divided by 1 plus r because again your first cash flow is not happening now it happens a year from now or 1 period from now so you need to discount it plus see if 1 over 1 plus r squared plus c if 2 over 1 plus R to the power of 3 and finally CF 3 or 1 plus R to the power of 4 ok so if you blindly calculate net present value using Excel you will you will get the wrong number now the good news is that the sign would still be intact so whether you use correct NPV calculation or Excel calculation it's not gonna affect the sign it's gonna be positive both ways or negative in both cases so you're not gonna make a terrible strategic mistake of rejecting investment where it should be accepted we're accepting it where it should be reject it so that's not a problem the only problem is that the value the magnitude the magnitude of your NPV is not going to be what you're looking for now again I'm not saying Excel is wrong I'm just saying that they using different assumption so how do you then rectify the problem how do you correct it well turns out that it's very easy to do as you can see if I take this whole thing right and multiply it by 1 plus R ok I will just have exactly what I need here okay so all I need to do so let me erase that so that you're not confused all I need to do now is to calculate my NPV as NPV Excel times 1 plus R so it's very very simple so from now on anytime you do net present value in Excel just don't worry about anything just calculated normally using Excel but don't forget to multiply by 1 plus R if you do it that way you will have absolutely no problem ok so let me try to do an example so let's see where my Excel is ok so that's what we have from last time so let me just put some some numbers here so let's say you are oopsie so your initial investment is I don't know - 1000 I'm still struggling with using iPad for this so you invest $1,000 and then you get let's say I don't know $800 in year 1 and let's say $600 in here - ok let's assume that you were you know benchmark R is equal to let me just say here's your are okay and let's say it's equal to I don't know 8% 0.08 okay so the question is is it good investment or not so if you look at you invest $1,000 you're getting for $1400 back total so you might think yes it's a good investment but again I keep you know giving you this wrong approach because I want to emphasize that it's wrong so you do not want you should never add these cash flows so what you need to do instead you need to discount those cash flows using appropriate R so one option is just to use the formula but another option is to use Excel so what we're gonna do now you're gonna say equal to + PV okay so I'm gonna click on this so that it gives me all the inputs so that you know what we are doing so your net present value your rate is 0.08 you could either input it directly or you could just click here ok and now you just have values all you have to do is just to highlight your cash flows okay that's pretty much it then you click enter okay return and that's your NPV in Excel but what I mentioned to you is you should be very careful and not leave it like that because again you still get positive NPV and you should not be concerned in terms of sign so yes regardless of your assumptions NPV is gonna be positive in this case so you will accept that investment opportunity but to be precise you want to know your value of net present value you know assuming your assumptions that the first cash flow happened right now so what you need to do you need to multiply it by 1 plus R so one way of doing it is to pull it right here in your formula right away so that you make it you know more elegant so I would do now x in parenthesis 1 plus hey where is my plus one plus and again I will refer to this cell right here so that it's all connected okay and now I click enter there you go now you have correct net present value 255 so as you can see it's still positive it's not going to be different in terms of sign so you would still accept the project but if you need to report the actual value right if you need to talk to your board and explain the actual economic profit abnormal profit you want to have a more accurate number and that's how you do it you multiply by 1 plus R okay very good so so that's your net present value so as you will see we will always compare all of those investment methods to net present value because net present value is our gold and standard you should understand it that's the best possible rule okay now let's talk about some other options so the next you know relatively common measures of investment desirability if you wish is the payback period so what payback period does it simply looks at cash flows at projected cash flows and calculates how many years it will take to repay original investment okay so it's extremely simplistic tool ok so again it just tells you how long does it take for the project to pay back its initial investment and payback period is measured as a number of years to recover that initial cost now the question becomes what is the minimum acceptance criteria is it two years is it five years six years ten years and unfortunately there is no theoretically justified benchmark here with net present value you know that it has to be greater than zero with payback period it's all set by the management so there's a lot of arbitrary aspects here so it's totally up to discretion up to up to the management okay and that's that's one of the biggest problems with payback period that it could be manipulated okay there is no theoretical justification for how many years is considered to be appropriate okay now so so for example I could have something like this so let me do it let me do it here actually so let me move it here so for example you could have your project a okay and let's say you have your C of 0 let's say CF 1 CF 2 and let's say C of 3 I'm just making it very simple so your initial cash flow is minus 1000 dollars after year 1 you get $500 after year 2 you get another 500 and then in year 3 you get let's say 200 okay so as you can see after 2 years right somewhere here your project is paid back so you payback period is equal to 2 very simple is equal to 2 years okay so that's just that's just an example okay so turns out that it's it's not a good method to rely on so payback period is okay if you use it in addition to net present value for example just as an additional piece of information but you should never base your entire investment decision exclusively on the basis of payback period you will make a very bad mistake so here's why one of the most important disadvantages of payback period is that it absolutely ignores time value of money so as you can see if you look at this example I just added up these two cash flows as if they happen at the same time but they don't happen at the same time okay so I need to discount them but I don't okay so in payback period cash flows at different points in time are treated the same way and this is again absolutely wrong from a financial perspective so that's number one number two it ignores cash flows that happen after payback period so for example let's say I have project B here okay so let's suppose it has the following structure okay so initial investment is also 1,000 in the first year it gives me 400 in the second year it gives me 400 and then in the third year okay it gives me 200 okay and then let's say there is another cash flow here cash flow for that is equal to you know you can put as many zeros as you want okay so here's the problem if I look at payback I know that it's gonna be three years so payback period is three years so now remember with payback period you just you know your ranking criteria are such that you choose the project that has the shorter payback period so it looks like payback period is better for project a so project a should be favored compared to project B but now anybody who has brain you would realize that there is a huge cash flow that happens after the payback period happens and that's in year four so of course it's very extreme and of course you know nobody would really choose project a over B but this extreme example just highlights the problem that if you focus on payback period only you will always be biased towards projects that have faster payback but you will ignore what happens in the long run okay so you may be really biased against any longer-term projects automatically okay so that's exactly what's going on it ignores cash flows that happen after payback period and as a result it's biased against anything that is long term okay and finally it requires an arbitrary acceptance criteria so again we mentioned that before there is no theoretical a justified rule about what is appropriate payback period two years ten years to one years nobody knows as a result of all of these the fact that it ignores time value of money the fact that it ignores all of the cash flows of the project only focuses on you know the ones that happens before payback it results in the possibility that a project that might be accepted on the basis of payback period may not even have positive NPV okay and converse could be true a project might actually have very good positive NPV but also very long payback period and as a result it might be rejected so the bottom line never use payback period as the only rule okay so the big advantage of payback period is that it's easy to understand and it does give you important information about liquidity so it does emphasize liquidity so how to reconcile all of those advantages and disadvantages of payback period the answer is very simple use payback period only as an additional piece of information so you want to supplement your net present value calculation with your payback period number but not as the main rule so for example if you're building you know a stadium all right the Yankee Stadium in New York City okay you report to your board that the net present value is positive which makes you port happy and then you say and by the way the payback period is let's say six years meaning that the original investment will be recouped within six years but it should not be again your only decision making rule you should always report NPV make sure that the project has positive NPV and therefore justified from theoretical financial perspective okay but then you can supplement it with information about payback period okay now somewhat there is somewhat corrected way of dealing with payback period which is called discounted payback period so this one addresses one of the concerns so now it takes time value of money in the account okay so what it does for example if I look at let's say my project a what I'm going to do now instead of looking at cash flow one plus cash flow two I'm going to convert it into present values okay so in other words I'm now calculating how many years it will take to pay back investment if I convert each of my future cash flows in present value terms okay so what you're gonna do you will calculate see if zero which you already have versus the present value see if one over one plus r plus CF two or one plus R squared and so on so you will keep adding you will be keeping adding those present values until you make it exactly equal so discounted payback period happens when C of 0 is exactly equal to C if 1 over 1 plus R plus C if 2 over 1 plus R squared plus up to some period I'm gonna call it C of n 1 plus R to the power of n so in this case n is your discounted payback period okay so it's a much better measure so now you're asking you know when do you get your money back in present value terms so you're not adding up cash flows anymore blindly you're discounting them first okay so it's it's better it's better than your regular payback period but still it doesn't care about what happens afterwards alright so you still have this problem of not taking into account all of the cash flows so you're just looking at the timing of when you just break even in terms of net present value but you're not worried about what happens afterwards so it's still flawed it's still very flawed method okay so that's kind of what discounted payback period does and another problem with it is that it kind of loses its simplicity so on the one hand on one hand it attempts to solve one of the major problems which is time value of money but on the other hand it loses its appeal one of the appeals of baibek period is that you don't need to worry about discounting you don't need to worry about estimating risk all you have to do is just to project your cash flows add them up and see when you're gonna get your money back that was the other attractive feature of payback period but once you start discounting you might as well just go ahead and do NPV anyway so there is no real point of calculating discounted payback period because you're already halfway there in terms of calculation of net present value so what happens most firms still use regular payback period but of course not as the main decision rule but as a supplement for net present value