so let's now consider an example so we kind of fine-tuned our general understanding of the capital budgeting process so now now let's look at an example that would be very similar although not as detailed not as involved as UK study but relatively similar so it's a Baldwin company that decides to sell and produce bowling ball okay bowling balls so what they do they just invest in test marketing so they spent two hundred and fifty thousand dollars so right there you realize that it's a sunk cost so you ignore so you don't need to worry about it it's gone there is nothing you can do about it then you have current market value of proposed factory site which we own one hundred and fifty thousand dollars so you don't spend one hundred and fifty thousand dollars because you own that factory site it's piece of land it's piece of piece of property that you already own but it does have market value that is equal to hundred and fifty thousand dollars immediately you need to realize that that's your opportunity cost okay and I'll show you how to deal with that I'll show you how to take that and take out then you have cost of bowling ball machine equal to a hundred thousand so that's gonna be our direct investment so you buy machine for hundred thousand dollars you also invest in networking capital ten thousand dollars so that's your Delta network in capital immediately in period zero and then you expect certain production pattern yearly over five year life of the project so those are in units those are actual bowling balls not in dollars but in units five thousand eight twelve ten and six so why five years well it's not clear in this example so again you could imagine that after five years the industry is not lucrative anymore the profit margins are too low so it doesn't make sense to continue so it's a relatively short-term project but you're thinking okay over five years maybe it's worth it okay what do we also know we know that the price for the first year that's the price of your bowling ball is equal to $20 and then prices will increase at two percent annually the production cost on the other hand so to produce one bowling ball you will need to spend $10 initially but then it will rise by 10% annually so as you can see the growth in your cost per unit far exceeds the growth in your final price so obviously your profit margin will get smaller and smaller and smaller you also know that inflation rate is going to be is equal to 5% so in this case it's going to be irrelevant and I'll explain to you later why and also as I mentioned before your initial work in capital is equal to 10,000 which is right here okay increase in net working capital equal to 10,000 but then it changes with sales so how does it change with sales well in this example it will be just given to you all right you will know exactly what net working capital is going to be in reality you want to project it one middle ground which is kind of you know the simple way to deal with net working capital is to assume that it varies directly with sales just like percentage of sales approach and that's what's going to happen in your case study so for your case study you will know what is that fixed proportion fixed percentage of sales that goes to net working capital so you will always be able to calculate it once you know your projected sales all right okay so with that in mind let's start working on it so you have your a timeline that starts from period zero and goes all the way to period five period zero is the time when you make your investment but you cash inflows do not happen until period one and that's normal that's why if you remember your NPV is equal to minus C of 0 plus present value of future cash flows ok so we need to start with figuring out that C of 0 okay so let's think about it you spend 100,000 on bowling ball so it's right here that's minus 100 that's you see of 0 then you have your net working capital equal to 10 so that means that you get you actually spent another $10,000 okay on investment in net working capital and that makes sense think about it intuitively if I am if I want to launch some production process I need to buy raw materials okay at the very least and maybe I need to invest in cash so that I hold it for transaction purposes so I need some kind of upstart I need some kind of starting working capital and that would that $10,000 is here so so far is relatively clear you have hundred thousand that you directly invest in bowling ball machine ten thousand that you invest in networking capital but then there is quite big investment here what is it that's the opportunity cost because if you remember you have hundred and fifty thousand dollars value of proposed factory site the fact that you are using that factory site for your project means that you are not able to sell that factory site so hundred and fifty thousand value is lost for you that's why you have minus 150 right here but then you might say wait a minute unlike our previous example where you gave up that land and decided to build apartment complex forever so yes indeed you were given up that land forever in this case you'll not given up that factory site forever okay so why do we say that the opportunity cost is 150 well we don't all they're saying is that it's equivalent to invest in hundred and fifty thousand dollars right now so you sacrifice 150 now but you are getting it back in year five okay so the way to think about the opportunity cost in this case is this your opportunity cost in general would be equal to minus 150 plus 150 divided by one plus R to the power of five okay so what you're really losing is not the entire value of the of the factory site you're losing time value of money the fact that you don't sell it now but instead do it after five years means that you miss your chance to make money on that hundred and fifty if you sold it now you could have put that money in the market make some market rate of return so what you are really losing is just this time value of money and the way to incorporate it is to either calculate opportunity cost directly like this or the way I prefer to do it is just to pull 150 here with negative sign 150 here with positive sign and then we will combine that with all other cash flows okay the result is going to be the same but it's a lot cleaner okay excuse me so so now we have pretty good idea about what happens in period zero so if you take and take out the bowling ball machine the opportunity cost and the net working capital our total initial and assessment is minus 260 so we are done with cf0 okay now let's see if there is anything else here so basically now we are looking at let me just uh let me just tell you what we are doing here I would say we are doing minus capital spending minus Delta net working capital so we took that part okay so if you remember again you're actually then write that down but your cash flow from assets are equal to operating cash flow minus capital spending minus Delta net working capital so in this first table we are focusing on this part okay we're looking at capital spending and net working capital then we're gonna worry about operating cash flow so now if you go back here you see that for for period 0 we are done we already know your capital spending in a.m. net working capital let's see what happens in period one in here one you have a depreciation expense which we don't care about because from cash flow perspective it doesn't do anything but you will need it in the moment I'll show you you needed to calculate salvage value of equipment our net working capital stays at the same level so your Delta your change in net working capital is zero okay how do we know that it stays again it's given to you in this case it's just the way the the case is presented alright in year two your net working capital is sixteen point thirty two which means that it increased by six point 32 so you subtracted so that's your Delta net working capital with minus sign then it goes up to twenty four point ninety seven so that's your cash outflow then it goes to 21 so you have cash inflow because your net working capital actually went down and finally as I mentioned to you earlier in the end of the project it has to go to zero so you have big inflow of money associated with liquidation of net working capital okay so all in all we now have pretty good idea of what happens in year one two three and four and year zero the only thing left is year five so in year five we know that you get big inflow of net working capital you know that you know that we get our opportunity cost back the only last thing that is left is this part right here which is called salvage value of equipment remember I mentioned to you that when your project is done you normally sell your equipment back in the market so what you need to do you need to calculate how much cash you will generate as a result so why isn't it just the market price and the answer is is because you also have to pay taxes so here's how it works so if you want to calculate salvage value of equipment here's what you need to do is going to be the market price - tax okay well you might wonder why do you pay taxes well because you know the way the accounting works and the way the government regulation works if you sell any piece of equipment at the price that exceeds the equipment's Book value we call it capital gain and as a result you have to pay taxes so think about it this way on your books after depreciation the machine is let's say $10 value but you sold it by 420 immediately the government realizes that you generated capital gain you sold it for at the price that exceeds its actual book value is it fair that's a different story but that's the way it is so that capital gain is a taxable income so what's gonna happen now you will have market price - and now your tax base is gonna be market price - Book value and then you multiply by tax right okay so that's what's going on so in this particular example as far as I remember I don't have textbook in front of me but I think the market price of equipment is 30 so you bought that machine for 100 in the end you sold it for 30 but the book value of the machine is 576 how do I know that well because I subtract depreciation in every period ok and as a result if I take that depreciation I subtracted from the original value of equipment this is my adjusted book value so again in zero my machine was worth 100,000 then after year one when I subtracted $20 depreciation the machine is only $88 on my books okay then I added another $32 of depreciation which result in accumulated depreciation equal to 52 and overall value of equipment only 48 and so on after year five your machine is worth only 5.76 on your books so what it means it means that you saw the machine at the price that is much higher planets book value again the fairness of that rule may be debatable you might say how can account in depreciation know the true market value of anything so why should I be taxed for selling the machine at a certain market price reach six which exceeds some kind of imaginary depreciation schedule and you would be absolutely right I mean nobody knows the true value the market speaks and markets believe that the price of the machine is thirty so you might say that it's very unfair that I have to pay taxes here but we are not here to debate that it's just the way it is so you book value is 576 but you market value is 30 so you need to do this so 30 minus 576 that's gonna be your taxable taxable capital gain okay and finally you multiply by tax rate and I think again as far as I remember I think it's equal to 34% the tax rate is equal to 34% so I hope again I don't have time to verify you can do that but I hope if everything is right here you should be able your you should be able to get twenty one point seven two six okay so I'm gonna put twenty one twenty seventy six but you guys I need to check so I'm gonna write check please make sure that all the information is correct here all right so now you're ready to combine all these cash flows together okay and that would give you your capital spending and net working capital so what it means it means that in year one you spent two hundred and sixty thousand dollars in year one no spending in year two you spent six thirty two in year three you spent 865 in here for you gain three seventy five and in year five you gain a lot which is one ninety two ninety eight now if you look at this cash flow clearly you're losing money okay in present value terms no doubt about it but that's because we haven't considered operating cash flows all right of course you're gonna lose money on your capital expenditure and network in capital because the reason why you're investing in capital is because you want to generate sales so the next step is to consider the most important cash flow which is your operating cash flow ocf and that's what we're gonna do here so the first step is project your sales so you project your sales by using very simple strategy you just take price and multiply by quantity so by definition sales are equal to price times quantity for example how did I get hundred here well you have five thousand bowling balls and the initial price is 20 so that's where your hundred is coming from okay five thousand volts times $20 price gives you $100,000 revenue okay but the trick here is to realize that the final price is growing so for example in year three as you can see in this example you sell 12,000 units but the price now is going to be 20 times 1 or 2 to the power of 2 it's because again your price is growing so it's actually going to be twenty point 81 and that's how you get this number right here and so on so in your case study you will have multiple markets you will have multiple products multiple prices and they will grow at different rates so it's a little bit more sophisticated but the logic is still the same you just figure out quantities and prices very very careful and the best way to do it of course is to use Excel all right then you do exactly the same with operating cost so for example again how did they get that fifty five thousand units times ten dollars per unit expense that gives you fifty thousand dollar expense similarly your expenses are growing at the constant rate in this case they're growing at ten percent annually so for example in year two it's gonna be eight thousand units but now your price is ten times one point one okay and that's how you get this eighty eight thousand and so on then you have your depreciation expense so how do I get all these numbers how do I know that this is my depreciation expense because they look rather random and the answer is it depends on your depreciation schedule and usually it will be given to you in your case you it will be given to you and also if you work for a company the accountants will always tell you what is the correct depreciation schedule so depreciation schedule is not something that we do it's given to you by certain accounting standards okay so it's called accelerated cost recovery system so you classify your asset into certain categories and depending on in which category your asset is you put it in the right MACRS OAC RS schedule so okay those percentages are given to us so for example in year one i'd appretiate 20% and that's why i have 20 here in year 4 i do appreciate 11.52 percent and that's why these numbers here and so on you just apply these percentages to the original value of your equipment okay so now you have sales depreciation you can calculate your EBIT earnings before interest in taxes so in this case interest doesn't exist anyway so EBIT is the same as EBT then you have your taxes thirty-four percent okay so those are your taxes and finally you have your net income now that would be your income statement but that's not what you want you want operating operating cash flow so what you're going to do you're going to calculate the operating cash flow and how you do it well basically if I go back here I would do OC f as EBIT plus depreciation and then minus taxes okay so for instance let's do it for year one my EBIT in year one is 30 so I will have 30 my depreciation is 20 so I will add 20 and then my taxes are 10.2 so minus 10.2 so I'm going to have 50 minus 10.2 that gives me 38 hold on a second 50 40 30 9.8 okay and that's exactly what you have right here okay so excuse me this particular table tells you that ocf is equal to 1 minus 2 minus 3 which is sales minus operating revenue excuse me operating cost minus taxes which is also correct but I strongly encourage you instead to use EBIT plus depreciation sorry - Texas this is more common more more theoretically correct formula okay because sales minus operating cost minus taxes may not always work it depends on if you have interest expense a lot so I would rather use more universal formula EBIT plus depreciation minus taxes okay so now you have all these operating cash flows for all of the years now you also have all of those capital expenditures and networking capital you combine them and you arrive at something that is very important which is your total cash flow from assets that are generated in this project so that would be overall cfa which is you know operating cash flow minus capital spending minus delta net working capital now you are in a position to actually calculate your NPV so you apply a net present value analysis to this cash flow so it's minus 260 plus thirty nine point eight divided by 1.1 plus 50 for 19 divided by 1.1 square and so on and so forth the reason why it's one point one is because you are is equal to ten percent so if you remember you are is equal to ten percent now you calculated your NPV so your NPV is greater than zero so you invest or in other words you accept the project okay so as you can see it's not that it's not that bad it's it's pretty simple you just need to be extremely careful and again in your case study you'll have a lot more details but it's all doable you just need to carefully go step by step and make sure you do not miss any important information so in reality the process is a lot more difficult because here your sales already to you okay in reality forecasting those sales is the most difficult task also your cost of production is given to you forecasting that is also very difficult and even things like net working capital is given to you but you don't know in reality what is going to be so again your case study or this particular example is a gross simplification of reality but remember we are just starting right this is basic finance course so you need to understand the process in general if you want to go deeper into finance world you will learn a lot more techniques about forecasting and how to incorporate those things in your analysis but again the key for now is just to understand the skeleton to understand the main approach to this problem all right finally let me explain the relationship between inflation and capital budgeting and I'm gonna tell you right away it turns out that you don't need to worry about inflation at all and here's the reason why so let me pull out this stuff here let me open the new one so you might think about it this way okay so I project certain cash flows so I have a CF 0 CF 1 CF 2 and let's say C of 3 okay those cash flows are forecasted in nominal dollars okay I don't make any adjustment for inflation because all I can do is just to just forecast how much I will have in dollars just think about it right you just say okay I am able to produce that much at that price then next year I'm gonna be able to produce that much at that price and so on and so forth so your final price may not be very correlated with general inflation rate in the economy at all your final price might be absolutely stable because of fierce competition while overall inflation in the economy is 3 to 5 percent for example okay alternatively your price might even go down right if you are if you're dependent on certain commodities for example so whatever that is you just forecast your cash flows without thinking about how inflation overall might influence your well-being because you might make an argument that inflation will eat some of the purchasing power that you will be able to generate so even though you get those cash flows you will not be able to buy goods and services or your shareholders will not be able to buy the same amount of goods and services when they receive that money back so the question is shouldn't you take into account inflation when you do your capital budgeting and the answer is no and the reason for it is because it's already done for you it turns out that when you use your are okay when you discount your future cash flows without even knowing it you already discount your cash flows taking into account inflation so let me try to explain to you what's going on here so first of all let's introduce the notion of nominal cash flow that would be cash flow in nominal period t dollars okay so for example see if two is nominal cash flow because it's in dollars that will exist right or valuable would be valuable at period two real cash flow on the other hand is cash flow in real period zero dollars so in other words if I have $100 today and a year from now I have 110 110 is going to be actual dollars so that would be nominal cash flow but if I convert that nominal cash flow in real terms I will express the value of that hundred and ten dollars in today's dollars how do I do it I take into account inflation so suppose your PI is inflation rate so the reason I use PI is because it's excuse me in economics that's it that's a common practice to use PI so obviously it's not 3.14 okay that's just the Greek letter that is commonly commonly used to you know to denote excuse me to denote inflation in the economy so what I'm gonna do now I could say that my C if one my real actually as let's do it this way my real see if one would be equal to Nala know see if 1/1 plus inflation rate okay or in other words I could say that my nominal see if one is equal to real cash flow one times one plus inflation okay so why is it the case well again think about it this way my nominal cash flows are growing but part of that growth is real purchasing power so yes you're really able to buy more goods and services but also part of it is just due to inflation so you could think of real cash flow is your purchasing power but one plus pi is that additional inflationary growth that has nothing to do with your true purchasing power okay alright then the same applies to our it turns out that 1 plus R is equal to 1 plus small R times 1 plus pi so what is big R that's your nominal rate of return and small R is your real rate of return ok so what happens is your accumulated return which is 1 plus R is split in 2 factors so it's factorized 1 is real growth and another one is growth due to inflation ok so again if I invest $100 at 10% rate of return I'm not going to get 10 percent in real terms part of it is going to be eaten up by inflation so basically I factorize my overall growth in my onions into two factors the real growth and the inflationary growth and by the way is called Fisher equation okay so now let me show you what does it all mean for your capital budgeting so your net present value is equal to minus C of 0 plus nominal right because normally we don't even think about inflation we don't factorizing anything we just say nominal cash flow 1/1 plus nominal R and then plus nominal cash flow 2 divided by 1 plus R squared so let's say we're talking about two periods only but now see what I'm gonna do see if 0 is already nominal and real at the same time because it's right now anything that is current is already expressed in real terms but now I'm gonna factorize that nominal cash flow one into two components two factors it's going to be real cash flow one times one plus inflation rate okay now in the denominator I'm gonna factorize my 1 plus big R as 1 plus real R times 1 plus inflation and I'm gonna do the same here my nominal cash flow 2 is gonna be equal to real cash flow 2 times 1 plus inflation squared right because now you have inflationary growth during two periods so it's 1 plus inflation Square same as here you're gonna have 1 plus R squared times 1 plus inflation square so what do you notice inflation just cancels out which means that if I simply you know cancel out inflation I will get real careful 1 over 1 plus real R plus real cash flow 2 or what was real R squared so what do we have it turns out that if I calculate my net present value using nominal cash flows and discount them using nominal required rate of return without even knowing I'm doing identical thing to if I just converted everything in real terms so if I was really concerned about inflation and started converting everything into real terms real cash flows a real rate of return turns out that I would get exactly the same answer if I was using just blindly nominal cash flows and not an alarm ok and it makes sense because inflation is driving your cash flows but it's also driving your R so it shows up in numerator and denominator and as a result whatever you know spurious growth that you are getting in your cash flows is gonna be cancelled by the spurious growth that you're getting in you are so they will compensate each other so the bottom line you don't need to worry about inflation at all the only thing you need to be careful about is to make sure ok that you always okay compare a real cash flows using real discount rates or if you're using nominal cash flows you have to use nominal discount rates as long as you're doing it consistently you should be perfectly fine so that's exactly what I have here so this part is nominal cash flows in nominal this part is real cash flows in real art and as you can see it doesn't really matter okay one last thing I'm going to show you here is if I go back to my Fisher equation 1 plus big R is equal to 1 plus small R times 1 plus pi let me now expand it so I have 1 plus PI plus R plus r times pi ok 1 and 1 will cancel out so your big R is equal to real r plus inflation rate plus R times inflation rate now it turns out that for most developed economies in normal times R times pi is very small so it's approximated by 0 think about it if your real rate is you know 5% a new inflation rate is 2% so you have 0.05 times point O 2 that results in a very small number so what it means is that very often we say that nominal R is approximately equal to R which is real R plus inflation rate and that's what we called modified Fisher equation or simplified simplified Fisher equation now why this important because that's how most people think about the relationship between nominal or in real are you see it everywhere when people say that my nominal R is equal to 5 percent but the inflation rate in the economy is equal to 2 percent it means that in real terms I'm getting only 3 percent so when people do that automatically they apply this modified or simplified Fisher equation it's not exactly right if you really want to do it right this is how you need to do it so either this or this okay so in this case your real R is equal to R big R minus inflation okay I actually know you can't even solve for it yeah you're right because yeah because you cannot factor it out so anyway in order to figure out the the real are you just basically need to do some calculations here you cannot solve for it analytically so that's why people like that simplified version which is not bad it's not far off but keep in mind that it's not exactly right okay so that's what we have here it's called you know modified or simplified Fisher equations so it's approximation okay in this case it's just expressed as real rate we call the nominal minus inflation basically the other way around okay alright so that does it for the capital budgeting so now you should be ready to start working on your case study as I said case study is much more complicated more detailed but fundamentally it's no different it's the same process the same ideas just a lot more information