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hi everyone this is the fourth video of investment decision chapter and in the previous three videos we have seen the concept of this chapter and we have solved problem on these two techniques right the payback period an accounting rate of return these two techniques of capital budgeting we have seen those and we have also solved problems right so those techniques where non discounting techniques now we are going to start the discounting techniques of capital budgeting right so in this video what are we going to do is in this video we are going to start with the net present value technique of capital budgeting right so let's start let's start and let's see how does this technique works and how to evaluate a project with these techniques okay all right then let's do it now let's try to understand this technique of capital budgeting net present value see here I have written the meaning over here right so let's go through that once the NPV technique is a discounted cash flow method that considers time value of money in evaluating capital investments right so basically what here they are trying to say is that this technique right net present value it is a technique where the cash flows what cash flows how much money will come in and how much money will go out due to that project which we are evaluating we are evaluating the projects here right different different projects are there that the company wants to invest in and they want to evaluate those projects whether they are profitable or not right so to do that this is one of the evaluation techniques net present value right so in this technique what happens is in this technique whatever cash flows will be there inflow and outflow those will be discounted right now here the cash flows are based on estimates they are not 100% true know they are estimates if we invest in this project this much cash flow would be there right this much outflow this much inflow will be there so those inflow and outflow right those will be discounted now what do you mean by discounting of cash flows we'll get to that don't worry so just understand that those cash flows will be discounted and here the most important thing is the time value of money it's the same thing it's interrelated discounting and the time value of money time value of money we have to understand these things time value of money and discounting right so let's do that first and then we'll come back to this okay so you understood right what do we do here here the cash flows are discounted that's the main core of this technique of capital budgeting net present value that's all this is okay so we'll just see you understand value of money and what is this discounting that we are talking about right so let's do that first now here's the time value of money so let's understand the time value of money with this small scenario so let me start by asking you one question which is better to have 500 rupees today in your hand or to have the same 500 a year later in future tell me which is better 500 now or 500 a year later in future which is better of course now is better right now it's better why is that why now is better because because the purchasing power of money falls down as the time passes by the purchasing power will fall down whatever you can purchase today with that 500 rupees you wouldn't be able to purchase the same thing in future right with that 500 you wouldn't be able to do that because the purchasing power Falls inflation is there there are lots of things right there's very much uncertainty right so that is why there is value of money and the value of money falls down as the time passes by so that is why in financial management what do we do is we always okay what we do is whenever we are going to receive anything in future any money in future what do we do is we discount that to present value whatever future value whatever money that we are going to receive in future we discount that we reduce that we bring that to the present value okay that is what is discounting fine so that is it that is the time value of money due to time value of money what will happen is we are going to discount our cash flows okay so now let's see what is the discounting okay let's see that now here is discounting CEO C discounting is nothing but converting the future value into present value okay let's take this example the same four hundred rupees right if we are supposed to receive five hundred rupees a year later then we want to know what is the value of this 500 rupees in today's terms that is called discounting converting this future value into the present value right present value is four fifty five but how did we get that right see we discount using a discount factor okay and a rate a percentage right so that person will be given to him the question okay don't worry right so this is what is we do by using a certain rate we discount the values fine see here the formula is nothing this year present value is equal to future value into 1 divided by 1 plus R raised to power n okay so here R is nothing but a rate any rate cost of capital interest right it could be anything and then n is the number of years now here it's one year so the power is one so we don't have to take that right so 500 into one over right one by one point 10 1 plus R we have taken it as 10% okay just one example so one point 10 if it was 11% one point eleven if it was 7% one point zero seven like that so 500 yeah 500 into one divided by one point ten that gives us the value for fifty four point five right so have just rounded it off for fifty five right that is the value so this is how you discount okay you just apply this formula we see that in the detail while solving the problem don't worry it's very simple you just have to use the discounting factor and just multiply you will get the you will get the present value okay discounting is nothing but converting the future value to the present value by just using the discount factor and a percentage should be given to you you just have to multiply that's it alright okay then let's go back to the net present value now I'm sure you have got an idea about time value of money and discounting right so this is what is net present value we discount the cash flows right it's a method of calculating the present value of cash flows inflows and outflows of an investment proposal using the cost of capital so here we don't use interest rate and all we use cost of capital or weighted average cost of capital okay it will be given to you in the question don't worry the rate we use write to discounted cash flows as an appropriate discounting rate fine so now let's see the format of this NPV how do we go about it see here there are four columns that you have to remember right it's very simple your cash flows discounting factor and present value right so yours right 0 1 2 3 now 0 right 0 would be the first day of the first year and then 1 2 3 these are the end ok and end off your 1 end of year 2 end of year 3 like that and then cash flows will be there but in the beginning there will be initial investment whatever money that you invested in in any project right that would be the initial investment all right so that would be negative ok because that is outflow and then the inflows would be there fine and then there will be discounting factor is given to you the question and then you're just gonna multiply you will get the present values add it all up right you will get the net present value and if net present value is greater than 0 you accept the project right and if net present value is less than 0 if it is negative then you reject the project right and if there are many projects then you will choose the project you will select the project which has the highest net present value right that is the basic idea of net present value right so now let's solve the problem and we're gonna see how does this works practically right so okay then that's all problem now here is the question let's go to it once see here calculate npv of the two projects and suggest which of the two projects should be accepted assuming discount rate at 10% so here we have been given two projects project x and project y right so now here we have to suggest the management which project to go for and we are gonna do that with the help of to present value this technique of capital budgeting right so here we have been given information of project X and project Y see here initial investment of project X is 40 thousand and then of project Y is 60 thousand and the estimated life of both the project is same five years five years right right and then there is scrap value that is two thousand of project X and four thousand of project Y the termination value the value which we are going to get at the end right the scrap value and then there is cash inflows see here the cash inflows of project X are ten thousand in one year one at the end of year one okay at the end of year one at the end of year two at the end of year three at the end of year four at the end of year five these are the cash inflows right ten thousand twenty thousand twenty thousand six thousand four thousand and half project why it's forty twenty ten six four like that so cash inflows are given now you know that these inflows are of future right these are estimates we are gonna get these cash inflows in future so we have to bring them to the present value they are future values we have to discount them to the present value so to do that we need discounting factors and discounting factors are given in the question you don't have to worry just have to multiply the cash flow with the discounting factors and you will get the present value right that's how you do it right so now let's solve this problems okay now let's solve this problem see here now you know right you have to remember these four columns here cash flows discounting factor and then the present value right this is the format of net present value table now let's start with the project X see at first what you have to do is first you have to look for the initial investment what money are we going to invest right the outflow of cash that is what you have to see so in case of project X it is 40,000 we are going to invest 40,000 in Project X so you have to take that first in the cash flow column but this is negative this is outflow of cash not inflow this is outflow the money is going out so you have to take that in negative way cash flow 40,000 negative and this is happening on the first day of the project that is the first day of the first year right that is year Z we take that as your zero so 40,000 negative and then this is happening on the day one okay keep that in mind and then take all the years that are there five years right the project is off five years estimated life of the project so take all that one two three four five fine and then they have set scrap value is two thousand right so scrap value is also in your five that is the last year we are gonna get scratched and you worked last and the last year is five so the scrap value will also be in the year five okay and then take all the cash flows whatever that is there right the inflows are ten thousand twenty thousand twenty thousand six thousand four thousand take all that ten twenty twenty six four and then the scrap value also you have to take fine but these are future values isn't it only this is present value right forty thousand is now today but these are future values so you have to discount them to the present value so how are you going to do that with the help of the discounting factor at 10% and the discounting factors are already given in the question right of every years see here your one 0.909 year to zero point eight two six year three 0.751 ef4 zero point six eight three year five zero point six two one you just have to copy them down right just take them down 0.909 of first year zero point eight two six of second year 0.75 one third year like that and then at last for scrap value also you have to take the discounting factor of the fifth year because this is happening in the year five right at the end of your five so you have to take that okay and all these are happening at the end of year like year for like that okay at the end of the year fine so these are the discounting factor you just have to multiply them you will get the present value right but one thing you have to remember is that this initial investment is happening on the day one no time has been passed so you cannot use any discounting factor there you just have to multiply it by one okay because the value of 40,000 today is 40,000 write the value of 10,000 after a year would be 9090 but the value of ten thousand today if I asked you it is ten thousand so the money which you're investing today forty thousand negative is today it's forty thousand only that is what you have to multiply it by one only okay not any decimals right okay so once you multiply I'm just gonna show you one see here this one let's see this one twenty thousand into zero point eight two six yeah twenty thousand into zero point eight two six that gives you 16 five two zero see this is how you do it simply just multiply you will get all the present values then you have to add up all the present values you will get the net present value right let's see first start with a negative figure minus forty thousand plus nine zero nine zero plus sixteen five to zero + 15 0 - 0 + 4 0 9 8 + 2 4 8 4 + 1 - 4 - that gives you 8 4 5 4 right 8450 4 that is the net present value see this is how you do it simple right now let's do project wife now let's do project YC here it's so simple the same thing you have to repeat right see here initial investment is 60,000 you have to take that in negative right and this is happening on the day one that is year zero take down all the years five years is the life so one two three four five and scrap value that will also happen in the at the end of your five so take that right and take down all the cash inflows that are there see here project Y 40 2010 6-4 40 2010 6-4 and then the scrap value also you have to take write this graph value right so that is it right and then the discounting factor here also you have to use the same discounting factor at 10% and this is happening on the day 1 itself so it will be multiplied by 1 okay it will not be discounted right so that would be minus 80,000 and we are using this negative because this is an outflow right so you take down all the discounting factor that are there here all the discounting factors take them down multiply that you will get the present value and add up all of these you will get the net present value let's add okay simple right it's the same thing it's very simple start with a negative right - 60,000 plus 36 360 plus 16 5 - 0 + 7 5 1 0 + 4 0 9 8 + 2 4 8 4 + 2 4 sorry 2 4 8 4 that gives you 9450 6 that is the net present value right it's so simple right so this is how you do it you just multiply the cash flow to the discounting factor you will get the present value but now the main question arises what if in the question discounting factors are not given don't worry it's very simple if the discounting factors are not given in the question all you have to do is you have to make use of that formula what formula the simple formula see here all you have to do is you just have to take 1 divided by 1 + R right this is what you have to do okay and then there will be power n there's a number of years but how do we do that in this calculator see it's very simple let's say the discounting factors were not given the question okay so all you have to do is 1 divided by the rate is given as 10 percent right so that is the rate okay so what you have to do is divide by okay see here divided by one point 10 okay one divided by one point n if it was seven percent one divided by one point zero seven if it was six percent one divided by one point zero six like that okay so what I did 1 divided by one point ten is equal to zero point nine zero nine take three decimals right again equal to zero point eight two six right that's the second year equal to zero point seven five one there's the third year equal to zero point six eight three that's the forty or equal to zero point six two zero that's a fifty or again if you want if the project is of seven years equal to sixty or equal to 70 or like that simple all you have to do is one divided by one point one zero equal to after one year equal to after two year equal to after three year okay light is you have to do it right if it is not given that is counting factors are not given you don't have to worry it's a simple thing okay to do in the calculator right so this is how you do it right always remember you have to take the initial investment here only okay it's very easy now in some books words they have done is they take the initial investment over here and then they subtract that okay don't do like that do this way it's very simple okay right okay then see you in the next video or I totally forgot to tell you the most important thing see here they have asked us which project would you suggest to the management that should be accepted right so we will select the project which has the highest net present value so tell me which has the highest net present value this is the project wife nine thousand four hundred fifty six is the present value of project Y and of project x the present value is eight thousand four hundred and fifty four so the highest is of project y so you will tell the management that we have to go for project Y right that's it okay then all right