#5 Internal Rate of Return (IRR) – Investment Decision – Financial Management ~ B.COM / CMA / CA #Finance

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fifth CashNews.co of investment decision chapter now in the previous CashNews.cos we have seen the payback period Accounting rate of return and also the net present value technique of Capital Budgeting yes so now here in this CashNews.co we are

going to see this another technique of Capital Budgeting that is internal rate of return yes so to understand this technique properly you must be perfectly clear with the net present value if you don’t know net present value time value of money and how to

discount the Cash Flows and everything then you cannot understand internal rate of return eeeh and we are not going to discuss the net present value in detail over here yes so for that please make sure you have what the previous the fourth CashNews.co of investment position in

which we have solved a problem of net present value and there I have also you know discussed the concept of that so that’s very important for you to understand so please make sure you have watched that first yeah I will put a link in the description below now coming back to this CashNews.co

what is this internal rate of return internal rate of return it’s nothing but just the percentage it’s a rate the name says itself internal rate of return yes so now in this method of Capital Budgeting what we do is you know we first calculate this

percentage to interpolation year through trial and error method yes we first calculate the IRR this percentage and then we compare the IRR with the required rate of return if the IRR is more than that that required rate of return or the cost of Capital then we accept the project if

IRR is less than that then we reject the project simple as that that is the technique of this Capital Budgeting yeah but first you have to understand what is this internal rate of return what does it signifies yeah see here the IRR represents the discount rate at

which the NPV of an investment is zero what does this mean see here this rate if you use this rate in NPV calculation in net present value calculation then what would happen is you know your NPV last which our answer you get it will be zero so if the NPV is zero then that means your present value

of the expert cash inflows is equal to initial cash outflow yes in NPV calculation what do you have you have expected inflows right over the years one two three four five years and then the er0 in the year zero what you have you have initial cash investment initial investment yes and that is

negative because that is outflow and these are inflows so if these two are equal then only your NPV will be zero is entered yes so IRR is the rate at which your NPV will be 0 so if NPV is zero that means these two are equal and then you have covered the cost ya breakeven you have driven the cost is

that clear yes so this is what IRR signifies okay so now the acceptance rules is very simple you understood this right if IRR is greater than cost of Capital except if IRR is less than cost of Capital reject simple as that yeah and here the time value of money is

considered because here what we do you know we use discounting area right so of course time value of money is taken into account is that clear yes now coming to the calculation part so how do you calculate this rate that’s what you have to do right you have to calculate this percentage IRR so

how do you do that it’s very simple you do that by trial and error method okay interpolation so see here first what you have to do is you have to calculate 2 NP B’s okay you have to do two NPV calculation and calculate two NPVs for a single project okay and at two different cost of

Capital yes you will calculate two NPVs with two different rates okay and you have to assume those rates okay you can take any rate you like it’s very simple we will see that while solving the problem but see here and then what you do is use the following formula to find the

IRR and then you have to apply this formula now what is this formula see here IRR is equal to Y a lower rate yeah lower rate plus then what are you going to do NPV at the lower rate yeah all the lower first lower rate NPV at the lower rate NPV at the lower rate we are divided by NPV at the lower

rate – NPV at the higher rate into higher rate – lower rate okay so this is what you have to do first you would do this and then this and then add it up clear we’ll see that so this is what you have to do but if you want to visualize this see here you have one project calculate

first one NPV okay if that NPV is negative or positive you have to see that if it is negative then what are you going to do the second NPV you are going to calculate with the lower rate so if you use lower rate what would happen you will get a positive NPV okay and if the NPV the first NPV is

positive then you are going to use higher rate ok higher discounting rate for the next NPV for the second NPD right and then you will get the negative and be real so what do you need over here to calculate the IRR you have to interpolate you need to NPVs as I said and one should be positive and

another should be negative okay negative NPV positive in P so what are you going to do you are going to try to calculate that rate at which the NPV is zero yes so we have to use this formula to interpolate yeah we are going to interpolate is that clear yes so this is the rate we need the rate at

which the NPV is zero okay so this formula you have to use it’s very simple all the lower first okay lower rate plus NPV at the lower rate and PV at the lower rate then minus NPV at higher rate and then into higher rate minus lower it’s simple as that let’s solve the problem and

then you’ll understand how simple and easy this is okay now here we have the problem see the question over here calculate the internal rate of return of an investment of rupees one lakh thirty-six thousand which Yields the following cash inflows now here they are asking us to

calculate IRR internal rate of return of a project which has an initial investment initial outflow of rupees one lakh thirty six thousand and then they have given us the projected cash inflows that they expect to receive over the years yeah 1 2 3 4 5 these are the years yeah and the inflows are

here thirty forty sixty thousand thirty thousand twenty thousand and so on yep so now what do we have to do here first to calculate IRR to calculate IRR first we need to ndb’s one positive and one negative and then we are going to use the formula of IRR interpolation formula and then we are

going to get the that I are rate yeah internal rate of return simple so let’s start let’s solve this problem so let’s calculate the first NPV yeah so how do we calculate npv simple we have to discount all the cash inflows yes to discount the cash inflows we need a discounting rate

isn’t it so now here the discounting rate is not given and it will not be given in the question all right you have to pick a random random any rate okay now here let’s take ten percent all right so let’s take discounting factor yeah discounting rate as 10% and take the discounting

factors of those and just calculate the present value of all the cash inflows ya see here it’s very simple what are we going to do is here column one two three four five and then year zero on your zero what happens in Year Zero we invest the money on the day one and that is the present value

itself it’s not the future value so we don’t have to discount this directly multiply it by one and take it as it is one lakh thirty-six thousand because this is happening at the day one yeah but these are happening after a year after two year of the three year of a four-year after five

years here so these are future values we have to discount them so to discount them we have to multiply with the discount factors yes now the discount factor now discount factors will not be given to you in the problem in the question but now in some exams what they do is they give you discounting

tables yes if they provide you that then that’s better but if they don’t then you have to calculate it by the calculator how do you calculate discounting factor it’s very simple here the rate is discounting rate is 10% so to calculate what you’re going to do one divided by

one point ten if it was seven percent one divided by one point zero seven one point zero six one point zero five like that yeah one divided by one point 10 is equal to first discounting rate after a year is equal to next discounting rate after two years zero point eight to six yeah is equal to 0.75

and like that you can easily calculate how one divided by one point 10 is equal to first year is equal to second year is equal to third year like that you can easily calculate yeah not a big deal then what you have to do to discount these thing you just have to multiply 30,000 into 0.909 let me

just show you one yeah let’s not waste time here 30,000 into zero point nine zero nine yeah two seven two zero two seven two zero you see this simple that’s what you have to do everywhere forty days 60 days 30 days 20 days yeah so you get all the present values now to calculate the NPV

what do we do to calculate the NPV we added up everything yeah now here if you see if we added up everything yeah twenty seven two seven zero plus thirty three zero four zero plus forty five zero six zero plus or you can’t see that plus 24 9 0 plus then what 12 4 to 0 that is equal to 138 but

then you have to subtract this right one like 36 so one like 3600 so that’s equal to two two eight zero yeah so NPV is positive over here yeah if NPV is positive now what do we have to do the first NP which we calculated with a random discount rate yeah it’s positive now the NPV is

positive is NP these positives now you need a negative NPV we need to NPV is right one positive one negative to calculate the IRR and interpolate yes so what do we need we need negative NPV so for that what we have to do is now we have used you know 10% as our discounting rate and got this positive

NPV so now to get a negative NPV you have to use a higher rate does that make sense you have to use higher rate yeah so what I’m going to do is I’m going to use a higher rate 12 percent yeah you can also take 13% 14% yeah but 2% margin is good yeah so discounting factor at 12% yeah and

then discount in factors you have to calculate just like how I showed you right now yeah how’s that 1 divided by 1 point 12 is equal to first year you see this 8 9 2 so zero point 8 9 3 close yeah I just copied directly from the discounting table they have been you know little bit rounded off

yeah is equal to zero point seven nine seven yeah like that you have to calculate simple yes then the same thing you have to follow you know cash inflows multiplied with the discounting factor you will get the present values yeah thirty thousand into zero point eight nine three you get twenty six

seven ninety let me just show you one thirty thousand into zero point eight nine three that’s equal to twenty six seven nine zero you see this simple thing just have to multiply the future values with a discounting factor to get the present values clear then you add up everything then you get

this NPV now we have negative and beanie you see we have two NPV is now one positive one negative now what we can do is easily yeah we have got a negative NPV and a positive NPV so what do we need we need to calculate a rate at which our NPV is zero yes use the formula to interpolate that’s

what we do so now we can apply the formula directly now yeah we have got two NTV’s simple so you see here the formula is very simple all the lower first L ya lower rate plus NDVI deliberate and P via the lower rate and then minus NPV at the higher rate into higher rate minus lower rate yes so

now it’s very simple lower rate is what ten percent yes so 10 + bracket yeah two two eight zero now what is this NPV at the lower rate so NPV at the lower it is the ten percent right lower rate and this is the higher rate so this is the NPV at the lower rate two two eight zero a 2002 80 then

divided by and PV at the lower rate same thing two two eight zero then you see in formula here we have – yes and then here the NPV will also be negative so minus minus becomes plus isn’t it so this will be plus here so four one nine zero yeah minus into minus plus right yes so four one

nine zero and then into higher rate minus lower rate 12 minus 10 higher rate lower II you see yes so first solve this and then add it up simple as that so let’s do it see here so this 12-10 too simple yeah then here you see this 2 2 8 0 + 4 1 9 0 that is equal to 6 4 7 0 yes so just divide

that 2 2 8 0 divided by 6 4 7 0 that is equal to some decimals in two – yeah you have to do this first all right okay yeah into 2 that is equal to some decimals then you have to just add it with the lower rate at last you have to add okay plus 10 that is equal to 10 point 70 I’m just

taking 2 decimals 10 point 7 T is our IRR at this rate if we use this rate in our calculation what could happen our you know present value of all these cash inflows will be equal to our initial investment and then the NB will be 0 is that clear so this is our internal rate of return you see this is

how you have to calculate it’s very simple