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Case Study: Breakeven Point

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Namaste, in the last few sessions we have discussed CVP, BEP.In the last session, we have also discussed the relevant cost versus sunk costs, we have done cases based on few decision-making scenarios. Let us go for the next case again based on decision making and we have to calculate BEP, but this case is very interesting because we are going for a picnic. So, we have to decide on pricing for a school picnic please read the case yourself. So, Rhishi Prashala has a total of 160 students and they are proposing to go for a picnic to Bhimashankar. Now, Bhimashankar is a very important pilgrimage place in Maharashtra, it also has a very interesting sanctuary there wherein you can see wildlife. So, please go through this there is a reserve forest there cost details are also mentioned. Now, based on the cost, the question is you are required to compute a: If the school decides to charge 500 per student, what is a BEP in terms of a number of students and what is PV ratio? The interesting thing is you can have multiple answers, you can have up to 4 columns, I mean 4 sales are given, you can have up to 4 answers for BEP and 4 answers for PVR. In b part now school has decided to take a few students from Municipal school at a concession fee.So, that they would be charged enough fee just to cover the incremental cost, now what will be the concessional fee again there are 4 possible answers. And in part c as per the estimated number of students you need to make 4 columns. Now, instead of charging 500 school wants to just cover enough fee to cover the cost, so lower fee 1, 2, 3, 4. So, these three calculations are required please go through the case once again and then we will discuss the solution.So, you are ready, you enjoyed the picnic, but to go on a picnic, first, we need to decide regarding, what are the costs involved and what is a price we are going to charge? So, let us start collecting the important data and we know in marginal costing or CVP we segregate the cost as per their nature.So, please list down the fixed cost, variable cost and semi-variable cost if any ok.So, are you able to identify, there is a cost of donation at the temple that is 3000 that is a fixed cost, gifts are fixed cost, bus rent one more fixed cost, prices shall we take bus rent permit. How much has a bus rent permit cost? I think it is based on anything is missed out special permit fee of 700 is per bus. So, we will not take it as a fixed cost, it becomes a semi-variable cost. So, let us list out what are the semi-variable cost.Teachers allowances, how much is an allowance to the teacher? 200 per teacher for 2 teachers. So, in each bus the for each bus the cost will be 400, entry fee for the bus, bus permit fee, then the variable costs; variable cost is 108, are you getting it. So, we have made a list of cost on food etcetera which is 20, 60, 80 and 20 making the variable cost per unit as 108 and the variable cost per teacher is 128 right. Now, this 128 though is variable per teacher for us the cost unit is a student. So, for every student, the variable cost is 108, for the teacher it is 128, but the variable cost of the teacher will need to be considered as the semi-variable cost right and there are two teachers in one bus. So, per bus cost is a cost calculation which we have made which includes teacher allowances, entry fee, food and another variable cost for the two teachers 258, 256, 4,700 is a bus rent, so it becomes 5756 per bus, fixed cost is 12000. Bus rent permit though I have entered will not be included in fixed cost; it will rather be included in the semi-variable cost which changes per bus not per student.So, are you getting it now we have got three types of costs one which is totally changed with the variable student, one which is changing with the bus, so SVC Semi Variable and the third ones are not changing at all they are fixed?Now, let us go for they have actually asked us to calculate BEP and other things, but in the c part, they have also asked us to calculate different costs as per the number of students. So, it will be better to make it different, so please open your netbook prepare column for 80, 120, 150 and 160 students right. So, how many buses will be required for 80 students? There will be 2 buses like that for each of the range let us go for a number of buses 2,3, 3 and 4 as per the number of students.Now, how much will be the variable cost for 80 students? Now, there is no point in writing each variable cost for each student, we are essentially calculating the total variable cost for 80 students and we know that variable cost is 108 per unit. So, 108 into 80 will be the VC for 80 students, so it comes 1680 are you getting.Now, much will be a semi-variable cost? It depends on the number of buses, there are 2 buses and one bus cost 5756.So, total SVC for 80 students comes to 11512 which is for 2 buses and a total fixed cost is 12000 which is anyway fixed. So, the total cost is 35152 for 80 students are you getting and what is an average cost?If we divide by 80 we get it as 401 around 400 rupees per student, if there are 80 students.Now, we have been asked in the c part of the question compute for 80, 120, 150 and 160. So, we will try to calculate it for all these four. In fact, we can also calculate it for50 just for our own sake.Now, same calculation please make it for 120 students.Now, what is VC?12960 right 108 into 120?Then semi-variable cost how much it is? Now, it is for 3 buses.So, it comes to 17268, fixed cost is unchanged, so it is 12000, the total cost is 42228 and now the average cost you can see there is a drop in average cost is 351.9.So, almost 50 rupees reduction has happened because the number of students has gone up.Now, let us see what happens if the number of students goes up to 150. So, how much is a VC now?It is 16200 at the rate of 108 into 150.Semi variable cost will be same now because it is now also its three buses, fixed cost is always constant at 1200, the total cost will be now 45468 and the average cost goes down to 303 because this is called also known as economies of scale. Now, you are having more students, so the total cost is going down. Now, if you go for 160 students will the total cost further go down? You can see here the total cost is falling from 80 to 120 to 150, for 160 will it fall further?It may not because economies of scale are not always true you can just calculate it and then we will discuss.So, VC is now 17280, SVC will go up because now there are 4 buses, fixed cost is constant, the total cost is now 52304 and you can just see that average cost has slightly gone up.Why has it gone up? Because SVC has gone up.If you remember, semi-variable costs are a step in nature. So, we can have 1 bus, 2 buses, 3 buses, 4 buses, now because just for the last 10 students you have to take one more bus that is why your average cost has gone up. Normally it is true that average cost will fall because the variable cost per unit is same108, fixed cost is constant at 12000 and gets spread over more and more number of students; however, the semi-variable cost is unique, it has a steep nature. So, while increasing the level of operations we have to keep a close eye on semi-variable cost. Are you getting ok, so these were basic calculations? Now, let us go to what has been asked.Now, you were asked to calculate BEP and it was told that you can have more than one answer.Now, what is a formula BEP?Fixed cost upon in this case since its number of students we will go for fixed cost upon contribution per unit, now the selling price is known that is 500, so compute the contribution.So, 500 minus 108, so very high contribution of 392 per unit. Breakeven point, so we go for FC upon contribution per unit.So, how much will be the breakeven point, will it be 12000 upon 392? Let us check. So, I think you will have to apply your mind and then only we will get the answer are you able to apply your mind because the fixed cost is not going to be fixed here.Normally we know that fixed cost is defined as a cost which does not change with the level of activity, but in this case, what is happening in the bus-related cost are semi-variable in nature and we are not including them in the variable cost.So, they are they have to be included in the fixed cost. So, what happens is if you have 2 buses the fixed cost becomes 23512 it is 12000 plus the cost of 2 buses that is 5756 into 2 are you getting it.So, for 80 students the fixed cost is 23512 when the number of students touches in fact when a number of students across 50 that is you have to go for sorry when the number of students crosses 100 that is you have to go for 3 buses. The fixed cost becomes 29268 and when you go for 4 buses the fixed cost becomes 35024,contribution is unchanged at 392.So, you get multiple breaks even points are you getting me.Now, the breakeven points are 59, 74, 89 that is why there was a possibility of having 3 breakevens. Can you have one more break even with just 50 students? I think we will need to calculate what happens for 50 students. If you just take 50 students that are only 1 bus the SVC is 5756 the total cost is 23000.So, the average cost is 463 although it was not asked in the problem we have done this extra calculation because for these you will need to calculate BEP. So, you will realize now it is just one bus, so the fixed cost is 17756 and BEP is 45. So, in the first part of the question, it was asked to calculate the BEP and you can have up to four alternate answers.I hope you have got the answers now. So, possible answers are 45, 63 sorry 45, 59, 74 and 89 are you getting it. Now, so far in earlier problems we never encountered with multiple BEP, but here you will realize that because of the existence of semi-variable cost you can approach a scenario where you can have more than 1 BEPs.If the cost structure is a straight line that is you have got same fixed cost and only one PV ratio or only one contribution per unit, then there will be only one BEP, but if the cost structure is a curve or if it is a step nature you can have more BEPs that is why while answering the first part of the question you will have to come out with four answers of BEP.Now, what are the 4 PV ratios can you calculate? PV ratio all of you know the formula contribution upon selling price.So, how much is a PVR are you able to calculate PV ratio for each of the scenarios in the first case it becomes 0.7840 that is 5 392 upon 500.What will happen for 2, 3, 4 buses?What will be the other PVRs, will they change?Actually no because PVR has nothing do with fixed costs or semi-variable cost, it is purely a relationship between contribution and sales that is why I was repeatedly asking what could be other PVRs, they are just asked here to confuse you.And mind well sometimes students are so intelligent that they come out with two three four PVRs because it is asked in the problem.Actually answer for the second part that is this PVR is only 1 because you can have just1 PVR which is 0.7480 are you getting me.Now, let us go to the b part.Now, in b part, it has been asked that school wants to help out some Municipal school students and they would be taken with our normal students at a concessional fee because they may not be able to afford 500 rupees. We want to charge them just enough to cover incremental costs, we do not want to make any profit from them at the same time we do not want to subsidize them so whatever is their cost will be recovered. So, what will be the concessional fee from these students in scenario 1, 2, 3, 4? Actually, the concessional fee will be just 108 because we know that variable cost per student is 108, we want to cover from them just enough that is just enough to cover their variable cost which is 108.Whether we have got 1 bus, 2 bus, 3 bus, 4 bus does not make any difference because we don't want to cover the rent of the bus from them only difference will be whatever is our free seats that are whatever our vacant seats we may want to take those students that number may vary, but the fee will not change.So, again four answers have been asked is just to trick you, concessional fee the only one answer is there that is 108 are you getting me.Now, the c part, maybe there are some complaints from the students that they don't want to pay 500 rupees.So, the school has now decided to charge the fee at cost without taking any profit from students, they will just take a fee at cost. So, what will be the lower fee in these four scenarios?So, what is the answer?I think we have already calculated the average cost now there will be no profit-taking there are 4 possible scenarios, there are 4 possible fees. So, for 80 students it's 401, for 120 students 351, then 303 and 326 got it.So, what have we learned in this case? There are two three extra things you already knew how to calculate breakeven point, but in this case, we have seen that there can be multiple break even points especially if cost structure is not linear. If you remember in my earlier session I had told you that some of the assumptions can be liberalized you can waive the assumption. So, we have waved the assumption that cost structure must be linear and we have allowed semi-variable cost that is why you have got multiple BEPs, but there is no multiple PVratio. Unless and until the selling price and variable cost do not change there will be only one PVR. Concessional fee if you remember we have discussed special pricing say for government contracts in one of our earlier cases this is similar, this is also special pricing for this for the municipal school students. So, that we can charge them a lower fee and we can take them just at 108 without any loss to our own students.And the c part was simple we had to just calculate the average cost and you can see that average cost normally goes down, but in some cases, it can go up also like it has happened for160 students when you compare with 150 students are you getting it ok. So, with this we will stop this case Namaste, thank you.