 Next, we will look at the profit volume ratio. So, profit volume ratio is another useful tool for finding the break even point for sales, especially for the multipurpose firm. So, this is the break even point in the short form is known as BEP that is of sales especially for the multipurpose firm. And what is the PV ratio? PV ratio is S minus B upon S multiplied by 100, where S is the selling price B is the average variable cost. So, the profit volume ratio is the difference between the selling price and the average variable cost. And this is PV ratio is generally used as the break even point for the sales particularly in the multipurpose firm. So, if you the selling price is S is equal to 5 unit, the average variable cost B is equal to rupees 4 unit, then the PV ratio is selling price that is 5 minus variable cost 4 upon 5 multiplied by 100 that is 20 percent. So, we can say that 20 percent is the PV volume ratio. Then we will take another example to understand this PV ratio. Suppose we have product, in two products since we are saying multipurpose firm. So, A and B will take selling price here and will take variable cost per unit and will take machine hour per unit. So, in case of selling price in case of A this is 2, in case of B this is 2.5, variable cost per unit is 1 in case of A, 1.5 in case of B, machine hour per unit is 2 in case of A and 1.0 in case of B. Now, to find out the PV ratio for A, PV ratio for A will take selling price minus variable cost upon selling price multiplied by 100. So, this will 2 is the selling price minus 1 is the variable cost per unit divided by 2 multiplied by 100 that gives to 50 percent. So, 50 percent is the break even level price that is through the PV ratio. So, now, to find out the PV ratio for machine hour because if you look at machine hour required is 2 unit. So, in this case to find out the PV ratio for each machine hour, PV ratio for A for each machine hour this 50 percent will be divided by 2 that is 25 percent. So, 25 percent is the PV ratio and that leads to the break even sales price of the break even price for the sales. Similarly, how to find out the PV ratio for B? PV ratio for B is again S minus B by S. So, there it comes to 2.5 minus 1.5 by 2.5 multiplied by 100 that comes to 40 percent so PV ratio for B will be 40 percent. And since this is the machine hour is only 1 this is the total PV ratio in term of the machine hour also. So, in case of A the PV ratio is 25 percent in case of B the PV ratio is 40 percent. So, in this case B will be preferable to A or the in the other word we can say the firm will get more break even or may get may more profit from B as compared to the A because the PV ratio is more in case of B as compared to A and PV ratio is nothing, but the difference between the selling price and the selling price and the variable cost of production. So, the larger is the larger is the variation more profit to the firm because that that finally, lead to the break even price for the sales for the typical product. Then we will discuss about the so break even point in the sales value is calculated by dividing the fixed expenses F by the PV ratio. So, BEP sales value is the fixed expenses by PV ratio which is equal to F by S minus B divided by S. Then we will talk about the margin of a safety and margin of safety generally represents the difference between sales at the break even point and the total actual cost. So, the difference between the sales at the break even point and the total actual cost leads to the margin of safety. There are three measures to this margin of safety. One that is profit multiplied by sales by PV ratio, second profit by PV ratio and third margin of safety is S A minus S B divided by S A multiplied by 100 where S A is the actual sales S B is the sales at BEP. So, we will just take an example to understand this margin of safety. So, here total revenue is 10 Q, total cost is 50 plus 5 Q and S A is 20. So, given the total revenue and total cost function sale at BEP S B can be if you look at so total revenue is 10 S B and total cost is 50 plus 5 S B because this is the sales at the break even level of output which is equal to Q. Then at the break even point total revenue is equal to total cost. So, substituting the value of total revenue and total cost that is 10 S B is equal to 50 plus 5 S B. So, 10 S B minus 5 S B which is equal to 50. So, 5 S B is equal to 50 and S B is equal to 10. Now, in order to find the margin of safety we know that S B is equal to 10 and S A is equal to 20. So, following the third measure that is S A minus S B by S A multiplied by 100 will give us the margin of safety. Here S A is the actual sales, this is the break even sales. So, corresponding to this we will get marginal load of safety is equal to 20 minus 10 by 20 multiplied by 100 which is equal to 50 percent. So, this margin of safety can be increased by increasing the selling price provided that demand of four product is in elastic because if it is elastic then small change in the price is going to get influenced by the consumer and they will change the demand pattern. So, the margin of safety is the difference between the actual sales and the break even sales and break even sales can be find out from total cost and total revenue. So, margin of safety in the last place if you look at the more is the actual sale that is S A that more is the margin of safety. So, it can be increased by increasing the selling price the sales can be increased by increasing the selling price provide the sales are not seriously affected and it can happen only when the demand for product is in elastic because if it is elastic whenever there is change in the change in the price selling price that leads to affect the demand and in one way that will reduce the sales the quantity of the sales. Also this margin of safety can be increased by increasing the production and sales up to the capacity of the plant even by reducing the selling price provided the demand is elastic. So, it can be also increased by increasing the production and sales up to the capacity of the plant even by reducing the selling price and here again the precondition is the demand has to be elastic. So, this for a margin of safety the other method includes reduction in the fixed absence in order to increase the margin of safety. The other methods to increase the margin of safety is to reduction in the fixed expenses, reduction in the variable expenses or having a product mix with a greater share of one that assure a greater contribution per unit which has a higher PV ratio. So, either the margin of safety can be increased by reducing the fixed expenses, reducing the variable expenses or using a product mix which gives more contribution that is more than the fixed cost and also a higher PV ratio the profit volume ratio. So, margin of safety can be increased by reducing the expenses, both fixed expenses and the variable expenses or greater share of contribution or the greatest value of the PV ratio. So, when it comes to this break even analysis whether it is contribution analysis through the PV ratio or through any other method if you look at it can be only applied to the single product system or cannot be applied when the cost and price data cannot be determined beforehand. So, there is a limitation to the break even analysis if it is applicable only to the single product system and it can be applied only if the cost and price data is known beforehand. Then we will talk about the concept of a learning curve and if you look at we are going on discussing one fact across this session that this long run average cost curve is u shape and this long this u shape the decreasing part is because of economies of scale, the reduced cost is because of economies of scale and the increasing part is because of diseconomies of scale. But if you look at there may be other reason also to understand that this reduced cost it not only because of economies of scale or the increase cost is not because of diseconomies of scale there may be few other factors which influence the increasing and decreasing average cost of production when there is the scale of output increases. So, one of the fact here is that the acquire knowledge and experience help firms in reducing the long run average cost curve most continuously. The learn about time to get work done in shorter period of time reduce cost of production and increase factor productivity like if you take the case of labour if you take the case of capital I think when you the opinion of the firm or the opinion of the learning proponent of learning curve is that when the firm does the same type of production over a period of time they get experience in doing that and that leads to less time that leads to less cost of production and increase the factor of productivity. So, the efficiency of the inputs increases efficiency of the firm increases and that is the reason the cost is decreasing. So, the learning cost the theory behind learning cost is that it is not because of economies of scale or the diseconomies of scale there is one more fact that the knowledge and experience in doing the same kind of activity they learn through it and that leads to the average cost decreases. Suppose someone new to operate that machine and if the labourer is operating that machine over a period of time he gain the skill he gain the exposure to operate this operate the machine and he is doing the whatever the time he is requiring time requires to operate the machine that has come down and maybe also the the productivity of the labour has increased because in the same time he can do something else now. Similarly, if you look at the process itself the process itself initially there is a time to fix up or set up the process, but in the long run when you do it over a period of time the process is set up the system is in place and that leads to less time and the inputs become more productive. So, in case of learning of the opinion is that the acquire knowledge and experience help the firms to reduce the average cost and that leads to the shorter period of time reduce cost of production and increase the factor productivity. And this learning curve is one that is applicable to the cumulative output and it is not the output may be average output the major difference between the long run average cost curve and the learning curve is in case of long run average cost curve we take the average cost of production with the increase in the scale of output, but in case of learning curve we take the cumulative output that is the total product from the beginning of the scale. So, if you look at this curve is showing a declining trend in the. So, if this is the learning curve it is decreasing, but in case of long run average cost curve it is always increases after a point, but is in case of learning curve in case of learning curve it the cumulative cost cumulative output in case of cumulative the average cost goes on decreasing there is no shine to increase the cost of production when the output in the scale of output increases. So, this curve shows a declining trend in long term average cost of production and learning curve is different from the conventional long run average cost curve as long run average cost curve gives the cost of plant wise production learning curve gives the average cost of cumulative output the total output right from the beginning of a production of the commodity. Now, we will say we will take a small numerical to understand this learning curve or we will do the we will estimate the unit of the learning. So, if you take a cost function where c is equal to a q to the power b, where c is the average cost and q is the average cost for unit of output q, a is the cost of first unit of output and b is the rate of decrease in rate of decrease in average cost with cumulative increase in output the value of b is negative because decrease in q will always increase the or may be decrease in the cost with cumulative increase in the output the greater the value of b the faster is the decrease in the average cost. So, this learning of this c a q b can be converted into a logarithmic form that is c a q to the power b. So, this can be log c is equal to log a plus b log q. So, b gives the slope of the learning curve b gives the slope of the learning curve a is the intercept. So, if you look at this if you take this that log c is equal to 5 minus 0.4 log 100 suppose if assign the value of q is equal to 100, b is equal to 0.4 and a is equal to 5 then this equation will be log c is equal to 5 minus 0.4 log 100 and since log of 100 is 2 then we can again reframe this equation as log c is equal to 5.0.4 multiplied by 2 and which is equal to 5 minus 0.8 which is equal to 4.2. So, if you take a antilog of 4.2 that comes to 15849 and if you summarize this then unit cost of 100 unit of output is equal to 15849 is the cost of production. So, similarly you can find out for any level of output that is you can find out the cost for any level of output simply changing the value of q and getting the value of log a and log b. So, if you summarize whatever we have discussed today taking this break even analysis learning curve and PV ratio the business manager must plan for the long run administration of the cost revenue and profit and because in the long run firm will be in a position to expand the scale of production by increasing all inputs. So, it is a kind of scenario analysis it is a kind of long term horizon how the firm because the firm's decision firm's business decision depends upon the cost and revenue because that gives us the profitable and non profitable range of output. So, in the long run with the increase in output the total cost of production first increases at the decreasing rate then at an increasing rate and as a result the long run average cost initially decreases until the optimum utilization of new plant capacity and then it began to increase. And the cost and output relation always follow a laws of return to scale and that is the reason the long run average cost curve is show a u shape. So, the decreasing part of the long run average cost curve is because of economies of scale and long run increasing part is because of diseconomies of scale. So, the cost are assumed to plan their production activity much better if the level of production for which total cost and total revenue break even is known and this implies the profitable and non profitable range of output. So, we analyze the break even analysis for both linear and the non-linear total cost and revenue analysis. So, the break even analysis or the profit contribution analysis is the analytical technique used in studying the relationship between the total cost, total revenue, total profit losses over a range of stipulated output and basically there is a technique of previewing the profit prospect and tool of profit planning. So, if you remember in case of linear cost and revenue we get one break even level of output where the profitable range of output is unlimited. But in the real life this is not possible to get a unlimited profitable range of output that brings the non-linearity in the total revenue and total cost function and in case of non-linear total revenue and total cost function we get two break even level of output. So, rather than getting a profitable range of output we get a upper limit and lower limit for the profitable range of output. Then we discuss about the PV ratio and the PV ratio which is specifically deals and the contribution analysis which is specifically deals with the incremental revenue and the incremental cost. Incremental revenue and incremental cost comes to the fact where we cannot do the analysis with the marginal cost and marginal revenue where the per unit change is not possible. In this case the contribution is the guiding factor for the contribution is the guiding factor for the business manager to decide the range of output. So, in case of contribution analysis beyond the before the break even analysis before the break even level of level of output the contribution is less than fixed cost that is that the firm incur loss. But in case of beyond the break even level of output the contribution is more than fixed cost and that leads to the profit. So, here in case of incremental analysis the guiding factor is the contribution and that helps the manager to decide whether to go for that range of output or not. And finally, we discuss about the learning curve which is alternate to the economies of scale as the reason behind the decreasing cost of production. And here it is different from the long run average cost curve because the learning curve is one where the average cost goes on decreasing for the cumulative output and that achieve through the experience that achieve through the productivity of the factor input. So, we will continue our discussion on this cost again typically on economies and diseconomies of scale in the next session. And for preparing this session these are the session references that is being exclusively followed for this.