How to calculate learning curve on scientific calculator

The function of this article is twofold: first, it is to summarise the background of the learning curve impact and help candidays understand why it is crucial. 2nd, it is to look at what past learning curve inquiries have required of candidates and to clarify how future concerns might go beyond this.

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A brief background of the finding out curve

In exercise, it is often discovered that the resources compelled to make a product decrease as production volumes increase. It costs more to create the initially unit of a product than it does to develop the one hundredth unit. In part, this is because of economic situations of scale given that costs usually fall when products are made on a bigger scale. This might be because of bulk quantity discounts received from providers, for instance. The learning curve, effect, but, is not about this; it is not around price reduction. It is a huguy phenomenon that occurs because of the reality that civilization gain much faster at performing repeated tasks once they have actually been doing them for a while. The initially time a new procedure is perdeveloped, the employees are unacquainted with it given that the process is untried. As the procedure is repeated, but, the workers come to be even more familiar through it and much better at percreating it. This suggests that it takes them less time to finish it.

The initially reported observation of the learning curve goes as much back as 1925 once aircraft manufacturers observed that the number of guy hrs taken to assemble planes decreased as more planes were developed. TP Wappropriate consequently establiburned from his research of the aircraft industry in the 1920s and 1930s that the price at which finding out took place was not random at all and also that it was actually possible to accurately predict just how much work time would be compelled to construct planes later. During World War II, US federal government contractors then provided the discovering curve to predict price and also time for ship and aircraft building and construction. In time, private sector companies likewise adopted it after the battle.

The certain finding out curve result figured out by Wideal was that the cumulative average time per unit decreased by a solved percent each time cumulative output doubled. While in the aircraft industry this price of finding out was mostly seen to be about 80%, in various industries various other rates happen. Similarly, depending upon the sector in question, it is regularly more correct for the unit of measurement to be a batch fairly than an individual unit.

The finding out process starts as soon as the first unit or batch comes off the manufacturing line. Because a doubling of cumulative production is forced in order for the cumulative average time per unit to decrease, it is plainly the instance that the result of the discovering rate on labour time will certainly become a lot much less substantial as production increases. At some point, the discovering impact will certainly pertained to an end altogether. You deserve to see this in Figure 1 listed below. When output is low, the learning curve is really steep but the curve becomes flast as cumulative output boosts, through the curve ultimately ending up being a directly line as soon as the finding out impact ends.

Figure 1


The discovering curve impact will not constantly use, of course. It flourishes wright here certain conditions are current. It is vital for the procedure to be a repeated one, for instance. Also, tright here requirements to be a continuity of workers and also they mustn’t be taking prolonged breaks in the time of the manufacturing procedure.

The prestige of the discovering curve effect

Learning curve models allow customers to predict just how long it will certainly require to finish a future task. Management accountants should therefore be certain to take right into account any kind of finding out price as soon as they are transporting out planning, regulate and decision-making. If they fail to do this, major results will outcome. As regards its importance in decision-making, let us look at the instance of a company that is introducing a brand-new product onto the market. The firm desires to make its price as attrenergetic as possible to customers but still wants to make a profit, so it prices it based upon the full absorption price plus a small 5% mark-up for profit. The first unit of that product may take one hour to make. If the labour price is $15 per hour, then the price of the product will certainly be based on the inclusion of that expense of $15 per hour. Other costs might total $45. The product is therefore released onto the industry at a price of $63. Subsequently, it becomes obvious that the learning effect has been ignored and the correct work time per unit have to is actually 0.5 hours. Without crunching through the numbers aobtain, it is obvious that the product will certainly have actually been introduced onto the sector at a price which is much also high. This might expect that initial sales are much reduced than they otherwise would certainly have actually been and the product launch might fail. Worse still, the agency might have made a decision not to launch it in the initially location as it believed it could not market a competitive price.

Let us now think about its importance in planning and manage. If typical costing is to be offered, it is essential that conventional expenses provide an exact basis for the calculation of variances. If typical prices have actually been calculated without taking into account the learning effect, then all the work consumption variances will certainly be favourable bereason the traditional work hours that they are based upon will be as well high. This will certainly make their usage for control purposes pointmuch less.

Finally, it is worth noting that the usage of discovering curve is not restricted to the assembly industries it is traditionally associated via. It is also offered in other much less standard sectors such as professional exercise, financial solutions, publishing and also take a trip. In fact, research has shown that simply under fifty percent of users are in the business sector.

How discovering curves have actually been examined in the past

The learning curve impact has actually routinely been examined in Performance Management. For instance, in December 2011, it was examined in conjunction through life cycle costing. Candidates were asked to calculate a revised lifecycle expense per unit after taking into account the learning result. This affiliated working out the incremental labour time taken to create the last 100th unit made before the discovering result finished. This is a fairly widespread exam requirement which tests candidates’ knowledge of the distinction between cumulative and also incremental time taken to create a product and also the application of the finding out curve formula. It is worth mentioning at this suggest that you need to never before round discovering curve calculations to much less than 3 decimal locations. In some inquiries, where the discovering result is little, over-rounding will bring about a candiday wiping out the whole discovering effect and then the question becomes pointless.

The learning curve formula, as displayed below, is always provided on the formula sheet in the exam:

Y = axbWhere Y = cumulative average time per unit to create x unitsa = the time taken for the first unit of outputx = the cumulative number of units producedb = the index of learning (log LR/log2)LR = the finding out rate as a decimal

While a value for ‘b’ has usually been given in past exams there is no factor why this have to constantly be the situation. All candidays have to recognize just how to use a clinical calculator and also need to be certain to take one right into the exam hall.

In June 2013, the discovering impact was aget examined in conjunction through lifecycle costing. Aobtain, as has actually historically been the case, the learning rate was provided in the question, as was the value for ‘b’.

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Back in June 2009, the finding out curve impact was examined in conjunction with targain costing. Once aobtain, the learning rate was given, and also a worth for ‘b’ was offered, however this time, an average cost for the first 128 units made was required. It was after this allude that the discovering impact ended, so the question then went on to ask candidates to calculate the cost for the last unit made, considering that this was going to be the price of making one unit going forward in the organization.

It can be viewed, just from the examples provided above, that learning curve inquiries have tfinished to follow a relatively regular pattern in the past. The difficulty through this is that candidates don’t always actually think around the calculations they are performing. They ssuggest practise past files, learn just how to answer concerns, and never before really think beyond this. In the worklocation, once challenged with calculations entailing the finding out effect, candidays may not have the ability to tackle them. In the worklocation, the discovering price will certainly not be known in advance for a new process and also secondly, also if it has actually been estimated, differences may well aincrease in between intended finding out prices and actual finding out price skilled. Thus, it appeared only right that future inquiries should study candidates’ capacity to calculate the learning price itself. This leads us on to the next section of the write-up.

Calculating the learning rate

The discovering result deserve to proceed to be examined with candidays being asked to calculate the moment taken to develop an individual unit or a variety of devices of a product either as soon as the discovering curve is still in result or when it has actually finished. In a lot of concerns ‘b’ has actually generally been given, however candidates have the right to additionally be supposed to calculate the finding out rate itself. Here, the tabular strategy is the most basic means to answer the question.

Example 1

P Co operates a typical costing mechanism. The typical work time per batch for its newest product was estimated to be 200 hours, and also reresource alplace and expense information were ready on this basis.

The actual number of batches developed in the time of the initially 6 months and the actual time taken to develop them is presented below:



Learning rate:176/200 = 88%154.88/176 = 88%136.29/154.88 = 88%

Thus the monthly rate of learning was 88%.

(b) End of discovering rate and implications

The finding out period finished at the end of September. This intended that from October onwards the moment taken to create each batch of the product was continuous. Because of this, in future, as soon as P Co provides decisions around allocating its resources and costing the product, it should base these decisions on the moment taken to produce the eighth batch, which was the last batch produced prior to the learning period pertained to an end. The reresource allocations and also expense data ready for the last six months will certainly have been inexact considering that they were based on a standard time per batch of 200 hrs.

P Co can try and also improve its manufacturing procedure so that the discovering duration can be extended. It may have the ability to do this by raising the level of staff training offered. Alternatively, it might attempt to incentivise staff to work harder with payment of bonsupplies, although the high quality of production would certainly should be preserved.

Example 2

The initially batch of a new product took 6 hours to make and the total time for the initially 16 systems was 42.8 hours, at which suggest the finding out impact involved an finish.

Required: (a) Calculate the rate of discovering.

Solution: Aget, the simplest way to fix this problem and discover the actual discovering price is to use a combination of the tabular method plus, in this case, a tiny bit of maths. Tbelow is an alternate approach that have the right to be provided that would involve some even more challenging maths and also usage of the inverse log button on the calculator, however this have the right to be rather tricky and also candidays would not be expected to use this strategy. Should they choose to carry out so, yet, complete marks would certainly be awarded, of course.


Using algebra:

Step 1: Write out the equation:42.8 = 16 x (6 x r4)

Step 2: Divide each side by 16 in order to remove the ’16 x’ on the right hand side of the equation:2.675 = (6 x r4)

Tip 3: Divide each side by 6 in order to eliminate the ‘6 x’ on the best hand side of the equation:0.4458333 = r4

Tip 4: take the fourth root of each side in order to remove the r4on the ideal hand side of the equation. You must have a switch on your calculator that saysr4or x1/y. Either of these can be supplied to discover the fourth root (or any root, in fact) of a number. The key is to make sure that you deserve to usage your calculator properly prior to you enter the exam hall rather than trying to work-related it out under exam press. You then obtain the answer:r = 0.8171

This indicates that the finding out rate = 81.71%.


The above 2 examples show the type of requirements that you might uncover in concerns where you are asked to uncover the learning price. All that we are doing is encouraging you to think a little and also, in some situation, perhaps usage a tiny little of the maths that, as a trainee accountant, you have to be even more than capable of applying.