The learning curve effect will not always apply, of course. It flourishes where certain conditions are present. It is necessary for the process to be a repetitive one, for example. Also, there needs to be a continuity of workers and they mustn’t be taking prolonged breaks during the production process.
The importance of the learning curve effect
Learning curve models enable users to predict how long it will take to complete a future task. Management accountants must therefore be sure to take into account any learning rate when they are carrying out planning, control and decision-making. If they fail to do this, serious consequences will result. As regards its importance in decision-making, let us look at the example of a company that is introducing a new product onto the market. The company wants to make its price as attractive as possible to customers but still wants to make a profit, so it prices it based on the full absorption cost plus a small 5% mark-up for profit. The first unit of that product may take one hour to make. If the labour cost is $15 per hour, then the price of the product will be based on the inclusion of that cost of $15 per hour. Other costs may total $45. The product is therefore released onto the market at a price of $63. Subsequently, it becomes apparent that the learning effect has been ignored and the correct labour time per unit should is actually 0.5 hours. Without crunching through the numbers again, it is obvious that the product will have been launched onto the market at a price which is far too high. This may mean that initial sales are much lower than they otherwise would have been and the product launch may fail. Worse still, the company may have decided not to launch it in the first place as it believed it could not offer a competitive price.
Let us now consider its importance in planning and control. If standard costing is to be used, it is important that standard costs provide an accurate basis for the calculation of variances. If standard costs have been calculated without taking into account the learning effect, then all the labour usage variances will be favourable because the standard labour hours that they are based on will be too high. This will make their use for control purposes pointless.
Finally, it is worth noting that the use of learning curve is not restricted to the assembly industries it is traditionally associated with. It is also used in other less traditional sectors such as professional practice, financial services, publishing and travel. In fact, research has shown that just under half of users are in the service sector.
How learning curves have been examined in the past
The learning curve effect has regularly been examined in Performance Management. For example, in December 2011, it was examined in conjunction with life cycle costing. Candidates were asked to calculate a revised lifecycle cost per unit after taking into account the learning effect. This involved working out the incremental labour time taken to produce the final 100th unit made before the learning effect ended. This is a fairly common exam requirement which tests candidates’ understanding of the difference between cumulative and incremental time taken to produce a product and the application of the learning curve formula. It is worth mentioning at this point that you should never round learning curve calculations to less than three decimal places. In some questions, where the learning effect is small, over-rounding will lead to a candidate wiping out the entire learning effect and then the question becomes pointless.
The learning curve formula, as shown below, is always given on the formula sheet in the exam:
Y = axb
Where Y = cumulative average time per unit to produce x units
a = the time taken for the first unit of output
x = the cumulative number of units produced
b = the index of learning (log LR/log2)
LR = the learning rate as a decimal
While a value for ‘b’ has usually been given in past exams there is no reason why this should always be the case. All candidates should know how to use a scientific calculator and should be sure to take one into the exam hall.
In June 2013, the learning effect was again examined in conjunction with lifecycle costing. Again, as has historically been the case, the learning rate was given in the question, as was the value for ‘b’.
Back in June 2009, the learning curve effect was examined in conjunction with target costing. Once again, the learning rate was given, and a value for ‘b’ was given, but this time, an average cost for the first 128 units made was required. It was after this point that the learning effect ended, so the question then went on to ask candidates to calculate the cost for the last unit made, since this was going to be the cost of making one unit going forward in the business.
It can be seen, just from the examples given above, that learning curve questions have tended to follow a fairly regular pattern in the past. The problem with this is that candidates don’t always actually think about the calculations they are performing. They simply practise past papers, learn how to answer questions, and never really think beyond this. In the workplace, when faced with calculations involving the learning effect, candidates may not be able to tackle them. In the workplace, the learning rate will not be known in advance for a new process and secondly, even if it has been estimated, differences may well arise between expected learning rates and actual learning rate experienced. Therefore, it seemed only right that future questions should examine candidates’ ability to calculate the learning rate itself. This leads us on to the next section of the article.
Calculating the learning rate
The learning effect can continue to be examined with candidates being asked to calculate the time taken to produce an individual unit or a number of units of a product either when the learning curve is still in effect or when it has ended. In most questions ‘b’ has usually been given, however candidates can also be expected to calculate the learning rate itself. Here, the tabular method is the simplest way to answer the question.
P Co operates a standard costing system. The standard labour time per batch for its newest product was estimated to be 200 hours, and resource allocation and cost data were prepared on this basis.
The actual number of batches produced during the first six months and the actual time taken to produce them is shown below: