MANAGEMENT ACCOUNTING APPLICATIONS The learning …

[Pages:2]CIMA Student 8

MANAGEMENT ACCOUNTING APPLICATIONS

The learning curve: from aircraft to spacecraft?

G.J. Steven, Napier University

This article on the learning curve: ? explains the learning effect; ? identifies sectors where it can be

used; ? explains how it is calculated; ? explains, with examples, how it

can be used for planning, control and decision-making; ? discusses the other factors that have to be considered in relation to its use.

W hile this article was principally written for Management Accounting Applications, it is also relevant for Management Science Applications (MSA). MSA students, however, are only expected to have knowledge of this technique, i.e. no calculations are required for this technique at Stage 2.

Introduction

The learning curve was first observed by Wright in the 1930s in the American aircraft industry, and his pioneering work was confirmed by Crawford in the 1940s. But what is the learning effect? Where can it be used? What can it be used for? And is it relevant for the modern business environment?

Economies of scale

Most students will be familiar with economies of scale. However, it is important to appreciate that the learning effect is not concerned with reduction in unit cost as production increases and/or production facilities are scaled up to manufacture larger batches of products. So what is the learning effect?

Learning effect

The learning effect is concerned with cumulative production over time--not the manufacture of a single product/batch at a particular moment in time--and recognises that it takes less time to assemble a product the more times that product is made by the same worker, or group of workers.

The most effective way of describing the learning effect is to consider the assembly of selfassembly furniture in your own home! Let's assume that you decide to purchase three selfassembly chests of drawers for your home.

The first chest of drawers will take considerable time to assemble since you are unfamiliar with the

instructions, the components, and how to assemble them. In addition, you may also lack confidence in your ability to produce an acceptable product.

The second one, however, will take you less time, as you will be more familiar with the instructions, the components, and the assembly procedures. You will also be confident of your ability to assemble this product.

The third one will take even less time, as you will have learned from your earlier mistakes and determined more efficient assembly procedures. That is the learning effect.

Cost reduction tool?

It is important to appreciate that the learning curve is not a cost-reduction technique since the rate of future time reduction can be predicted accurately by the learning curve model. Cost reduction only occurs if management action is taken, for example, to increase the rate of time reduction by providing additional training, provision of better tools etc.

The learning effect occurs because people are inventive, learn from earlier mistakes, and are (generally) keen to take less time to complete tasks, for a variety of reasons. It should also be noted that the learning process may be done consciously and/or intuitively. The learning curve consequently reflects human behaviour.

Learning curve sectors

While the learning curve can be applied to many sectors, its impact is most pronounced in sectors which have repetitive, complex operations where the pace of work is principally determined by people, not machines. If the pace of work is determined by machines, the learning effect will not be observed since (at present!) people learn, not machines.

Examples of sectors where the learning effect is pronounced include: ? aerospace; ? electronics; ? shipbuilding; ? construction; ? defence. The learning curve is also being utilised by the refurbishment sectors. Rail operators, for example, seek to extend cost-effectively the lives of their assets, e.g. London Underground, privatised rail companies etc.

Another sector which makes considerable use of this technique is the space industry. NASA, for example, uses the learning curve to estimate costs for the production of space shuttles, time to

complete tasks in space etc. The phenomenon observed by Wright and Crawford is now being used for extra terrestrial activities!

Learning curve model

Wright observed that the cumulative average time per unit decreases by a fixed percentage each time cumulative production doubles over time. The following table illustrates this effect:

Cumulative output

1 unit 2 units 4 units 8 units

Cumulative time

1,000 hrs 1,800 hrs 3,240 hrs 5,832 hrs

Average time

1,000 hrs 900 hrs 810 hrs 729 hrs

The above table indicates that the cumulative average time per unit falls by 10% each time cumulative production doubles, i.e. it is depicting a 90% learning curve.

The above relationship between cumulative output and time can be represented by the following formula:

Yx = axb where Yx = cumulative average time to

produce a cumulative number of units a = time to produce the first unit x = cumulative number of units b = index of learning

The index of learning is the log of the learning curve divided by the log of 2.

NB: At present, CIMA does not require students to calculate the index of learning.

Use your calculator to confirm that b = -0.152 for a learning rate of 90%;

Calculator instructions Press LOG Enter 0.9 Press DIVIDE Press LOG Enter 2 Press EQUALS to obtain answer, i.e. -0.152

NB: The above instructions may not apply to all types of scientific calculator

and the cumulative average time per unit is 7,329 hours for a cumulative output of eight units.

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Management Accounting May 1999

CIMA Student 9

Calculator instructions Enter a, i.e. 1000 Press MULTIPLY Enter x, i.e. 8 Press XY Enter b as a positive, i.e. 0.152 Change b to -b with +/-, i.e. 0.152 Press EQUALS to obtain answer, i.e. 729

NB: The above instructions may not apply to all types of scientific calculators.

NASA's web site--see below for URL--contains a learning curve calculator based on Wright's and Crawford's models. Unfortunately, students do not have access to this resource in CIMA's examinations! Please note that the preceding calculations are based on Wright's model.

Budgeting and control

While the learning curve can be used for a number of purposes as it predicts time reduction, it is normally associated with budgeting. This is because budgets and standards will only provide reliable benchmarks to measure actual performance against if account is taken of the learning effect.

For example, if it is assumed that the above data covered the first year's production of this product, and demand in year 2 was expected to be 24, a simplistic analysis which ignored the learning effect would produce an estimate of 17,496 hours to produce 24 additional items. This would produce a large favourable variance if the actual time taken to produce these 24 items was 13,800 hours.

Additional production (24 items) Multiplied by Cumulative average time for last year's production (729 hours) Equals 17,496

A very different picture emerges, however, if account is taken of the learning effect since the expected time to produce the additional 24 items would be 13,064 hours. That is, it would generate a significant adverse variance which would provide a more accurate indication of performance.

Cumulative average time for 32 items x 32 (= 18,896 hours) Less Cumulative average time for 8 items x 8 (= 5,832 hours) Equals 13,064 hours

Decision-making

While a great deal has been written about the use of the learning curve for control purposes, this technique can also be used to determine costs for potential contracts in sectors which exhibit the learning effect.

For example, Above & Beyond Ltd, which produces high-technology guidance systems, is preparing a tender for the Aurora project, the new generation of space shuttles. The guidance systems for the Aurora project will be very similar to those recently supplied by the company for the Dark Star project, experimental Stealth aircraft

capable of flying outside the earth's atmosphere. The company has been asked to submit a tender to install ten guidance systems for this project.

While a tender would take account of all costs that would apply to a particular project, one of the key costs for a high-technology project is labour time, as highly skilled personnel (who are highly paid) are required to assemble and test such systems. The following analysis will focus on the labour time required for this project.

Aurora project

Above & Beyond Ltd's engineers believe it is possible to estimate the time required to install the guidance systems for the new generation of space shuttles from the learning derived from the Dark Star project. The same system will be installed in the space shuttles. The following data was consequently obtained in respect of the Stealth project: ? Time to install first system: 12,000 hours; ? Total installed: to date 9 systems; ? Total cumulative time: 69,595 hours. The first figure to be calculated is b, the index of learning, and this can be derived from the learning curve equation, Yx = axb, since all the other figures are known.

Yx = aXb 69,595/9 = 12,000 x 9b

9b = 7733/12000 9b = 0.6444 b log 9 = log 0.6444

b = log 0.6444 / log 9 b = - 0.2

- 0.2 is equivalent to a learning rate of 87%, i.e. the antilog of (-0.2 multiplied by log 2).

It is now possible to estimate the time required to install the guidance systems for this project.

Cumulative average time for 19 systems x 19 (= 126,527 hours) Less Cumulative average time for 9 systems x 9 (= 69,595 hours) Equals 56,932 hours

Please note that the learning curve would produce an estimate of 75,715 hours to install the guidance systems using a learning rate of 87% if no account was taken of the learning derived from Dark Star. This difference of 18,783 hours is extremely significant since the costs of hiring specialist engineers, and supporting these engineers, could be ?100+ per hour, i.e. ?1.8m+.

Other factors

The calculations for the Aurora project assumed it was possible to continue down the learning curve from the learning obtained in respect of the Dark star project. This might not be a realistic starting point, however, as it may be necessary to take account of the following factors: ? the guidance system for the Aurora project may

have to be modified for the shuttles since they have, for example, a different airframe; ? the work teams may be different from those used for the Dark star project; ? the time lapse since the completion of the Dark Star project.

It may consequently be necessary to take a more realistic view of the initial efficiency levels that can be achieved for the Aurora project. It may be prudent, for example, to use a cumulative total production of seven to estimate the time required for this project, i.e. 58,836 hours. While this will be a subjective judgment, hopefully based on past experience, it must be made to avoid underestimating the time required for this project. it may also be necessary to determine whether or not the learning rate for Dark Star was affected, adversely or favourably, by illness, holidays, changes to work groups etc, to determine whether or not a reasonable learning rate resulted from that project.

Conclusion

The learning effect, which was first recognised by Wright and Crawford, still applies to today's business environment since people haven't changed since the 1930s. It is also possible that the learning curve will be used more widely in the future due to the demand for sophisticated hightechnology systems, and the increasing interest in refurbishment to extend asset life. While much has been written in relation to the use of the learning curve for budgeting and control, there has been little recognition of its potential for decisionmaking. The learning curve is a vital decisionmaking tool, however, since it can be used to prepare competitive tenders by utilising earlier learning for new contracts for the same, or a similar, product. Customers are also increasingly aware of the learning effect, and expect tenders to take account of this factor. The phenomenon observed by Wright and Crawford is, consequently, still relevant for the modem business environment.

References and further reading DRURY, C. (1996): Management and Cost Accounting, International Thomson Business Press, pp.687- 691 DUGDALE, D., KENNEDY, A., SUGDEN, K. and SCARLETT, R. (1996): Management Accounting Applications: Practical Elements, pp.61-66 KENNEDY, A. and SUGDEN, K. (1996): Management Accounting Applications: Knowledge, pp.37-41 NASA . bu2/learn.html UPCHURCH (1998): Management Accounting: Principles and Practice, pp.78 - 85, Pitman

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