Management accounting--decision management: the learning curve equation has a number of applications in the manufacturing sector. Fortunately, the formula itself is fairly straightforward to learn for paper P2.
| Author | Brookfield, Bill |
| Position | Study Notes |
The principle underlying learning curves is generally well understood: if we perform tasks of a repetitive nature, the time we take to complete subsequent tasks reduces until it can reduce no more. This is relevant to management accounting in the two key areas of cost estimation and standard costing.
Before we look at these we need to understand the maths. Imagine that we have collected the following information for the production of eight units of a product: it takes 1,000 hours to produce the first unit; 600 hours to produce the second unit; 960 hours to produce the third and fourth units; and 1,536 hours to produce the remaining four units. There is clearly a learning curve effect here, as the production time per unit is reducing from the initial 1,000 hours.
Learning curves are initially concerned with the relationship between cumulative quantities and cumulative average times (total cumulative time divided by cumulative quantity). The relationship in this case is shown in table 1. Notice that, as the cumulative quantity doubles, the cumulative average time reduces by 20 per cent. In other words, subsequent cumulative average times can be obtained by multiplying the previous cumulative average time by 80 per cent. This is an example of an 80 per cent learning curve. A learning curve is addressed in percentage terms, depending upon the relationship between the cumulative average times when the cumulative quantities are doubling. For example, if the cumulative average time were 1,000 hours at the production of the first unit, 700 hours at the production of the second, 490 hours at the fourth, 343 hours at the eighth and so on, this would be a 70 per cent learning curve.
The learning curve formula is needed when dealing with situations that do not fit into this doubling-up pattern.
A learning curve is geometric with the general form Y = a[X.sup.b].
Y = cumulative average time per unit or batch.
a = time taken to produce initial quantity.
X = the cumulative units of production or, if in batches, the cumulative number of batches.
b = the learning index or coefficient, which is calculated as: log learning curve percentage / log 2. So b for an 80 per cent curve would be Log 0.8 / log 2 = - 0.322.
Example one: unit accumulation
The first unit took 100 hours to produce. It is expected that an 80 per cent learning curve will apply. You are required to estimate the following times:
a The cumulative average time per unit to produce three units.
b The total time it will take to produce three units.
c The incremental time for the fourth and fifth units, in total.
The solutions are as follows:
a Y = 100([3.sup.-0.322]) = 70.2 hours per unit.
b We need to multiply Y by the cumulative number of units (X) to derive the total time: 70.2 x 3 = 210.6 hours.
c The incremental time to produce the fourth and fifth units equates to the total time to produce five units minus the total time to produce three units.
Cumulative average time to produce five units:
Y = 100([5.sup.-0.322]) = 59.56 hours per...
To continue reading
Request your trialCOPYRIGHT GALE, Cengage Learning. All rights reserved.
