FINANCIAL
44 MANAGEMENT April 2005
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 = aXb.
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:
BILL BROOKFIELD
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.
TABLE 1 CUMULATIVE QUANTITY VERSUS
CUMULATIVE AVERAGE TIME
Cumulative quantity Cumulative production time Cumulative average
production time per unit
1 unit 1,000 hours 1,000 hours
2 units 1,600 hours 800 hours
4 units 2,560 hours 640 hours
8 units 4,096 hours 512 hours
