This helpsto understand learning curve theory

1. LEARNING CURVE THEORY

2. INTRODUCTION
The first time a new operation is performed both workers and operating
procedures are untried but as the operation is replaced the workers
becomes more familiar with the work so that less hours are required.
This phenomena is known as the learning curve effect.
This is also referred to as improvement curve theory. It occurs when
new production methods are introduced, new products (either goods or
services) are made or when new employees are hired. It is based on the
proposition that as workers gain experience in a task, they need less time
to complete the job and productivity increases.
The learning curve theory affects not only direct labour costs but also
impacts direct labour related costs such as supervision, and direct
material costs due to reduced spoilage and waste as experience is gained.

3. The time to perform many operations begins slowly and speeds
up as employees become more skilled. Gradually, the time needed
to complete an operation becomes progressively smaller at a
constant percentage.
Since this rate of improvement has a regular pattern, a learning
curve can be drawn (see diagrams) to estimate the labour hours
required as workers become more familiar.
These curves are also referred to as progress functions or
experience curves.
INTRODUCTION

4. COST ESTIMATION AND FORECASTING 8 7
Cumulative quantity
INTRODUCTION

5. The effect of experience on cost is summarized by a learning
ratio (improvement ratio or learning rate) defined by the
following;
Learning ratio = Average labour cost for the first 2x units
Average labour cost for the first x units
Example 1:
The first 500 units have an average labour cost of sh.12.50 and
the average labour cost for the first 1000 units is sh.10.
Required: Calculate the learning ratio.
Learning ratio = Sh.10/12.5 x100 = 80%
INTRODUCTION

6. Interpretation
Every time cumulative output doubles, average cost declines to 80 percent of the
previous amount. Since the average cost of the first 1000 units was sh.10, the
average cost of the first 2000 units will be expected to be 20% or sh.8 per unit.
Learning curve equation:
The basic learning curve equation is
Y = abx
Where: a is the labour cost of the first unit
b is the cumulative production
x is the improvement exponent or an index learning given by:
x = logarithm of the learning ratio = log (1- proportional decrease)
logarithm of 2 log 2 x can take any value between -1 and zero.

Y is defined depending on whether a cumulative model or incremental model is
being applied.
The above equation can be restated in the logarithmic form Log Y = log a + x log b
INTRODUCTION

7. Incremental cost
If producing a second 1000 units is to reduce cumulative average cost from
sh.10 to sh.8, the cost of the second 1000 units will have to be only sh.6000, or
sh.6 each. Hence;
Total Cost (Sh.) No. of Units Average Cost (sh.)
First 1000 units 10,000 1,000 10
Second 1000 units 6,000 1,000 6
16,000 2,000 8
EXAMPLE

8. Defining the learning curve in terms of this incremental
relationship would be more useful but is more difficult to work
with. As a result, learning curve improvement ratios are usually
stated as percentage reductions in cumulative average labour cost.

9. APPLICATION OF LEARNING CURVE
The learning phenomenon applies to time and it could thus affect any
costs which are functions of time. Examples are hourly labour costs,
indirect labour, supervision, etc.
Whenever costs are estimated, the potential impact of learning should
be considered.
The phenomenon can also affect costs used in inventory valuation,
costs used in decision making and costs used in performance
evaluation. However, learning curves only apply to the early phases of
production. After the steady state is achieved, costs tend to stabilise.
In Inventory valuation- failing to recognise learning effects can have
some unexpected consequences. (See example below).

10. Production of a new product starts in January and continues through
the year. Direct material cost is sh.100 per unit through out the year.
Because of the learning effect, the labour hours per unit drop from 1
hour (at sh.160 per hour) in January to 0.25 hour in December.
Manufacturing overhead is all fixed at sh.80,000. If 1000 units will be
produced in January the overhead application rate is sh.80 per hour. This
rate is (mistakenly) applied throughout the year.
Unit inventory Value
January December
Sh. Is (Sh.) Should be (Sh.)
Direct materials 100 100 100
Direct labour 160 40(0.25x160) 40
Overheads applied 80 20(0.25x80) 80
340 160 220
EXAMPLE

11. Decision making making” – A product newly launched may at a
glance appear to be unprofitable, however because of learning
effect, the variable costs would drop by the end of the period
making the product profitable.
Performance evaluation. A bank has developed labour time and
cost standards of some of its clerical activities. These activities
are subject to the learning curve effect. The management has also
found that the time on these activities exceeded the standard.
On investigation, it was found that there was high personnel
turnover meaning the activities were done by inexperienced
people. Changes were made in personnel policy and the personnel
turnover was reduced. The time spent on clerical activities no
longer exceeded standards.
APPLICATION OF LEARNING CURVE