Cost and Management Accounting - Learning Curve

 

COST AND MANAGEMENT ACCOUNTING

LEARNING CURVE

 

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 as given below:

 

Table: 1

  Cumulative Quantity VS 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

 

Notice that, as the cumulative quantity doubles the cumulative average time reduces by 20%. In other words, subsequent cumulative average times can be obtained by multiplying the previous cumulative average time by 80%. This is an example of an 80% 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 second, 490 hours at the fourth, and 343 hours at the eighth and so on, this would be a 70% learning curve.

 

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  = aX^b

Where,

Y  =  Cumulative average time per unit or per batch.

a  =  Time taken to produce the first (initial) unit or first batch.

X  =  Cumulative units of production or, if in batches, the cumulative number of batches.

b  =  Learning Index or Learning Coefficient, which is calculated as: log (learning curve percentage) ÷ log 2.

So ‘b’ for an 80% learning curve would be log 0.8 ÷ log 2 = – 0.322.

 

Example: 1

The first unit took 100 hours to produce. It is expected that an 80% 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.

 

Solution: 1

Example: 2

The first batch of a new product has just been made. The batch size was 20 units and the total time taken was 200 hours – i.e. an average of 10 hours per unit. A 90% learning curve is expected to apply. You are required to estimate the following:

(a)    The cumulative average time for the first two batches.

(b)    The total time to produce 40 units.

(c)     The incremental time for 41 to 60 units.

 

Solution: 2

Example: 3

Aryan Limited uses a marginal costing system. You have been asked to provide calculations of total variable costs for a contract for one of its products, based on the following alternative situations:

i.     A contract for one order of 600 units.

ii.    Contracts for a sequence of individual orders of 200, 100, 100 and 200 units. Four separate costings are required. It’s expected that the average unit variable cost data for an initial batch of 200 units will be as follows:

(a)    Direct material: 15 kg at Rs 8 per kg.

(b)    Direct labour: department A: 8 hours at Rs 8 per hour; and department B: 100 hours at Rs 10 per hour.

(c)     Variable overhead: 25% of labour cost.

 

Labour times in Department A are expected to follow an 80% learning curve. Department B labour times are expected to follow a 70% learning curve.

 

Solution: 3

The cost estimates are as follows:

1.   Cost estimates for one order for 600 units

2.   Cost estimates for sequential individual orders of

200, 100, 100 and 200 units