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Learning Curve Theory
LEARNING OBJECTIVES :
After studying this unit, you will be able to : l Understand, visualize and explain learning curve phenomenon. l Measure how in some industries and in some situations the incremental cost per unit of output continues to fall for each extra unit produced l Understand how the percentage learning rate applies to the doubling of output l Know that cumulative average time means the average time per unit for all units produced so far back to and including the first unit produced. l Successfully use learning curve theory in such situations as pricing decisions, work scheduling and standard setting l Describe and identify the situations where learn effect can be incorporated l Calculate average hours/cost per unit of cumulative productions and incremental hours/ cost per order using the learning curve
17.1 INTRODUCTION
Learning is the process by which an individual acquires skill, knowledge and ability. When a new product or process is started, performance of worker is not at its best and learning phenomenon takes place. As the experience is gained, the performance of worker improves, time taken per unit reduces and thus his productivity goes up. This improvement in productivity of workers is due to learning effect. Cost predictions especially those relating to direct labour must allow for the effect of learning process. This technique is a mathematical technique. It is a graphical tech- nique used widely to predict cost. Learning curve is a geometrical progression, which reveals that there is steadily decreasing cost for the accomplishment of a given repetitive operation, as the identical operation is increasingly repeated. The amount of decrease will be less and less with each successive unit produced. The slope of the decision curve is expressed as a percent- age. The other names given to learning curve are Experience curve, Improvement curve and Progress curve. It is essentially a measure of the experience gained in production of an article by an organisation. As more units are produced, people involved in production become more effi- cient than before. Each additional unit takes less time to produce. The amount of improvement
17.2 Advanced Management Accounting
or experience gained is reflected in a decrease in man-hours or cost. The application of learning curve can be extended to commercial and industrial activities as well as defence production.
The learning effect exists during a worker’s start up or familiarization period on a particular job. After the limits of experimental learning are reached, productivity tends to stabilise and no further improvement is possible. The rate at which learning occurs is influenced by many factors includ- ing the relative unfamiliarity of workers with the task, the relative novelty and uniqueness of the job, the complexity of the process, the impact of incentive plans, supervision, etc.
17.2 DISTINCTIVE FEATURES OF LEARNING CURVE THEORY IN MANUFACTURING ENVIRONMENT
The Theory of learning curve was first introduced by T.P. Wright of Curtiss—Wright, Buffalo, U.S.A. engaged in production of airframes. As the production quantity of a given item doubled, the cost of that item decrease at a fixed rate. This phenomenon is the basic premise on which the theory of learning curve has been formulated. The key words, ‘doubled’ and ‘rate’ are important as the quantity produced doubles, the absolute amount of cost increase will be successively smaller but the rate of decrease will remain fixed. This is the essence of the learning curve theory and it occurs due to following distinctive features of manufacturing environment :
( i ) Better tooling methods are developed and used; ( ii ) More productive equipments are designed and used to make the product; ( iii ) Designed bugs are detected and corrected; ( iv ) Engineering changes decrease over the time. Designed engineering are prompted to achieve better design for reducing material and labour cost. ( v ) Earlier teething problems are overcome. As the product involves monthly, management is prompted to strive for better planning and better management. ( vi ) Rejections and rework tend to diminish over time.
There happen a significant influence of all these features on labour as the quantity produced increases and the cost per unit drops. The reasons for this are that each unit will entail : (a) less labour; (b) less material; (c) more units produced from the same equipments; (d) cost of fewer delays and less loss time. Every Time Study engineer or industrial engineer experienced in work measurement has seen this phenomenon happening. Learning curve applications are fast grow- ing with time in manufacturing environment. A company should never blindly adopt another company's learning curve. The product approach for a company should be to develop knowl- edge of its own learning preference in its plant.
17.3. THE LEARNING CURVE RATIO
In the initial stage of a new product or a new process, the learning effect pattern is so regular that the rate of decline established at the outset can be used to predict labour cost well in advance. The effect of experience on cost is summaries in the learning ratio or improvement ratio :
Learning Curve Ratio = (^) AveragelabourcostoffirstNunits
Averagelabourcostoffirst2N units
17.4 Advanced Management Accounting
Learning Curve
Columns (2) and (4) have been used for drawing the learning curve. Last column is not used in drawing the 80 per cent learning curve. This column shows how the cumulative time consump- tion will increase with decrease in cumulative average per unit. Cumulative quantity is plotted on X-axis and cumulative average time consumption per unit is plotted on Y-axis. After the learning effect phase is over, steady-state phase will start. Learning effect advantage will not be there is steady-state phase, when the product or the process gets well stabilised.
17.4 LEARNING CURVE EQUATION
Mathematicians have been able to express relationship in equations. The basic equation
Yx = KXs^ ...(1)
where,
X is the cumulative number of units or lots produced Y is the cumulative average unit cost of those units X or lots. K is the average cost of the first unit or lot
s is the improvement exponent or the learning coefficient or the index of learning which is calculated as follows :
s = (^) logarithmof 2
logarithmoflearning ratio
Learning curve equation Yx = KXs^ becomes a linear equation when it is written in its logarithmic form :
log Yx = log K + s log X ...(2)
Each of the above two equations defines cumulative average cost. Either of them can be con- verted to a formula for the total labour cost of all units produced up to a given point. Total cost under equation I can be found out by the following formula :
Total cost = XYx = KXs^ = KXs+1^ ...(3)
17.5 LEARNING CURVE APPLICATION
Knowledge of learning curve can be useful both in planning and control. Standard cost for new operations should be revised frequently to reflect the anticipated learning pattern. Its main uses are summarised below :
17.5.1 Helps to analyse CVP Relationship during familiarisation phase : Learning curve helps to analyse cost-volume-profit relationship during familiarisation phase of product or pro- cess and thus it is very useful for cost estimates. Learning curve is of immense value as a tool for forecasting.
Illustration
XYZ Co., has observed that a 90% learning curve ratio applies to all labour related costs each time a new model enters production. It is anticipated that 320 units will be manufactured during
Learning Curve Theory 17.
- Direct labour cost for the first lot of 10 units amounts to 1,000 hours at Rs. 8 per hour. Variable overhead cost is assigned to products at the rate of Rs. 2 per direct labour hour. You are required to determine :
(i) Total labour and labour-related costs to manufacture 320 units of output.
(ii) Average cost of (a) the first 40 units produced (b) the first 80 units, (c) the first 100 units.
(iii) Incremental cost of (a) units 41–80 and (b) units 101–200.
Solution
Table showing cost projections based on 90 per cent learning curve.
Incremental Cumulative Average Cumulative Incremental quantity quantity time per unit time taken hours
10 10 100 1,000 — 10 20 90 1,800 800 20 40 81 3,240 1, 40 80 72.9 5,832 2, 80 160 65.61 10,497.6 4,665. 160 320 59.049 18,895.68 8,398.
Following cost information can be derived from the data given in the above table :
(i) Total cost of 320 units = 18,895.68 × Rs. 10 = Rs. 1,88,956.
(ii) Average cost of first 40 units = 81 × Rs. 10 = Rs. 810 per unit.
Average cost of first 80 units = 72.9 × Rs. 10 or Rs. 729 per unit.
(iii) Incremental cost of units 41 – 80 = 2592 × Rs. 10 or Rs. 25,920.
The basic learning curve formula must be used to derive the average cost of the first 100 units and the incremental cost of units 101 – 200.
We know that Yx = KXs
The first production lot contained 10 units. K = 1,000 hrs. (time taken for the first lot) and X = 10 (the number of lots needed to produce 100 units).
Taking the logarithm of the above relation, we get
log Y 10 = log 1000 + (–0.1518 log 10) = 3.0 – 0. = 2. Y 10 = 705
Learning Curve Theory 17.
(b) Those which are being performed by new workmen, new employees or others not familiar with the particular activity. In contrast, activities being performed by experi- enced workmen, who are thoroughly familiar with those activities will not be subject to learning effect. (c) Those involving utilization of material not used by firm so far.
- It is correct that learning effect does take place and average time taken is likely to reduce. But in practice it is highly unlikely that there will be a regular consistent rate of decrease, as exemplified earlier. Therefore any cost predictions based on covernational learning curves should be viewed with caution.
- Considerable difficulty arises in obtaining valid data, that will form basis for computation of learning effect.
- Even slight change in circumstances quickly renders the learning curve obsolete. While the regularity of conventional learning curves can be questioned, it would be wrong to ignore learning effect altogether in predicting future costs for decision purposes.
Illustration
Illustrate the use of leaning curves for calculating the expected average unit cost of making.
(a) 4 machines; (b) 8 machines
Using the data below :
Data : Direct labour needed to make first machine 1,000 hours Learning curve = 90% Direct labour cost Rs. 15/per hour Direct materials cost Rs. 1,50, Fixed cost for either size orders — Rs. 60,000.
Solution
Learning curve (90%) for calculating the expected average unit cost
Cumulative Cum. Avg. Cum. Avg. Materials Overheads Total order size hours labour cost @ Rs. 15 per hr.
1 1,000 Rs. 15,000 — — — 2 (90% of 1,000) = 900 13,500 — — — (a) 4 (90% of 900) = 810 12,150 1,50,000 60,000 2,22, (b) 8 (90% of 810) = 729 10,935 1,50,000 30,000 1,90,
17.8 Advanced Management Accounting
Illustration
XYZ & Co. has given the following data : 80% Average – Time Curve
Cumulative Average Total Marginal Units (x) Hours Hours Hours
1 100 100 100 2 80 160 60 3??? 4 64 256?
Required : Fill in the blanks
Solution
We know that : Y = axb
where, Y = average time per unit
a = total time for the first unit x = the cumulative number of units manufactured. b = the learning index
The learning coefficient, b, is determined as follows :
b = (^) log 2
log ( (^1) − %decrease ) = (^) log 2
log ( (^1) − 0. 20 ) = (^) log 2
log 0. 80
- 3010
By inserting the proper values into the equation, average time for any given number of units can be computed. For three cumulative units, we find that
Y = 100 (3)–.^322 = 100. . 322 *
= 100 (.7020) or 70.
*Log 3 = 0.
0.15363 Antilog = 1.
17.10 Advanced Management Accounting
Illustration
A customer has asked your company to prepare a bid on supplying 800 units of a new product. Production will be in batches of 100 units. You estimate that costs for the first batch of 100 units will average Rs. 100 a unit. You also expect that a 90% learning curve will apply to the cumulative labour cost on this contract.
Required : (a) Prepare an estimate of the labour costs of fulfilling this contract.
(b) Estimate the incremental labour cost of extending the production run to produce an additional 800 units.
(c) Estimate the incremental labour cost of extending the production run from 800 units to 900 units.
Solution
(a) Average cost decreases by 10 per cent every time when the cumulative production doubles.
Therefore,
Average cost of first 200 units = 0.9 × Avg. cost of 100 units
Average cost of first 400 units = 0.9 × Avg. cost of 200 units
Average cost of first 800 units = 0.9 × Avg. cost of 400 units
Combining these, we find that average cost of the first 800 units = 0.9 × 0.9 × 0.9 × Rs.100 = Rs. 72.
Total cost = 800 × Rs. 72.90 = Rs. 58,
(b) Average cost of the first 1,600 units = 0.9 × Rs. 72.9 = Rs. 65.
∴ Total cost of 1,600 units = 1,600 × Rs. 65.61 = Rs. 1,04,
Additional cost of 2nd 800 units
= Rs. 1,04,976 – Rs. 58,320 = Rs. 46,656 or Rs. 58.32 per unit
(c) Because this increase will not increase cumulative production to twice of some figure we already have, formula has to be used :
Y = axb^ where b = .0458 ÷ 0.301 = – 0.
log ax cost = log 10,000 – 0.15216 log 9
= 4 – 0.1452 = 3. Average cost = Rs. 71.5833 per unit
Total cost = 900 × 71.5833 = Rs. 64,
Incremental cost = Rs. 64,425 – Rs. 58,320 = Rs. 6,105 or Rs. 61.50 per unit.
Learning Curve Theory 17.
SUMMARY
- Learning Curve Effect applies only to direct labour costs and those variable overheads, which are direct function of labour hours of input. It does not apply to material costs, non- variable costs or items which vary with output.
- Incremental hours cannot be directly determined from the learning curve graph or formula, as the results are expressed in terms of cumulative average hours.
SELF-EXAMINATION QUESTIONS
- What is learning curve. How the learning curve ratio to calculated?
- Explain the application of learning curve in business situations.
