The document discusses the learning curve phenomenon, which is the mathematical expression that unit labor time decreases at a constant rate when complex labor-intensive procedures are repeated. It was observed during WWII that aircraft assembly times declined regularly as cumulative production increased. The learning curve models this reduction in unit production time as a percentage, typically 80% in aircraft manufacturing. Examples are given to illustrate how learning rates are calculated and applied to estimate labor hours and costs for production runs.

1. A presentation by
Ahmad Tariq Bhatti
FCMA, FPA, MA (Economics), BSc

2. It was found at Boeing, the aircraft manufacturing company,
during WW-II period, that the time taken to assemble an
individual aircraft declined as the number of aircrafts assembled
increased. It was noted that the rate of improvement (known as
rate of learning) was so regular that it was presented in the form of
a mathematical formula. Thus, the labor hours required for the
assembly of aircrafts could be predicted with reasonable
precision. The name given to this effect of increased efficiency
was Learning Curve (LC) phenomenon. The phenomenon was
tested in a number of manufacturing setups across the industries
and it was found invariably everywhere. However, the learning
rate of laborers differed from one industry to another.
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3. Definition
The mathematical expression of the phenomenon that,
when complex and labor–intensive
procedures are repeated, unit labor time tend
to decrease at a constant rate.
LC models mathematically this reduction in unit production time.
– Cima Official Terminology
The LC is based on the idea that labor hours decrease in a definite
pattern as labor operations are repeated. More specifically, it is derived
from statistical findings that as cumulative production doubles, cumulative
average time required per unit will be reduced by some constant
percentage, say 10% to 20%.
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4. The Concept
It was found that the cumulative average time per unit decreased by a fixed percentage
each time the cumulative production doubled.
In aircraft industry, the percentage by which cumulative average time per unit decreased
was typically 80%. Similarly different learning rates were noted for different industries.
Let us examine an example of production where learning rate is noted at 90%:
Units Avg. time/unit (hrs.) Cumulative production time (hrs.)
1 100.00 100.00
2 90.00 (100x90%) 190.00
4 81.00 (90x90%) 271.00
8 72.90 (81x90%) 343.90
16 65.61 (72.90x90%) 409.51
32 59.05 (65.61x90%) 568.56
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5. An Illustrative Model
Total Time
No. of Units
@LR of 80%
Order #
Per Cumulative Per Unit All Units
order Production (Hours) (Hours)
1 2 3 4 5=3x4
1 1 1 2,000 2,000
2 1 2 1,600 (2,000 x 80%) 3,200
3 2 4 1,280 (1,600 x 80%) 5,120
4 4 8 1,024 (1,280 x 80%) 8,192
5 8 16 819 (1,024 x 80%) 13,104
6 16 32 655 (819 x 80%) 20,960
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6. The Shape of LC
Learning Curve W. 80% LR
2500
2,000
2000
1,600
1500 1,280
1,024
1000 819
655
500
1 2 4 8 16 32
0
1 2 3 4 5 6
Avge. Hrs./Unit of Cumulative Production (Col. 4)
Cumulative Quantity in Units (Col. 3)
(Data used from table given at slide 5)
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7. The Formula
Where,
Y = the cumulative average time required to produce X units
a = the time required to produce the first unit of output
b = the learning /improvement rate/index of learning
X = number of units to be produced
Important Note ,
This formula calculates only direct labor time against given number of units.
The direct labor cost shall be calculated, thereafter, by multiplying the time
calculated by this formula with standard labor rate.
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8. Calculation
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9. Calculating Incremental Hours
To calculate incremental hours, we need to examine the differences
between total hours for various combinations of cumulative hours. For
instance, in our foregoing illustrative model , the company has completed an
order for 4 units and an enquiry has been received for 6 units later.
The calculation for the time required for the production of additional 6
units shall proceed in the manner given as below:
Total hours if an additional 6 units are produced (10 x 953) = 9530 …..(a)
Total hours for the first four units (4 x 1280) = 5120…..(b)
Hours required for 6 units after completion of 4 units = 4410 ……(a-b)
(Data used from table given at slide 5)
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10. Calculating LR by Using Logs
Illustration 1
Data relating to the production of first 12 batches of Product X are given
as follows:
Time taken to produce the first unit = 15 hours
Cumulative time taken to produce first 12 batches 81 hours.
Requirement: Calculate the learning rate???
Solution
Where:
Y = Average time/batch = 81/12 = 6.75 hours
a= 15 hours
X = 12
b = Rate of learning = Log of learning rate/ Log2 ……(a)
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11. Calculation
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12. Calculating Total Time - Tabular Method
Illustration 2
XYZ Ltd is calculating the time taken for product Y and found that a 90% LC applies
to the behavior of labor working on its production. The time taken for the first unit
produced is 4 hours.
Requirement: Calculate total time taken for 8 units to be produced of product Y???
Solution
# of units Average Time/ Unit Cumulative Time
Hours Hours
1 4.000 4
2 3.600 (4.00 x 90%) 7.2
4 3.240 (3.60 x 90%) 12.960
8 2.916 (3.24 x 90%) 23.328
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13. Calculating Total Time by Using
Formula
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14. Pricing a Contract by Using LC
Illustration 4
ABC Company, finds that product M has 80% learning effect. The company
has just produced 50 units at 100 hours per unit. Detail of cost incurred is
given in the table given below.
The company has just received a contract calling for another 50 units. The
company has decided to have a 50% markup on the cost.
Requirement: Determine price for the contract for the 50 units????
Description Amount in AED.
Materials (50 units @ AED. 20 each) 1,000
Labor & related cost:
-- Direct Labor (100 hours @ AED.8 each) 800
-- Variable Overheads (100 hours @ AED. 2 each) 200
Total cost of 1st 50 units 2,000
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15. Calculation
Solution
Quantity Total Time Average Time /Unit
Units Hours Hours
50 100 2
100 160 (1.6 x 2 x 100) 1.6 (2hrs x 80%)
Calculation of Contract Price: Amount
Description of Cost & Price Components: AED.
Materials (50 units @ AED. 20 each) 1,000
Direct labor (60 hours @ AED. 8 each) 480
Variable Overhead (60 hours @ AED. 2 each) 120
Total cost for additional 50 units 1,600
Add: Markup 50% 800
Contract Price for 50 units 2,400
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16. Important Note
The LC formula is used to estimate direct labor time for a given
number of units and thus is helpful in the calculation of direct labor
cost estimates. Further, the learning effect is applied to those
variables also that are dependent upon direct labor time for their
time and cost estimation.
The concept of LC is not applied to direct material costs or
overhead costs relating to production.
The concept of LC is applicable where operations are complex and
carried out manually by labor. Where operations are so simple that
apply very low level of intelligence, there shall be little scope for
learning effect. Hence, there shall be no LC.
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17. Applications
 Pricing Decisions
It requires the ability of the management to use the learning effect to forecast and make the
cost reductions and obtain a considerable lead over the competitors by giving better prices.
 Work Scheduling
Useful in the management of delivery orders and related schedules. Scheduling labor work
requirements.
 Standard Setting & Budgeting
Plays meaningful role in standard costing and applying budgetary controls. Standard costs
should reflect the point that has been reached on LC.
 Pricing Contracts
The LC has been quite useful in determining the likely costs relating to various contracts. It
provides a rational basis for price negotiation and cost control.
 Setting Incentive Wage Rates
The LC concept is applied in determining incentive wage rates across the industries.
 Inventory Management
The LC concept can be used in the planning, budgeting and purchasing of inventory.
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18. Abbreviations Used
# Abbreviation Description
1 AED Emirati Dirham
2 LC Learning Curve
3 LR Learning Rate
4 WW-II World War Two
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19. References
 Management & Cost Accounting by Colin Drury 5/e
 Cima Official Terminology
 Business Finance by Joel G. Siegel, Jae K. Shim, Stephan W. Hartman
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