A bus body builder in Kano has a contract to fit out forty vehicles. The labour manager says that the first vehicle took 100 hours, that the crew is learning quickly, and that the average will fall as they go. The sales director wants to quote a price that reflects this, and the production manager wants to know how many people to book for the next ten months.
Then the training manager adds a warning: the crew will learn for about sixteen vehicles, and after that each vehicle will take about the same time, whatever happens. Applying the learning curve formula to all forty vehicles as if learning never stopped would underestimate the labour needed.
This topic deals with the use of the learning curve in budgeting and pricing, the steady state when learning ends and how to calculate the total time when learning continues only for part of a production run, the conditions under which a learning curve applies, and the problems that limit its use. It builds on the earlier topic on the learning curve: the learning rate and the learning effect.
The next topic covers standard costing: its uses, how standards are set and the types of standard.
In 30 seconds
The learning effect only applies when conditions are right:
- stable conditions with low labour turnover and short gaps between units
- labour-intensive, repetitive work
- no change in production method, which would restart learning
- motivated employees
It reduces labour cost and overhead that varies with labour time, not materials. When learning ends, time per unit becomes constant, a steady state.
To cost a run longer than the learning period: (1) find the total time for the units during the learning period from the formula; (2) find the time of the last unit in that period (total for n − total for n − 1); (3) multiply that time by the remaining units; (4) add.
Implications: budgets must allow for falling hours per unit and so the labour force needed; cost-plus prices can allow for savings, which will lower the expected price; control reports should compare actual hours with expected hours allowing for learning.
Problems: the rate and first-unit time are hard to measure; automation removes learning; design changes restart it; the product may be at a steady state already; and labour turnover destroys the experience. Full marks come from the calculation and from applying the conditions to the facts.
Conditions, steady state and costing
When a learning curve applies
The learning curve will only be seen if these conditions are met.
- Stable conditions that allow learning to take place. If labour turnover is high, the experience leaves with the people. If the interval between units is long, workers forget what they learned.
- The activity is labour-intensive and repetitive, so that learning affects the time to complete the work. In a highly mechanised process the machine sets the pace and there is little to learn.
- No change in production techniques, which would require the learning process to start again from the beginning.
- Employees are motivated to learn.
The costs that fall are those that vary with labour time: direct labour and any overhead that varies with labour hours. Materials do not fall, since their use has no relation to labour efficiency (waste may fall, but that is a separate effect).
The steady state
After a time the learning effect wears out, and the time to make each additional unit becomes constant. This is the steady state. The formula y = axb assumes learning goes on for ever, so if a run is longer than the learning period, the formula must be used only up to the point where learning stops. The units after that are costed at the steady-state time.
In a question the steady state is given as a number of units, after which each unit takes the same time as the last unit in the learning period.
- Total time for the learning period = n × a × nb, where n is the last unit in the learning period.
- Steady-state time per unit = total for n units − total for n − 1 units.
- Units after the learning period × the steady-state time.
- Total time = (1) + (3).
Implications for budgeting, pricing and control
- Budgets. Labour hours per unit fall, so total labour requirements and the size of the workforce needed are lower than a first-unit estimate. Cost budgets, cash budgets and production schedules should reflect this. The budget can be built period by period using the totals for cumulative units at the start and end of each period.
- Pricing. If prices are cost-plus, quotations should allow for the future savings, so the expected selling price and the sales budget fall. A firm that quotes on the first-unit cost may lose the contract or fail to pass savings on; one that quotes below cost on the strength of an unproven rate carries the risk if the learning does not happen.
- Control. Variance reports should compare actual hours with hours expected allowing for learning. Comparing with the first-unit time shows false favourable variances, and comparing with a steady-state time too early shows false adverse ones.
Problems with applying learning curve theory
In practice the technique is not used widely, for several reasons.
- Measurement. It is difficult to measure the learning rate and the time for the first unit accurately, and small errors in the rate give large errors over many units.
- Automation. In a modern, mechanised process, the learning effect does not apply to the mechanised part.
- Changing designs. The theory assumes stable conditions and the same specification for all units; product designs are often changed after the first unit, and each change restarts learning.
- Steady state already reached. For many skilled products there is already no further learning, because the workforce has long experience.
- Labour turnover. A high rate prevents the workforce from gaining collective experience.
- Motivation. Staff who are demotivated, for example after a reorganisation, will not look for faster methods.
An evaluation therefore looks at each condition in turn. If the process is repetitive but 60% automated, the 40% that is manual may show learning but the effect on the whole process is probably small; if the workforce is demotivated and resignations are rising, the learning curve is unlikely to appear at all.
The conclusion should be that a learning curve is possible but should be treated with caution, and the budget should not rely on it without supporting evidence.
Layouts for steady state and learning curve costing
- Learning period: total hours for n units = n × a × nb.
- Steady-state time: total(n) − total(n − 1).
- Remaining units × steady-state time.
- Total hours, then × labour rate (and variable overhead rate); add materials.
- Price: total cost × (1 + mark-up).
Hours to two decimal places where needed; money in naira; each answer rounded once, at the end.
Worked examples
Example 1: a steady state. The first of forty vehicles takes 100 hours. An 80% learning curve applies for the first 16 vehicles; after that every vehicle takes the same time as the sixteenth. Required: the total labour hours, and the effect of ignoring the steady state.
- Learning period.
Total for 16 units = 16 × 100 × 0.84 = 16 × 40.96 = 655.36 hours. - Steady-state time.
Total for 15 units = 15 × 100 × 15−0.32193 = 627.3 hours, so the sixteenth takes 655.36 − 627.30 = 28.06 hours. - Remaining 24 vehicles.
24 × 28.06 = 673.4 hours. - Total.
655.36 + 673.44 = 1,328.8 hours, an average of 33.2 hours a vehicle. - Ignoring the steady state.
Applying the formula to all 40: 40 × 100 × 40−0.32193 = 40 × 30.52 = 1,220.6 hours.
This under-estimates labour by about 108 hours, because it assumes that later vehicles keep getting faster.
With no learning at all the figure would be 40 × 100 = 4,000 hours.
Example 2: pricing. Labour costs ₦1,000 an hour, materials ₦20,000 a vehicle, and the mark-up is 25% on cost. Required: the price of the forty-vehicle contract, with and without allowing for learning.
- With learning.
Labour 1,328.8 × 1,000 = ₦1,328,800; materials 40 × 20,000 = ₦800,000; cost ₦2,128,800; price × 1.25 = ₦2,661,000. - Without learning.
Labour 4,000 × 1,000 = ₦4,000,000; cost ₦4,800,000; price ₦6,000,000. - Comment. The difference is more than ₦3.3m. A firm that quoted on first-unit time would price itself out of the contract. If the learning rate were wrong, the contract could lose money, so the rate and the conditions should be checked before the quote is made.
Expect variants: a steady state given after a different number of units, an evaluation of whether a learning curve will apply to a described process, a budget by period, or a discussion of the problems.
Deriving the learning rate, and pricing a special order when labour is scarce
When two points are given, find the cumulative average time at each and divide. Example. The first 20 units took 800 hours (average 40) and the first 40 units took 1,360 hours (average 34): learning rate = 34 ÷ 40 = 85%; b = log 0.85 ÷ log 2 = −0.2345. For 200 units the cumulative average is 40 × (200 ÷ 20)^−0.2345 = 23.32 hours, a total of 4,663 hours. If 80 units have already been made (average 40 × 4^−0.2345 = 28.89, total 2,311 hours), the hours needed now are 4,663 − 2,311 = 2,352 hours.
If labour is scarce, each hour used on the special order loses the contribution it would have earned elsewhere, so the relevant cost per hour is wage + variable overhead + contribution forgone per hour (the contribution being measured after labour and overhead): wage ₦150, variable overhead ₦50 and contribution forgone ₦100 give ₦300 an hour, or 2,352 × 300 = ₦705,600 before materials and any direct fixed costs. Ignoring the learning effect would overstate the labour needed and the price.
Why a learning curve forecast may be wrong
Reasons include:
- inflation (the costs are not adjusted)
- ageing equipment, so that maintenance costs rise
- learning may stop earlier or later than assumed, or the rate may differ
- changes in staff or methods
- the data being too few points to fix the rate
When learning stops, use the cost of the last unit, not the cumulative average, for every later unit.
Common mistakes
- Applying the formula beyond the learning period.
- Using the average of the learning period as the steady-state time. It is the time of the last unit.
- Applying learning to materials.
- Accepting a learning curve without testing the conditions in the case.
- Comparing actual hours with the first-unit time.
- Forgetting the effect on price and sales budget.
Quick revision
- Conditions: stable, labour-intensive and repetitive, no change in method, motivated staff.
- Steady state: total for n units, plus remaining units × time of the n-th unit.
- Affects labour and labour-related overhead; budgets, prices and control reports must allow for it.
- Problems: measurement, automation, design change, steady state already, turnover.
How the marks are earned
- Calculate the learning period, steady-state time and total.
- Apply to budget and price.
- Evaluate the conditions in the case.
Practice questions
These are original questions, written in the style of the Skills examination. Work each one before you open the answer.
Recall check: multiple choice
Question 1. A steady state is reached when:
- The time per additional unit becomes constant
- The first unit is made
- Costs double
- Output stops
Show the answer
A. Learning has ended.
Question 2. After the steady state each unit takes:
- Less time each time
- Twice as long
- The same time as the last unit in the learning period
- The first-unit time
Show the answer
C. The time is now constant.
Question 3. For learning to apply the work must be:
- Highly mechanised
- Labour-intensive and repetitive
- Changing constantly
- One-off
Show the answer
B. Otherwise there is nothing to learn.
Question 4. A condition for a learning curve is:
- High labour turnover
- Frequent design changes
- Long gaps between units
- Stable conditions and motivated employees
Show the answer
D. Experience must be kept.
Question 5. A change in production technique:
- Restarts the learning process
- Speeds learning
- Has no effect
- Ends costs
Show the answer
A. Workers have a new task to learn.
Question 6. Budgets should allow for:
- Rising labour hours per unit
- Constant hours
- Falling labour hours per unit
- No labour
Show the answer
C. Until the steady state.
Question 7. Cost-plus prices on a learning process:
- Should ignore savings
- Should allow for expected later cost savings
- Should rise
- Should be fixed
Show the answer
B. Otherwise the quote is too high.
Question 8. A problem with learning curve theory is that:
- It is too simple
- It needs no data
- It always applies
- The rate and first-unit time are hard to measure accurately
Show the answer
D. Automation and design changes also limit it.
Question 9. In a highly automated process the learning effect is likely to be:
- Small
- Large
- Increasing
- Constant
Show the answer
A. Machines set the pace.
Question 10. Actual hours should be compared with:
- The first-unit time
- Last year’s hours
- Expected hours allowing for learning
- Zero
Show the answer
C. Otherwise the variances mislead.
Section B style: written questions
Question 11 (10 marks). (a) State FOUR conditions for the learning curve to apply. (4 marks) (b) State FOUR problems in applying it. (4 marks) (c) State which costs it affects. (2 marks)
Question 12 (15 marks). The first unit of a product takes 200 hours. A 90% learning curve applies to the first 8 units; after that each unit takes the same time as the eighth. Twenty units are to be made and labour costs ₦1,400 an hour.
(a) Calculate the total time for the first 8 units. (3 marks) (b) Calculate the time of the eighth unit. (4 marks) (c) Calculate the total time for 20 units. (3 marks) (d) Calculate the labour cost. (2 marks) (e) Explain why applying the formula to all 20 units would be wrong. (3 marks)
Question 13 (20 marks). A company makes a new product by a repetitive process that is 70% automated. After a reorganisation the workforce is less motivated and resignations have risen. The design is expected to change after the first year.
(a) Evaluate the extent to which a learning curve will occur. (6 marks) (b) Explain how a learning curve would affect the budget, the price and control reports if it did apply. (8 marks) (c) Explain TWO other problems in applying the theory. (6 marks)
Model answers
Show the model answer to Question 11
(a) Stable conditions with low labour turnover and short gaps; labour-intensive, repetitive work; no change in production method; motivated employees (4).
(b) Any four: rate and first-unit time hard to measure; automation; design changes; steady state already reached; high labour turnover; demotivated staff (1 each).
(c) Labour and overhead that varies with labour time; not materials (2).
Show the model answer to Question 12
(a)
- Cumulative average for 8 units = 200 × 0.93 = 145.8
- total 8 × 145.8 = 1,166.4 hours (3).
(b)
- Total for 7 units = 7 × 200 × 7−0.152 = 1,041.5
- the eighth unit.
1,166.4 − 1,041.5 = 124.87 hours (4).
(c)
- 12 more units × 124.87 = 1,498.4
- total 1,166.4 + 1,498.4 = 2,664.9 hours (3).
(d) 2,664.9 × 1,400 = ₦3,730,860 (2).
(e) The formula assumes learning never stops, so it would give 2,536.9 hours for 20 units and underestimate the time, since after the eighth unit the time per unit stays constant (3).
Show the model answer to Question 13
(a) The process is repetitive, which favours learning; but it is 70% automated, so only 30% of the work could show learning and the overall effect would be small; staff are demotivated and turnover is rising, both of which prevent learning; and the design change will restart learning. A learning curve is unlikely to be significant (6).
(b) Budget: labour hours per unit would fall, so total labour and workforce needs, cost and cash budgets would be lower. Price: cost-plus prices should allow for future savings, lowering the price and the sales budget. Control: actual hours should be compared with hours expected allowing for learning, not with the first-unit time (8).
(c) Any two, explained: difficulty measuring the rate and first-unit time; steady state already reached; materials are not affected (6).
Pathfinder on Learning curve in budgeting
These are the ICAN Pathfinder questions that test this topic. ICAN owns the questions and the suggested solutions, so we point you to them and do not copy them. Open your Pathfinder, attempt each question under exam conditions, then check your answer against the notes above.
Learning curve concept, learning rate from quarterly shut-down costs, forecast year costs, steady state.
Revise first: Layouts for steady state and learning curve costing
Learning rate from batch times, time for 400 more units, minimum price with opportunity cost of scarce labour.
Revise first: Layouts for steady state and learning curve costing
Source: ICAN Pathfinder, Performance Management. Diets covered: March/July Diet, 2020 to May Diet, 2026. All 13 diets in the Pathfinder are mapped.
Spotted a mistake? Tell us and we will check it.
