Question

1. The Company just began making boingos at the beginning of Year 1. During Year 1, the company produced 10 boingos and used a total of 20,000 pounds of direct materials and 10,000 direct labor hours (these are both totals, NOT per unit). Each pound of direct material costs $50 and each hour of direct labor costs $30. These 10 units will make up the baseline for your learning curve computations. The class example and the homework problem both had a baseline of only 1 unit, but this problem is different. The management of the company expects a 90% learning curve to be in effect over the first 4 years of producing boingos. The company produced 14 units in Year 2, 16 units in Year 3, and 40 units in Year 4. Compute the total estimated direct labor COST for Year 4.

2. Refer to question 1. Compute the total estimated direct materials COST for Year 4.

Answer 1

It is our common belief that people and organizations become more efficient over time. Such difference in efficiency rate over time is having a major impact on business decisions. To illustrate, an organization may estimate the production rate of a given product, and can determine from the same what would be the time and money resources requirement for future production. Such effect of increased efficiency with production volume is known as the ‘learning curve’ effect. The ‘curve’ is the idea that if we plot ‘production time per unit’ over time, the amount will curve down.

There are three major assumptions in the learning curve effect:

1. The time required to complete a given task will decrease the more times the task is performed.

2. The decrease will decrease in a decreasing rate.

3. The decrease will follow a predictable pattern.

Calculations:

The most common form of learning curve calculation is an exponential decay function (i.e., production rates decay—or decrease—following an exponential curve).

Tn=T1nb

Where, n = the unit number (1 for the first unit, 2 for the second unit, etc.)

T1 = the amount of time to produce the first unit

Tn = the amount of time to produce unit n

b = the learning curve factor, calculated as In (p)/ln(2), where ln(x) is the natural logarithm of x

p = the learning percentage

The learning percentage p is interpreted as follows:

Every time the cumulative production quantity doubles, the unit production rate will decrease by the percentage p.

This is shown in the following calculation:

Imagine that we have T1 = 10 hours and p = 90% = 0.90. We can calculate the production time for the first 4 units as

This means that even though the 1st unit will take 10 hours, the 4th unit will only take 8.10 hours. Observe that the improvement from the 1st to the 2nd units was 10-9 = 1 hour of improvement.

From the above calculation it is clear that at 90% learning curve to be in effect over the first 4 years, the effective cost will be only 81% for the year 4

Calculation for the total estimated direct labor cost and direct material cost for Year 4
Particulars	Year 1	Year 4	Remarks
No. of units produced	10	40
Direct Materials required = (20,000/10*40)*81%	20,000	64,800	Only 81% materials as compared to year 1 is required
Direct labors required = (10,000/10*40)*81%	10,000	32,400	Only 81% labor hours as compared to year 1 is required
Direct Material cost per unit		$              50
Direct labor cost per hour		$              30
1. the total estimated direct labor COST for Year 4 = (32,400 hours @ $30 per hour)		$    972,000
2. the total estimated direct material COST for Year 4 = (64,800 hours @ $50 per unit)		$ 3,240,000