Question

LEARNING CURVE TABLE 1.0000 0.8000 1.0000 0.8500 0.7021 0.6400 0.7729 0.5957 0.5618 0.5345 0.5120 0.7225 0.6856 0.6569 0.6336 0.6141 1.0000 0.9000 0.8462 0.8100 0.7830 0.7616 0.7440 0.7290 1.0000 0.9500 0.9219 0.9025 0.8877 0.8758 0.8659 0.8574 Question 1 (13 marks) ABC produces equipment. It has just completed the manufacture of its first newly designed AB-XY Data is as follows: Direct Materials $ 5,000 Direct labor-first unit 180 hrs Learning curve - Incremental 90% Direct labor cost $45/DM labour hour Variable Manufacuring OH costs $75/DM labour hour Calculate the variable cost of producing 8 units of AB-XY (4 marks) Assume a cumulative average learning curve of 90%-what are the variable costs of producing 8 units of AB-XY (3 marks) Assume no learning curve - What is the variable cost of producing 8 units of product AB-XY 12 marks) If a cumulative Learning curve and wanted to save $5760. What would the LC need to be (4 marks)

Answer 1

Units	cumulative production time	avg per unit
1	180	180
2	(180*2)*90% = 324	162
4	(324*2)*90%=583.2	145.8
8	(583.22*2)*90% = 1049.76	131.22

1 and 2. Variable costs with assumption of Learning Curve:

• Direct Labour: 1049.76 hours * 45 $ = $ 47,239
• Variable Man. O/H costs: 1049.76 hours * 75 $ = $ 78732.

3. Variable costs without assumption of Learning Curve:

• Direct labour: (180 hours * 8 units) *45 = $ 64800
• Variable Man. O/H costs: (180 hours * 8 units) *75 = 108000

4. Save $ 5760. So, total Variable cost should be [(64800+108000)-5760] = $ 167040. Total Direct labour hours => 167040/(75+45) = 1392 hours. That means, time required for producing the 8th unit = 1392/8 = 174 hours

as per the LC theory, Y = ax^b
Y = cumulative average time per unit to produce N units
a = the time taken for the first unit of output
x = the cumulative number of units produced
b = the index of learning

So, 174 = (180)*(8)^?

ie, 0.9667 = 8^?

Taking log and solving we get ? = 0.9838 or 98.38%.

Please comment for any query regarding the solution to this problem.