Question

2-49 Randy Duckout has been asked to develop an esti- mate of the per-unit selling price (the price that each unit will be sold for) of a new line of handcrafted booklets that offer excuses for missed appoint- ments. His assistant Doc Duckout has collected information that Randy will need in developing his estimate: Cost of direct labor $20 per hour Cost of materials $43.75 per batch of 25 booklets Cost of overhead items 50% of direct labor cost Desired profit 20% of total manufacturing cost Doc also finds out that (1) they should use a 75% learning curve for estimating the cost of direct labor, (2) the time to complete the 1st booklet is estimated at 0.60 hour, and (3) the estimated time to complete the 25th booklet should be used as their standard time for the purpose of determining the unit selling price. What would Randy and Doc's estimate be for the unit selling price?

I NEED A VERY WELL DETAILED EXPLANATION

Answer 1

Learning is the process by which an individual acquires knowledge and skill. When a new process or product is started , performance of a worker is not best at initiation but with learning and experience gained, the performance of worker improves and time taken is reduced. Thus productivity goes up. This improvement in working of a labour is due to learning effect.

Learning Curve Ratio = Average Labour cost for first 2N units *100 / Average Labour cost for first N units

If average labour cost for first 500 units is $100 and Average labour cost for first 1000 units is $75 then Learning Curve Ratio = 75%

Learning Curve ratio Goes in a twice manner, that is improvement comes on a level twice of the production of previous level. Like For 1st unit Average Labour cost is $100 then applying the learning curve effect Average cost for First 2 units will be $100*75% = $75 Then for first 4 units it will be $75*75% = $56.25 then for 8 Units then for 16 units and 32 units it will be $ 42.1875, $31.64 and $23.73 per unit respectively.

For achieving the learning at any production level which is not the twice of the previous level we have a mathematical formula, application of which we will see in our solution:

Learning Curve Table @ 75% Learning Curve Ratio Incremental Quantity (1) Cumulative Quantity (2) Working of Incremental Average time Cumulative time Time/increm per unit (Hours) taken (Hours) ental unit (3) (4) (5) Avg. time at previous level of production XL. C. Ratio 0.600 0.600 0.450 0.900 0.300 0.338 1.350 0.225 0.253 2.025 0.169 0.190 3.038 0.127 Formula Level 1 Level 2 Level 3 Level 4 Level 5 Desired Level Level 6 0.142 4.556 As we can see that simple approach does not show the estimated time taken for 25th booklet. Now we have to apply the mathematical formula for arriving at the solution for 25th booklet.

the formula is given as y = ax Where b always has a negative value. 'x' is the cumulative no. of units or lots produced, in our case it is 25 booklets 'y' is cumulative average unit cost of those 'x' units or lots 'a' is the average unit cost of first unit or lot. 'b' is the learning coefficient or index of learning which is calculated as follows b = log L.R./log 2 For our solution, b = log10 0.75 / log10 2 = -0.4150 Now, y = 0.60*2504150 0.158 hours/unit Level 5 Desired Level Level 6 0.190 0.158 0.142 3.038 3.944 4.556 0.127 0.101 0.087

Calculation of unit selling price (25 booklets) Time Taken Cost of direct labour 3.944 hours Cost/ unit $20/hour Cost $78.88 Cost of Material Cost of Overhead Manufacturing Cost $43.75/25 books 50% of DL $43.75 $39.44 $162.07 162.07 20% of Mfg. Cost 32.414 Desired Profit Selling Price $32.41 $194.48 Total No. of Booklets Unit Selling Price $7.78