# learning index of learning curve

#### Vinod

A company is developing a new product. During its expected life, 16,000 units of the product will be sold for 82 dollars per unit.
Production will be in batches of 1,000 units throughout the life of the product. The direct labour cost is expected to reduce due to the effects of learning for the first eight batches produced. Thereafter, the direct labour cost will remain constant at the same cost per batch as the 8th batch.
The direct labour cost of the first batch of 1,000 units is expected to be 35,000 dollars and a 90% learning effect is expected to occur.
The direct material and other non-labour related variable costs will be $40 per unit throughout the life of the product. There are no fixed costs that are specific to the product. a)I want to calculate the expected direct labour cost for the 8th batch. b)I want to calculate the expected contribution to be earned from the product over its lifetime. Note:- The learning index for a 90% learning curve is -0.152. It is now thought that a learning effect will continue for all of the 16 batches that will be produced. c)I want to calculate the rate of learning required to achieve a lifetime product contribution of 400,000 dollars, assuming that a constant rate of learning applies throughout the product’s life. Last edited by a moderator: #### HallsofIvy MHF Helper A company is developing a new product. During its expected life, 16,000 units of the product will be sold for 82 dollars per unit. Production will be in batches of 1,000 units throughout the life of the product. The direct labour cost is expected to reduce due to the effects of learning for the first eight batches produced. Thereafter, the direct labour cost will remain constant at the same cost per batch as the 8th batch. The direct labour cost of the first batch of 1,000 units is expected to be 35,000 dollars and a 90% learning effect is expected to occur. I presume this means that the second batch would cost 0.9(35000)= 31500, the third will cost 0.9(31500)= 0.81(35000)= 28350, the fourth will cost 0.9(28350)= (.9^3)(35000)= 25515, etc. direct material and other non-labour related variable costs will be$40 per unit throughout the life of the product.
There are no fixed costs that are specific to the product.

a)I want to calculate the expected direct labour cost for the 8th batch.
The 8th batch will cost (0.9^7)(35000)= $16740.39 b)I want to calculate the expected contribution to be earned from the product over its lifetime. Note:- The learning index for a 90% learning curve is -0.152. It is now thought that a learning effect will continue for all of the 16 batches that will be produced. c)I want to calculate the rate of learning required to achieve a lifetime product contribution of 400,000 dollars, assuming that a constant rate of learning applies throughout the product’s life. #### Vinod I presume this means that the second batch would cost 0.9(35000)= 31500, the third will cost 0.9(31500)= 0.81(35000)= 28350, the fourth will cost 0.9(28350)= (.9^3)(35000)= 25515, etc. The 8th batch will cost (0.9^7)(35000)=$16740.39
Hello HallsofIvy,
I am presenting here the answers provided to me.
a)Cumulative direct average labour cost for 8 batches.$y=ax^b, y=dollars 35000*8^{-0.152}=dollars 25515.16$
The total direct labour cost for 8 batches=8*dollars 25515.16 =dollars 204121.

Cumulative average direct labour cost for 7 batches. $y=ax^b,y=dollars 35000*7^{-0.152}=dollars 26038.33$ The total direct labour cost for 7 batches=7*dollars 26038.33=dollars 182268.32.

Direct labour cost for the 8th batch is dollars 204121-dollars182268.32=dollars 21852.68

b) i)Sales less non labour related cost over the product's life=16000*(dollars 82- dollars 40)=dollars 6,72000
ii)Total labour cost over the product's life=dollars 204515.16+(8*dollars 21852.68)=dollars 378942.47
Subtracting ii)from i) we get contribution of dollars 293057.53.

c) In order to achieve a contribution of dollars 400000, the total labour cost over the product's lifetime would haveto equal(dollars 672000-dollars 400000)=dollars 272000. This equals an average batch cost of dollars 272000/16= dollars 17000.

This represents dollars 17000/dollars35000=48.571% of the cost of first batch.

Therefore the rate of learning required $16^{-x}=0.48571\Rightarrow x=0.260458$

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