CMA Study Group

learning Curve

  • 1.  learning Curve

    Posted 23 days ago
    Fact Pattern: Donehart Corporation produces agricultural vehicles. Most of the component
    parts for these vehicles are subcontracted to reliable vendors. The final assembly of all vehicles
    is accomplished at Donehart's plant. Donehart's Engineering Department has developed a new
    fuel injection system that can be produced in-house because of the availability of production
    capacity. The first production run of the new fuel injection system has already been completed
    in-house. This 80-unit production run took 60 direct labor hours per unit to produce based on the
    cumulative average labor hours per fuel injection unit. Donehart has experienced an 80%
    learning curve with similar products, and this experience indicates that learning tends to cease by
    the time 640 systems are produced. Donehart's direct labor cost (including employee benefits) is
    $18 per direct labor hour. Donehart's management must decide whether to continue producing
    the fuel injection system or to subcontract the work. Donehart's purchasing agent has received a
    proposal from Midland, Inc., a company specializing in fuel injection systems. From past
    contracts, Midland has proven to be efficient and reliable. The terms of Midland's proposal are
    outlined below.
    - Donehart must supply all materials required for the fuel injection system units.
    - The first 80 units produced by Midland will require direct labor input at the rate of 56 hours per unit. Current direct
    labor cost is $20 per hour.
    - The direct labor cost charged to Donehart will be the hourly rate in effect at the time the work is performed.
    Midland is currently negotiating its labor contract, which includes a 4% increase in direct labor cost and should be
    applicable when Donehart signs the contract.
    - A learning curve factor of 75% will be applied through the first 640 units produced, and all benefits derived from
    the learning factor will accrue to Donehart.
    - Donehart must pay the actual labor cost incurred plus a 5% margin.
    Question: 19If Donehart manufactures the units in-house, how many total hours will it take to complete 1,000

    A. 8,294.4 hours.
    B. 19,660.8 hours.
    C. 24,330 hours.
    D. 27,955.2 hours

    Please help me to understand?

    Ahmed Kamel
    Accountant at CEMEX

  • 2.  RE: learning Curve

    Posted 23 days ago

    There is key assumption we need to focus on:

    - "Donehart has experienced an 80% learning curve with similar products, and this experience indicates that learning tends to cease by the time 640 systems are produced." => It means learning curve will have peaked. Any additional production unit will have a same average hour spent within fourth batch.
    - To calculate an average hours spent per unit for any additional production unit after batch 4, please see the table below. It will be 23.04 hours/unit.
    -  To calculate total hours spent to complete 1000 units:
    + The first 640 unit = 640 x 30.72 = 19,660.8  hours
    + The remaining 360 unit = 360 x 23.04 = 8,294.4  hours
    So, the total will be 27,955.2 hours

    Hope this helps