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Math Help - Break even Volume ( i think )

  1. #1
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    Break even Volume ( i think )

    During an economic slowdown, an automobile plant lost $6,000,000 on the production and sale of 9000 cars. Total revenue for the year was $ 135,000,000. If the break even volume for the plant is 10,000 cars per year, calcuate

    a) The plant's total fixed costs for a year.
    b) the net income if unit sales for the year had been equal to the five
    year average of 12,000

    somehow i think i screwed up with a which in result screwed be over to b

    T.R. : 135,000,000
    BEV : 10,000
    N. i : 6,000,000

    N. i = ( s - vc ) x - FC
    T.R. = (S)x

    135,000,000 = 9,000s

    s = 15,000
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  2. #2
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    Quote Originally Posted by diehardmath4 View Post
    During an economic slowdown, an automobile plant lost $6,000,000 on the production and sale of 9000 cars. Total revenue for the year was $ 135,000,000. If the break even volume for the plant is 10,000 cars per year, calcuate

    a) The plant's total fixed costs for a year.
    b) the net income if unit sales for the year had been equal to the five
    year average of 12,000

    somehow i think i screwed up with a which in result screwed be over to b

    T.R. : 135,000,000
    BEV : 10,000
    N. i : 6,000,000

    N. i = ( s - vc ) x - FC
    T.R. = (S)x

    135,000,000 = 9,000s

    s = 15,000
    You have two equations: for breakeven

    0=10000*UnitPrice-(FixedCosts+10000*UnitCost)

    and for this year:

    -6000000=9000*UnitPrice-(FixedCosts+9000*UnitCost)

    We are told that the total revenue on 9000 sales is 135000000, so the UnitPrice is 135000000/9000=15000


    So we have the two simultaneous linear equations:

    FixedCosts+10000*UnitCost=150000000

    FixedCosts+9000*UnitCost=9000*1500+6000000=1350000 00+6000000=141000000


    Which you now have to solve.

    Subtracting the second from the first gives:

    1000*UnitCost=9000000

    or UnitCost=9000

    So the FixedCost=150000000-10000*9000=60000000

    Though the arithmetic still needs checking

    CB
    Last edited by CaptainBlack; April 11th 2010 at 09:17 AM. Reason: typos
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  3. #3
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    F.C. + 10,000 * U.C. = 1,500,000
    F.C + 9,000 * u.c =

    1,000uc = 1,500,000

    u.c. = 1,500
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by diehardmath4 View Post
    F.C. + 10,000 * U.C. = 1,500,000
    F.C + 9,000 * u.c =

    1,000uc = 1,500,000

    u.c. = 1,500
    My earlier post has been updated with the errors corrected

    CB
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