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Math Help - Selling Shares

  1. #1
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    Selling Shares

    Hi all,

    I have a question relating to share trading, I hope someone can help me out with.

    Here is the scenario:

    I buy 120,000 shares in stock AAA at $1.00 per share.
    I buy another 57,000 shares in stock AAA at $1.46 per share.
    I then buy 80,000 shares in AAA at $0.96 per share.

    To sum this up, I have 257,000 shares. (120,000 + 57,000 + 80,000)

    and this cost a total of $280,020.
    ((120,000 x 1) + (57,000 x 1.46) + (80,000 x 0.96))

    Therefore my average price per share is 257,000 / 280,020

    = $0.91779158 per share.

    I decide to transfer 100,000 shares to a friend using this price.

    So the question is: How many shares do I need to sell from each parcel to get the average price per share?

    I would love it if someone could post the steps involved to work this out.

    Cheers!
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  2. #2
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    1) I'm a little puzzled by the description. Are these "stock AAA" the same stock? In other words, did your first 120,000 increase in value by the time you purchased the 57,000?

    2) You seem to have Share / Dollar, rather than the intended Dollar / Share.

    3) Just keep the same proportions.

    100,000 * (120,000)/(257,000) = 46,693

    etc.
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  3. #3
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    Sorry about the complexity of the numbers. I'll put in an example which is easier to follow...it confused me as well! and you are correct, average price per share is Dollar/Share. And yes, AAA is the same stock, which I bought at different times when the price increased in value.

    I buy 1000 shares in AAA at $1 per share. So cost = $1000

    The stock went up and I decide to buy another 5000 shares in AAA at $2 per share. So cost = $10,000

    I again buy another 4000 shares in AAA at $3 per share. So cost = $12,000

    So totally, I have 10,000 shares and it cost $23,000

    Therefore my average price per share is $2.30 (23,000 / 10,000)

    I decide to sell 3000 shares at $2.30, and I want to take in out in proportion to the the parcels. (pro rata)

    So question: How many shares should I sell from each parcel to maintain the average?
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  4. #4
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    Hint: 1:5:4 = 300:1500:1200
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  5. #5
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    Thanks Wilmer,

    Would you be able to kindly write out the steps as to how you derived that answer?
    The example above is simplistic with round dollar prices but in reality, the numbers are quite complex.

    ie. I buy 16,467 shares at 0.385
    then 364,000 at 0.415...etc

    so if i had a template i could use it in any situation.

    Much appreciated for your time!
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  6. #6
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    Quote Originally Posted by tintin00 View Post
    I buy 120,000 shares in stock AAA at $1.00 per share.
    I buy another 57,000 shares in stock AAA at $1.46 per share.
    I then buy 80,000 shares in AAA at $0.96 per share.
    To sum this up, I have 257,000 shares. (120,000 + 57,000 + 80,000)
    and this cost a total of $280,020.
    ((120,000 x 1) + (57,000 x 1.46) + (80,000 x 0.96))
    Therefore my average price per share is 257,000 / 280,020 = $0.91779158 per share.
    I decide to transfer 100,000 shares to a friend using this price.
    So the question is: How many shares do I need to sell from each parcel to get the average price per share?
    I'll use your original example. First, you're not calculating the average correctly:
    should be 280020 / 257000 = 1.089572 *******

    a =120000
    b = 57000
    c = 80000
    t = a + b + c (257000)
    s = 100000 (shares sold)

    Calculating shares sold (round, since part share not sold):
    "a" shares: s * a/t ; 100000 * 120000/257000 = 46693 (rounded) @ 1.00
    "b" shares: s * b/t ; 100000 * 57000/257000 = 22179 (rounded) @ 1.46
    "c" shares: s * c/t ; 100000 * 80000/257000 = 31128 (rounded) @ .96

    Shares sold: 46693 + 22179 + 31128 = 100000

    Proof (you must get initial average):
    (46693 * 1.00 + 22179 * 1.46 + 31128 * .96) / 100000 = 1.089572 *******
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  7. #7
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    Brilliant!

    Thanks again Wilmer
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