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Math Help - Growth Rates

  1. #1
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    Growth Rates

    Hi, I need to measure uptake / success of a program. This success is being evaluated based on transaction volumes.

    Here's what I am thinking in terms of an approach. I'm not sure it's a good way to go. And I don't know for sure how to do the necessary calculations:

    I have monthly transaction volume data from January 2011 to December 2011, inclusive. I am trying to figure out:

    The annual growth rate
    The monthly growth rate

    I want the monthly growth rate because it (and the 2011 data) will be used as a baseline. The baseline will then be used to predict the volumes in 2012 and onward. The difference between the predicted volumes (based on the historical growth rate) and actual volumes will be the uptake and help evaluate effectiveness of a program.

    I've found several sites on the web that provide answers but I don't feel confident in them. I don't think I want compound growth rate. Is that the same as Constant Growth Rate?

    P.S. I also need the formula in a format that i can use with Excel.

    Thank you!!
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: Growth Rates

    The formula to use for growth rate is change in volume divided by initial volume:

    \frac {V_2-V_1}{V_1}

    So the growth rate for a month would be: the volume for that month minus the volume for previous month divided by volume of the previous month. For example if cell A1 = volume for March and cell A2 = volume for April, then the April growth is (cellA2-cellA1)/cell A1. Similarly the growth rate for a year would be the volume for the year minus the volume for the previous year divided by the volume of previous year. You may want to convert these to a percentage.
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  3. #3
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    Re: Growth Rates

    thank you. The above formula will result in a different growth rate for each month. How can I find one number that would be applied to forecast the future? or would I have to apply the growth for a given month this year to the same month in 2012? Or do I use the annual growth rate and divide it by 12 to get one number for a forecast?
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  4. #4
    MHF Contributor ebaines's Avatar
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    Re: Growth Rates

    If you want to calculate an average monthly growth rate for n months you can use this formula:

     V_1(1+ R) ^{n} = V_{1+n}

    This can be rearranged to give:

     R = e^{\frac {\ln ( \frac {V_{1+n}}{V_1} )}n}-1

    For example if the monthly volume for January of year 1 is 1000 units, and the volume for December of year 1 is 1500 unites, the average monthly growth over the 11 months is:

     R = e^{\frac {\ln (\frac {1500}{1000})}{11}} - 1= e^{0.369} -1 = 0.0375

    or 3.75% per month.
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  5. #5
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    Re: Growth Rates

    do you happen to know how this formula for the average monthly growth rate can be done using excel?
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  6. #6
    MHF Contributor ebaines's Avatar
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    Re: Growth Rates

    Sure. If V1 is in cell A1, V_(1+n) is in cell A2, and the value for N is in cell A3, then:

    R=exp(ln(A2/A1)/A3)-1
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  7. #7
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    Re: Growth Rates

    ugggh.
    Unfortunately I only have basic skills in excel so the formula you've provided is almost lost on me...so:

    My January 2011 value is 4712
    My December 2011 value is 6505

    Using your formula, would it look like this?

    =exp(ln(6505/4712)/11)-1 = 0.0297 (or 3%)
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  8. #8
    MHF Contributor ebaines's Avatar
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    Re: Growth Rates

    Quote Originally Posted by galinthefrontrow View Post
    ugggh.
    Using your formula, would it look like this?

    =exp(ln(6505/4712)/11)-1 = 0.0297 (or 3%)
    Yes! This means that the average monthly growth was 2.97%. Hence the expected volumes each month is 2.97% greater than the month before:

    Jan: 4712
    Feb: 4852
    Mar: 4997
    Apr: 5156
    May: 5298
    Jun: 5456
    Jul: 5618
    Aug: 5785
    Sep: 5957
    Oct: 6136
    Nov: 6317
    Dec: 6505
    Last edited by ebaines; October 3rd 2012 at 05:28 AM.
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  9. #9
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    Re: Growth Rates

    Yaayy!! Thank you sooo much for your help!
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