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Thread: Formula for compounding exponential curve to pay employee bonus

  1. #1
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    Formula for compounding exponential curve to pay employee bonus

    Jim (the owner of AcmeCo) recently sold his business to TitanTek. In addition to the cash paid when the sale occurred, TitanTek is willing to pay Jim up to $40,000,000 in additional "Earnout" payments depending upon AcmeCo's attainment of various performance targets in the 12 months following the sale. Jim wants to share a portion of the earnout payments received from Titantek with his employees, as follows:
    a.) if the earnout received is less than $10 million, Jim will not share anything with his employees;
    b.) if the earnout payment received is exactly $10 million, Jim will share $100,000 with employees;
    c.) if the earnout payment received is exactly $40 million, Jim will share $8,000,000 with employees; and
    d.) if the earnout payment received is between $10 million and $40 million, Jim wants to share between $100,000 and $8,000,000, the exact amount to be calculated on an exponential compounding curve.


    What is the formula to solve d.)? What formula will draw the exponential compounding curve and calculate the exact amount of bonus that Jim will share with employees?
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    Re: Formula for compounding exponential curve to pay employee bonus

    Without worrying about specific numbers, what would the form of the formula be?
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  3. #3
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    Re: Formula for compounding exponential curve to pay employee bonus

    Quote Originally Posted by ptgallant View Post
    Jim (the owner of AcmeCo) recently sold his business to TitanTek. In addition to the cash paid when the sale occurred, TitanTek is willing to pay Jim up to $40,000,000 in additional "Earnout" payments depending upon AcmeCo's attainment of various performance targets in the 12 months following the sale. Jim wants to share a portion of the earnout payments received from Titantek with his employees, as follows:
    a.) if the earnout received is less than $10 million, Jim will not share anything with his employees;
    So the percentage he shares with employees is 0%.

    b.) if the earnout payment received is exactly $10 million, Jim will share $100,000 with employees;
    So the percentage shared is \frac{100000}{10000000}= \frac{1}{100} or 1%.

    c.) if the earnout payment received is exactly $40 million, Jim will share $8,000,000 with employees; and
    So the percentage shared is \frac{8000000}{40000000}= \frac{8}{40}= \frac{1}{50}= 2%.

    d.) if the earnout payment received is between $10 million and $40 million, Jim wants to share between $100,000 and $8,000,000, the exact amount to be calculated on an exponential compounding curve.
    A "compounding exponential" can be written in the form y= Ae^{bx} for some numbers A and b. When x= 10,000,000, you want y to be equal to 100,000 so you want 100,000= Ae^{10,000,000b} and, when x= 40,000,000, you want y= 8,000,000 so you want 8,000,000= Ae^{40,000,000b}. That gives you two equations to solve for A and b. For example, if you divide the second equation by the first, A is eliminated: \frac{8,000,000}{100,000}= 80= \frac{Ae^{40,000,000b}}{Ae^{10,000,000b}}= e^{30,000,000b}.


    What is the formula to solve d.)? What formula will draw the exponential compounding curve and calculate the exact amount of bonus that Jim will share with employees?
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