My Math Forum Revenue Growth, which formula?

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 November 19th, 2014, 01:04 PM #1 Newbie   Joined: Nov 2014 From: GA Posts: 3 Thanks: 0 Revenue Growth, which formula? Should be a fairly simple question, but I'm drawing a blank on the proper formula. Given a company X, revenues are expected to grow 5% to \$200 million by end of year 1. Building a monthly revenue schedule for the company for year 1 (months 1-12). What formula could I use to project what month 1 starting balance would be allowing for a smooth growth profile which would give us \$200 million by year end? I can't use a simple annuity PV formula, so what should I use? January- starting balance + February- Jan balance * percent growth + March-Feb balance * percent growth etc. End of year =200 million Last edited by skipjack; November 23rd, 2014 at 04:03 PM.
November 19th, 2014, 08:54 PM   #2
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Quote:
 Originally Posted by pbutler22 Should be a fairly simple question, but I'm drawing a blank on the proper formula. Given a company X, revenues are expected to grow 5% to \$200 million by end of year 1. Building a monthly revenue schedule for the company for year 1 (months 1-12). What formula could I use to project what month 1 starting balance would be allowing for a smooth growth profile which would give us \$200 million by year end? I can't use a simple annuity PV formula, so what should I use? January- starting balance + February- Jan balance * percent growth + March-Feb balance * percent growth etc. End of year =200 million
If the monthly growth is $\displaystyle x$, and in 12 months you see a $\displaystyle 5\%$ ($\displaystyle 0.05$) growth you have:

$\displaystyle (1+x)^{12}=1+0.05$

Rearrange this to give:

$\displaystyle x=(1+0.05)^{1/12}-1\approx 0.00407$ or $\displaystyle 0.407\%$ monthly growth

CB

Last edited by skipjack; November 23rd, 2014 at 04:03 PM.

 November 19th, 2014, 10:55 PM #3 Global Moderator   Joined: Dec 2006 Posts: 20,747 Thanks: 2133 Please don't quote the entire immediately previous post, as that can needlessly double the length of the topic. The equations in the original post don't make much sense. If the monthly revenue amounts form a GP, CB's formula is incorrect.
November 20th, 2014, 10:40 AM   #4
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Not quite, an additional wrinkle that makes it more complicated

Quote:
 Originally Posted by CaptainBlack If the monthly growth is $\displaystyle x$, and in 12 months you see a $\displaystyle 5\%$ ($\displaystyle 0.05$) growth you have: $\displaystyle (1+x)^{12}=1+0.05$ Rearrange this to give: $\displaystyle x=(1+0.05)^{1/12}-1\approx 0.00407$ or $\displaystyle 0.407\%$ monthly growth CB
Unfortunately, this is just giving me the monthly compounding rate, which isn't quite what I'm asking for. I know the monthly growth rate as that's very easy to solve. Essentially, I'm asking what is the base value of revenue for the month JANUARY (1), that by the end of the year (December) all the monthly revenue values sum to $200 million and have grown at a rate of 5% a year. For reference the correct answer is 16,296,495.13 (solved using what is basically an amortization schedule). I'm hoping to get a shortcut formula to use in the future, or at least a method of solving, that doesn't involve guess and check. Last edited by skipjack; November 23rd, 2014 at 03:59 PM.  November 20th, 2014, 10:58 AM #5 Global Moderator Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms You want to solve for y in y(1 + x + ... + x^11) =$\$$200 million, where x^12 = 1.05. Note that$$ 1+x+\cdots+x^{11}=\frac{1-x^{12}}{1-x} $$and so$$ 1+x+\cdots+x^{11}=\frac{1-(1.05^{1/12})^{12}}{1-1.05^{1/12}}=\frac{0.05}{1.05^{1/12}-1}\approx12.27257753 $$and so the answer is \$$16,296,495.13, as expected. You should be able to adapt the formula to solve similar problems. For example, what if it were 500 million dollars over 3 years at 6% growth?
November 20th, 2014, 02:19 PM   #6
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Quote:
 Originally Posted by CRGreathouse You want to solve for y in y(1 + x + ... + x^11) = $\$$200 million, where x^12 = 1.05. Note that$$ 1+x+\cdots+x^{11}=\frac{1-x^{12}}{1-x} $$and so$$ 1+x+\cdots+x^{11}=\frac{1-(1.05^{1/12})^{12}}{1-1.05^{1/12}}=\frac{0.05}{1.05^{1/12}-1}\approx12.27257753 $$and so the answer is \$$16,296,495.13, as expected. You should be able to adapt the formula to solve similar problems. For example, what if it were 500 million dollars over 3 years at 6% growth? Ok I KNOW this is the right answer, so forgive me for a couple more stupid questions. The 12.272, how does that relate to the$16 million? I know you're right and it's the end of the long day so I'm missing a step between the two.

Last edited by skipjack; November 23rd, 2014 at 04:00 PM.

November 20th, 2014, 05:49 PM   #7
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Quote:
 Originally Posted by pbutler22 Ok I KNOw this is the right answer, so forgive me for a couple more sutpid questions. The 12.272, how does that relate to the \$16 million. I know you're right and its the end of the long day so I'm missing a step between the two
You know: y(1 + x + ... + x^11) = 200 million
You also know: 1 + x + ... + x^11 = 12.27257753...

So divide 200 million by 12.27... to get the value of y.

 November 21st, 2014, 09:23 PM #8 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,587 Thanks: 1038 Why don't you simply use the ordinary annuity formula: A = F*i / ((1 + i)^n - 1) Where: A = annuity Amount (?) F = Future value (200,000,000) n = number of periods (12) i = periodic rate (1.05^(1/12) - 1)

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