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November 19th, 2014, 02:04 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 112). 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 + MarchFeb balance * percent growth etc. End of year =200 million Last edited by skipjack; November 23rd, 2014 at 05:03 PM. 
November 19th, 2014, 09:54 PM  #2  
Senior Member Joined: Jan 2012 From: Erewhon Posts: 245 Thanks: 112  Quote:
$\displaystyle (1+x)^{12}=1+0.05$ 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 05:03 PM.  
November 19th, 2014, 11:55 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,281 Thanks: 1965 
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, 11:40 AM  #4  
Newbie Joined: Nov 2014 From: GA Posts: 3 Thanks: 0  Not quite, an additional wrinkle that makes it more complicated Quote:
Last edited by skipjack; November 23rd, 2014 at 04:59 PM.  
November 20th, 2014, 11:58 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 $$ 1+x+\cdots+x^{11}=\frac{1x^{12}}{1x} $$ and so $$ 1+x+\cdots+x^{11}=\frac{1(1.05^{1/12})^{12}}{11.05^{1/12}}=\frac{0.05}{1.05^{1/12}1}\approx12.27257753 $$ 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, 03:19 PM  #6  
Newbie Joined: Nov 2014 From: GA Posts: 3 Thanks: 0  Quote:
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 05:00 PM.  
November 20th, 2014, 06:49 PM  #7  
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  Quote:
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, 10:23 PM  #8 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,955 Thanks: 988 
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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