
Economics Economics Forum  Financial Mathematics, Econometrics, Operations Research, Mathematical Finance, Computational Finance 
 LinkBack  Thread Tools  Display Modes 
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 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 04:03 PM. 
November 19th, 2014, 08:54 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 04:03 PM.  
November 19th, 2014, 10:55 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,373 Thanks: 2010 
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  
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 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 $$ 1+x+\cdots+x^{11}=\frac{1x^{12}}{1x} $$ 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, 02:19 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 04:00 PM.  
November 20th, 2014, 05:49 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, 09:23 PM  #8 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,124 Thanks: 1003 
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) 

Tags 
formula, growth, revenue 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
marginal revenue  mdog4229  Calculus  1  February 25th, 2014 04:28 AM 
Growth rates for rows and growth rate for columns  cjejung  Linear Algebra  1  January 17th, 2012 08:38 AM 
Growth Rate Formula Manipulation  hawaiiruss  Economics  3  May 9th, 2010 01:45 PM 
Population Growth Rate Formula  manich44  Algebra  3  January 25th, 2010 10:04 AM 
Marginal revenue  happy8588  Real Analysis  0  December 31st, 1969 04:00 PM 