Mathematics desk
< August 6	<< Jul \| August \| Sep >>	August 8 >

Welcome to the Wikipedia Mathematics Reference Desk Archives
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages.

August 7

Forecasting Return on Capital Employed

Hi, I started a small business almost 12 months ago and was just sitting down trying to forecast my full year growth estimations when my mathematical handicap came back to haunt me! Essentially I started my business on August 24th 2012 with $30,570.77 of start-up funds, and by August 4th 2013 (346 days later) I had grown my initial investment to $107,640.89. So I made 252.103954202004% return on capital employed in the first 346 days, however I want to estimate what my full year (365 day) percentage return on capital employed will be. You can assume that my business model is perfectly scalable, and moreover that profits are continually recycled back into the business, where the entire capital base is constantly being utilized. I look forward to your answers! Flaming Ferrari (talk) 22:52, 7 August 2013 (UTC)[reply]

Wow, good job on your business. I believe this is the formula you need:

R = (3.521^(365/346))-1

Then just multiply by 100 to put it back into percentage form. BTW, you have way too many digits listed above, see false precision. I'm reminded of the kid in the museum who asks the guard how old the dinosaur is: "Well, it was 200 million years old when I started working here seven years ago, so now it's 200,000,007". :-) StuRat (talk) 00:00, 8 August 2013 (UTC)[reply]

Thanks very much! I get the answer 277.3% which looks to be an accurate forecast. :) Flaming Ferrari (talk) 02:24, 8 August 2013 (UTC)[reply]

You're quite welcome. I do see a problem with this model going forward, though, as presumably you will want to take some of those profits out of the business at some point to have something to live on (unless you already subtract this before you figure the profit). StuRat (talk) 06:44, 8 August 2013 (UTC)[reply]

Or maybe he has a job or some other income, and is running this business as a side-line. -- Jack of Oz ^{[pleasantries]} 20:35, 8 August 2013 (UTC)[reply]

The problem with the model is that exponential growth is always increasing, and always accelerating, so that it increases faster and faster as time goes by. While businesses can grow for indeterminate time periods, usually the rate of growth declines after competitors enter the field, markets saturate, etc. While I think this is a fine extrapolation for a few days, if you plug in e.g. 10^10 days into your formula, the result will be unreasonably high. (Good point on false precision though :) SemanticMantis (talk) 23:27, 8 August 2013 (UTC)[reply]