The reality is no matter how much you work with things in your head, no matter how confident you may be and how much you think you already have a great vision for your business, there are so many great reasons why you should get it down on paper.
Remember the proverbial expression 'not seeing the wood for the trees'? You need to see the 'wood' first, then delve in and start examining the individual 'trees', meaning the individual items which you will be breaking down later. So a great point is to make sure that you have that overarching vision - and if you cannot find one, then maybe it is an indication that you are obsessing on a few technical aspects that do not necessarily make up a whole business as you had imagined it.
I say that because of course you need to be careful with commercially sensitive ideas, as you do not want to pass your plan on to someone in the pub who then starts your idea before you across the road.
I teach that you should seek to learn from competitors; obviously never copy another business's idea or what they are doing, but you can absolutely learn from their mistakes or see what they are doing and discover ways to improve it. All of that analysis belongs in your business plan: make sure you have your competitors under the microscope and make sure that is a solid chunk of your plan. That is some of the best research and information you will gather about what will make your business successful in future.
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