First of all, it depends on whether you need and want to receive funding from a financial institution or from a private investor. If this is the case, then, writing a business plan is mandatory.
Even though you may not need the capital, the business plan can play a significant part in the success of your business because by writing it you are able to get a better understanding of the market in which your company activates (one of the chapters of the business plan is market analysis), and a solid knowledge of your market will help you avoid certain risks, while also exploiting the opportunities that may arise.
For this you don’t need to create a 70 page document with complicated graphics; your business plan should be around 10-12 pages and include the mission of the company, the reason behind its creation, a market and potential competitor analysis, several information regarding the prices of your products/services and how you intend to sell your products/services. Moreover, you should also include some financial details: revenue and expense budget, operational costs, and a break-even point analysis.