According to Dictionary.com, an assumption is, "a thing that is accepted as true or as certain to happen, without proof." For both business and personal budgeting purposes, budget assumptions are expectations -- usually expected or presumed income and expenses. Making reasonable assumptions when creating a budget for the first time gives you starting numbers to work with for planning purposes.
Since a budget is a plan for spending money, there must first be money to spend. When you create a personal budget, the income from your job provides the source of funds to pay your bills. If you have a job already, it is reasonable to assume you will continue receiving the same paycheck over a period of time. When you're creating a budget for a business, the income assumptions might be created based on projected sales levels of a specific product or service.
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The expenses you expect to pay from your budget are also assumptions. Even if each expenditure expectation is based on previous expenditures, it is still an assumption that the expense will not change. For personal budgeting, expense assumptions are often the non-fixed expenses you have, such as groceries and transportation costs. On a business budget, expense assumptions might include the cost of raw materials needed to create products.
When creating either a personal or a business budget, using budget assumptions is normal -- particularly when you're creating the budget for the first time, or with unknown elements in the plan. Budget assumptions must be reasonable, however, otherwise you could be setting yourself up for failure. A reasonable budget assumption is based on research or existing data. On a personal budget for example, it's reasonable to assume your electric bill will be $100 per month when it has averaged that for the last three months. In business, it's reasonable to assume raw materials may cost $8.62 a bushel if that was the average going price for them from suppliers in the past three months.
The best research and supporting data for budget assumptions cannot guarantee the success of the budget. Sometimes local or world events arise unexpectedly that change everything, and require the budget to be completely re-created from scratch. A personal budget may have to be completely changed if you're laid off from work for example, and a business budget may need to change if a major supplier goes out of business.