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Forecasts and projections are the two types of prospective financial statements.

forecast is management's estimate of future results and is based on assumptions reflecting conditions it expects to exist and the course of actions it expects to take. It can take the form of a specific amount or can be a range. For example when a sales forecast is made by management consideration must not only be made about sales for various products for each geographic location and type of customers but costs directly related to sales must also be forecast. Sales will be determined to some extent by the amount spent for the selling effort and distribution costs will be a function of the units sold. Moreover the sales budget is dependent about what will be with the advertising and sales expense budgets because sales will be a function of the selling effort. They are all intertwined, so-to-speak.

projection presents an entities expected financial position given one or more hypothetical assumptions. It is sometimes used to present one or more hypothetical courses of actions for evaluation. It often answers the a "what if” question. A projection like a forecast may contain a range of results based on the hypothetical course of actions. Projections are quite useful where management wants to test how a hypothetical course of action such as changing the product mix of sales or changing price levels might impact results of operations or financial condition.
A budget can be a forecast or a projection depending upon whether it is based on  whether management's assumptions and actions are expected or hypothetical. The budgeting process is often broken down into component parts such as a budget capital expenditures, or for sales, a budget for costs - purchases, hiring employees, scheduling production, so that arranging for the supply of sufficient cash can be planned and available at the appropriate time. Using budgets allow management to predict the results of a specific course of action and compare the results to what actually happens. This can be very extremely useful, because management may be able to change its strategy before the event has occurred, rather than after it.