CMA Intermediate · Management Accounting

Forecasting, Budgeting and Budgetary Control: formula sheet

Full chapter guide

Key formulas

Simple moving average (n periods): Moving average = (sum of n consecutive period values) ÷ n; Place each average against the middle period if n is odd. For an even n, centre it by averaging two successive averages.
Linear trend line: Y = a + bX; Y is the forecast value, X is the time period (or the independent variable), a is the intercept and b is the slope.
Regression slope (least squares): b = (nΣXY − ΣX·ΣY) ÷ (nΣX² − (ΣX)²); n is the number of pairs of observations.
Regression intercept: a = (ΣY − b·ΣX) ÷ n; Equivalent to a = Ȳ − b·X̄.
Trend by deviation from mean time (X taken from the middle): When ΣX = 0: a = ΣY ÷ n and b = ΣXY ÷ ΣX²; Useful shortcut for time series with coded time values.
Time series components: Y = T + S + C + R (additive model); T is trend, S seasonal, C cyclical, R random. A multiplicative model uses Y = T × S × C × R.
Budgetary control: Budgetary control = Budgeting + Comparison of actual with budget + Corrective action; Use this to separate it from budgeting, which is only preparing the plan.
Key factor rule: Prepare the key factor budget first; all other budgets are built around it; Sales is the usual key factor in normal times; it changes with the business situation.
Classification by function: Operating budgets (sales, production, cost) + Financial budgets (cash, capital expenditure, budgeted balance sheet) → Master budget; The master budget is the summary budget approved by the budget committee.
Classification by flexibility: Fixed budget = one activity level; Flexible budget = several activity levels or recast to actual activity; Flexible budgets need costs split into fixed, variable and semi-variable.
Classification by time: Long-term (usually over one year) | Short-term (up to one year) | Current (very short, tied to present conditions); Do not give exact year limits beyond these ideas unless the question does.
Budget allowance for actual activity (flexible budget): Flexed budget cost = Fixed cost + (Variable cost per unit × Actual units); For semi-variable costs, split into fixed and variable parts first.
Variance: Variance = Actual result − Flexed budget result; Label as favourable (F) or adverse (A) by effect on profit.
Rolling budget horizon: New budget period added = Period just completed; The total number of budgeted periods stays constant, for example four quarters.
Incremental budget: New budget = Previous budget (or actual) ± Expected change; Existing activities are assumed to continue.
ZBB decision package ranking: Rank packages by benefit relative to cost, then fund in order until the budget limit; Minimum-level package comes first, followed by incremental levels.
Sales budget (value): Budgeted sales ₹ = Budgeted sales units × Selling price per unit; For several products, calculate each product separately and then total.
Production budget (units): Production = Sales units + Closing stock of finished goods − Opening stock of finished goods; Closing stock is often given as a percentage of next period's sales. The closing stock of one period is the opening stock of the next.
Raw material usage: Material required = Units produced × Material per unit; If normal loss is given, first find the input needed per good unit.
Material purchase budget (quantity): Purchases = Material required for production + Closing stock of material − Opening stock of material; Purchase cost = Purchase quantity × Price per unit.
Labour hours and cost: Hours = Units produced × Hours per unit; Labour cost = Hours × Wage rate; If idle time is given as a % of hours paid, then Hours paid = Productive hours ÷ (1 − idle time %).
Overhead budget: Variable overhead = Activity × Rate per unit or hour; Total overhead = Variable + Fixed; Cash overhead = Total overhead − Non-cash items such as depreciation.
Closing cash balance: Closing cash = Opening cash + Total receipts − Total payments; The closing balance of one period becomes the opening balance of the next.
Cash collected from credit sales: Collection in a month = Credit sales of earlier month(s) × % collected as per the credit policy; Reduce the collection by any cash discount allowed if the discount is taken.
Cash paid for purchases: Payment in a month = Purchases of the month(s) per the credit period; A one-month credit period means January purchases are paid in February.
Budgeted debtors: Closing debtors = Credit sales of the uncollected months; Use the collection pattern to find which months are still outstanding.
Budgeted retained profit: Closing reserves = Opening reserves + Budgeted net profit − Dividends; Dividends are deducted when appropriated or paid, as the question states.
Budgeted fixed asset balance: Closing net block = Opening net block + Additions − Depreciation − Book value of disposals; Depreciation reduces the asset but is not a cash item.
Total cost at any activity: Total cost = Fixed cost + (Variable cost per unit × Units); Use for any cost that has been split into fixed and variable parts.
Variable cost per unit (high-low method): Variable rate = (Cost at high activity − Cost at low activity) ÷ (High activity − Low activity); Use for semi-variable costs when two activity levels and their costs are given.
Fixed element (high-low method): Fixed cost = Total cost at either level − (Variable rate × Activity at that level); Check by using both levels; you should get the same fixed amount.
Variable cost at changed activity: Variable cost at new level = Variable cost at base level × (New activity ÷ Base activity); Shortcut when a variable cost is given only at one capacity level.
Fixed cost at changed activity: Total fixed cost is unchanged within the relevant range; Fixed cost per unit changes, but total fixed cost does not.
Contribution and profit: Contribution = Sales − Variable cost; Profit = Contribution − Fixed cost; Use this layout to get profit at each activity level.

Quick revision

Forecast is an estimate of what will probably happen; a budget is a plan of what you intend to happen.
The key factor, or limiting factor, is the constraint that decides which budget you prepare first.
Production budget units = Sales units + Closing stock units − Opening stock units.
Material purchase units = Material needed for production + Closing stock − Opening stock.
The cash budget includes only cash flows. Leave out depreciation and other non-cash items.
Credit sales appear in the cash budget when the money is collected, not when the sale is made.
The master budget consolidates all functional budgets and is presented as the budgeted profit and loss account and budgeted balance sheet.
A fixed budget does not change with activity. A flexible budget is recast for the actual level of activity.
In a flexible budget, variable cost per unit stays the same and total fixed cost stays the same within the relevant range.
Zero-base budgeting justifies each activity from scratch. A rolling budget is updated as each period ends.
Budgetary control means setting budgets, comparing actuals, finding variances and taking action.
There is no negative marking in Section A, so attempt all 15 MCQs.

Common mistakes

Treating a forecast and a budget as the same thing. Fix: Say that the forecast is a prediction and the budget is a plan with targets and responsibility. Write at least two differences in the theory answer.
Placing moving averages against the wrong period. Fix: For a 3-period average, place it against the middle period. For an even period, centre it by averaging two consecutive averages.
Treating budgeting and budgetary control as the same thing Fix: Say that budgeting is preparing the plan, while budgetary control also compares actual with budget and takes action.
Saying sales is always the key factor Fix: Say the key factor is whatever limits activity. It could be material, labour, plant capacity or cash. Use the facts in the question.
Comparing actual cost with the original fixed budget and calling the difference a variance. Fix: Flex the budget to actual activity first. Compare only like with like.
Changing fixed costs in proportion to output when flexing. Fix: Hold fixed costs constant within the relevant range. Split semi-variable costs.
Taking production equal to sales. Fix: Always write the adjustment rows. Production = Sales + closing stock − opening stock.
Using the wrong opening stock for the second and later periods. Fix: Only the first period's opening stock is given. For every later period, opening stock = previous period's closing stock.
Including depreciation as a cash payment. Fix: Remove depreciation, provisions and write-offs from the cash budget. Only items that move cash belong there.
Showing sales and purchases in the month they are made rather than the month cash moves. Fix: Apply the credit period first. Prepare a collections and payments working note before the main table.

Exam tips

In theory questions, give the forecast vs budget difference as a short point-wise list. Four points are enough.
In numerical questions, always show the working table. Examiners award marks for ΣXY, ΣX² and the equation even if the final answer is off.
Use coded time whenever the periods are equally spaced. It saves time and reduces errors.
For MCQs, remember what each method suits: Delphi is qualitative, moving average smooths data, regression links two variables.
End every forecast with a note on its assumption. It costs one line and shows understanding.
In theory questions, structure the answer with numbered points and one-line explanations. This earns step marks even when you forget a point.
For MCQs, watch the exact words: a question that says budgetary control needs comparison and action is pointing past budgeting alone.
If a case gives several limits, the key factor is the one that binds first, which is the lowest limit on activity.