Preparing Fixed and Flexed Budgets and Analysing Variances Between Them

In January a company in Port Harcourt budgets to make and sell 10,000 units. By December it has sold 11,200, spent more in total than the budget allowed, and earned more profit than planned. Was the performance good?

A simple comparison of actual and budget says costs are adverse and profit is favourable. But it cannot say how much of the difference is due to the extra volume, which was welcome, and how much is due to prices and efficiency, which management controls. To answer that, the budget has to be restated at the level of activity actually achieved.

This is the flexed budget. This topic explains the fixed (static) budget and the steps for preparing it, how to prepare a flexed budget from the cost behaviour of each item, how to separate semi-variable costs, and how to compare actual results with the fixed and the flexed budgets so that the profit variance splits into a volume element and a spending element.

It builds on the earlier topic on budgetary systems and types of budget. The next topic covers rolling, activity based, functional and master budgets.

Fixed and flexed budgets

The fixed (static) budget

A fixed budget is prepared in advance for a stated period at a planned level of activity, and it does not change when actual activity differs from plan. It is built using historical analysis, top-down or bottom-up approaches, zero-based budgeting or activity based budgeting.

The steps are: define the period; set the goals and targets; estimate revenue and expenses; allocate the expenses to responsible centres; monitor actual performance; and review and revise as needed. It is used for sales, production, overhead, personnel, capital expenditure and marketing budgets.

Advantages: useful for planning and for setting goals and targets; it is simple; it supports control and accountability and gives a source of motivation and an overall financial plan against which to authorise spending.

Disadvantages: it is inflexible, because the figures do not change with activity; it can set unrealistic goals when conditions change; and above all, when actual volume differs from budget, a comparison of actual with the fixed budget mixes the effect of volume with the effects of price and efficiency, which makes it a poor basis for judging managers.

The flexed (flexible) budget

A flexed budget is a budget restated for a different level of activity, normally the actual level. It recognises that costs behave differently when activity changes. The steps are:

1. Identify fixed and variable costs. Variable costs change in total in proportion to activity; fixed costs stay the same in total within the relevant range; semi-variable (mixed) costs have both elements.
2. Separate semi-variable costs into fixed and variable parts, for example by the high-low method: variable cost per unit = change in cost ÷ change in activity; fixed cost = total cost − variable cost per unit × activity.
3. Calculate the variable cost per unit for each variable item.
4. Write the flexed budget formula: total cost = total fixed cost + (variable cost per unit × activity).
5. Apply it to the required activity level, flexing revenue (price × units sold) as well as costs.

Benefits: better cost control, since actual costs are compared with what they should have been at the actual activity; fairer performance evaluation; the ability to plan for different scenarios (what if volume is 10% higher); and better resource allocation.

Limits: it depends on reliable splits between fixed and variable costs; fixed costs and unit variable costs are not constant over very wide ranges (the relevant range) or when costs are stepped; and the activity measure chosen must really drive the cost.

Using the two budgets together

Three sets of figures are needed: the fixed budget (planned activity), the flexed budget (actual activity at budgeted prices and costs) and the actual results. The differences between them have different meanings.

• Fixed budget profit → flexed budget profit is the sales volume variance (in profit terms): the effect of selling a different number of units than planned, at budgeted margins. It is favourable when more are sold at a positive contribution.
• Flexed budget → actual is the spending (or price and efficiency) variance: the effect of actual prices, costs and efficiency being different from budget at the same level of activity. This is the part that managers can be held responsible for.
• The two add to the total difference between actual and fixed budget profit.

Line by line, revenue is compared with revenue (a difference reflects selling price), each variable cost with the flexed figure (a difference reflects price or usage of the resource) and fixed costs with the fixed budget (a difference reflects spending). The detailed variances (material price and usage, labour rate and efficiency, and so on) are the subject of the later topics on standard costing.

Flexing is needed because a fixed budget does not allow for the fact that costs rise with volume. A manager who sold more than budgeted will certainly spend more on materials; the question is whether the spending was more than it should have been for that volume. Only a flexed budget answers it.

Flexible and flexed budgets are not the same, and budgeting under uncertainty

A fixed annual budget is unsatisfactory because, when it is prepared, there is a great deal of uncertainty and it rests on estimates that may turn out wrong; and because unexpected events during the year may make it unrealistic.

Risk and uncertainty mean that forecasts in a budget are unlikely to be exactly right, so managers should look at several forecasts when preparing budgets and, when monitoring results, remember that a variance may come from a weak forecast rather than from good or bad performance. Approaches include flexible budgets, probabilities and expected values, feed-forward control, spreadsheet “what if” analysis and stress testing.

A flexible budget is prepared before the period (ex ante) for different volumes of output and sales from the master budget: for example a master budget on sales of ₦100 million, with flexible budgets at ₦80 million, ₦90 million, ₦110 million and ₦120 million, each allowing for changes in fixed cost above or below some level of sales and for changes in unit variable cost at some volume.

If actual activity is far from the plan, a suitable flexible budget can replace the fixed one. Its disadvantage is the time and effort of preparing them, which may cost more than the information is worth. A flexed budget is prepared after the period (ex post): the budget redrafted to the actual level of activity, for control and variance analysis, as above.

Expected values can be used in a sales budget.

If sales will be ₦40m with probability 0.6, ₦50m with 0.3 and ₦70m with 0.1, the expected value is 24 + 15 + 7 = ₦46m. But that figure is not one of the possible outcomes, and sales for a year happen only once, so it may be more sensible to base the fixed budget on the most likely outcome (₦40m) and prepare flexible budgets for ₦50m and ₦70m. Expected values are best where the event happens many times in the period, and probabilities should have a rational basis.

With a spreadsheet model, a new budget can be produced by changing a few inputs, allowing “what if” questions: sales 5% below forecast, a different product mix, a six-month delay in a new system, interest rates 2% higher than expected. Sensitivity analysis uses variations that are reasonably likely (costs up 5%, sales down 5%); stress testing uses much larger changes (sales 20% below forecast, a key material 50% dearer) to see how far results could fall.

Layouts for flexed budgets and variance analysis

1. Cost classification and rates. Variable per unit; fixed total; split mixed costs by high-low.
2. Flexed budget. Revenue = price × actual units. Variable costs = rate × actual units. Fixed costs as budgeted.
3. Three columns. Fixed budget; flexed budget; actual.
4. Variances. Volume = flexed − fixed profit. Spending = actual − flexed profit, by line.
5. Label each as favourable (F) or adverse (A).

Money is in naira and each answer is rounded once, at the end.

Worked examples

1. Variable cost per unit. Materials 150; labour 120; variable overhead 40.
2. Selling expenses.
   Variable per unit = (380,000 − 300,000) ÷ (14,000 − 10,000) = 80,000 ÷ 4,000 = ₦20.
   Fixed = 300,000 − 20 × 10,000 = ₦100,000.
3. Totals.
   Variable cost per unit 150 + 120 + 40 + 20 = ₦330.
   Fixed costs 900,000 + 250,000 + 100,000 = ₦1,250,000.
4. Flexed budget.
   At 10,000 units: 3,300,000 + 1,250,000 = ₦4,550,000.
   At 8,000 units: 2,640,000 + 1,250,000 = ₦3,890,000.
   At 12,000 units: 3,960,000 + 1,250,000 = ₦5,210,000.
5. Check. A 20% fall in volume reduces total cost by only 14.5% (4,550 to 3,890), because the fixed costs do not fall.

1. Fixed budget profit.
   Revenue 10,000 × 500 = 5,000,000; costs 4,550,000; profit ₦450,000.
2. Flexed budget profit at 11,200 units.
   Revenue 11,200 × 500 = 5,600,000; costs 330 × 11,200 + 1,250,000 = 3,696,000 + 1,250,000 = 4,946,000; profit ₦654,000.
3. Actual profit.
   Revenue 11,200 × 495 = 5,544,000; costs 4,990,000; profit ₦554,000.
4. Sales volume variance.
   654,000 − 450,000 = ₦204,000 F.
5. Spending variance.
   554,000 − 654,000 = ₦100,000 A.
   Of this, revenue is ₦56,000 A (5,544,000 − 5,600,000, the price cut of ₦5 on 11,200 units) and costs are ₦44,000 A (4,990,000 − 4,946,000).
6. Total.
   204,000 F − 100,000 A = ₦104,000 F, which equals actual profit less fixed budget profit (554,000 − 450,000).
   The comparison with the fixed budget alone would have praised the manager for a ₦104,000 improvement.
   The flexed budget shows that the extra volume was worth ₦204,000 and that spending and pricing lost ₦100,000.

Expect variants: a stepped cost in the range, flexing at more than one level, an incomplete budget that must be completed from percentages, or a question that asks which budget should be used to judge a manager and why.

Common mistakes

• Flexing fixed costs. They stay as budgeted within the relevant range.
• Flexing using the wrong activity. Use units sold for revenue and units produced for production costs.
• Comparing actual with the fixed budget and calling the difference a spending variance.
• Leaving semi-variable costs unsplit.
• Using budgeted price on actual revenue in the flexed column, but actual price in the actual column.
• No F or A labels.

Quick revision

• Fixed budget: one activity level, not changed. Flexed: restated at actual activity.
• Flex = fixed cost + variable per unit × units; split mixed costs (high-low).
• Volume variance = flexed − fixed profit; spending variance = actual − flexed profit.
• Judge managers against the flexed budget.

How the marks are earned

• Classify costs and calculate rates.
• Flex each line correctly.
• Analyse the variance and comment on the right basis for judging performance.

Practice questions

These are original questions, written in the style of the Skills examination. Work each one before you open the answer.

Recall check: multiple choice

Section B style: written questions

Model answers

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