# Sensitivity Analysis

## What is Sensitivity Analysis? – Definition

Sensitivity analysis involves examining what happens to a budget when changes are made in the assumption on which it is based. It is also known as ‘what-if’ analysis, and can be carried out using a spreadsheet or with manual calculations. Manual calculations are easier if they focus only on the parts of the budget that are subject to change.

## Importance of Sensitivity Analysis

The problem that arises, therefore, is to determine how sensitive the cash budget is to possible changes in the initial assumptions. If a change in one assumption produced a cash difference of only a small amount we would not be too concerned. However, sometimes a change in one assumption can lead to severe changes in the cash position. Sensitivity analysis helps us to determine which assumptions are critical and which have less impact. The technique investigates the impact that changes would have on the budget so that we are aware of how the situation could vary from our expected position.

Sensitivity analysis is sometimes called ‘what-if’ analysis and that really sums up what it does. The techniques simply show us what will happen to the budget if changes occur.

The procedure involves ‘trying out’ various alterations from our original assumptions to assess the impact. This can be done by changing one category of receipt or payment (for example – what if our purchase prices go up by 5%?), or using more than one change in combination (for example – what if our purchase price goes up by 5% and we have to pay for them after one month instead of two months?). You may be asked to carry out some sensitivity analysis in a given task, and we will look at the numerical techniques shortly. Before we do that it is worth examining an important practical tool for carrying out sensitivity analysis – the computer spreadsheet.

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### Using a spreadsheet for sensitivity analysis

The format of a cash budget is very easy to reproduce on a computer spreadsheet, using formulas to carry out the arithmetic.

Once a spreadsheet is set up it is a simple matter to change any of the data, or to add lines for additional receipts or payments. The totals of receipts and payment will automatically adjust when changes are made; together with the bank/cash balances at the bottom of the budget. An example of a cash budget layout is shown below. It is illustrated twice:

• a normal view, showing the figures (upper illustration)
• a view showing the formulas used (lower illustration)

Although the practical use of spreadsheets is difficult to incorporate into AAT simulations, the knowledge and understanding requirements of the Unit include computer modeling.

### Carrying out sensitivity analysis manually

The type of change to data that can be carried out in sensitivity analysis generally falls into one of three categories:

1. Changes in underlying volumes

Here we mean changes in the sales units, or the production or purchase units. It could also apply to some extent to overheads or fixed assets (e.g. hiring or buying additional equipment not included in the original budget).

2. Changes in prices

We will initially deal with some straightforward price changes, and then in the next section examine the impact of inflation and how to deal with it.

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3. Timing changes

We also need to see the impact when the receipts and payments are the same as the original cash budget, but they occur at different times. Examples would be allowing longer (or shorter) credit terms on sales, or paying for purchases or other outgoings at a different time than was originally planned.

There are two approaches to change the cash budget data:

1. The whole cash budget could be redrafted. While this would be a simple matter when using a spreadsheet model, it would be very time consuming manually, especially if there were several alternative options to consider.
2. The impact on the cash movements for each month could be calculated from just examining the changes proposed. This approach requires the application of some logic to the problem but is a quicker technique than redrafting the whole budget.

The second technique is often required in AAT simulations and we will now in more detail at how this is carried out. The key is to look at each month separately and calculate for that month:

• any change in receipts, and
• any change in payments, that together result in
• a change in cash movement.

The revised closing cash balance for that month can then be calculated and carried forward to the next month. The exercise can be carried out in the form of a table.

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## Sensitivity Analysis Examples

We will use a straightforward example to demonstrate the process.

The following cash budget is based on all sales being made on two month’s credit. March sales are estimated at \$8,000.

Suppose that we wanted to see the impact of changing our terms of sale to one month’s credit, with effect from January sales. For simplicity, we will assume that all our customers comply with the revised terms. Buy following the procedure outlined above we would get the following results:

In the above example, two months’ sales receipts would arise in February, increasing the receipts for that month by \$6,000. The changes in receipts for March and April result from receiving different month’s sales than originally planned. The overall result is a new bank balance at the end of April of \$5,000 instead of the original \$3,000 overdrawn figure.

Note that using this technique, it is only necessary to examine those lines in the cash budget that are subject to change. Here there was no impact on payments so there was no need to revisit those figures.

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