When should numbers in a financial model be positive, and when should they be negative?
This question is one that modellers often feel quite strongly about. Although the FAST Standard has a well established position on this, I want to open this up for discussion ahead of writing the guide. The whole idea of this collaborative, “publish as we go” model is that we can explore topics iteratively, and hopefully all gain from perspectives we hadn’t considered previously.
The reality is that we can’t escape sign switching. It’s going to happen somewhere in our model. The question is therefore not “whether to sign switch” but rather “how to sign switch and where”.
Before we get into what the FAST Standard says about sign convention, and why it takes the position it does, we’ll look at the advantages and disadvantages of two approaches: inflow / outflow and positive as normal.
1. Inflow / outflow
In this approach all values which represent inflows to the business are positive numbers. All values that represent outflows from the business are negative numbers.
Advantage: Inherent readability of financial statements
Users expect to see financial statements presented according to the inflow / flow convention, with inflows represented as positive numbers, and outflows represented as negative numbers.
Advantage: Simpler logic in arithmetic expressions
When inflows are expressed as positive numbers, and outflows as negative numbers, arithmetic expressions can be more simple. i.e. a column of numbers can just be added up, without worrying which are being added and which subtracted from the total.
Weakness: Sign switching of inputs
Sometimes modelling assumptions are provided as positive numbers. They therefore have to either be sign switched on input, or sign switched within calculations. It’s often the case that values have to be sign switched numerous times to accommodate the requirements of functions and presentation. This increases the risk of error.
However, the flip side of this is that forecasts are often driven off “actuals” which are provided on inflow / outflow convention. More on this below.
Weakness: Mid calc sign switching often required
Let’s take an example. When calculating say, the balance of non current assets, one will need to know the amount of capex and the amount of depreciation (ignoring asset disposals for the moment). Under inflow / outflow convention capex is a (cash) outflow, depreciation is a (noncash) outflow. Yet capex increases the balance of noncurrent assets, whereas depreciation reduces that balance. There will need to be some kind of sign switching going on in the middle of this, very often buried within the calculation.
Weakness: Sea of negatives
On occasion in a model a value will become unintentionally negative when it should be positive, or positive when it should be negative.
Which is more like to be spotted . . .
This single positive among the negatives?
Or the single negative among the positives?
2. “Positive as normal”
In this convention all numbers are positive, and the “direction of flow” is indicated by the label. Inflow numbers will include labels like Revenue, Income, Receipts, Drawdown, Borrowings. Outflow line items will have labels like Expenses, Costs, Payments, Expenditure, Repayments, Distribution.
Advantage: How assumptions are often provided
Assumptions are often provided as positive numbers. Sign switching is not required on input or within calculations and in many cases logic can be simpler as a result. However this is not universally true, especially where forecasts pick up from a last set of actuals.
Advantage: Negatives stand out as unusual
See the side by side comparison above. I suspect that different people will have different views about which is easier to spot. Please leave a comment with your thoughts on this.
Weakness: Can’t just “add up”
In the inflow / outflow convention we can usually just add up the numbers and let the sign convention take care of itself. In “positive as normal” whether a line is being added or subtracted has to be written into the formula.
Weakness: Not appropriate for financial statements
Most users will be used to seeing financial statements expressed using “inflow / outflow” convention and will expect to see the model’s financial statement outputs presented in this way.
Note however that there are regional variations about how the balance sheet is presented. Sometimes both the asset and liability balances are presented as positive numbers. Sometimes only the asset values are expressed as positives, with the liability balances expressed as negatives.
3. What FAST recommends
FAST recommends a “mixed economy” of sign convention. “Positive as normal” in the calculation engine / working sheets of a model, and inflow / outflow on the presentation / financial statements. The reason for this can be hopefully seen from the diagram below: the advantages of each of the two conventions apply to specific parts of the model.
How sign switching is done in FAST models
Only line items that are going to flow into the financial statements are sign switched. The suffix “POS” is added to the positive version in order to maintain distinction between the line items, and thus maintain consistency and integrity about row labels being unique. The example above, “Fuel costs” are being exported to the financial statements, and are therefore give “export” line item formatting.
4. Issues with this approach
The mixed economy of “positive as normal” in the calculation sheets and “inflow / outflow” on the financial statements works really well, especially in “bottom up” models where all line items are built up from provided assumptions. This is typical of project finance and infra modelling.
It’s less typical in Corporate Finance and FP&A where we’re often starting from a set of actuals, expressed in inflow / outflow convention. FAST is not currently sufficiently clear on this.
In this regard are three possibilities:
1. Adopt FAST positive as normal in calculations and sign switch the actuals prior to input
Benefits:
 avoids a lot of additional sign switch calcs.
 The calculations are all positives which avoid mid calc sign switching and is simpler.
Weaknesses:
 The actuals inputs don’t match the actuals outputs – this gets horribly confusing when trying to ensure alignment of outputs.
 The sign switching is done outside the model and is not transparent. When the actuals are updated this could cause confusion.
2. Adopt FAST positive as normal in calculations and explicitly sign switch the actuals before using them
Benefits:
 The actuals inputs match the actuals outputs.
 The calculations are all positives which avoid mid calc sign switching and is simpler.
 The sign switching is explicit.
Weaknesses:
 More sign switch calcs – switching “pre calc” as well as the normal “post calc”
3. Adopt inflow / outflow throughout the model
Benefits:
 Avoids having to worry about what to do with the inflow / outflow actuals
Weaknesses:
 We get into sign switching in the middle of calculations e.g. capex / depreciation issue.
 Have to deal with all the other weaknesses of inflow / outflow
At F1F9 we’ve been following the second approach in our Corporate Finance and FP&A modelling.

How have you approached this problem in your models?

Have I missed anything on the “advantages” and “weaknesses” of each approach?

Do you have any recommendations for a better approach?
At Grant Thornton, we hold that we take whatever sign convention is judged most appropriate for the case and requirement, and then make sure:
– it is applied consistently throughout the model; and
– it is clearly documented through guidance notes and units instructions.
In our Infrastructure modelling, we follow the FAST standard approach.
For our Corporate Finance and wider Advisory modelling, we differ marginally and generally use the following:
– all assumption and driver inputs are entered as positive only (KISS);
– actual inputs in Financial Statements format are entered in an ‘accounting’ convention (see below), as client data is usually in this format);
– outputs, especially Financial Statements, are shown in the accounting convention; and
– calculations are under the accounting convention, as we feel the signs should match the outputs.
There will be exceptions, for example, with capital structure and insolvency models, which are far more safely done with everything positive throughout (doing cash waterfalls with negative numbers is just asking for trouble!).
By an ‘accounting’ convention, I mean with signs that match typical UK financial statements, so:
– for P&L items – income is positive, expenses are negative;
– for BS items – assets and equity are positive, liabilities are negative; and
– for CF items – receipts are positive, payments are negative.
This is pretty close to the FAST approach, and will lead to sign changes in the calculations when a positive input (annual rent expense, for example) comes through to drive a calculated cost or liability item. We do the sign change as soon as feasible. Incidentally, we don’t typically do this with an extra step, or label the positive version as ‘POS’, which we feel is artificial and makes thing less easy for clients to understand, not more.
As for Capex? The input is positive – our clients usually have budget files where the data is positive, anyway. In the workings, it hits our Balance Sheet workings, where it’s increasing an asset, and is positive. For the cash flow, we’d flip the sign at the end (‘capex for cash flow’ line) and link that to the output.
Most of our model users are accountants – we want things to be as intuitive as possible for them. And we want all sums to work as sums.
Switching signs can cause errors and the simplest approach is to adopt ‘HP 12C’ methodology with all outflows as negative. This mean you only have to add the line items and makes it much easier to balance cash flows and other statements.
I prefer using whatever sign allows a straight sum per block approach, favouring positive normal. I find this provides for high reliability and readability. For example; a capex cost buildup is positive with possible savings/offsets shown as negative such that the straight subtotal is correct. But when it appears as part of net revenue, revenue is positive and costs negative.
Interesting that you say you need to flip capex from positive to negative to positive – I would leave it negative in the core calculation part of the model – let me explain. Assets are debits in the general journal (in accounting speak). Debits and credits is just a convenience for double entry bookkeeping to work; accountants understand this – you need to ignore the common meaning conjured in your mind. If I am creating accounts from general journals I use the convention ve for debits, +ve for credits. This makes account creation absolutely bullet proof especially for those tricky accounting entries. I may need to switch the sign in a balance sheet representation for example – but that’s an output/presentation function. The calculation engine robustly accords to the convention.
Hope that makes sense.
The approach I prefer (so far) is:
a) On calculation sheets and financial statements, inflow/outflow.
b) On input (assumptions) sheets, positive as normal – but “revenue” (inflow) and cost (outflow) items are normally grouped on separate sheets. E.g. for a visitor attraction, there’s typically one sheet for admissions income (ticket sales), another for retail and catering income, another for staff costs, another for revenue costs, and so on. The change of sign is done implicitly between the input sheet and the calculation sheet.
To make it easier to spot negatives that should be positive and vice versa, I format negative numbers as red and positive as black on the input and calculation sheets. (On the output sheets, of course, the formatting is whatever the client wants.)
Nice explanations.
We tend to do the calculations of income, costs and capex in separate sheets, where they are positive numbers. The costs will switch to negative when they are read by the PL sheet or in case of CAPEX when they are read by the CF sheet. I guess this follows more or less what FAST recommends.
Most published financial statements (e.g. of listed companies) do NOT follow the Inflow / Outflow convention purported by FAST, as the balances (in both P&L and Balance Sheet) are usually in blocks of similarly signed values (e.g. Revenues, Expenses, Assets, Liabilities). It is only where the values in the statement or Note to the Accounts are mixed (e.g. Statement of Cashflows) are the signs also mixed to reflect an inflow / outflow characteristic.
In financial modelling, I think it is difficult to set a hard and fast (pardon the pun!) rule – rather, it’s ‘horses for courses’. Personally, I think brackets (which is the only acceptable format to display negative values) are “noise” or clutter that can be done without where doing so doesn’t interfere with the logic flow and review of the model.
Where inflows and outflows are mixed in a calculation block then the values should be signed accordingly. However, in separate calculation blocks costs can be positive.