Is there a synonym for pro rata?

English is not my first language and I am writing a university assignment where I am trying to find a word appropriate to the following situation :

A business' expense in a particular region is valued at \$100 in January. If you were to calculate the estimated expenses by the end of the quarter it would be \$300, by the end of the first 6 months it would be \$600 and by the end of the year the estimated expense would be \$1200.

Is there a word I can use to name the estimated figure in all cases? For the estimated expense by the end of the year, the word annualized comes to mind but it is not appropriate for the bi-yearly and quarterly estimations. The way I describe this is a reverse pro rata. The only word I can think of is "periodized" which I really don't like.

• Rework to use 'proportional' or 'proportionally'. "A business' expense in a particular region is valued at \$100 in January. The expenses at quarter-end, bi-yearly, and yearly are proportional."
– JEL
Sep 21, 2016 at 7:05
• The case you describe is not one for which I would normally use the term pro-rata. It is merely a rate per month. Pro-rata which is used both as an adverb and a verb by accountants, is used where a cost which cannot otherwise be individually allocated (e.g. to a department, cost centre, project, or between separate participants), is apportioned on the basis of something else.
– WS2
Sep 21, 2016 at 7:12
• AFAICT, you are describing a total or aggregated amount. Sep 21, 2016 at 7:15
• You "extrapolate" quaterly/yearly expenses from January expense. Sep 21, 2016 at 10:38
• propotionate(-ly) it is.
– Kris
Sep 21, 2016 at 10:56

@Graffito, in the comment above, suggested the word, extrapolate. The Oxford Dictionaries site offers this definition:

Extend the application of (a method or conclusion) to an unknown situation by assuming that existing trends will continue or similar methods will be applicable.

That sounds to me exactly like your situation. Your estimates are extrapolated from current data. An alternate word with a similar meaning is project [VERB](accent on the second syllable):

Estimate or forecast (something) on the basis of present trends.

In this case the estimates are projected expenses.

I will approach your question from my own point of view as a retired accountant. Pro-rata is accountancy jargon, usually in adverbial context, though sometimes as a verb, for the dictionary verb prorate.

The latter is not an expression restricted to matters of finance. The Oxford Dictionary Online meaning is given as allocate, distribute or assess pro-rata.

From an accountant's point of view, the case you describe is not one for which I would normally use the term pro-rata. It is merely a rate per month. But I see nothing wrong, in this context, with the terms periodize or annualize which you suggest.

Pro-rata is used where a cost, capital expense, or item of income, which cannot otherwise be individually allocated (e.g. to a department, cost centre, project, or between separate participants), is apportioned on the basis of something else.

Example. A building is used by a number of different businesses. How can the rent and other building costs be allocated to each individual entity? A common method would be to pro-rata those expenses based on floor area occupied. The overall cost would be calculated as a rate per square foot and then charged to the different entities based on the area each occupies.

Inside an individual company overheads are pro-rated in this way based on a number of different factors e.g. personnel costs on the basis of employee headcount etc.

So in answer to the question, the most suitable synonym I can think of would be apportion, but both distribute and allocate are often used.