The Arithmetic Memo
How to build a business case for automation that gets CFO approval: the one-page memo, where every number comes from, and the conservative column.
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Problem: You found the bottleneck, you know what to build, and you cannot get it funded. The person who has to sell this internally is almost never the person who signs the invoice, and the document that has to travel upward is one you have never had to write.
Quick Win: Send one page of arithmetic, not a business case. The business case for automation is the internal document that turns a problem into approved budget, and the version that gets approved contains no return-on-investment number you calculated. It contains four or five inputs your finance team can recompute from systems they already trust, the formula connecting them, and a deliberately pessimistic column most memos leave out. The house rule: every figure should be one the CFO's own team can dispute. That is not a weakness. It is the entire reason it works.
Your Memo Is Competing Against Every Other Request
The first mistake is treating the memo as an argument for doing this versus doing nothing. Money is not sitting idle waiting to be justified. It is allocated, and allocation is a ranked queue.
In a Gartner survey of more than 200 finance chiefs, 56% ranked enterprise-wide cost optimization among their top five urgent actions for 2026, and 47% ranked allocating capital to new growth opportunities in that same top five (CFO.com, on Gartner). Cutting and funding at once. That is not a company deciding whether to spend. It is a company deciding where to move money it has already decided to move.
The academic work says the same thing more quietly. Asked why they set the bar for a project higher than what money genuinely costs the company, finance executives cite the desire to pursue the best available among all projects, plus limits on management time and a margin for error in the analysis (Graham, Corporate Finance and Reality, NBER).
Your competition is not inertia. It is the best of everything else on the list, and the padding is deliberate.
Good Projects Get Rejected On Format, Not Merit
Now add the credibility problem specific to this moment, because it raises the bar for you personally.
RGP surveyed 200 US finance chiefs in late 2025 at companies between $500 million and $10 billion in revenue. 66% expect significant returns from AI within two years. Only 14% report clear, measurable impact today (RGP, covered by CFO.com). The same survey found 48% say they are ultimately responsible for making sure AI delivers measurable value, and only 10% fully trust their own company data.
That is your reader. Personally accountable for the outcome, sitting on a two-year expectation, holding a 14% hit rate, not fully trusting the systems your numbers come from. Only 36% of CFOs feel assured they can achieve meaningful AI outcomes at all (CFO.com, on Gartner). And the reasons projects get abandoned are consistent: escalating costs, unclear business value, poor data quality, weak risk controls (Gartner). "Unclear business value" is a document problem as much as a project problem.
Behind all of it sits the number your CFO has almost certainly seen: MIT's Project NANDA reported that the large majority of organizations investing in generative AI saw no measurable impact on profit, with only about 5% of integrated pilots producing real value (MIT Project NANDA).
You are not writing into a neutral room.
We Will Not Give You An ROI Number
Any return-on-investment figure calculated by the party being paid is worth nothing. Your CFO discounts it automatically, so a memo led by a confident percentage has already spent its credibility on the first line. Worse, one number invites one question: how did you get that? Now you are defending a calculation instead of describing a problem.
So do not submit an ROI number. Submit the arithmetic: the inputs, the source of each, and the formula connecting them. Then stop. Let the finance team press the equals key.
That changes the question from "do we believe this person" to "do we believe our own numbers." One of those is a debate you cannot win. The other is a debate you do not need to have.
The Six Blocks Of A One-Page Memo
One page, not a deck. A deck gets presented, and presentation is where optimism creeps in.
| # | Block | What goes in it |
|---|---|---|
| 1 | The number that is bleeding | One metric, its current value, the system it came from, the date range. Nothing else. |
| 2 | What it costs per year | That metric converted to money, multiplication written out in full so it checks in thirty seconds. |
| 3 | What changes | One paragraph of plain language on the mechanism. No product names, no technology names. |
| 4 | The cost of finding out | A fixed price and an end date for a first phase that proves or disproves the claim. Not the whole program. |
| 5 | Three columns | Conservative, expected, upside. Each with its assumption stated and its payback period in months. |
| 6 | The ask | The exact decision you need, from whom, by what date, and what happens if the date slips. |
Block 4 is the one most memos get wrong and the one that most often frees the money. You are not asking a CFO to approve a return. You are asking them to approve the cost of finding out whether the return exists, on a date certain, with a defined stopping point. Far smaller decision. We build first phases this way, which is why our pricing is fixed and scoped rather than open-ended.
Where Your Numbers Come From, And Where They Must Not
This is what decides whether the memo survives contact with a finance analyst.
| Allowed | Banned |
|---|---|
| Payroll and headcount records | Any vendor case study or customer story |
| Timestamps from the software you use to track customers and deals | Analyst estimates of productivity gains in your industry |
| Invoice dates and payment dates | Benchmarks from companies that are not you |
| Support ticket open and close times | Your team's self-reported estimate of hours spent |
| The actual quote from whoever will do the work | A number whose origin you cannot name in one sentence |
The rule behind the table: a number is allowed if a system created it for some other purpose, before anyone had a reason to make this project look good. Invoice dates were not recorded to justify automation. That is exactly why they are credible.
People push back on the ban against self-reported hours. Do not budge. If you have not captured what the work costs today from a system rather than a survey, you do not have a memo, you have an anecdote with a budget request attached. Fix that first: baseline the process before you start, then write.
And if you do not yet know which number is bleeding hardest, that is a different project and it is the one to run first. A ranked, evidence-backed map of where the company loses time and money is what a bottleneck diagnosis produces, and it is far easier to fund than a solution to a problem nobody has sized.
The Conservative Column Most Memos Leave Out
Almost every rejected memo submits one scenario. One scenario reads as a forecast, and finance discounts forecasts by habit, silently and by more than you would like.
Three columns instead, and one rule that makes them work: you are judged on the conservative column.
Build it from the unglamorous things that actually happen. Adoption is partial, so only a fraction of the volume goes through the new process in year one. Rework does not drop at all. The first version takes longer to stabilize than planned. Two of the intended users leave.
Then the discipline: if the conservative column does not clear your company's bar, do not send the memo. Go find a bigger problem.
That is uncomfortable and it is the single strongest move in the document. A memo whose worst case clears the bar is not asking for faith. And when the project lands between conservative and expected, which is where most land, you were right rather than optimistic. That is what makes the next approval easy.
Hurdle Rate, In Plain English
A hurdle rate is the minimum yearly return a project has to beat before finance considers it worth doing. It is set on purpose above what money actually costs the company, as a margin of error and because projects compete against each other.
The gap is measurable. In a survey of 306 finance executives, the median hurdle rate was 12% and the mean 13.6%, against a median cost of capital of 9.8% and a mean of 10.6% (CFO.com, on Graham's Duke survey). Two to three points of deliberate padding, and the executives quoted are explicit about why: risk the calculation does not capture, plus an added spread on growth projects.
So ask your finance team what your company's hurdle rate is before you write a word. It is a two-sentence email, almost nobody sends it, and sending it is the moment your memo stops being a pitch and becomes a submission, because you are writing to a standard they set rather than one you invented.
Then ask which measure they use for this kind of spending. Many teams judge operating costs on payback period, meaning how many months until the thing has paid for itself, rather than on a rate of return. Payback remains the most-used method after the standard discounted cash flow approaches, and more common still at smaller companies (Graham, NBER). If your finance team thinks in months, give them months. Answering in the wrong unit is itself a format failure.
Where This Breaks
One number your finance team can disprove. The big one. Claim 340 hours a year when payroll shows the team is 2.5 people and every other figure is suspect. Check the load-bearing inputs against the source system yourself, before sending.
You included a vendor's ROI claim. One borrowed percentage discounts the entire page. Cut it even if it is true.
You asked for the program, not the cost of finding out. Big asks get deferred rather than rejected, which is worse, because deferred requests do not come back.
Your savings are hours, not money. Hours become money three ways: revenue produced with the same team, a hire not made, or a cost actually stopped. Say which one, by name.
Nobody owns it after go-live. Name the person in block 6, or the memo reads as a launch date with no end state. If an outside partner will carry it, pressure-test them first.
The data underneath cannot bear weight. With only 10% of CFOs fully trusting their company data and 35% naming data trust as their top barrier to returns (RGP), a memo built on a system your CFO already distrusts fails for reasons unrelated to your project.
What Happens In The Meeting After You Send It
Send it at least 48 hours ahead. A memo read out loud is a pitch. A memo read alone, with a calculator open, is a submission. You want the second one.
Expect three questions.
"Where did this number come from?" A system name and a date range, never a person's estimate. If you cannot do that for a figure, delete the figure before the meeting.
"What happens if it does not work?" The cost to stop and the date you would know. Block 4 doing its job: a number small enough to be uninteresting, a date close enough to be checkable.
"Who else wants this money?" Do not try to answer. You cannot see the queue. The conservative column answers it for you, which is precisely why it is there.
One last thing about the room you are walking into. In Deloitte's Q4 2025 CFO Signals survey of 200 North American finance chiefs at companies above $1 billion in revenue, 59% said now is a good time to be taking greater risks, up from 36% the previous quarter, and 50% named digital transformation of finance their top priority for 2026 (Deloitte). The appetite is there. It is the format that is failing, not the idea.
Related Reading
- Baseline it first, the numbers to capture before you write
- AI for the CFO, which finance work pays back fastest
- The 30-day pilot that ships, what block 4 looks like in practice
Frequently Asked Questions
How long should the memo actually be?
One page, treated as a hard limit rather than a target. The constraint does the work: it forces you to pick the single number that is bleeding instead of listing seven, and it forces block 3 into plain language rather than an architecture description. Anything that does not fit is an appendix, and an appendix is optional reading by definition.
Should the memo name the vendor or partner?
Not in the first version. Block 3 describes the mechanism, block 4 carries the price. The moment a name appears it becomes a procurement conversation about that name rather than a capital conversation about the problem.
If the honest blocker is that you cannot name the number that is bleeding, no amount of formatting will fix it. That is where we usually start: a ranked, evidence-backed map of where a company loses time and money, built from its own data, so the arithmetic in the memo comes from systems the CFO already trusts. See what we install inside companies →
Quer o framework por trás destes projetos?
Obtenha o sistema Claude Code que usamos para planejar, construir, testar e lançar software em produção.