The arithmetic of a task
Price a task by hand and automated, build and run and review, then find the month it pays back or the review minute after which it never will.
On this page
Every automation is a bet that a cost paid once beats a cost paid every week. The bet can be priced before anyone opens a tool, with two sums: what the task costs a person each month, and what the automation costs to build once and then to run and review each month. Most automations that disappoint were priced on the first sum alone.
The running example
The company is the 14-person marketing agency from how to use this course: you, the founder; an operations manager who also keeps the books; two account managers; ten people doing client work across 40 active projects. Every figure is an assumption to swap for your own: a staff hour costs $30 loaded and a founder hour $100; a month is 52 ÷ 12 ≈ 4.33 weeks; a large model costs $2 per million input tokens and $8 per million output.
The task priced here is the Friday invoice run. Each of the 40 projects is invoiced weekly from the time tracker's export: the operations manager filters the export to one client, adds up the hours, applies the rate, creates the invoice in the accounting system and sends it. About 6 minutes an invoice.
Sum 1: what the task costs a person
Frequency × minutes × loaded hourly cost, taken to a month:
40 invoices a week × 6 min = 240 min = 4 h a week
4 h × 4.33 weeks = 17.3 h a month
17.3 h × $30 = $520 a month
$520 a month is the ceiling on what the automation can save, and every line of the second sum comes out of it.
The sum that stops at one line
The usual pitch goes: it saves 4 hours a week, $520 a month; the founder can build it in 12 hours, $1,200; so it pays back in $1,200 ÷ $520 = 2.3 months. Every number is right and the conclusion is wrong, because the automation is not free once built. It calls a model, it runs on a platform that charges monthly, and someone looks at each invoice before it reaches a client.
Sum 2: what the automation costs
Three lines, as on every page of the course: build once, run monthly, people monthly.
Build, once. 12 founder hours at $100 is $1,200.
Run, monthly. One model call an invoice turns the timesheet notes into line descriptions and flags hours that look wrong. Assume 1,600 tokens in (1,200 of instructions, about 400 of timesheet rows) and 200 out:
in 1,600 × $2 ÷ 1,000,000 = $0.0032
out 200 × $8 ÷ 1,000,000 = $0.0016
per invoice = $0.0048
× 173 invoices a month ≈ $0.83, call it $1
Add an assumed $20 a month for the workflow platform and the run line is $21. How a model bill is built up call by call is in where the money goes; for this task it is the smallest number on the page.
People, monthly. Before an invoice goes out, the operations manager checks three numbers: the hours against the export, the rate against the rate card, the total against last week's. If the workflow lays those three side by side, the check takes about a minute:
173 invoices × 1 min = 173 min = 2.9 h a month
2.9 h × $30 = $87 a month
Sum 2 is $1,200 once, then $21 + $87 = $108 a month.
The payback line
The automation saves $520 − $108 = $412 a month and pays back in $1,200 ÷ $412 ≈ 2.9 months. From then on it is $412 a month ahead for as long as it keeps working.
Change one number. Suppose the check takes 5 minutes, because the workflow shows only the finished invoice and the reviewer re-adds the hours before trusting it:
173 × 5 min = 865 min = 14.4 h × $30 = $433 a month
monthly cost $21 + $433 = $454
saving $520 − $454 = $66 a month
payback $1,200 ÷ $66 ≈ 18 months
The model, the platform and the build did not change; the review minute moved payback from three months to a year and a half. The break-even is the check length at which people cost everything the run leaves of the $520: ($520 − $21) ÷ $30 = 16.6 hours a month, or 5.8 minutes an invoice. A reviewer who spends six minutes checking a six-minute task has kept the task and added a build to it.
That is the commonest way an automation fails to pay: not a weak model, but a review step nobody priced. The design target for the build is the review minute, and the screen with three numbers on it is part of the 12 hours.
Why the review is there at all
Dropping the check would save the $87, which is a good trade only if errors are cheap. Assume an unchecked invoice is wrong 2% of the time (a missed internal tag, a stale rate) and that each wrong invoice costs about $50 of rework: a credit note, a reissue, an awkward email. That is 173 × 2% ≈ 3.5 bad invoices a month, about $173. The 1-minute check costs $87 and catches most of them, so it earns its place. A 5-minute check costs $433 to protect $173, and does not.
The cost of one error is the third input after frequency and minutes. The scoring frame makes it a factor, so a $50 error and an $8,000 one are not ranked on hours alone.
How sure the sums need to be
Every input is an estimate, so test the decision, not the number. A payback past 12 months is a no, since every automation gets a 12-month retirement date; estimates this rough want margin, so aim for six. Double the build to 24 hours, $2,400: payback $2,400 ÷ $412 ≈ 5.8 months, still inside six. Double the run to $42: saving $391, payback 3.1 months. Neither moves the decision. Move the check from 1 minute to 4: saving $520 − $21 − $347 = $152, payback 7.9 months, and the margin is gone. The decision turns on one input, the one to measure before building.
Measure three numbers rather than remembering them: the minutes per item, timed on ten real items; the review minutes, timed on a prototype's output; and the cost of one error, from the last time one happened. The method is back-of-the-envelope estimation applied to a task: state the assumption, show the multiplication, find the input the answer turns on.
In practice
Hand the builder, or the vendor, the two sums before the brief. "The invoice run costs us $520 a month. With a 12-hour build and a 1-minute check it pays back in about three months. The check is the part we are buying: show me the screen the operations manager will use, and how long one invoice takes on it." A vendor who answers with the model's accuracy and not the reviewer's minutes is pricing the wrong line.
Tell the operations manager the same numbers: 4 hours a week become 40 minutes of checking, and those 40 minutes are how everyone will know whether the build worked.
The mistake that costs money: pricing the hours saved and not the review minutes added. At 5 minutes a check, the invoice automation costs $1,200 to build and saves $66 a month.
Check yourself
1. The account managers write up 30 client meetings a week at 15 minutes each. An automation would take 16 founder hours to build, $22 a month to run, and 3 minutes of checking per meeting. Do you build it?
Sum 1: 30 × 15 min = 7.5 h a week × 4.33 ≈ 32.5 h × $30 ≈ $975 a month. Sum 2: build 16 × $100 = $1,600; checking 30 × 4.33 ≈ 130 meetings × 3 min = 6.5 h × $30 = $195; run $22; so $217 a month. Saving $758, payback $1,600 ÷ $758 ≈ 2.1 months. Build it, but time the check on a prototype first: at 12 minutes a meeting the saving falls to $173 and payback stretches to about 9 months.
2. A vendor offers the invoice run as a service at $300 a month, no build, with the same 1-minute check. Over a year, is it cheaper than building?
Vendor: $300 + $87 = $387 a month, $4,644 over 12 months. Build: $1,200 + 12 × $108 = $2,496. The lines cross where $1,200 + $108m = $387m, at m ≈ 4.3 months; after that, building is $279 a month ahead. Buy only if the run will be retired within about four months, or the founder's 12 hours are worth more elsewhere than the year's $2,148 difference.
3. The check is taking 4 minutes because the reviewer re-adds every invoice's hours. What do you change, and what is the change worth?
At 4 minutes, people cost 173 × 4 ≈ 692 min ≈ 11.5 h × $30 ≈ $347 a month, so the saving is $152 and payback 7.9 months. Change the screen, not the reviewer: put the export total, the invoiced total and last week's total side by side so the check is a comparison, not a recount. Back at 1 minute the saving is $412 a month, so the screen is worth about $260 a month.