{"id":"fpa-cac-payback-with-free-months-lines","audience":"fpa","category":"finance-work","track":"finance","technique":"verification","level":"intermediate","title":"Compute CAC payback on gross margin including free promo months","free":false,"task":"You're calculating CAC payback for the CMO. Write a prompt for plain text with lines starting \"Monthly margin:\", \"Paid months to recover CAC:\", \"Free months:\", \"Payback:\" and \"Versus marketing's figure:\". Use gross margin dollars, not revenue. Free promo months earn nothing and count toward the payback time. Show the math. Under 90 words.","materialLabel":"Source material (attached to your prompt automatically)","material":"CAC PAYBACK INPUTS - new SMB customers, Q3\n\nCustomer acquisition cost (CAC): $12,000 per customer\nPrice: $1,000 per month\nGross margin: 75% of revenue\nPromo: the first 2 months of service are free (no revenue, no margin; the cost to serve is ignored in the free months for this exercise)\n\nMarketing's figure in the board deck: \"CAC payback is 12 months\" (calculated as $12,000 divided by $1,000 of monthly revenue, ignoring margin and the free months).\n\nNotes: the CMO wants a figure that can stand up to the CFO's questions. The promo applies to every new customer this quarter. Churn is not considered in the payback; a separate analysis covers retention. All amounts are in US dollars and exclude taxes.","rules":[{"type":"plainText"},{"type":"maxWords","max":90}],"promptHints":[{"label":"Names the five lines","patterns":["monthly margin","paid months","free months","payback","versus marketing"]},{"label":"Uses margin","patterns":["gross margin","75%","margin dollars"]},{"label":"Adds free months","patterns":["free months","count toward"]},{"label":"Asks for the math","patterns":["show the math","math"]},{"label":"Caps length","patterns":["\\d+\\s*words","under \\d+"]}],"mistakes":[{"title":"Using revenue","why":"The AI divides CAC by $1,000 and gets 12.","fix":"Say: \"Use gross margin dollars, not revenue.\"","checks":["r0","r1"]},{"title":"Ignoring the free months","why":"The AI stops at 16.","fix":"Add: \"Free months count toward the payback time.\"","checks":["r1"]},{"title":"Skipping the comparison","why":"The AI leaves out marketing's figure.","fix":"Add: \"Versus marketing's figure: the difference in months.\"","checks":["r2"]},{"title":"Markdown extras","why":"The AI adds bold labels, headings and a closing note.","fix":"Say: \"Plain text, no bold. Output only the lines asked for.\"","checks":["plainText"]},{"title":"Trusting the AI to count words","why":"AI is bad at counting and runs past word limits.","fix":"Ask for fewer words than the real cap and keep each part short.","checks":["maxWords"]}],"hint":"Payback uses margin dollars and counts the months with no revenue. Say both.","rubricLabels":["Monthly margin shows $1,000 x 75% = $750 and Paid months to recover CAC shows $12,000 / $750 = 16","Free months shows 2 and Payback shows 16 + 2 = 18 months","Versus marketing's figure shows 18 - 12 = 6 months longer (and says marketing used revenue and ignored the free months)"]}