{"id":"fpa-ltv-cac-corrected-cfo","audience":"fpa","category":"finance-work","track":"finance","technique":"verification","level":"intermediate","title":"Compute CAC, payback and LTV:CAC after a cost correction","free":false,"task":"You're preparing a unit-economics note for the CFO. Write a prompt for plain text with exactly four lines, no intro, starting \"CAC:\", \"Payback:\", \"LTV:\" and \"LTV:CAC:\", each showing the arithmetic. Use only sales and marketing spend after the controller's reclass. Give figures only and make no recommendation about spending. Under 75 words. No bullets or numbering.","materialLabel":"Q3 sales and marketing data and notes (attached to your prompt automatically)","material":"Q3 2026 - unit economics inputs, Willow CRM Inc.\n\nSales & marketing spend per the GL: $540,000\nNew customers won in Q3: 60\nAverage revenue per account (ARPA): $500 per month\nGross margin: 80%\nMonthly customer churn: 2%\n\nController note (Nov 3): $60,000 of the Q3 sales & marketing line is customer success salaries that were coded there by mistake. They are not acquisition costs. The reclass entry will post in the November close, so the GL still shows $540,000.\n\nFormulas used by FP&A:\n- CAC = acquisition spend / new customers\n- Payback (months) = CAC / (ARPA x gross margin)\n- Customer lifetime (months) = 1 / monthly churn\n- LTV = ARPA x gross margin x lifetime\n\nA board member asked last month whether the company should \"double marketing spend\". Not part of this analysis.","rules":[{"type":"plainText"},{"type":"maxWords","max":75},{"type":"maxBullets","max":0}],"promptHints":[{"label":"Lists the four lines","patterns":["cac:","payback:","ltv:"]},{"label":"Applies the reclass","patterns":["reclass","60,000","remove"]},{"label":"Uses given formulas","patterns":["formulas","gross margin","1 /"]},{"label":"Bans recommendations","patterns":["no recommendation","figures only"]},{"label":"Caps length","patterns":["\\d+\\s*words","plain"]}],"mistakes":[{"title":"Using the GL spend","why":"The AI divides $540,000 by 60 for a $9,000 CAC.","fix":"Say: \"Remove the $60,000 reclass before dividing.\"","checks":["r0"]},{"title":"Payback on revenue, not margin","why":"The AI divides CAC by $500, not $400.","fix":"Add: \"Gross profit per month = ARPA x gross margin.\"","checks":["r1"]},{"title":"Recommending spend","why":"The AI answers the board member's question about doubling marketing.","fix":"Add: \"Figures only. No recommendation about spending.\"","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","maxBullets"]},{"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 line short.","checks":["maxWords"]}],"hint":"The GL has a known miscoding. Tell the AI the reclass, the formulas and to avoid recommendations.","rubricLabels":["Has exactly four lines starting CAC:, Payback:, LTV: and LTV:CAC: (no intro), and the CAC line uses $480,000 ($540,000 - $60,000 reclass) / 60 = $8,000","Payback line shows $8,000 / ($500 x 80% = $400) = 20 months, and LTV line shows $400 x 50 months (1 / 2%) = $20,000","LTV:CAC line shows $20,000 / $8,000 = 2.5 and nothing recommends spending more or less"]}