{"id":"data2-cac-payback-months-math-steps","audience":"marketing","category":"data","track":"data","technique":"verification","level":"advanced","title":"Calculate CAC payback in months with each step shown","free":false,"task":"Your CFO asks how many months it takes to earn back what you spend to win a customer. Write exactly 4 numbered lines with the math shown: 1 CAC, 2 monthly gross profit per customer, 3 payback in months, 4 a verdict against the 12-month target. Plain text, under 90 words, round months to one decimal. Use the average discounted price, not the list price.","materialLabel":"Q3 acquisition numbers (attached to your prompt automatically)","material":"Q3 acquisition - Wavecrest Fitness App\n\nMarketing and sales spend to acquire customers in Q3: $60,000\nNew paying customers in Q3: 120\n\nPricing:\n- List price: $80 per month.\n- Average price actually paid after discounts and promotions: $60 per month.\n- Gross margin on subscription revenue: 75%.\n\nFinance target: CAC payback of 12 months or less.\n\nOther facts:\n- Payback months = CAC divided by monthly gross profit per customer.\n- Monthly gross profit per customer = monthly price paid x gross margin.\n- 8 of the 120 customers were free trials converted by a partner at no marketing cost; they are included in the 120 and the spend figure already covers everything.\n- Churn is ignored in this simple calculation.","rules":[{"type":"numberedItems","count":4},{"type":"plainText"},{"type":"maxWords","max":90}],"mistakes":[{"title":"Using the list price","why":"The AI uses $80, giving a payback of 8.3 months.","fix":"Add: \"Use the $60 price actually paid, not the $80 list price.\"","checks":["r0"]},{"title":"Skipping steps","why":"The AI jumps to the payback figure.","fix":"Add: \"Show CAC, monthly gross profit, payback, then the verdict, each with its math.\"","checks":["r1"]},{"title":"No verdict","why":"The AI never compares the result to the 12-month target.","fix":"Add: \"Line 4: within or over the 12-month target.\"","checks":["r2"]},{"title":"Leaving the format to chance","why":"The AI picks its own length and layout unless told the exact shape.","fix":"Add: \"Exactly 4 numbered lines. Plain text, no bold or headings.\"","checks":["numberedItems","plainText"]},{"title":"Trusting the AI to count words","why":"AI is bad at counting. Ask for a total word limit and it often lands over it.","fix":"Cap each part instead, for example \"each line under 15 words.\"","checks":["maxWords"]}],"promptHints":[{"label":"Asks for four steps","patterns":["4 numbered","1\\.","exactly 4"]},{"label":"Uses the paid price","patterns":["\\$60","price (actually )?paid","not the \\$80"]},{"label":"Shows the math","patterns":["60,?000 ?/ ?120","\\$500","x 75%"]},{"label":"Asks for a verdict","patterns":["verdict","12.month","target"]},{"label":"Rules out notes","patterns":["no notes","nothing else"]}],"hint":"Make the AI write each step and tell it which price to use; otherwise it grabs the list price.","mission":"What is our CAC payback?","musts":["Four numbered steps","Use the discounted price","Verdict vs 12 months"],"rubricLabels":["Line 1 shows CAC as $60,000 / 120 = $500","Line 2 shows monthly gross profit per customer as $60 x 75% = $45 (using the discounted price, not $80)","Line 3 shows $500 / $45 = 11.1 months and line 4 says payback is within the 12-month target (or meets it), with no extra text"]}