Customer lifetime value (simple and discounted)

Illustrative STUD.com buyer LTV (STUD is pre-seed, pre-revenue soft launch, so every figure here is illustrative and modeled, not measured). The per-year profit series models one active launch-scenario buyer: an active buyer spends about $25 a month on prepaid credit packs ($300 per year, roughly 1.25 plays a month at the typical 500-credit, $20 price), the estimated 87 percent gross margin makes that $261.00 of year-one profit, and the illustrative 6 percent monthly logo churn compounds to a 0.4759 annual retention factor, so expected per-year profit rounds to 261, 124, 59, 28 over four years. All four years are profitable, so the customer lifetime is 4 years and the simple LTV is the plain sum, $472.00. Discounting each year at a 10 percent annual rate (year t divided by 1.1 to the power t) gives a discounted LTV of $403.20. Read against the illustrative $40 blended content-led CAC, even the discount-adjusted LTV covers acquisition roughly 10 times over, which is the number that matters when deciding whether STUD can afford to spend more to acquire a buyer as the catalog compounds what the system knows about each venture.