How can ROAS be calculated using Retention, ARPU, and LTV metrics?

If you have an LTV metric, it means you have an LTV curve, which is really all you need to calculate ROAS.

Remember that ROAS is time-indexed; you don't really talk about ROAS in the abstract ("the ROAS on this campaign is 100%") because the extent to which ad spend has been recouped changes over time. You'd more commonly hear about Day 1 ROAS or Day 7 ROAS or Day 90 ROAS; those numbers provide a sense of how cash flows back into the company after being expended on marketing campaigns (of course, that cash recoup is usually staggered on some timeline based on payments from vendors and platforms; cash doesn't get deposited into a company's bank account in real time). More on this topic in my MDM article, Building a marketing P&L using LTV and ROAS:

If you don't actually have an LTV curve available, you can use retention rates and ARPDAU numbers to roughly estimate cumulative monetization over time. ROAS is calculated by: