If the acquisition cost of a customer is less than life-time value of the customer you should pay. Otherwise not.
Generally the life-time value of a customer (how much money you make on an average customer in the time you do business together) is an important metric that you would want to estimate anyway.
Subject to liquidity constraints. If you have a product that has regular payments from a customer, and customers stay customers for a long time, creating a high lifetime value, then it is likely that there are many marketing activities that exceed lifetime value but will take six months or more to break even. Some marketing activities have the above characteristic but require a sizable minimum investment, such as ad campaigns. This limits your ability to implement them.
This constraint doesn't apply to public (or large) companies who can raise whatever money they need if they have a high value marketing activity to invest in.
I would also add that many people don't necessarily have the operating history to know what lifetime value is, so they begin making assumptions, and the assumptions are almost always too optimistic. This can lead to excessive marketing.
I actually model allowable acquisition cost on expected first year average revenue per user (less any marginal service costs like bandwidth or storage). The key variables are % of users that have a transaction and the average transaction size. If you have a monthly recurring fee, then you also have to consider churn. I'd recommend a conservative estimate of an average of six months of revenue in the first year for each paying customer on a monthy recurring fee. Annual fee is obviously the entire transaction size. Hope this makes sense.
Sean Ellis (startup-marketing.com, led early marketing at both Dropbox and Xobni)
Generally the life-time value of a customer (how much money you make on an average customer in the time you do business together) is an important metric that you would want to estimate anyway.