Average cost of magazine layout?

Hello, i'm trying to quote a potential client for a full magazine layout, 15-20 pages, including cover. After that, they plan on having a quartley with 40-60 pages. It's for the travel industry, and has many high end ad spaces for Prada, Gucci, Dior and others. I was thinking something like $150-$200 / page and $400 for each cover. So twenty pages like $4200, and 60 like $12200. I know this is alot cheaper than a professional design firm would charge for a magazine as such, but im curious, am i low balling myself? It seems cheap for such a magazine. I know that that there are freelancers who would do it for almost nothing, but don't have the experience they're looking for.

Thanks for any input.

That depends on the budget of your client and the hour require to complete specific task.