You don't explain too much what is your application and why there is a need to calculate something, so it's difficult to answer someting precise. In all cases, you say that you have a choice between letting the user wait for 15 seconds or for 90 seconds. In both cases, there is a problem. Every application I used loaded in less then ten seconds, except in some very specific circumstances (for example, Visual Studio can take up to 30 - 40 seconds when loading for the first time after a clean install).
In general, the user don't have to wait neither at startup, nor during the workflow. If the app takes 15 seconds to start, most users will attempt to never close it, or to start it when leaving take a cup of coffee. In all cases, they will probably think: "I should invest more in buying a correct software instead of loosing my precious time".
The cases when you really need a lot of calculation immediately are extremely rare and can be easily removed. For example, Adobe Lightroom, when starting, must show the last catalog with the thumbnails of the photos. When I start it with a catalog containing several hundreds of photos, 20 MB on disk per photo, it requires a lot of hard disk and CPU to load those photos, read them, make transformations (including perspective distorsion etc.) and generate a thumbnail. Actually, Lightroom spends less then five seconds to load on a not-so-new PC, because data is cached intelligently and because it doesn't show every of those hundreds of thumbnails immediately after startup, but rather one by one once the main window is already displayed.
So in your case, you should probably think less about when the user must wait, and more about how to avoid your users to waste their time.
Edit: of course, I've forgotten a group of applications which can behave differently: video games. In a video game, you can let the user wait for one minute to load graphics. This is done because 2D/3D rendering can be CPU-intensive, and you can't afford wasting machine resources loading and calculating things during the game: the visual performance must be the best possible, and game experience must be extremely smooth.
But even in this case, I think those applications try to spend less than a minute loading stuff. Or they load small chunks, letting the user start the game very fast, play smooth, but wait for free to five seconds when going from one level to another (that's what I've seen in Half Life series for example).