How do I convert 120FPS video from the iPhone 5s to 60FPS?

When I shoot 120FPS video on the iPhone 5s, I can easily export it as a 30FPS video, slowed down four times. But I want to export it as a 60FPS video, slowed down twice.

Ideally, I'd like to do this without transcoding the video (because that reduces quality and increases file size), but merely having an app change the fields in the header to say that rather than playing for 1 minute at 120FPS, this video should play for 2 minutes at 60FPS.

I'm looking for:

• A Mac app, but if that's not possible, an iPhone app will do.
• A less expensive ($20) or free app.
• A GUI app, rather than a command line one.

I have iMovie 10, iPhoto 11, Picasa and Lightroom 5, but none of them seem to have this function. iMovie 10 can only export a 30FPS video, not a 60FPS one.

Is there any software that does this?

Update2: Official Apple Support iMovie (2013): Slow down and speed up clips:

Make a clip play more slowly
In the timeline, select the clip you want to slow down.

Choose Modify > Slow Motion, and choose a speed percentage from the submenu.

Update: Maybe i misunderstood the question, you just want to make it half the FPS without changing the play speed, right? iMovie 11 for Mac is supported to export 60 FPS videos:

So, here is what you have to do if you want to export a 60p movie made with your 60p footage :
- create a NTSC (29.97 fps) project in iMovie
- choose "export using quicktime" in the "Sharing" menu
- choose the correct codec settings (I choose a Quicktime movie with the H264 and AAC codecs, max quality, and recompress the movies with Handbrake afterwards)
- be sure to check the correct framerate (59.94 fps for my 2 cameras, I guess it should be pretty standard - you can always check it in the information window in Quicktime Player for a raw file from your camera)
- export and enjoy.

Source

You can slow it down using iMovie on iOS:

Or you can use different applications for record, like SloPro - 1000fps Slow Motion Video.