M4V is a file container format with MPEG-4 file extension, used and downloaded from Apple iTunes store. It is very similar to .mp4 file, however, the M4V file may be copy-protected with Apple's FairPlay DRM copyright protection. To play protected M4V file, you should firstly authorized with the account. When comes to the unprotected M4V, you can try to rename the file extension to .mp4, before editing in iMovie.
However, if you find the renamed MP4 still can't be recognized by iMovie, you may have to render to a third party software-M4V to iMovie Converter, which can help you to convert compatible MOV or DV, etc. Then you can transfer the output .mov or .dv files into iMovie for further editing. Moreover, it can convert versatile video or audio file formats, but also allows you to set video codec, bit rarte, frame rate, resolution, audio codec, sampling rate, channels, etc.
After download the on your Mac, you can go on the specific steps to finish the conversion. If you are also the FCP user, you can use it edit M4V in Final Cut Pro as well.
Step 1. Add M4V video files to the application
Click "Add files" button into the M4V to iMovie Converter.
Step 2. Directly choose "iMovie" as the output format
Select profile drop-down list to choose ".mp4" as the output format.
Step 3. Start M4V to iMovie converting
When all settings are done, click the "convert" button to start convert M4V video to iMovie.
Finally, when the conversion is done, you can open the iMovie application, go go to "file > import movies" to import M4V video into iMovie directly.
Resource from the details about M4V video editing in iMovie at doremisoft.net/guides/convert-m4v/import-m4v-into-imovie.html