This is the general troubleshooting steps for Office 2013, or Office 365. That's usually caused a third party application having conflict with the installation files. Sometimes it will stop or hangs on 87% etc...
Here is the general troubleshooting steps on how to sort it out. I tried this several times with great success.
Steps:
1. Perform computer clean boot (disable Non MS Services/Startup) = Visit this Clean Boot Link for the steps.
2. Create and Login to a new Admin Account = Visit this Create New User Account link for the steps.
3. Delete temp files. Press windows key + R. On the run box type the following;
a. %temp%
b. C:/Windows/temp
c. C:/Windows/Prefetch
4. Optimize the Internet Explorer.
1. Type inetcpl.cpl on run and click OK
2. Under General, click on delete browsing history, put a check on all boxes, and click delete
3. Under Security Tab, click on reset all zones to default level
4. Under Privacy, click on clear sites
5. Under Content, click on clear SSL state
6. Under Advanced, click on restore advanced settings, and click on reset, put a check on delete personal settings, and click reset
2. Under General, click on delete browsing history, put a check on all boxes, and click delete
3. Under Security Tab, click on reset all zones to default level
4. Under Privacy, click on clear sites
5. Under Content, click on clear SSL state
6. Under Advanced, click on restore advanced settings, and click on reset, put a check on delete personal settings, and click reset
5. Run the Office 365 uninstaller fixit http://support.microsoft.com/kb/2739501
6. Delete Microsoft Office 15 in Program Files and Program Files(x86)
7. Run IE in private mode;
Press control shift + P
8. Download the 64bit and 32bit Office setup file… login to http://office.com/myaccount
9. Run first the 64bit. An error may appear regarding integrated... Just click on OK.
10. Run the 32bit installer.
