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Office 2016 not compatible with Office 2013 Standalone Apps
Office 2016 Installation Routine Deleting Older Stand-alone Apps
More here:I can't say I wasn't warned. I was part way through installing Microsoft Office 2016 on my primary workstation when I got a message that said, "Stop, you should wait to install Office 2016." The error message went on to say that if I decided to continue anyway, my copy of Microsoft Visio Standard 2013 would be removed. Since I had the original disk from when I purchased the software, I went ahead. Bad move. It turns out that when Microsoft says that Visio 2013 won't work with Office 2016, it means it won't even have the chance to work. Any attempt to reinstall the software will be thwarted. The fact that you paid for the software is beside the point. You're basically out of luck. When I went to the Microsoft community forums, which is where Microsoft handles much of its tech support, I discovered that I wasn't alone. Apparently hundreds of people who'd purchased stand-alone Microsoft Office products were affected, and they weren't happy about it.
Furthermore, the problem extended far beyond Visio. Users with Microsoft Project, Publisher, Access, InfoPath and SharePoint Designer were also affected. Likewise, Microsoft customers who purchased Office Apps that are normally part of Office suites but may have been purchased separately, such as Outlook 2013, were also affected.
Office 2016 Installation Routine Deleting Older Stand-alone Apps
Special offer for customers with Office 2016 and Office 2013 standalone applications
More here:Office 2016 and standalone Office 2013 applications (purchased separately via a retailer and not part of a suite of applications) cannot be installed on the same device. To resolve this issue, you'll need to upgrade your standalone applications to the Office 2016 version of the products. Please contact Accounts & billing at the Microsoft Answer Desk to obtain a free upgrade for your qualifying standalone applications.
Special offer for customers with Office 2016 and Office 2013 standalone applications - Office Support