Moving the CharacterSet setting to a property file in Visual Studio

Question

I have few Visual Studio projects that should compile either in MultiByte or in Unicode mode.

Looking at the project xml file, the compilation is controlled by a Property named CharacterSet that can have value either MultiByte or Unicode.

I'm trying to move this setting to a property file so that when I want to switch from one mode to the other I can change simply in one place. My property file is like:

<?xml version="1.0" encoding="utf-8"?>
<Project DefaultTargets="Build" ToolsVersion="4.0" xmlns="http://schemas.microsoft.com/developer/msbuild/2003">
  <PropertyGroup>
    <CharacterSet>Unicode</CharacterSet>
  </PropertyGroup>
</Project>

Including this property file seems to have no effect (but adding the property everywhere in the project file, properly sets the encoding).

What am I doing wrong? Which is the correct way of moving this setting to a property file?