Exchange 2013: Shell does not start (EventID 23, MSExchange RBAC)

After a new installation of Exchange 2013, the following error could occur, which prevents ECP and Shell from working, EventID 23:

Source: MSExchange RBAC

ID: 23

(process w3wp.exe, PID 13160) "Exchange-AuthZPlugin cannot use the method "GetApplicationPrivateData" due to the application exception "Microsoft.Exchange.Diagnostics.SetupVersionInformationCorruptException: The installed file version cannot be determined from the registry key 'HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\PowerShell\1\PowerShellEngine'.
for Microsoft.Exchange.Diagnostics.ExchangeSetupContext.get_PSHostPath()
for Microsoft.Exchange.Configuration.Authorization.InitialSessionStateBuilder.InitializeWellKnownSnapinsIfNeeded(ExchangeRunspaceConfigurationSettings settings, Boolean isPowerShellWebServiceSession)
for Microsoft.Exchange.Configuration.Authorization.InitialSessionStateBuilder.Build(List`1 allCmdlets, List`1 allScripts, ExchangeRunspaceConfiguration runspaceConfig)
for Microsoft.Exchange.Configuration.Authorization.ExchangeRunspaceConfiguration.CreateInitialSessionState()
for Microsoft.Exchange.Configuration.Authorization.ExchangeAuthorizationPlugin.GetInitialSessionStateCore(PSSenderInfo senderInfo)
for Microsoft.Exchange.Configuration.Authorization.ExchangeAuthorizationPlugin.c__DisplayClass4.b__3()
for Microsoft.Exchange.Configuration.Authorization.AuthZLogHelper.HandleExceptionAndRetry[T](String methodName, Func`1 func, Boolean throwException, T defaultReturnValue)"."

The solution is to enter the corresponding registry keys by copying and pasting the following text into a .REG file:

Windows Registry Editor Version 5.00
[HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\PowerShell\1\PowerShellEngine]
"ApplicationBase"="C:\\Windows\\System32\\WindowsPowerShell\\v1.0"
"PSCompatibleVersion"="1.0, 2.0"
"RuntimeVersion"="v2.0.50727"
"ConsoleHostAssemblyName"="Microsoft.PowerShell.ConsoleHost, Version=1.0.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35, ProcessorArchitecture=msil"
"ConsoleHostModuleName"="C:\\Windows\\System32\\WindowsPowerShell\\v1.0\\Microsoft.PowerShell.ConsoleHost.dll"
"PowerShellVersion"="2.0"