Yahoo Messenger can access the following on your device:

Device & app history

• retrieve running apps
• read sensitive log data

Identity

• find accounts on the device
• add or remove accounts

Contacts

• read your contacts
• modify your contacts

Location

• precise location (GPS and network-based)
• approximate location (network-based)

SMS

• send SMS messages
• receive text messages (SMS)

Phone

• read call log
• write call log

Photos/Media/Files

• modify or delete the contents of your USB storage
• read the contents of your USB storage

Wi-Fi connection information

• view Wi-Fi connections

Device ID & call information

• read phone status and identity

Other

• read sync statistics
• run at startup
• full network access
• view network connections
• control vibration
• use accounts on the device
• create accounts and set passwords
• modify system settings
• read sync settings
• toggle sync on and off
• prevent device from sleeping
• control Near Field Communication

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Last Update: 06/12/2015

Source:
https://play.google.com/store/apps/details?id=com.yahoo.mobile.client.android.im