A promise by industry super fund Cbus to invest $500 million in the government’s controversial affordable housing plan came despite its own concerns that the scheme’s design meant “no investor would provide capital up front”.

The $85 billion fund in January told Treasury that the Housing Australia Future Fund’s original $500 million limit on disbursements and annual approval process would turn off institutional investors, emails released under freedom of information revealed two months after pledging its members’ retirement savings to the scheme.