Before revision:  We show that when the interest rate process is correlated with the price process of the risky asset, the value of the information is  infinite, as is usually the case for initial-enlargement-type problems.
After revision:  Incidentally we show that an affine process conditioned to its future value is still an affine process. When the interest rate process is correlated with the price process of the risky asset, the value of the information is infinite, as is usually the case for initial-enlargement-type problems.