Influence of Recapitalization on Stock Price

Let's say a company wants to do a recapitalization in which it issues debt to buy back equity.

This will effectively reduce the market capitalization by the value of the repurchased shares and increase it by the NPV of the recap (due to the tax shield).

However, in an efficient market, wouldn't the market price slightly decrease again, since the recapitalization would increase the leveraged beta, and thus the PV to equity investors would be discounted more strongly? Thus, the share price would have to be slightly higher than before (thanks to PV(ITS), but lower than if one simply added the NPV and divided by the share count?