If you bought treasuries at the prevailing rate and swapped them at the same rate then the market price of the swap will be zero. You'll still have to pay credi

If you bought treasuries at the prevailing rate and swapped them at the same rate then the market price of the swap will be zero. You'll still have to pay credit and funding premia though. If, however, you only hedge once the prevailing rate moves against you, you'll pay a market premium in the form of a spread.