shootingstar

You are right that it is the right for the issuer to call back the bond. A callable bond is a bond with an embedded call option.

The reason for subtracting the price of the embedded call is because the advantage is to the issuer, therefore the investor has to be compensated for the the fact that he could potentially lose his expected return. The effect on price between a regular bond and a bond with embedded options is the movement in the option. Thus, the option is price is subtracted because the issuer can call back the bonds.