When a bond has a call provision, the potential for price appreciation is reduced, because the call caps the price of the bond near the call price. Even if interest rates fall considerably, it is unlikely that investors would pay a price that exceeds the call price.

The other statements are false. To calculate the value of a putable bond, it is correct to add the option value to the value of a similar straight bond. However, to calculate the callable bond value, subtract the option value from that of a similar straight bond. As a result, when yield volatility increases (thus increasing the option value), the value of a callable bond decreases and the value of a putable bond increases. A call option does benefit the issuer, but a put option benefits the holder.  Embedded options (puts and calls) increase in value when volatility increases.