Why is higher the call price, the higher the price of a callable bond?

Question

I am preparing for FRM level 2, but I ran into a question whose answer was confusing to me:

In the answer, it says "all other things remaining the same, the higher the call price, the higher the price of a callable bond." I thought a higher call price is benefit to the seller and harmful to the investor, why does a higher call price lead to a higher callable bond price? Is it because for a callable bond with a higher call price, the seller will have to pay more to the investors, therefore the price of the callable bond with a high call price is higher?

Please correct me my understanding is not correct, thank you so much!

Answer 1

A callable bond is a little like a put. Companies issue them to protect against a drop in interest rates, and with a higher call price, interest rates need to drop even further to be called.

In essence, in the same way a put with a lower strike is more desirable to a buyer, a callable bond with higher call value will be priced higher than otherwise equivalent bonds.

Answer 2

To the investor, a callable bond can be seen a ordinary bond plus a short position in a call. If the strike price is higher, the call has less value, and the "package" ordinary bond minus call has more value.