Currently I am reading Basic Black Scholes: Option Pricing and Trading by Timothy Falcon Crack.
At page $47,$ the author mentions the following.
Higher interest rates decrease the present value of the strike price. Other things being equal, this increases the value of a call because the strike price you potentially give up has lower present value; conversely for a put.
I do not understand the bold sentence.
Intuitively, I thought that if interest rate increases, then stock price decreases (which is the same as above). But wouldn't this decrease the value of a call option as the difference between terminal stock price and strike price is smaller.
Can someone verify whether my reasoning is correct and explain the bold sentence?