# Why would a lower stock price leads to higher value of a call option?

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?