A compound option then has two expiration dates and two strike prices.
Suppose that you purchase a CoC and sell a PoC on the same underlying call option and with the same strike price and time to maturity.
The payoff of this portfolio is always the same: you will purchase the underlying call at the time of maturity of the compound options.
Thus, there will always be a cash outflow equal to the strike price and you will come into possession of a call option.
Suppose that you also borrow an amount equal to the strike price of the CoC/PoC from the above portfolio discounted at the risk free rate from the CoC/PoC maturity date to today.