Imagine the following binary option modification: if the stock price at t = 0,5 is greater that 100 roubles, the owner of the option receives 1 rouble at t = 1. Otherwise, he gets 0 roubles.So this is just a binary call option, but with the payment being made not at the expiry date, but some time later.Analytical formulae for valuing standard binary options are available. The question is: how to value those a bit altered binary options?I have come to the following solution and would like to make sure that I didn't make any mistakes.First, we calculate the PV of the cash flow "+ 1 rouble at t = 1" at t = 0,5. We can do that if we assume that the percent rate is constant. Let's assume that the PV of this cash flow is 0,95 roubles.We then use the standard binary option value formula and use 0,95 as the binary option cash flow. The idea is that the holder of the option gets 0,95 roubles, invests them at the risk-free rate and gets 1 rouble at t = 1, which is the same as buying our binary option with delayed payment.So the value of our binary option with delayed payment is as follows: StandardBinaryCallValue (Strike = 100, Years to expiry = 1, Volatility = ..., Risk-free rate = ..., Cash Flow = PV (1)).Is this logic correct?