Suppose the calendar time is 23-Feb-2021. Todays price of stock XYZ is $75. For the remainder of the year 2021 the stock will pay a dividend of $0.50 per share on 30-Apr-2021, 31-July-2021, and 31-Oct-2021. The interest rate is 2%.

[a] Compute the forward price of the stock for delivery date 31-Aug-2021.

[b] Consider a forward contract (delivery date 15-Sep-2021: invoice price $70) that was originated back in 2020. What is its value today?

[c] Let V(t) denote the value (at time t) of that legacy forward contract (part [b]). Let C(t) denote the value of a call option on XYZ (expiration 15-Sep-2021; strike price $70). Show that for any time t and any stock price S(t) we must have C(t) >= V(t).