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I am self-studying for an actuarial exam on financial economics. This statement in the following problem/solution seems to imply that the prepaid forward price on a stock is the same as the prepaid forward price on a futures contract for the stock, or $F_{0, T}^P(S) = F_{0, T}^P(\text{Future}(S))$. (Not sure if this is correct notation).

So why does the second statement underlined in red follow from the first statement?

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It is a very badly worded question in my humble opinion.

There are three "prices" to contend with.

(1) If you want to buy a stock and pay for it now, you pay the current stock price S.

(2) If you want to buy a stock and not have to pay for it until a future delivery date T, then you enter into a "forward" or (in the United States) a "futures contract" which specifies a price F, with $F=S e^{(r-d)T}$. No money is due when you enter into this contract.

(3) There is also an odd thing called a "prepaid forward" which is not much used except to get around tax and other regulations, in which you pay now the sum P in order to get the the stock later. This is priced at $P=F e^{-(r-d)T}$. Perhaps not surprisingly we have $P=S$ since you have to pay now, just like when buying the stock outright.

So there are only two prices for a stock: one if you want to pay now, and a slightly higher one (due to the time value of money) if you want to pay later.

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