Forward Agreement Question

Simple question about 16.58.a If I enter an agreement to sell stock at in 3 months $80 and its currently $75, the study materials say to discount the $80 strike price. That doesn’t make sense to me. Why wouldn’t we just discount the $5 profit to the present? For example, if we were certain that stock would still be at $75 in 3 months, then we know we’ll be getting $75. Since the forward agreement uses no margin, the value to us is $5 discounted to today. Why discount the $80? Thanks, Ari

You should not think in terms of the $5 because that’s based on a mix between forward agreement price and spot price today… you don’t know whether it will be $5 or $10 or $100. You only know that you will sell it for $80. It might be easier to calculate the future value of today’s stock ($75 * (1+r)^t), and compare that to the $80 you will get in 3 months.

Sorry, I don’t have the books with me so I may be confusing your question - in any case: If you agreed to sell a stock at $80, and the current value is at $75, discounting the $5 would not account for the entire effect of the discount rate. For example, you and I enter into a 1-year forward agreement. I agree to sell my stock in 1 year at $105, and it is currently worth $100. Why? Because the risk-free (discount) rate is 5%, and if I were to sell this to you in 1 year I would want to be compensated for the 1 year return I could earn at the discount rate. I wouldn’t want to be discounting the $5 difference.

Thanks guys, now it makes sense to me.