# 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.