# Purchase price equals present value of future price

Suppose we need to decide if to acquire A now for \$95.24 or in one year for$100. If the opportunity cost is 5% annual, what option would you choose?

My possible solution: as the present value of \$100 is \$95.24 given the discount rate of 5%, the value of A now equals the present value of the future quantity. In this case, I would argue that the opportunity cost includes a notion of risk, and is possible that I would not get exactly $100. But I'm not sure this is correct as, mathematically, options are equivalent. ## 1 Answer The correct opportunity cost should already reflect things like default risk. But equivalence in your case only comes from rounding. The present value of \$100 at 5% discounting is \$95.2381, which is lower than the purchase price of \$95.24. Thus, A is too expensive today, and you would not buy it.

• Thanks. What would be the argument if they were the same? Feb 12 at 13:15
• If they were the same, you'd be indifferent. And btw: The title of your question makes no sense here. Feb 12 at 13:28
• Thank you! I will change the name Feb 12 at 14:36