A sum received today can be used, saved or set to work. The same sum received later cannot do any of that in the meantime. That difference is the starting point for a great deal of finance, and it is easy to lose sight of under the formulas built on top of it.
Discounting is the formal version of the idea. A future amount is translated into a present one by asking what would have to be set aside now to arrive at it later. The rate used for that translation carries a judgement about patience, risk and what else the money could have done.1
A judgement, not a constant
Because the rate is a judgement, two careful people can value the same future quite differently. Neither has made an arithmetic mistake. They have made different assumptions about waiting, and the arithmetic faithfully reports the difference.
They have made different assumptions about waiting, and the arithmetic faithfully reports the difference.
Reading the assumption
When a valuation surprises, the most useful thing to examine is often not the projected amounts but the price put on waiting for them. Small changes there can move the answer more than large changes elsewhere, especially when the amounts sit far in the future.