present value and discounting
/ P-V /
You are promised $1,100 one year from now. How much is that worth to you right now? Clearly less than $1,100, because you would rather have cash today. Present value answers exactly this question: it is the amount of money today that is equivalent to a given amount in the future, once you account for the return you could have earned in the meantime. The mental move of turning future money into today's money is called discounting.
The arithmetic is just compound interest run backwards. If the interest rate is 10%, then $1,000 today grows to $1,100 in a year, so $1,100 in a year is worth $1,000 today — its present value. The formula is present value = future amount divided by (1 + r) raised to the number of periods, where r is the discount rate. A higher discount rate or a more distant payment both shrink the present value: at 10%, $1,000 due in 20 years is worth only about $149 today. When several payments arrive over time, you discount each one to today and add them up; that sum is the net present value, the workhorse tool for judging whether an investment is worthwhile.
Present value is how the entire financial world prices things that pay off over time: bonds, shares, pensions, mortgages, factories, even the cost of climate change. It also exposes a quiet but crucial assumption — the choice of discount rate. A small change in that rate can swing the present value of far-off cash flows wildly, which is why debates over long-horizon questions (like how much to spend today to prevent harm decades from now) often boil down to a fierce argument about which discount rate is fair.
A company can build a machine that will earn $10,000 a year for five years. Adding those cash flows gives $50,000, but that overstates the value. Discounted at 8%, the five payments are worth about $39,900 today. If the machine costs $35,000, its net present value is positive (about $4,900), so the project is worth doing.
Net present value compares discounted future earnings against the upfront cost.
Present value is extremely sensitive to the discount rate for distant cash flows. There is no single 'correct' rate — it reflects risk and the return available elsewhere — so honest analysts test a range of rates rather than trusting one number.