What is net present value?

The core idea behind NPV is the time value of money. If someone offers you $100 today or$100 next year, you always take the money today. You could put that $100 in the bank and earn interest, meaning it will be worth more than$100 next year. Because future cash is worth less than present cash, we have to shrink, or 'discount', future money to accurately compare it to money we are spending today. NPV does exactly this: it translates all future cash flows into today's purchasing power so we can make a fair, apples-to-apples comparison.

To calculate NPV, we use a specific formula that discounts each future cash flow. The formula is: $NPV = \sum \frac{C_t}{(1 + r)^t} - C_0$ Here, $C_t$ is the cash flow at a given time $t$, $r$ is the discount rate (like an interest rate), $t$ is the year, and $C_0$ is your initial investment (which is usually a negative number since it is an outgoing cost). You calculate the discounted value for each year, add them all up, and subtract your initial cost.

Recognizing a good investment using NPV is straightforward. If the NPV is greater than zero ($NPV > 0$), the investment is expected to add value and should generally be accepted. If the NPV is less than zero ($NPV < 0$), the investment will likely lose money in today's terms and should be rejected. If $NPV = 0$, the investment earns exactly the discount rate, meaning it breaks even.

A common mistake is discounting the initial investment ($C_0$). Remember, the initial investment happens at year 0, which is today. Money spent today is already in today's dollars, so you do not divide it by $(1 + r)$. Another frequent error is mixing up the signs: make sure costs (cash outflows) are negative and revenues (cash inflows) are positive.