Eli5: What is NPV (Net Present Value) in the most simplest terms? I have a non-finance background
In: 5
NPV is a number used to compare investments with different time periods.
Money in the future is less valuable than money today. In other words, when thinking about the value of future money, you don’t count the entire amount (don’t count == “discount”).
If you say that $100 in a year is equivalent to $97 today, you’re discounting 3%. If you say that $100 in a year is equivalent to $90 today, you’re discounting 10%. And so on.
The discount rate you choose to put into NPV calculations *represents how strongly you prefer current money to future money*. In other words, if Alice is patient and is willing to get tied up in long-term investments, she might choose a discount rate of 3%. If Bob is an impatient short-term thinker (or he knows that he’ll need money soon), he might choose a discount rate of 20% or even more.
In other words, the discount rate is *a number that you pick, to input to the calculation*. A higher discount rate means *you care more about the short-term and less about the long-term*.
NPV assumes that, whatever discount you apply in one year, you’ll repeat that discount twice for a two-year timeframe, five times for a five-year timeframe, and so on.
So if you choose a discount rate of 10%, that means you’d pay $90 to get $100 in a year, but you’d only pay $81 to get $100 in two years. (You knock off $10 for the first discount since it’s 10% of $100, but you only knock off $9 for the second discount since it’s 10% of $90.)
Mathematically, applying a 10% discount rate is multiplying by 100% – 10%, or 90%. Applying a 10% discount rate N times is multiplying by 90% to the power N. So a discount rate of 10% applied to money you’ll get in five years is 0.9 x 0.9 x 0.9 x 0.9 x 0.9. Which works out to paying about $59.05 for $100 in 5 years.
NPV just means you evaluate an investment by thinking about all the payments you’ll get in the future, and adding up each payment’s discounted value.
So if you have 10% discount rate, and a four-year investment that pays you $20 for years 1-3, then $40 at the end in year 4, you do the following calculation:
– First pmt: $20 in one year. Value = $20 x 0.9 = $18.
– Second pmt: $20 in 2 years. Value = $20 x 0.9 x 0.9 = $16.20.
– Third pmt: $20 in 3 years. Value = $20 x 0.9 x 0.9 x 0.9 = $14.58.
– Fourth pmt: $40 in 4 years. Value = $40 x 0.9 x 0.9 x 0.9 x 0.9 = $26.24.
The NPV of this 4-year investment is then $18 + $16.20 + $14.58 + $26.24 = $75.02.
NPV calculations sometimes use a couple mathematical tricks:
– Discount rates over different time periods. If 10% is your discount rate for a year, but your investment will make *monthly* payments instead of *yearly* payments, how do you convert an 10% annual discount rate to an equivalent monthly discount? [1]
– Partial sum of geometric series. If you’re considering loaning money for a 30-year mortgage with 360 monthly payments, there’s a “shortcut” you can use to avoid doing 360 calculations and adding up 360 numbers. This mathematical trick is less valuable in the computer age, a computer can easily add 360 numbers.
– Sum of infinite geometric series. The above “shortcut” also hints at how you could calculate the NPV of, say, buying a business that will produce $100 a year forever. This mathematical trick is less valuable in the computer age, a computer can easily run out the NPV calculation for such a business for 100 years (or 1000 years), which is close enough to “forever” for any practical purpose.
I should also mention that NPV calculation makes some simplifying assumptions:
– No risk of non-payment. NPV calculation ignores possibility that a company / individual will go bankrupt, or stop paying for other reasons.
– Payments known ahead of time. NPV calculation assumes you know income ahead of time, which isn’t true for all investments (“you know the payments ahead of time” is usually more true for debt investments like bonds / loans / mortgages, and less true for equity investments like stocks / businesses).
– Discount rate doesn’t change. NPV calculation assumes discount rate will always be the same. Many people use discount rates based on interest rates, which means the price at which they buy / sell investments drops when interest rates rise (and rises when interest rates fall). This explains why stock market reporting is currently obsessed with the US Federal Reserve switching from lowering interest rates to raising interest rates.
To some extent, you can mitigate the effects of these assumptions by inputting a higher discount rate, which gets the NPV calculations to be more “conservative.” But fundamentally NPV isn’t magic; it can’t turn a bad investment into a good one.
[1] The simple answer is divide 10% by 12 and get 0.833% per month. A “more correct” calculation raises 90% to the 1/12th power and subtracts that from 100%, which works out to 0.874%.
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