Eli5: What is NPV (Net Present Value) in the most simplest terms? I have a non-finance background

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Eli5: What is NPV (Net Present Value) in the most simplest terms? I have a non-finance background

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Anonymous 0 Comments

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%.

Anonymous 0 Comments

Simply put, the PV (present value) of money is the amount you would need to invest today to have that amount in the future.

So, say you’re expecting a $500 bill in a year. Depending on the interest rate, that’s worth less than $500 today, because you could invest, say, $450 today and it will have grown to $500 through interest by the time you need to pay it. So what is the “present” value of that $500 bill? $450, because that’s what you actually need today to be able to pay it when it’s due.

Companies use this for future profit. If you expect a product to make $1000 next year, how much would they need to invest today to make the same amount? That’s the PV (present value) of that cash flow. If the product is expected to make $2000 the year after that? The amount you’d invest to make $2000 in two years is the PV of that cash flow. You can find the PV of all the cash flows you expect over a number of years, add them up, and compare that to the cost it would take to develop and sell the product, usually by subtracting the cost from the PVs of the profits. That’s the ‘Net’ Present Value. If the NPV is negative, that means the present values of the cash flows (profits) the product will bring in over the years is less than the initial cost to develop the product. That means it’s not worth it, because you could make the same amount or more just by taking the money you’d have spent developing the product and investing it, and letting it grow.

So basically, NPV allows you to compare money in the future to money now by pretending all future money is money you invest today and take out in the future, and removing the ‘interest’ from that amount, leaving just what you would need to invest today.

Anonymous 0 Comments

“A bird in the hand is worth two in the bush.”

Or conversely, expected future income should be discounted, because … you might not get it for some reason, or inflation *will* reduce its worth, or the opportunity cost of not having it now.

Anonymous 0 Comments

What should this be worth to you RIGHT NOW. That is what NPV is. “This” could be an investment, loan, purchase etc.

The key fundamental concept is TVM – Time Value of Money. A dollar today is worth more than a dollar tomorrow because you can invest that dollar and earn something on it by tomorrow.

Using NPV, the idea is to value any activity in terms of today’s dollar. So they can be easily compared. The hyperbolic way to think of it is “would you prefer to be given $1,000 today or $10,000,000,000 in 200 years”. Since you’re almost certainly dead in 200 years, the rational answer would be $1,000 today even though $10,000,000,000 is a lot more money. That $1,000 now is more valuable to you and that is the idea behind NPV.

Anonymous 0 Comments

Risk is the number one thing being evaluated when determining if a financial decision is correct but there are other factors. Money today is worth more to me than money tomorrow. Net present value is how we quantify this concept, we use it to sort cash flows in order of payout, soonest first.

Anonymous 0 Comments

The value of money depends on when you get it. Getting 100$ today is better than getting 200$ in 30 years. Not only because of inflation but because if you want to spend 100$ now you’d have to take a loan and pay interest for 30 years. The earlier you get money the better, the later you pay something the better, makes sense?

Okay NPV tries to normalize that so money at different timepoints becomes comparable. Project A makes me 1 million next year, Project B makes me 1.3 million the year after, wich one is better?

NPV basically corrects every value to “now” by subtracting/adding the assumed interest rates