# Eli5: NPV, discount rate, IRR

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Can anyone explain to me how net present value relates to irr and discount rate

What’s the difference between discount rate and IRR

And in what situations can I use IRR instead of discount rate when I’m trying to calculate the value of future cash flows

Extra points if someone can tell me the difference between interest rate and discount rate

Can I use the interest rate as my discount rate when calculating NPV?

In: 0

NPV = value of a bunch of future cash flows right now.

Cash in the future isn’t worth as much as cash right now, so you reduce (discount) future cash flows by some percent to reflect that. That’s the discount rate.

You do not need IRR to calculate NPV, you just need the cash flows and the discount rate. The discount rate that makes sense for you depends on lots of things…how risk averse (or not) you want to be, what it costs you to borrow money, how your business works, how much you can earn by investing cash you have sitting around, etc. The discount can and will vary depending on who’s doing the analysis. Most companies will have established set discount rates for whatever it is they’re doing. Two companies assessing exactly the same cash flows may come up with different NPVs because they’re using different discount rates.

For any given set of cash flows (assuming they’re not all positive or all negative), there’s some discount rate that will give you NPV=0. That value is the IRR, internal rate of return. It’s basically the interest you’d have to actually get on your cash (on average) so all discounted cash flows balance out to zero, which is a fancy way of saying “you’ll be even…you won’t make or lose money.”

The IRR does *not* depend on the discount rate…it just depends on the cash flows (and has NPV=0 by definition).

Don’t use IRR to calculate the value of future cash flows. You only use discount rate for that.

Comparing IRR to discount rate tells you how good (or bad) the deal is. You’re comparing what the actual rate would need to be (to at least break even) to what you’re assuming it will be. It tells you how much trouble (or not) you’ll be in if your discount rate is wrong.

Interest rate is what you actually pay to borrow money (or receive if you’re saving money). Discount rates are typically higher than interest rates because you’re taking a bunch of other stuff into account, including opportunity cost, risk of putting money into higher return investments, etc.

For example, discount rates of 10-15% are fairly typical for large capital projects. Nobody’s paid that kind of interest rate on institutional loans for decades. So you shouldn’t use interest rate as your discount rate either, unless you’ve got a hyperconservative model that’s just going to stick your money in a bank account for years (bad idea…the treasury group will get mad at you).

Assume you have an investment that is expected to pay \$1,000 next year. This payment is the *nominal cash flow*.

You calculate the *net present value* of this cash flow by discounting them using a *discount rate*. The discount rate is the *opportunity cost of capital*. Essentially, if someone gave you \$1,000 right now instead of in one year, how much of a return could you earn on that money? If you could invest \$950 today and earn \$1,000 in one year, then your discount rate is \$1,000/\$950 = 5.26%. Another way of saying that is that the *present value* of \$1,000 one year from now is \$950, assuming a discount rate of 5.26%.

Alright, so that’s the background info for your questions. We know what a discount rate is and what a net value is – what’s a *Net Present Value*? Well the NPV is simply the present value less any cash outflows. If someone were to sell you a bond that pays \$1,000 in one year for \$900, your net present value would be the present value of the bond (\$950, per above) less the price (\$900). This gives a Net Present Value of \$50. At higher discount rates, the net present value goes down for a given price point, because the present value of the investment goes down.

This stands to reason – the more money you can make investing elsewhere, the higher return you’ll need to justify buying the bond. How low can the discount rate go before you won’t buy the bond? Well, that’s your *Internal Rate of Return*.

The IRR is some discount rate that gives you an NPV of \$0, and it’s used to evaluate different investments. In the above example, you’re essentially comparing your current discount rate (5.26%, which is the return you can get on some other investment) and your IRR of 11.11% (\$1,000 cash flow in one year/\$900 purchase price). Because the IRR is higher than the return on any other available investment, you’ll invest in this product.

Now, imagine if someone comes to you pitching a *new* investment that costs \$1,000 and pays out \$1,100 in one year – how would you compare that to your existing investment of \$900 for \$1,000 in one year?

Well, you can go two routes:

1) You can calculate the NPV of the second investment, but now you’ll use 11.11% as your discount rate (the IRR of the first investment, which is now your opportunity cost of capital), or,

2) You can calculate the IRR of the second investment and see if its higher or lower than the first investment.

You’re not using the IRR instead of a discount rate, but if an investment is available, its IRR *should become* your discount rate because ignoring that investment is an opportunity cost.

Lastly, interest rates play into discount rates but aren’t necessarily the same. Your discount rate is an available rate of return that could consist of interest, dividends, capital gains, etc..