# Discounted Cash Flow [Concepts Series]

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Economics nerds always complain that you should never compare stocks to flows. It’s meaningless to say that one company’s cash on hand is bigger than a country’s GDP, for example, because GDP is quoted in dollars *per year* and cash on hand is a cumulative quantity. It’s like saying a plane is faster than the distance from New York to Boston. Does not compute.

There’s a giant exception, though: stocks, bonds, loans, and other financial products *explicitly exist to convert flows to ‘stocks’ in the economic sense*. The mechanics of this are worth understanding, because they underpin the value of so many financial assets.

The basic idea of discounted cash flow is to convert future estimate cash flows into present values, by “discounting” them at some interest rate. Suppose you can earn 1% annual interest on a certificate of deposit. The present value of $100 in a year is equal to the amount you’d have to put in a CD today in order to have $100 a year from now, or $99.01. The present value of $100/year for the next three years, at a 1% discount rate, is $100/1.01 + $100/(1.01 * 1.01) + $100/(1.01 * 1.01 * 1.01), or $294.01.

This can get pretty tedious as you extend it (here I’m using a higher discount rate):

As you can see, the amounts dwindle after a while. I’ve modeled it out for the first 100 years, and the value will keep accumulating after that point, albeit slowly.

There’s another twist to the model, though. What about growth? We can look at a series of cash flows that grow over time at a known pace:

But that’s not a realistic description of any business. No company grows at a steady pace *forever*. Usually, you expect growth to slow at some point. Here’s a multi-stage model, with fast growth for a while followed by a deceleration.

All of these models are *close to* correct, but they’re all below the theoretical value. There’s a nice trick for calculating an actual net present value given steady assumptions: cash flows / (discount rate — growth rate). So $1, growing at 1% per year in perpetuity…