The Time Value of Money

This is the only math we'll do that goes beyond adding, subtracting, multiplying and dividing. The Time Value of Money is the most fundamental idea in finance, and it boils down to: A dollar today is worth more than a dollar tomorrow.

Not that a dollar bill under your pillow turns into a million in a year. Not even the tooth fairy pays that kind of return. It means money you have now always has more buying power than the same money later, for three reasons:

1. Inflation. There's always some. If it runs about 3% a year, a dollar a year from now buys about 97 cents of what it buys today.
2. Opportunity Cost. Money you have now can be put to work: stocks, crypto, or even a halfway decent bank rate. Wait for it, and you get the Pain of Missing Out.
3. Risk. There's always a chance you won't get that dollar next year. The Done Deal gets undone; the company you invested in goes under.

That's how VCs value your startup, so it matters when you raise money.

Present Value and Future Value

Money we have now is Present Value. Money we expect later is Future Value. They're not apples and oranges; more like apple seeds and ripe apples.

The average annual return of the US stock market is about 10%. That's our baseline: the long-run return you could get without picking startups at all. Put $1,000,000 in the market and you could reasonably expect about $1,100,000 a year from now (ignoring taxes):

Future Value = Present Value × (1 + r) = $1,000,000 × 1.1 = $1,100,000

Here r is the Rate of Return. Going the other way, r is called the Discount Rate:

Present Value = Future Value ÷ (1 + r) = $1,100,000 ÷ 1.1 = $1,000,000

Risk Lives in the Discount Rate

When we compare two investments, inflation and opportunity cost apply to both equally. The one that really differs is risk, and we put risk into the discount rate. The riskier an investment, the higher the discount rate, and the lower its value today.

With a zero discount rate, the future amount is the same as today's. That's the family member who borrows money and pays you back next year with no interest: you get the same dollars back, but you lost the 10% you could have earned in the market. For a startup, an investor might use 50% or more. The goal is a rate where you'd honestly be indifferent between the money today and the bigger amount later.

More Than One Year Out

For money several years away, divide by (1 + r) once for each year:

Present Value = Future Value ÷ (1 + r) to the power of the number of years

Here's a deal we'll use in the next lesson: invest $1,000,000 today and expect $2,500,000 back in three years. At a 35% discount rate:

$2,500,000 ÷ (1.35 × 1.35 × 1.35) = $2,500,000 ÷ 2.460375 = $1,016,105

Based on our own read of the risk, that $2,500,000 in three years is worth $1,016,105 to us today.