Discounting and the discount rate

Discounting is the act of converting future money into its value today. The rate you use to do it is the discount rate — and choosing it well is half the art of finance.

The discount factor

For a single cash flow n periods away, the discount factor is:

DF = 1 / (1 + i)^n

Multiply any future amount by its discount factor to get its present value:

PV = FV * DF

At a 10% per year discount rate, 1,000 units received in 3 years is worth:

DF = 1 / (1.10)^3 = 1 / 1.331 = 0.7513
PV = 1000 * 0.7513 = 751.31

So a promise of 1,000 units three years out is worth only about 751 units today at a 10% rate.

The rate drives everything

The higher the discount rate, the less future money is worth today. The same 1,000 units in 3 years:

• At 5%: PV = 1000 / (1.05)^3 = 863.84
• At 10%: PV = 1000 / (1.10)^3 = 751.31
• At 15%: PV = 1000 / (1.15)^3 = 657.52

Choosing the discount rate

The discount rate reflects the return you could earn elsewhere at similar risk — the opportunity cost of capital. A safe government bond yield is the floor; riskier cash flows demand a higher rate to compensate. This is exactly why rising interest rates tend to push asset prices down: a higher discount rate shrinks the present value of every future cash flow. Keep this in mind — it is the engine behind NPV, which we build next.