Investing
Net present value
Discount each year's cash flow and subtract the upfront cost. The present value of a level annuity simplifies the sum.
The Formula
NPV = -C0 + sum_{t=1..n} CF / (1 + r)^t
Discount each year's cash flow and subtract the upfront cost. The present value of a level annuity simplifies the sum.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| C0 | Initial cost | currency | Cash spent at time zero. |
| CF | Annual cash flow | currency | Cash received each year. |
| r | Discount rate | rate | Required annual return. |
| n | Years | count | Life of the investment. |
What Each Symbol Means
C0currency
Initial cost
Cash spent at time zero.
CFcurrency
Annual cash flow
Cash received each year.
rrate
Discount rate
Required annual return.
ncount
Years
Life of the investment.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate npv page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate NPV, filed under Finance. Every number the guide produces comes from substituting into this one line.