Net Present Value
Present value of a stream of cash flows.
Formula
Variables
Example
A positive NPV means the investment earns more than the discount rate — a go signal.
How it works
Net Present Value converts a sequence of future cash flows into today’s dollars by discounting each amount back to time 0 and then adding them together. This works because money received later is worth less than money received now: the discount rate represents the return you could earn elsewhere, so each future cash flow is scaled by the opportunity cost of waiting. If the total present value of inflows exceeds the upfront and later costs, the project adds value at that required rate of return.
When to use it
Use NPV when comparing investments, projects, or business decisions that produce cash flows over time, such as equipment purchases, product launches, or real-estate developments. It is especially useful when cash flows are uneven and you need to decide whether a project creates value at a given discount rate.
Worked example, step by step
A company is evaluating a project with these cash flows: C0 = -100,000 C1 = 30,000 C2 = 40,000 C3 = 50,000 Discount rate r = 8% Step 1: Write the NPV formula. NPV = C0/(1+r)^0 + C1/(1+r)^1 + C2/(1+r)^2 + C3/(1+r)^3 Step 2: Substitute the values. NPV = -100,000/(1.08)^0 + 30,000/(1.08)^1 + 40,000/(1.08)^2 + 50,000/(1.08)^3 Step 3: Compute each present value. -100,000/(1.00) = -100,000 30,000/1.08 = 27,777.78 40,000/1.1664 = 34,293.55 50,000/1.259712 = 39,690.72 Step 4: Add them up. NPV = -100,000 + 27,777.78 + 34,293.55 + 39,690.72 NPV = 1,762.05 Final answer: NPV ≈ $1,762.05, so the project is slightly value-creating at an 8% discount rate.
Common mistakes to avoid
- Using the discount rate as a percentage in the denominator without converting it to decimal form
- Forgetting that the time-0 cash flow is not discounted because it is already in present value
- Mixing cash flow timing by placing a payment in the wrong period, which changes the NPV
Did You Know?
Net present value is the gold-standard rule for corporate investment: take the project if NPV is positive.
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