Investment appraisal Updated November 2026

NPV (net present value)

Net present value discounts every future cash flow to today and subtracts the initial outlay: NPV = sum of CF_t / (1 + r)^t for t = 0 to n, with CF_0 negative. Positive NPV means the project earns more than the discount rate, so accept; negative means reject. Excel: =NPV(r, CF1:CFn) + CF0.

Syntax

NPV = CF_0 + CF_1 / (1 + r) + CF_2 / (1 + r)^2 + ... + CF_n / (1 + r)^n

Part	What it is
`CF_t`	Cash flow at the end of period t (CF_0 is the investment today, negative)
`r`	Discount rate (cost of capital or required return) per period
`n`	Number of periods

Examples

Invest 1,000 now; receive 500 a year for 3 years; r = 10%
NPV = -1,000 + 500/1.1 + 500/1.1^2 + 500/1.1^3

Result: NPV = 243.43 (accept)

Excel: =NPV(10%, 500, 500, 500) - 1000

Invest 10,000; receive 3,000, 4,000, 5,000; r = 8%
NPV = -10,000 + 3,000/1.08 + 4,000/1.08^2 + 5,000/1.08^3

Result: NPV = 176.29 (accept)

Invest 5,000; receive 2,000 a year for 3 years; r = 12%
NPV = -5,000 + 2,000 x (1 - 1.12^-3) / 0.12

Result: NPV = -196.34 (reject)

Common mistakes

Including the initial investment inside Excel's NPV range: the function discounts its first value by one period, so CF_0 must be added outside: =NPV(r, CF1:CFn) + CF0.
Discounting with a nominal rate while cash flows are in real (inflation-adjusted) terms, or vice versa; match them.
Comparing projects of different sizes by NPV alone when capital is limited; use the profitability index as well.

Practice NPV (net present value)

These drills check your answer on live data, free, no account needed.

Net present valueA project costs $25,000 today and returns $15,000, $13,000 and $12,000 at the end of years 1 to 3. At a cost of capital of 9.75%, what is its net present value? (Enter a negative number if NPV is below zero.)
Present value of a lump sumYou will need $6,000 in 25 years for a down payment. If your savings earn 3.25% per year, compounded annually, how much must you deposit today to have exactly that amount?

Questions

What does a positive NPV mean?

The project returns more than the discount rate and adds that amount of value today. An NPV of 243.43 at 10% means the investment is worth 243.43 more than putting the same money into a 10% alternative.

What discount rate should I use for NPV?

The return required for the project's risk: the company's WACC for projects of average risk, a higher rate for riskier ones. Small changes in r can flip the sign for long projects.

IRR (internal rate of return)The IRR is the discount rate that makes NPV zero. How to find it by trial, what Excel IRR returns, worked examples, the accept rule and where IRR fails.
Present valueHow to calculate present value with PV = FV / (1 + r)^n, what discounting means, examples with yearly and quarterly rates, the Excel PV function and mistakes.
Profitability indexThe profitability index is the present value of future cash flows divided by the initial investment, or 1 + NPV / investment. Examples and the accept rule.
WACCWACC = E/V x Re + D/V x Rd x (1 - T): the blended after-tax cost of a company equity and debt. Step-by-step examples, where each input comes from, errors.