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NPV Calculator

Discounts a series of end-of-period cash flows at a required rate of return, subtracts the initial investment and reports the net present value, the present value of each cash flow and the profitability index.

When to use

You are appraising a project or investment with an upfront cost followed by periodic cash flows and want to know whether it creates value at a given discount rate.

Do not use when: You want the rate that makes NPV zero (use irr), the time to recover the outlay (use payback-period), or a single future amount (use present-value).

Formula

NPV = −initial_investment + Σ_{t=1..n} cash_flows[t] / (1 + discount_rate_percent/100)^t; profitability_index = (NPV + initial_investment) / initial_investment

Cash flows occur at the end of each period and the rate is constant; the period of the rate must match the period of the cash flows (annual rate with annual flows).

Inputs

Parameter	Type	Unit	Required	Description
`discount_rate_percent`	number	% per period	yes	Required rate of return or cost of capital per period in percent (annual for yearly cash flows). Range: ≥ -99, ≤ 1000
`initial_investment`	number		yes	Outlay at time 0, entered as a positive number. Range: ≥ 0, ≤ 1000000000000000
`cash_flows`	number_list		yes	Net cash flow at the end of periods 1, 2, 3 … (negative values allowed).

Outputs

Output	Type	Description
`npv`	number	Σ CF_t / (1 + r)^t − initial_investment.
`present_value_of_cash_flows`	number	Σ CF_t / (1 + r)^t (before subtracting the investment).
`profitability_index`	number	present_value_of_cash_flows / initial_investment (only when the investment is > 0); above 1 means NPV > 0.
`discounted_cash_flows`	number_list	Each CF_t / (1 + r)^t in order.
`total_undiscounted_cash_flows`	number	Σ CF_t without discounting.
`net_undiscounted_gain`	number	Σ CF_t − initial_investment (NPV at 0 %).
`decision`	string	'Accept' when NPV > 0, 'Reject' when NPV < 0, 'Indifferent' at 0.

Example

−1,000 then 500, 400, 300 at 10 %: {"discount_rate_percent":10,"initial_investment":1000,"cash_flows":[500,400,300]} → {"npv":10.52,"present_value_of_cash_flows":1010.52,"profitability_index":1.0105,"discounted_cash_flows":[454.55,330.58,225.39],"total_undiscounted_cash_flows":1200,"net_undiscounted_gain":200,"decision":"Accept (NPV > 0)"}

−10,000 then 3,000, 4,000, 5,000, 2,000 at 8 %: {"discount_rate_percent":8,"initial_investment":10000,"cash_flows":[3000,4000,5000,2000]} → {"npv":1646.35,"present_value_of_cash_flows":11646.35,"profitability_index":1.1646,"decision":"Accept (NPV > 0)"}

GET https://tttkmbb.com/api/v1/calculate/npv?discount_rate_percent=10&initial_investment=1000&cash_flows=500%2C400%2C300

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/npv (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/npv · Markdown: https://tttkmbb.com/finance/npv.md · JSON definition: https://tttkmbb.com/finance/npv.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="npv"
OpenAPI operationId: calculate_npv
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

Investopedia – Net Present Value (NPV): What It Means and Steps to Calculate It (reference)
Wikipedia – Net present value (reference)

FAQ

Which discount rate should I use?

The return available on an alternative of similar risk: a company's weighted average cost of capital for projects, or a hurdle rate. A higher rate lowers NPV.

How do I handle monthly cash flows?

Use a monthly rate: annual_rate/12 for a nominal rate, or (1 + annual)^(1/12) − 1 for an effective one, and list one cash flow per month.

Related calculators

IRR Calculator — Rate of return that sets NPV to zero.
Payback Period Calculator — Time to recover the initial investment.
Present Value Calculator — Discount a single amount.