{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"payback-period"},"result":{"entity_type":"calculator","id":"payback-period","calculator_id":"payback-period","canonical_url":"https://tttkmbb.com/finance/payback-period","name":"Payback Period Calculator","title":"Payback Period Calculator – Simple and Discounted Payback from Cash Flows","category":"finance","category_name":"Finance","tool_name":"calculate_payback_period","featured_mcp_tool":false,"description":"Computes how long an investment takes to recover its initial outlay from a list of periodic cash flows or a constant annual cash flow, both undiscounted (simple payback) and discounted at a given rate (discounted payback), interpolating within the recovery period.","use_when":"You want a quick liquidity/risk measure of a project: the years until cumulative cash inflows equal the initial investment.","do_not_use_when":"You need the value created over the whole life (use npv) or the rate of return (use irr); payback ignores cash flows after recovery.","inputs":[{"name":"initial_investment","label":"Initial investment","type":"number","required":true,"max":1000000000000000,"exclusive_min":0,"description":"Outlay at time 0, entered as a positive number.","example":10000},{"name":"cash_flows","label":"Cash flows per period","type":"number_list","required":false,"description":"Net cash inflow at the end of each period; takes precedence over annual_cash_flow.","example":[3000,4000,5000,2000]},{"name":"annual_cash_flow","label":"Constant annual cash flow","type":"number","required":false,"max":1000000000000000,"exclusive_min":0,"description":"Used with `years` when cash_flows is omitted.","example":3500},{"name":"years","label":"Number of years","type":"integer","unit":"years","required":false,"default":20,"min":1,"max":60,"description":"Length of the constant cash-flow series (ignored when cash_flows is given).","example":5},{"name":"discount_rate_percent","label":"Discount rate","type":"number","unit":"% per period","required":false,"default":0,"min":0,"max":100,"description":"Rate for the discounted payback; 0 skips it.","example":8}],"outputs":[{"name":"payback_period_years","label":"Simple payback","type":"number","unit":"periods","decimals":2,"description":"Periods until cumulative undiscounted cash flow reaches the investment, interpolated within the final period."},{"name":"payback_time","label":"Simple payback (years and months)","type":"string","decimals":4,"description":"payback_period_years expressed in years and months."},{"name":"discounted_payback_period_years","label":"Discounted payback","type":"number","unit":"periods","decimals":2,"description":"Same using cash flows discounted at discount_rate_percent (only when the rate is > 0)."},{"name":"payback_reached","label":"Investment recovered","type":"boolean","decimals":4,"description":"False when the cash flows never add up to the investment."},{"name":"cumulative_cash_flows","label":"Cumulative cash flows","type":"number_list","decimals":2,"description":"Running total of undiscounted cash flows after each period."},{"name":"total_cash_flows","label":"Sum of cash flows","type":"number","decimals":2,"description":"Σ cash flows over the series."}],"input_schema":{"type":"object","properties":{"initial_investment":{"description":"Outlay at time 0, entered as a positive number.","type":"number","maximum":1000000000000000,"exclusiveMinimum":0,"examples":[10000]},"cash_flows":{"description":"Net cash inflow at the end of each period; takes precedence over annual_cash_flow.","type":"array","items":{"type":"number"},"examples":[[3000,4000,5000,2000]]},"annual_cash_flow":{"description":"Used with `years` when cash_flows is omitted.","type":"number","maximum":1000000000000000,"exclusiveMinimum":0,"examples":[3500]},"years":{"description":"Length of the constant cash-flow series (ignored when cash_flows is given). Unit: years.","type":"integer","minimum":1,"maximum":60,"default":20,"examples":[5],"x-unit":"years"},"discount_rate_percent":{"description":"Rate for the discounted payback; 0 skips it. Unit: % per period.","type":"number","minimum":0,"maximum":100,"default":0,"examples":[8],"x-unit":"% per period"}},"additionalProperties":false,"required":["initial_investment"]},"output_schema":{"type":"object","properties":{"payback_period_years":{"description":"Periods until cumulative undiscounted cash flow reaches the investment, interpolated within the final period. Unit: periods.","type":"number","x-unit":"periods"},"payback_time":{"description":"payback_period_years expressed in years and months.","type":"string"},"discounted_payback_period_years":{"description":"Same using cash flows discounted at discount_rate_percent (only when the rate is > 0). Unit: periods.","type":"number","x-unit":"periods"},"payback_reached":{"description":"False when the cash flows never add up to the investment.","type":"boolean"},"cumulative_cash_flows":{"description":"Running total of undiscounted cash flows after each period.","type":"array","items":{"type":"number"}},"total_cash_flows":{"description":"Σ cash flows over the series.","type":"number"}}},"formula":"Simple: payback = (k − 1) + (initial_investment − cumulative_{k−1}) / CF_k, where k is the first period with cumulative ≥ initial_investment. Discounted: same with CF_t / (1 + r)^t. Constant flow: payback = initial_investment / annual_cash_flow.","method":"Cash flows arrive at the end of each period but the fractional part assumes they accrue evenly within the recovery period. Payback ignores cash flows after recovery and (in the simple form) the time value of money.","sources":[{"name":"Investopedia – Payback Period: Definition, Formula and How to Calculate","url":"https://www.investopedia.com/terms/p/paybackperiod.asp","type":"reference","retrieved_at":"2026-09-24"},{"name":"Investopedia – Discounted Payback Period","url":"https://www.investopedia.com/terms/d/discounted-payback-period.asp","type":"reference","retrieved_at":"2026-09-24"},{"name":"Wikipedia – Payback period","url":"https://en.wikipedia.org/wiki/Payback_period","type":"reference","retrieved_at":"2026-09-24"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"examples":[{"name":"10,000 then 3,000, 4,000, 5,000, 2,000 at 8 %","inputs":{"initial_investment":10000,"cash_flows":[3000,4000,5000,2000],"discount_rate_percent":8},"expected":{"payback_period_years":2.6,"payback_time":"2 years 7 months","discounted_payback_period_years":2.96,"payback_reached":true,"cumulative_cash_flows":[3000,7000,12000,14000],"total_cash_flows":14000},"url":"https://tttkmbb.com/api/v1/calculate/payback-period?initial_investment=10000&cash_flows=3000%2C4000%2C5000%2C2000&discount_rate_percent=8"},{"name":"50,000 with 12,000 per year for 10 years at 10 %","inputs":{"initial_investment":50000,"annual_cash_flow":12000,"years":10,"discount_rate_percent":10},"expected":{"payback_period_years":4.17,"discounted_payback_period_years":5.67,"payback_reached":true},"url":"https://tttkmbb.com/api/v1/calculate/payback-period?initial_investment=50000&annual_cash_flow=12000&years=10&discount_rate_percent=10"}],"faq":[{"q":"Why is the discounted payback longer?","a":"Discounting shrinks later cash flows, so it takes more of them to add up to the investment: 2.96 instead of 2.6 years in the example at 8 %."},{"q":"What if the investment is never recovered?","a":"payback_reached is false and the payback outputs are omitted; the cumulative list shows how far the cash flows get."}],"tags":["payback period","discounted payback","break-even time","capital budgeting","investment recovery"],"related":[{"calculator_id":"npv","reason":"Value of all cash flows, including those after payback."},{"calculator_id":"irr","reason":"Rate of return of the same cash flows."},{"calculator_id":"break-even","reason":"Units needed to cover fixed costs."}],"links":{"html":"https://tttkmbb.com/finance/payback-period","markdown":"https://tttkmbb.com/finance/payback-period.md","json":"https://tttkmbb.com/finance/payback-period.json","api":"https://tttkmbb.com/api/v1/calculate/payback-period","schema":"https://tttkmbb.com/api/v1/calculators/payback-period","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-24"},"timestamp":"2026-09-24T01:47:10Z","next_actions":[{"tool":"run_calculator","calculator_id":"payback-period","reason":"Run Payback Period Calculator with the inputs above."}],"links":{"markdown":"https://tttkmbb.com/finance/payback-period.md"}}