Match rates to cash-flow periods
T0 occurs now; T1, T2 and later rows are equally spaced period ends. Use an annual rate for annual periods or a monthly rate for monthly periods. Removing a row leaves a gap with no cash flow; later period numbers retain their timing. These calculations do not use calendar dates or compute XIRR.
Net present value
NPV = Σ CFₜ / (1 + r)ᵗ, including T0 without discounting. Enter negative amounts for costs and positive amounts for receipts. Positive NPV means the entered forecast exceeds the selected discount hurdle in present-value terms; it does not guarantee future profit. Negative NPV can coexist with positive undiscounted receipts.
Worked scenario: −$100,000 now, followed by $30,000, $35,000, $40,000 and $45,000 at four annual period ends, gives NPV $16,986.54 at 10% per year. This is a calculation example, not investment performance.
Profitability index and later outlays
For a negative T0 investment followed only by nonnegative cash flows, PI = (NPV + initial investment) / initial investment. This page shows N/A when there are later outlays or no initial investment, rather than applying that initial-outlay formula to a different cash-flow pattern. NPV still includes every entered outlay.
Internal rate of return
IRR solves NPV(r) = 0. The numerical solver starts at 10%, checks the resulting NPV residual, and uses a bounded bisection fallback from −99% to 1,000% if needed. A failure to find a verified root is not proof that no root exists. Multiple sign changes may produce several roots or no root; one returned root does not establish uniqueness.
For a conventional initial outlay followed by inflows, an IRR above a hurdle rate corresponds to positive NPV at that hurdle. Borrowing-style cash flows can reverse that rule. Different project sizes and timing can also make IRR rankings conflict with NPV. Inspect the cash-flow pattern instead of treating a rate as an accept/reject instruction.
Modified internal rate of return
MIRR = (terminal value of positive cash flows / absolute present value of negative cash flows)^(1/n) − 1. The finance rate discounts negative flows to T0; the reinvestment rate compounds positive flows to the last entered period n. Both rates are per period and must exceed −100%. Positive and negative flows and a positive horizon are required.
MIRR makes those two assumptions explicit. It is not automatically a more accurate, lower or safer return measure. IRR is a root of the NPV equation; a claim about terminal reinvested wealth needs further assumptions.
Use and review the results
- Choose the matching calculator and enter finite amounts and rates.
- Calculate, then inspect the NPV period breakdown or the rate result.
- Changing any input clears the old result; calculate again before comparing.
- Keep units, inflation, tax treatment and discount-rate assumptions consistent. Those factors are not supplied automatically.