Markets & Trading

Financial Calculator (TVM, NPV, IRR)

A web emulation of the BA II Plus / HP 12C keys every CFA, CMA and finance candidate must master. Solve for any one of N, I/Y, PV, PMT or FV, then switch to the cash-flow worksheet for NPV, IRR and payback on an uneven stream — all in your browser, nothing sent to a server.

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Sign convention: cash you receive is positive, cash you pay out is negative. A loan you take is +PV with −PMT; a deposit you make is −PV.

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Period (t)Cash flow CFₜRepeat ×

“Repeat” groups consecutive equal cash flows (the BA II Plus Fj frequency). Up to 20 distinct cash flows.

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How it works

Every time-value-of-money problem is one equation in five unknowns. With the per-period rate i = (I/Y ÷ 100) ÷ freq baked into the inputs, the BA II Plus cash-flow identity is:

PV·(1 + i)N + PMT·[ (1 + i)N − 1 ] / i · (1 + i·begin) + FV = 0
where begin is 1 for an annuity due (BEGIN) and 0 for an ordinary annuity (END). If i = 0 the annuity term collapses to PMT · N.

Four of the five values are knowns; the tool rearranges the identity to solve algebraically for PV, FV or PMT, takes a logarithm for N, and uses Newton–Raphson with a bisection safety net for I/Y (the rate has no closed form). The effective annual rate that compares compounding frequencies is EAR = (1 + I/Y/100)freq − 1 when I/Y is the periodic rate.

The cash-flow worksheet handles an uneven stream. NPV discounts each cash flow back to today and sums them: NPV = Σ CFₜ / (1 + r)t. IRR is the rate that drives NPV to exactly zero, found here by bisection on the bracket [−99%, 100%]. Payback counts the periods until the running total of raw cash turns positive; discounted payback does the same on discounted cash, and the profitability index is the present value of inflows divided by the initial outlay.

Worked examples

TVM

Retirement gap

Have $25k, want $50k in 10 years, monthly compounding — solve for I/Y to see the return you need.

TVM

Loan payment

Borrow $25k at 6%/yr over 60 months — set PV +25000, I/Y blank or known, solve PMT.

NPV

Capital project

Lay out $100k, recover uneven inflows for 5 years — read NPV, IRR and discounted payback at once.

FAQ

Why does my answer flip sign? The calculator follows the BA II Plus cash-flow convention: money in is positive, money out is negative. PV and FV/PMT normally have opposite signs. If everything is the same sign there is no rate that balances the equation and I/Y has no solution.
END or BEGIN? Use END for loans and most bonds (payment at period end) and BEGIN for leases or rent (payment at period start). BEGIN makes an annuity worth a factor of (1 + i) more.
Can IRR be wrong? A stream that changes sign more than once can have multiple IRRs; this tool returns the first root in the bracket. When inflows and the rate conflict, trust NPV at your required rate over IRR.

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